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Berichte des Institutes für Erdwissenschaften, Karl

1. In the 50s and 60s of the last century the automobile industry in particular had to face the difficulty that freeform curves and surfaces couldn t be exactly reproduced owing to a lack of a proper mathematical description Carl de Boor solved this problem by depicting the shape of component parts as parametric curves defined piecewise by polynomials 2 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 As a result the curve s shape 15 determined by its so called control points or de Boor points which are the vertices of the control polygon It turned out that this way of characterizing curves and shapes was advantageous for other fields and generalized versions and enhancements of B splines were developed shortly after Representing curves and shapes using B splines and their further development is still employed in Computer Aided Design systems Nowadays the areas of application are manifold and diversified and reach far beyond technical mould design and construction Bartels 1987 Farin 2001 Hoschek and Lasser 1993 For our task the approximation of outline data B spline curves offer several advantages B spline curves are invariant under affine transformations the pixel data can be approximated by a numerically stable and accurate algorithm and we obtain an enormous data reduction The primary outline data consisting of approximately 1000 to 1400 pixels can be excellently depicted by a B spline curve determined
2. Norberg U 1994 Wing design flight performance and habitat use in bats In P C Wainwright and S M Reailly Eds Ecological Morphology University of Chicago Press Chicago pp 205 239 Pielou E C 1977 Mathematical Ecology Wiley Interscience Publication John Wiley and Sons New York Pielou E C 1984 The Interpretation of Ecological Data A Primer on Classification and Ordination John Wiley and Sons Inc USA Raup D M 1967 Geometric analysis of shell coiling Coiling in ammonoids Journal of Paleontology 41 43 65 Ray T S 1990 Application of eigenshape analysis to second order leaf shape ontogeny in Syngonium podophhyllum Araceae In F J Rohlf and F J Bookstein Eds Proceedings of the Michigan Morphometrics Workshop The University of Michigan Museum of Zoology Ann Arbor pp 201 213 Reilly S M 1990 Comparative Ontogeny of cranial shape in Salamanders using Resistant Fit Theta Rho Analysis In F J Rohlf and F L Bookstein Eds Proceedings of the Michigan Morphometrics Workshop Special Publication No 2 The Natural Museum of Natural History The Smithsonian Institution Washington Chapter 16 pp 311 321 Reyment R A and Abe K 1995 Morphometrics of Vargula hilgendorfii M ller Ostracoda Crustacea Mitteilungen aus dem Hamburgischen Zoologischen Museum und Institut 92 325 336 Reyment R A and Bookstein F L 1993 Infraspecific variability in shape in Neobuntonia airella an
3. 37 003 234 39 600 protzi 3 Zy m m vg 0 000 0 000 0 000 0 000 0 000 lt Mean Specimen gt 26 721 5225 641 311 21 345 439 29 023 Cluster Approximation for Specimen candida 10 l4m fvg TPS Index Control Point Delta vector Delta Length x y x y m Bow 155 0 000 79 230 0 000 9230 d 661 217 85 193 79 207 5 6165 73 406 d if la 224 205 57 B30 5 166 56 5542 d 477 259 363 250 3 704 45 649 49 609 d4 327 096 446 340 13 564 53 795 55 479 do 164 620 405 552 15 102 32 506 35 944 db 3 6359 453 057 3 100 Z4D 25 179 Arm Candoninae Exercise 2 Expor Ready les 2 sf Print a MORPHOMATICA document The contents of a MORPHOMATICA document can be printed with the menu item File Print The contents to be printed depend on the selected entry in the tree view Drucker Name asenlet 6 Eigenschatten Status Bereit Typ HF LaserJet BL Standort LPT1 Kommentar Ausgabe in Datei umleiten Druckbereich Esemplare Anzahl der Exemplare H RER Abbrechen Ce Alle Seiten von fi bis fi E Markieruna You can check the output before printing with the menu item File Print Preview 65 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Candoninae Exercise 2 mmd Morphomatica Drucken N chste Vorherige Specimen DiDateriDanM orph2icandida 10 l4m fvg TPS Seite 1 Coordinates num YA The printer set
4. Mean Delta Quad Is the square root of the Sum Delta Quad divided by the number of control points Remaining columns Coordinates of the calculated control points d dorsal v ventral The specimen selected in the tree view is marked in the cluster data view with a grey background The rows of the table can be sorted depending on the values in a column by clicking on this column header It 1s possible to copy either the whole sheet of displayed data or selected columns For this action for instance select Cluster Display coordinates click on a column Fig below see b press the right key mouse move arrow to Copy column Fig below see c Open in Excel a new file and click Insert b c ME ES JibleaHotarele Morphomatica 1 6 beth File Specimen Cluster View 2 7 E Specimen Ne Specimen _ Areatotal Ares der ot Aras ventral Maan Delta Square Sum Dekta Square mi coord di coo D J449 8 tps 0 J44941 tps 0 00 Jumm 0 00 00 000 000 0 00 696 29 0 00 652 88 115 E 2FHotarele tps 3 J44943 tps 13 04 gt 9 04 7 75 20 28 123 95 1306 85 697 94 0 00 657 627 118 E 3FHotarele tps 2 J449 42 tps 14 27 Copy sheet 10 80 8 91 1931 14257 1865 38 697 13 000 648 45 120 D 4FHotarele tps 1 J449 8 tps 28 86 Sopy column 14 10 12 10 2251 19357 3179 66 695 21 000 659 15 120 D 5FHotarele tps 4 J449 f4 tps 29 07 14 55 12 36 2702 207 34 3385 02 705 9070 00 668 237 123 D EFHotarele 12 6FHot
5. 2008 References Baltan s A and Geiger W 1998 Intraspecific Morphological Variability morphometry of valve outlines In K Martens Ed Sex and parthenogenesis evolutionary ecology of reproductive modes in non marine ostracods 127 142 Backhuys Publishers Leiden The Netherlands Baltanas A Alcorlo P and Danielopol D L 2002 Morphological disparity in populations with and without sexual reproduction a case study in Eucypris virens Crustacea Ostracoda Biol J Linnean Soc 75 9 19 Baltanas A Brauneis W Danielopol D L and Linhart J 2003 Morphometric methods for applied ostracodology tools for outline analysis of nonmarine ostracodes In L E Park and A J Smith Eds Bridging the gap trends in the ostracode biological and geological sciences Paleontol Soc Papers 9 101 118 Clarke K R and Gorley R N 2001 Primer v5 User manual tutorial Primer E Ltd Plymouth Clarke K R and Gorley R N 2006 Primer v6 User manual tutorial Primer E Ltd Plymouth Clarke K R and Warwick R M 2001 Change in marine communities an approach to statistical analysis and interpretation 2 Edition Primer E Ltd Plymouth Danielopol D L Ito E Wansard G Kamiya T Cronin T and Baltanas A 2002 Techniques for collection and study of Ostracoda In J A Holmes and A R Chivas Eds The Ostracoda applications in Quaternary research Geophys Monogr 131 65 98 American Geophy
6. Reveal All Arbitrary Histogram Flip Horizontal Flip vertical Trap Extract 9 Alk Ctrl x LiquiFy Shft tbrl The outline is checked any pieces of dirt that are connected to the valve are erased with the Eraser tool dirt somewhere in the background is ignored If the outline is very translucent there is too little contrast and the edge needs to be outlined with the Paintbrush Tool KARIN select the thickness of the stroke n the toolbar below the menubar 71 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 File Edit CR Layer 4 oe TOET le In the menubar under Window there is a heading Show History al kuer I if selected a window is shown where the modification steps are listed 1t 1s possible to undo the last 20 changes Po 4 Eraser e ec Eraser B i Eraser The original is shown in the header bar of the history window and can always gone back to ke x Pixel Dimensions 141 2 Width Emn pixels 128 Cancel Height 1320 pixels r Auto Document Size width 90 31 Height 67 73 310 Resolution 72 pixels inch B constrain Proportions e Resample Image Bicubic The Image Size under Image in the menubar is very important for the number of digitised points the outline is made up out of Think about an appropriate number gt 1000 pts before digitalizing since MORPHOMAT
7. Univ Graz ISSN 1608 8166 Band 13 Graz 2008 The new y axis 1s of course perpendicular to the new x axis and corresponds to the maximum moment of inertia Finally we have to define a congruence transformation f which moves the points of the contour as mentioned above Shifting S to the point Y 0 0 and rotating the vectors E 11 12 specifying the axis with minimum moment of inertia and E e21 22 specifying the axis with maximum moment to 1 0 resp 0 1 can be done by a transformation K i k EH 2 e21 Applying this transformation to each point moves the contour into the desired position 3 3 Approximation to Contour Data To prepare the point data for a good and meaningful approximation it is necessary to divide the contour into two halves If the B spline approximation is applied in a straightforward way to an outline it may happen that two very similar outlines lead to rather different control points This is the case for instance with the two artificial elliptical outlines of figure 5 One should note that this phenomenon occurs due to the fact that moving the control points simultaneously in a suitable way around the curve has only little influence on the shape of the curve Figure 5 Two rather similar elliptic outlines with different control points To avoid this problem we cut the outline in two pieces and approximate each half separately under the condition that the res
8. analysis as applied in morphometric studies Paleontology 43 765 783 Humphries J M Bookstein F L Chernoff B Smith G R Elder R L and Poss S G 1981 Multivariate discrimination by shape in relation size Systematic Zoology 30 3 291 308 Irizuki T and Sasaki O 1993 Analysis of morphological changes through ontogeny genera Baffinicythere and Elofsonella Hemicytherinae In K G McKenzie and P J Jones Eds Ostracoda in the earth and life sciences A A Balkema Rotterdam pp 335 350 James F C and McCulloch C E 1990 Multivariate Analysis in Ecology and Systematics Panacea or Pandora s box Annual Review of Ecology and Systematics 21 129 166 Jolicoeur P 1963 The multivariate generalization of the allometry equation Biometrics 19 497 499 Kaesler R L and Foster D W 1987 Ontogeny of Bradleya normani Brady Shape analysis of landmarks In Hanai T Ikeya N and Ishizaki K Eds Evolutionary Biology of Ostracoda Elsevier Kodansha pp 207 218 Kaesler R L and Maddocks R F 1984 Preliminary harmonic analysis of outlines of recent Macrocypridid Ostracoda In N Krstic Ed The Taxonomy Biostratigraphy and Distribution of Ostracodes Belgrade Serbian Geological Society 169 174 Kaesler R L and Waters J A 1972 Fourier analysis of the ostracode margin Geological Society of America Bulletin 83 1169 1178 11 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Ban
9. be the angle between the x axis and the vector OD If the cotangent values are in ascending order this means cot pi lt cot Yi 1 and cot Wj lt cot W541 we can confidently assume that points of intersection on a segment S can only be possible for segments 7 where cot 1341 gt cot pi and cot Yj lt cot pi 1 see figure 11 36 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 y axis Figure 11 For possible points of intersection of the segment S only the segments T and T 1 of the other polygon are worth considering Usually a segment of a polygon has to be compared with 2 or 3 segments of the other polygon This makes it possible to reduce the number of comparisons to about 150 as opposed to 2500 mentioned above Due to the structure of the algorithm certain outlines of specimens cannot be treated As described above the cotangent values of the successive vertices of the spline approximating polygon must be in ascending order In other words the B spline considered as a clockwise directed curve must not change its direction viewed from the origin As a rule such shapes occur only in faulty datasets To get a general idea of such uncalculable shapes a couple of exemplary specimens with their approximating B splines are indicated below na e Sa i E ns a vr N 7 Ki j j Br e Tr ha mg al Be Se IA Figure 12 Examples of uncalculable outlines black and th
10. it Fill in the column with abbreviations under Factors pick Plot key to give the abbreviations corresponding symbols that you like and sort the abbreviations with the up down arrows to have them displayed on the side of the plot n the right order When you are done confirm the abbreviations and plot key with OK Select Analyse in the menubar and MDS ten restarts are usually sufficient The resulting plot needs to be modified go to Graph and Properties select Display Symbol and Factor in the neighbouring field Label and None If you made several columns with factors it is possible to select a factor confirm with Ok The plot can be rotated to display the results best plot on the following page The first plots are based on a matrix with normalization for area Candona neglecta deep sites left valve dr Candona neglecta deep sites right valve sl Candona neglecta shallow sites left valve sr Candona neglecta shallow sites right valve Abbreviations used n the plots below 85 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Example 2 010708 MDS plot using Normalized for Area In this case a three dimensional display helps to better understand the differences between the populations see figure next page Go Graph and Properties again and select 3D instead of 2D in the dimensions field The resulting graph shows the samples positioned in a three dimensional space Most symbols ha
11. 10 DINO Co Cl OO Go Cl NOME ed ww ea t Cl eu si o ae 8 L CO Gi N ei HCOOH NN CORK E E oO Cl VO ei OM o tit ay gt noamnmsoyYsrm LD nor e O Oci Co D CC CO OO CH T MNN Y ANA s Ma rar m A Mm Orin H N 00 00 N amp OO ech we HS r oO si Ceci GO WO eo E ei ges in Tee O Y N O E M O 0 m L DANS GU s i Gi h Vi OG Ei 40 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Figure 14 Lateral view of female valves belonging to the species Pseudocandona eremita from Astileu Computing the above dissimilarity index for the Ada Kaleh and Astileu populations resemblance matrix table 1 yields TES mt s P 869 2 s Q 454 56 s P Q 3412 94 and diss P Q 2 58 Indiss P Q 0 947 References Baltan s A Brauneis W Danielopol D L and Linhart J 2003 Morphometric methods for applied ostracodology tools for outline analysis of nonmarine ostracodes In L E Park and A J Smith Eds Bridging the gap trends in the ostracode biological and geological sciences Paleontol Soc Papers 9 101 118 Bartels R H Beatty J C and Barsky B A 1987 An Introduction to Splines for use in Computer Graphics and Geometric Modeling Morgan Kaufmann Publishers Los Altros Bayer S Brauneis W and Trischitz U 2002 Approximierende B Splines Bachelor Thesis Department of Mathematics University of Salzburg De Boor C 1978 A Practical Guide to Splines Springer
12. 54 00 15 01 28 49 15 97 16 44 9 54 12 78 8 95 10 72 18 49 0 00 11 29 1 27 95 55 52 13 31 21 99 7 97 11 61 12 81 7 46 10 08 15 59 13 35 11 29 0 00 po Export to Image File o e cuter DN Loz absolon f vg TPS D i Caud 9 2W8m vd F tp E Caud Absolon f vg TF E Caud Kaufmann f vg D Caud Scharf f vg TPS Di CeLvilgm tps 5 E CcLY1SM6m tps 6 E CeL 214m tps 7 E CcLy25M6m tps 8 E CcLY3GF10m tps 9 E CcL 35M6m tps 10 E CeL 45M6m tps 11 E CeLYSSM m tps 12 E CcLY6SM6m tps 13 E CcLY7SM6m tps 14 E CcLY8SM6m tps 15 E CcLv95M6m tps 16 E CcLY105M6m tps 17 E CcRY1l4m tps 18 2 CcRY1SM6m tos 19 z gt Coordinates num u 78 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 The resulting sheet 1s a classical matrix that can easily be exported to Excel Right click the sheet and choose Copy Sheet open a new Excel table and paste the sheet into the field A3 Into field Al write a title copy the names of the specimen and paste 1t with Paste Special Transform into field B2 Save the Excel file El Microsoft Excel Example1 010708 x1s Schreibgeschiitzt Datei Bearbeiten Ansicht Einf gen Format Extras Daten Fenster 2 DSRS SAY BAS 0 0 BE A AR MB 0 A Cal HD ooo da EE Loz absolon f vg TPS Caud 9 ZVV 8m vd f tos Caud Absolon f vg TPS Caud Kaufmann f vg TPS Caud Schart f vg TPS CcL 1l4m tps CcLV1SM6m
13. CcLv45M6m tps B CcLY55M6m tps Ej CcLY6SM6m tps EY CcL 75M6m tps E CcL 8SM6 m tps EJ Col Y9SM6m tps E CcRV114m tps E CcRV1SM6m tps Y CcRY2I4m tps A Crav2SM m Fm Coordinates MN u It might be useful to change the number of control points to get a better resemblance between the calculated and the real shape 76 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Mark the Cluster folder select the specimen you want to compare and click Apply BEE File Specimen Cluster View Oe Sg Ej ClmLY1Mo041 28 tps Ej ClmLY1Mo041 29 tps Ej ClmLv15M15m tps Ej ClmLY15M6m tps EI ClmLv2GF10m tps D CimLv2I4m tps dy To add a RAE a and ins Select All Loz absolon f vg TPS E Clml 2Mo41 27 tps E ClmRV1GF10m tps Ej ClmRv1115m tps Ej ClmR il4m tps E ClmRV1Mo41 20 tps Ej ClmRV1Mo41 26 tps E ClmRV1Mo41 27 tps E ClmRV1Mo41 28 tps Ej ClmRV1Mo41 29 tps Ej ClmR 1SM15m tps Zen Selecta Zen Calculate Caud Absolon f vg TPS Caud Kaufmann f wg TPS Caud Scharf f wg TPS CcL105M6m tps Select None CcLW1l4m tps specimen CcL 1SM6m tps CeL 2l4m tps CcL 25M6m tps CcLV3GF10m tps Apply SI EI EI EI EI EI EI EI I EI 1 El ClmRvisM m tps CcLY35M6m tos Ej ClmR 2I4m tps E ClmRv2M041 26 tps E Caud 9 ZW8m wd f tp amp Cluster vv Coordinates NUM u Set the control points to the value that you determined earlier usually 8 contro
14. Geometric Morphometrics for Biologists Elsevier Academic Press Amsterdam 15 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 16 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Introduction to the Computer Programme MORPHOMATICA Dan L Danielopol Walter Neubauer Angel Baltanas Commission for the Stratigraphical 8 Palaeontological Research of Austria Austrian Academy of Sciences c o Institute of Earth Sciences Geology amp Palaeontology University of Graz Heinrichstrasse 26 A 8010 Graz E Mail dan danielopol oeaw ac at Unterfeldstra e 13 10 A 5101 Bergheim E Mail mathstud gmx at 3 Department Ecologia Universidad Autonoma de Madrid Edif Biologia E 28049 Madrid E Mail angel baltanas uam es MORPHOMATICA 1s a user friendly computer programme designed for the morphometric analysis of the shape of ostracods with a more or less smooth outline The software package Linhart et al 2006 with the same name is available at http palstrat uni graz at For the mathematical description of outline shapes MORPHOMATICA uses an original solution here called the Linhart algorithm cf details in the next chapter based on a B spline method a popular technique in computer aided geometric design cf Hill 1990 which has been applied to morphometric analysis of human skulls by Gu ziec 1996 The MORPHOMATICA project which started in 2001 at the Limnological
15. Institute Austrian Academy of Sciences in Mondsee and at the Department of Mathematics University of Salzburg is a spin off of a larger project on the morphometrics of non marine ostracods initiated ten years ago by one of us A B and from which various publications issued cf inter alia Baltanas and Geiger 1998 Baltanas et al 2002 2003 Danielopol et al 2002 Sanchez Gonzalez et al 2004 One should see the computer programme described here as a complement to other computer programmes using alternative approaches like Eigenshape analysis and or Fourier analysis see a review of morphometric methods used by ostracodologists in Danielopol et al 2002 MORPHOMATICA and the Linhart s B spline algorithm have interesting features as compared with other programmes 1 it uses a reduced number of parameters for the mathematical reconstruction of form 2 one can identify the segments of the outline described by the B spline functions 3 the computation is not excessively long for the solution proposed 4 it allows to estimate the precision with which the B spline curve fits the original digitised outline and 5 it allows to produce virtual arte factual outlines useful 17 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 for various topics dealing with theoretical and or applied morphology MORPHOMATICA as other programmes do cf those of the Eigenshape analysis method discussed by Rohlf 1996 suffers
16. M 1989 Perimeter based Fourier analysis a new morphometric method applied to the trilobite cranidium Journal of Paleontology 63 80 885 Foote M 1992 Paleozoic record of morphological diversity in blastozoan echinoderms Proc Natl Acad Sci USA 89 7325 7329 Foote M 1993a Discordance and concordance between morphological and taxonomic diversity Paleobiology 19 2 185 204 10 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Foote M 1993b Contributions of individual taxa to overall morphological disparity Paleobiology 19 4 403 419 Foote M 1995 Analysis of Morphological Data In N L Gilinsky and P W Signor Eds Analytical Paleobiology Short Courses in Paleontology University of Tennessee and the Paleontological Society Knoxville 14 59 86 Foote M 1997 The evolution of morphological diversity Annual Review of Ecology and Systematics 28 129 152 Foster D W and Kaesler R L 1988 Shape analysis Ideas from Ostracoda In M L McKinney Ed Heterochrony in Evolution Plenum Press New York pp 53 69 Galton F 1869 Hereditary genius an inquiry into its laws and consequences London Macmillan Galton F 1889 Natural Inheritance London Macmillan Goodall C R 1983 The statistical analysis of growth in two dimensions Doctoral dissertation Dept Statistics Harvard University Haines J A and Crampton J S 2000 Improvements to the method of Fourier shape
17. The aim of the present workshop Methods in Ostracodology is to intensify communication between specialists both palaeontologists and neontologists interested in taxonomy evolution and palaeo ecology of ostracods This goal can be achieved if we are aware or if we adopt some of the new research tools useful for the description of ostracods and their use for environmental reconstruction Therefore our intention is to make more available techniques used for three types of purposes 1 sampling sediments to gain a high resolution spatial and temporal record 2 applying geometric morphometrics for ostracod description and taxonomy 3 using stable isotope composition of ostracod valves for further use in palaeo environmental reconstructions Morphometrics the quantitative description analysis and interpretation of form 1s especially suited for ostracods particularly when combined with conventional multivariate statistical techniques and with methods used in computer graphical analysis As F J Rohlf noted Ann Rev Ecol Syst 1990 299 morphometrics is a fundamental area of research and techniques of description and comparison of shapes of structures are needed in any systematic study based on the morphology of organisms The present volume presents a series of contributions in this scientific field Dr A Baltanas Madrid provides a general overview on morphometrics including traditional methods but focussing on geometric mo
18. Verlag New York Deuflhard P and Hohmann A 1995 Numerical analysis A first course in scientific computation de Gruyter Berlin Farin G 1990 Curves and Surfaces for Computer Aided Geometric Design A Practical Guide pr ed Academic Press San Diego 41 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Farin G 2001 Shape In B Enqquist PdL Mathematics Unlimited 2001 and Beyond 463 477 Springer Verlag Berlin Hogben L 2007 Handbook of Linear Algebra Chapman and Hall CRC Boca Raton Hoschek J and Lasser D 1993 Fundamentals of Computer Aided Geometric Design A K Peters Wellesley MA Iepure S Namiotko T and Danielopol D L 2007 Evolutionary and taxonomic aspects within the species group Pseudocandona eremita Hydrobiologia 585 159 180 Kelly J B 1970 Metric Inequalities and Symmetric Differences In O Shisha Ed Inequalities 2 193 212 Academic Press New York Linhart J Brauneis W Neubauer W Danielopol D L 2006 Morphomatica Computer Program version 1 6 http palstrat uni graz at morphomatica morphomatica _e htm Loy A Busilacchi S Costa C Ferlin L and Cataudella S 2000 Comparing geometric morphometrics and outline fitting to monitor fish shape variability of Diplodus puntazzo Teleostea Sparidae Aquacultural Engineering 21 271 283 Minati K Cabral M C Pipik R Danielopol D L Linhart J and Neubauer W 2008 Morphological
19. are several studies that apply landmark methods Kaesler and Foster 1987 Reyment et al 1988 Abe et al 1988 Reyment and Bookstein 1993 Reyment 1995 1997 Elewa 2004 For a large number of ostracod species however it is not possible to identify landmarks or at least a number of landmarks large enough to make that approach feasible Under such circumstances there is an option Outline Analysis Rohlf 1990b Outline analysis operates on the following basis 1 when landmarks are not available one should record the 6 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 positions of a rather high number of points along the contour of the studied object 2 a mathematical function must the be fitted to such observationsin order to 3 explore differences between shapes through the analysis of the mathematical descriptors fitted to them This approach includes a variety of specific methods fig 1 among others Eigenshape analysis Lohmann 1983 Schweitzer et al 1986 Lohmann and Schweitzer 1990 standard Fourier descriptors Kaesler and Waters 1972 and Elliptic Fourier Analysis Kuhl and Giardina 1982 Kaesler and Maddocks 1984 Rohlf and Archie 1984 Foote 1989 Rohlf 1995 Lestrel 1997 McLellan and Endler 1998 Baltan s and Geiger 1998 Geometric Morphometrics Landmark analysis Outline analysis Polar coordinates Transformation grids Procrustes Finite element Least Squa
20. by just 16 control points A further important fact to mention in advance is a property called local control Thereby the shifting of a single control point of the B spline curve does not cause the change of the entire curve progression but just a deviation in the surrounding of the concerning control point This characteristic has proved very useful for the examination of morphological structures just having an effect on single parts of the outline This article gives an overview of the theoretical background of approximating B spline curves following the elaborations in Bartels 1987 de Boor 1978 Hoschek and Lasser 1993 Piegl 1995 A detailed description of the algorithm for the approximation of ostracods outlines is presented in Bayer et al 2002 and Neubauer 2007 The shape of a carapace offers the possibility of a fast and stable computation Moreover the area deviation provides us with demonstrative results for the application in palaeontology since a perspicuous graphical representation of the stated area 1s feasible and the output is in units of Square micrometers The last section deals with a method of distinguishing two populations of ostracods by using the data of a distance matrix which frequently finds application in biological research 22 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 2 B Spline Representation 2 1 B Spline Curves Definition 2 1 A pth degree B spline curve is
21. defined by C t N t P a lt t lt b gel The P are the control points and the N t are the pth degree B spline basis functions defined by Na o l Ju S lt ug E d otherwise New t Np t NN 1 p 1 t d where U us Um 18 a nondecreasing sequence of real numbers Le u lt uj 1 1 0 m 1 called knot vector The items u are called knots and the polygon formed by the P is the control polygon Particularly we use B spline curves of degree p 2 also called quadratic B spline curves for the approximation of ostracods outlines Their basis functions are already calculated given by 2 t u gt a for u St lt Uy T ru u u u yo t u u r1 usr3 t a AN ea IE _ 12 225 fcr u lt t lt Us Vi 2 t wi 2 us ui 2 4441 F Wi 3 Ui41 Ui 2 Ui41 I l GEI 142 ui43 t gt SA lt lt 0143 U 4 1 U 43 Ui 2 for wua t lt mus and N gt t O for t outside the interval u u 3 In these formulas division by zero may occur When this 1s the case the result of the division 1s set equal to zero A common choice for the knot vector of pth degree basis functions is setting the first p l knots 0 the last p 1 knots 1 and the interior knots equally spaced ig iby Gan AE PD e BS S OF St La mel m 2p 23 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 This so called unifor
22. different at your system enter the appropriate extension in the Filename field 46 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 In the next step an open dialog will be displayed in which you select the file s with the ostracod s you intend to import The open dialog allows you to select one ore more files at the same time xl Grosil O54R 2 H E Grosit Lvos5 2 J Grosit Lv056 2 EJ Grosi1 LYO57 2 d J oltidac 15072 FA OltBara2 16072 2 EJ candjMo9 130722 TPS 3 CandjMo9a 130722 TPS Dateiname Grosi1 053AV 210722 TPS Candjndant1307 Dateityp an Specimen Files tps msd v Abbrechen Z After confirming the dialog with open the specimens contained in the selected files are inserted into the document Those specimens will be added to the specimen directory in the tree view with their related file names If more than one specimen is stored in the imported file the entries in the tree view are extended with an enumeration Display the outline of a specimen To display the outline of an imported specimen you just have to select its name in the tree view on the left The currently selected specimen is marked in the tree view with a blue background The outline is displayed in the specimen view with additional information like the corresponding scaling of the outline or the coordinate axes Candoninae Exercise 2 mmd Morphom
23. exposition of geometric morphometry In K G McKenzie and P J Jones Eds Ostracoda in the Earth and Life Sciences Rotterdam AA Balkema pp 291 314 Reyment R A 1985 Multivariate Morphometrics and Analysis of Shape Mathematical Geology 17 6 591 609 Reyment R A Bookstein F L McKenzie K G and Majoran S 1988 Ecophenotypic variation in Mutilus pumilus Ostracoda from Australia studied by canonical variate analysis and tensor biometrics Journal of Micropalaeontology 7 11 20 13 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Reyment R A 1991 Multidimensional Paleobiology Pergamon Press Oxford Reyment R A 1995 On multivariate morphometrics applied to Ostracoda In J Riha Ed Ostracods and Biostratigraphy Rotterdam AA Balkema pp 43 48 Reyment R A 1997 Evolution of shape in Oligocen and Miocene Notocarinovalva Ostracoda Crustacea a multivariate statistical study Bulletin of Mathematical Biology 59 63 87 Rohlf F J and Archie J 1984 A comparison of Fourier methods for the description of wing shape in mosquitos Diptera Culicidae Systematic Zoology 33 3 302 317 Rohlf F J and Bookstein F L 1987 A comment on shearing as a method for size correction Systematic Zoology 36 4 356 367 Rohlf F J and Marcus L F 1993 A revolution in morphometrics Trends in Ecology and Evolution 8 129 132 Rohlf F J and Slice D 1990 Extensions of
24. for all j and adding them to control point P2 we obtain a B spline curve CO for each vector Owing to the measure defined above d C C for any vector of length a although intuitively speaking some of the curves deviate much more from C t than others fig 9 e A TEEN N K S VAN Figure 9 The primal B spline curve red and various B spline curves blue generated by N FI j V Y V adding different vectors with the same length to a control point This difficulty is of particular importance if we adjust several control points Each point of the curve is determined by at least 3 control points for degree gt 2 see property 2 4 Thereby neighbouring control points can be positioned in such a way that an almost identical curve emerges Figure 5 shows this effect The left B spline curve results from the right curve by rotating the control points by 30 It is obvious that both curves are nearly similar but our difference measure yields a high value of dissimilarity 34 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 4 2 Area Deviation The B spline curves we use to approximate ostracods outlines feature some nice characteristics We want to use these characteristics for computing a demonstrative and tangible measure to distinguish contours Our approximating B spline curves have no loops self intersections or other anomalies We obtain solely so called simply close
25. main axes of inertia This 15 why the above centroid should be replaced by the centre of gravity of the domain A surrounded by the given outline This centre 1s defined by 1 5 sy Bal H x y dz dy A a where s and s denote the coordinates of and a is the area of the domain 4 It turns out that S can be computed in the following rather simple way if x and y denote the coordinates of Or and the points are given in counterclockwise order TL Sa EA Yi i Yi 2 1 F Ziti 1 t SC Ja 4 Sy is computed in a similar way with x and y interchanged and the whole expression multiplied by 1 Of course xm1 yY11 18 understood to be equal to x1 y1 Analogical to the centroid the axes of inertia should also be calculated not only for the points but for the whole outline or more precisely for the domain surrounded by the outline The moment of inertia with regard to a certain axis passing through the origin 1s defined to be the integral of the squared distance from this axis taken over the considered domain It may be computed in a similar but somewhat more complicated way as the centre of gravity above If the moment of inertia 1s not equal for all directions of axes there is a unique direction which yields the minimum moment and this is taken to be the new x axis This direction is given by an eigenvector of a certain 2 by 2 matrix and thus it is not difficult to compute 29 Ber Inst Erdwiss K F
26. of the lake 100 ins Shallow sites DeltaVecScale 1 00 Number of Iterations 6 100 microns Deep sites DeltaVecScale 1 00 Number of Iterations 6 Valves from the deep shallow sediment No Normalization 84 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 The data obtained with MORPHOMATICA can be used for further analysis in other programs In both cases Normalize for Area Don t Normalize all specimen are used for the Cluster analysis Select Display Differences Area Total and copy the sheet with a click on the right mouse button Paste the matrix into field A3 of an Excel worksheet copy the list of specimen and insert it with Paste special Transpose into field B2 into field Al fill a title Save the Excel book Repeat the copy and paste with the other normalization and insert it into the next sheet of the workbook We use for further analysis the program Primer Start Primer and select Excel files to be opened in the dialog box choose sheet 1 and pick Similarities Ok and Dissimilarities Ok Make sure that the number of rows corresponds to the number of specimen that was used if it does not check in the Excel worksheet if something went wrong with copying the list of specimen any blank field in column A and row 2 other than A2 will be the signal that it is the end of the matrix Go to Edit and select Factors in the dialog box under Factors add a new factor and name
27. the computation of the amount of morphological differences represented by vector dimensions and Euclidean distances This latter data is further analysed using multivariate statistical methods In the examples we present it is shown how using non metric multi dimensional scaling and or hierarchical cluster analysis one can visualise the data within the framework of morphological spaces We use since several years the computer package Primer with its versions 5 and 6 Clarke and Gorley 2001 Clarke K R and Gorley R N 2001 Primer v5 User manual tutorial Primer E Ltd Plymouth 2006 specially designed for multivariate statistical analysis Note that there are other packages which can be as useful as the one mentioned here Our preference for Primer is due to the user friendly structure of the programmes to the excellent manual produced by Clarke and Warwick 2001 Finally we recommend to those interested in additional information on geometric morphometrics the various books issued during Morphometric Symposia like those of Marcus et al 1996 An excellent introductory text which has to be consulted 1s Geometric morphometrics for biologists a primer Zelditch et al 2004 18 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 For the practical use of MORPHOMATICA programme one should consult inter alia also Iepure et al 2007 2008 Minati et al 2008 Danielopol et al 2008 Gross et al
28. the procrustes method for the optimal superimposition of landmarks Systematic Zoology 39 1 40 59 Rohlf F J 1986 Relationship among eingenshape analysis Fourier analysis and analysis of coordinates Mathematical Geology 18 845 854 Rohlf F J 1990a Morphometrics Annual Review of Ecology and Systematics 21 299 316 Rohlf F J 1990b Fitting curves to outlines In F J Rohlf and F J Bookstein Eds Proceedings of the Michigan Morphometrics Workshop Ann Arbor Michigan The University of Michigan Museum of Zoology pp 167 177 Rohlf F J 2004 tpsDig digitize landmarks and outlines version 2 0 Department of Ecology and Evolution State University of New York at Stony Brook Roy K and Foote M 1997 Morphological diversity as a biodiversity metric Trends in Ecology and Evolution 12 Sampson P D Bookstein F L Sheehan F H and Bolson E L 1996 Eigenshape analysis of left ventricular outlines from contrast venticulograms In L F Marcus Ed Advances in Morphometrics Plenum Press New York pp 211 234 Schlichting C D and Pigliucci M 1998 Phenotypic Evolution a Reaction Norm perspective Sinauer Associates Inc Schweitzer P N and Lohmann G P 1990 Life history and the evolution of ontogeny 1n the ostracode genus Cyprideis Paleobiology 16 107 125 Schweitzer P N Kaesler R L and Lohmann G P 1986 Ontogeny and heterochrony in the ostracode Cavellina Coryell from Lower Permi
29. tps CcLV 2l4m tps CcLV25M6m tps Start Primer select Open and choose your Excel table in the pop up dialog field click Similarities on the second surface Dissimilarities check that the right number of lines is imported if not most likely a labelling mistake occurred If everything is correct click OK The matrix is displayed i Example1 010708 Example 1 010700 Dissimilarity 0 to 100 CcLv3sM a Loz absolom fCaud 9 ZWerl Caud Absolorl Caud Kaufma Caud Scharf CcL V1 4m tps CcL v1 SM im Cl wv 24m tpslCeLv2SM m 4CcLV3GF10m Loz absolon f vg TF a Caud 9 ZvV8m vd f 1 54 53 Caud Absolon f vg 54 62 34 84 74 87 413 36 67 41 59 22 75 21 84 42 62 44 92 45 9 423 74 99 33 69 42 91 31 67 25 58 56 53 17 36 19 78 37 36 35 43 35 37 65 58 23 48 13 82 12 72 30 39 28 43 31 74 55 43 17 53 28 12 17 63 18 14 39 85 27 42 25 75 50 6 11 29 27 13 11 67 16 07 15 84 40 04 23 51 32 72 55 67 15 77 23 29 15 19 12 78 14 09 12 25 a 4 Under the header Edit choose Factors a list of the specimen s displayed click Factors and select 4dd Edit Factors Rename Remove Plot key species sex Gesten Aassssensessssnssnssnnsssennennssnn H Cancel Ccl114m tps Ccl15M6m tps Cel214m tps Help CcLv25M6m tps Cel 3GF10m tps Col 5SM6m tps 79 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Yo
30. variability among European populations of Vestalenula cylindrica Straub Palaeogeogr Palaeoclimat Palaeoecol 264 296 305 Neubauer W 2007 Measuring the Difference of Approximating B Spline Curves with Application in Distinguishing Ostracoda Master thesis Dept of Mathematics Univ of Salzburg download at http palstrat uni graz at morphomatica morphomatica_e htm Piegl N and Tiller W 1995 The NURBS book Springer Verlag Berlin Rohlf F J 2001 tpsDIG Program version 1 43 Department of Ecology and Evolution State University of New York Stony Brook NY http life bio sunysb edu morph soft dataacq html 1 17 04 Strang G 1998 Lineare Algebra Springer Verlag Berlin Veltkamp R C 2001 Shape Matching Similarity Measures and Algorithms In SMI 2001 International Conference Shape Modeling and Applications download at http people cs uu nl marc asci sm12001 pdf 188 197 Zelditch M L Swiderski D L Sheets H D and Fink W L 2004 Geometric morphometrics for biologists a primer Elsevier Academic Press Amsterdam 42 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 MORPHOMATICA Programme Description Wolfgang Brauneis Walter Neubauer Anika Stracke Pfeifergasse 9 A 5020 Salzburg E Mail wolfgang brauneis e mundo at Unterfeldstra e 13 10 A 5101 Bergheim E Mail mathstud gmx at 3 Heinrichstrasse 55 A 8010 Graz E Mail anika_boriss ya
31. 2 Centre of Gravity and Axes of Inertia The positions of the valves on the pictures vary widely and the tps files do not tag any basing points Nevertheless a meaningful comparison of two valves should be independent of alignment and position in the picture Therefore to compare the shape of two outlines they first have to be superimposed Ideally this should be done in such a way that the difference between them 1s as small as possible But this would be a very difficult task so we choose to position the two outlines in such a way that the centroids and the main axes of inertia coincide The structure of the tps data suggests computing the centroid based on the pixels using the arithmetic mean of the coordinate vectors of the points Q that is But this is the centroid of these points and not of the whole outline Consequently this only makes sense 1f the points are distributed very uniformly If parts of the outline are a little bit rugged or jagged there will be relatively many points Q concentrated in these parts and S tends to move towards them So the centroids of two very similar outlines may be rather different if only one has some rugged parts Figure 4 illustrates this difficulty 28 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Figure Aa Centroid and main axes Figure 4b The origin now 1s the centre of computed with the outline points gravity of the domain and the axes correspond with the
32. 4 Color Options en 7 Information Black and White I Print Specimen List s Color Abbrechen The following settings can be applied Pen Width Specimen Specifies the pen width for the specimen in the printout Pen Width Delta Vectors Specifies the pen width for the delta vectors in the printout Colour Options Whether colour e g for a overhead beamer presentation or only black white e g for a paper should be used Print Specimen List Should a separate list with the names of the specimens in the cluster be printed 59 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Listening the calculated cluster data The calculated cluster data can be displayed with the menu item Cluster Display coordinates This replaces the cluster view in the right pane of the main application window with a spread sheet view which lists all the relevant data of the cluster such as the names of specimens all calculated control points and the delta vectors to the reference specimen Unbenannt Morphomatica 1 6 lol x File Specimen Cluster view Specimen E OltGrosi 160722 TPS OltGrosi7 160722 TPS B C kiefMlumina 130722 TP C kiefMlumina 130722 TP5 El candjinv130722 TPS candjinv130722 TPS El CandjMo9b 130722 TPS CandjMo9b 130722 TPS El c n fi1AMat tps Ilyocypris bradyi TPS flipc n FisaR z t Leucocythere mirabilis LY m 1 F tps B he d gt p E Leucocythere
33. Band 13 Graz 2008 Calculation of the cluster mean As soon as one or more specimens are added to the cluster the mean specimen of these can be calculated with the menu item Cluster Calculate mean specimen The outline of this mean specimen is drawn in the cluster view too using a different colour An entry named lt Mean Specimen gt is added in the cluster directory of the tree view representing this mean specimen Candoninae Exercise 2 mmd Morphomatica ned EN E a Oj x File Specimen Cluster View D sug amp Specimen Ei candida 10 I4m f wg TPS Ej candida 2 5M8m f wg TPS E candida 3 5M8m f wg TPS Ej candida 4 SM8m f wg TPS El neglectaS GF2m m vg TPS Ej protzi 3 ZW8m m wg TPS E E Cluster B candida 10 I4m f wg TPS 0 Ej candida 2 SM8m f wg TPS 1 Ej candida 3 5M8m f wg TPS 2 Ej protzi 3 ZW8m m wg TPS 3 Mean Specimen gt Normalised Area DeltaVecScale 1 00 Number of Iterations 6 Coordinates NUM 4 Remark The mean specimen is not recalculated if new specimens are added to the cluster or specimens are removed from it This behaviour is deliberate such that multiple ways of comparison with the mean specimen are possible Selecting a specimen as reference After two ore more specimens are present in the cluster one of these can be defined as the cluster reference To define a specimen in the cluster as reference select its name in the cluster directory of the tree view a
34. Berichte des Institutes f r Erdwissenschaften KarJ Franzens Universitat Graz Band 13 BEE w it IM Methods in Ostracodology CONTRIBUTION TO GEOMETRIC MORPHOMETRICS Landesmuseum Jo Geology and Palaeontology Berichte des Institutes f r Erdwissenschaften Karl Franzens Universitat Graz Band 13 Workshop Methods in Ostracodology Workshop y SC AR Mil dl 4 u pc Ih S Methods in Ostracodology Graz 14 17 July 2008 CONTRIBUTION TO GEOMETRIC MORPHOMETRICS Dedicated to Roger L Kaesler Organisation Karl Franzens University Institute of Earth Sciences Geology and Palaeontology Austrian Academy of Sciences Commission for the Stratigraphical amp Palaeontological Research of Austria Landesmuseum Joanneum Department of Geology amp Palaeontology Land J Geology and Palaeontology Zitiervorschlag dieses Bandes DANIELOPOL D L GROSS M amp PILLER W E Eds 2008 Contribution to Geometric Morphometrics Ber Inst Erdwiss K F Univ Graz 13 88 S Graz lt ISSN 1608 8166 gt Herausgeber und Verleger Institut fur Erdwissenschaften Bereich Geologie und Pal ontologie Karl Franzens Universit t HeinrichstraBe 26 A 8010 Graz Osterreich Redaktion Satz und Layout Institut fur Erdwissenschaften Landesmuseum Joanneum Druck Offsetdruckerei der Karl Franzens Universitat Graz Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Preface
35. Changing the approximation parameters The parameters of an existing approximation can be changed with the menu item Specimen Approximation Properties at any time In the general case a parameter change forces a recalculation of the approximation Delete the approximation of a specimen An approximation of a specimen can be deleted with the menu item Specimen Approximation Delete Change a control point interactively The user can change the calculated control points interactively To do this click on the yellow rectangle representing the control point you want the coordinates to change The fields of the upcoming dialog are initialised with the actual position You can now change the position by entering the new coordinates directly or by pressing the up and down cursor buttons next to the fields 53 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Candoninae Exercise 2 mmd Morphomatica S DO x Fie Specimen Cluster View D Bgl E E Specimen Ej candida 10 I4m f vg TPS Y candida 2 SM8m f vg TPS EY candida 3 SM8m f vg TPS E candida 4 SM8m f vg TPS B neglectaS GF2m m vg TPS El protzi 3 2W8m m vg TPS EE Cluster Control points E candida 10 I4m f wg TPS 0 E candida 2 SM8m F vg TPS 1 E candida 3 SM8m f wg TPS 2 DR protzi 3 ZW8m m wg TPS 3 X Coordinate S I E lt Mean Specimen gt 4 Y Coordinate 236 238 Abbrechen Number of Iterations 6 Mean Err
36. Graz E Mail dan danielopol oeaw ac at gt UnterfeldstraBe 13 10 A 5101 Bergheim E Mail mathstud gmx at 60 valves of Candona neglecta female from different depths of lake Mondsee are compared to see if there is a difference between specimens from deep 65 m and shallow 3 m 6 m sites Fuschler Ache Lake Mondsee 83 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Open MORPHOMATICA to insert the digitalized specimen into the specimen folder Activate the Cluster folder go to Cluster in the menubar and choose Select click the Select All button and Apply Check under Cluster Properties if Normalize for Area is selected The valves are projected on top of each other The difference between the valves is small to see if there is a difference between the valves from the shallow parts and the deep parts select valves from one depth only Deep site Normalised Area Shallow sites DeltaVecScale 1 00 Normalised Area DeltaVecScale 1 00 Number of Iterations 6 Number of Iterations 6 Valves from the deep shallow sites Normalized for Area More information concerning the differences between the different origins can be obtained if the valves are compared without normalization Activate Cluster in Properties change to Don t normalize and select the valves from the different sites again The valves from the deep sediment show a greater diversity in size than those from the shallow parts
37. ICA 1s sensible to variations of points used to calculate the outline The number of points depends on the size of the picture and the resolution Size and resolution should be adapted prior to producing the bitmap No example for resolution and size can be given because these parameters vary greatly depending on the way the picture was produced 12 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 The outline is digitalized from a bitmap of the CS x Resolution Input 7Z pixels inch SES Choose 50 Threshold for the bitmap Check if Suteut 72 pieisiinch valve to get the bitmap go to Image Mode Bitmap the valve has a continuous outline wherever there is a Method d Lisa 30 Threshold small gap it will disturb the digitalizing of the outline A TT Make changes not in the bitmap but go back in the history to the last point prior to bitmap to make modifications Finally the modified image is stored go to File Save as and store it either under a new name or a different format do not simply Save since this way the original picture will be lost This step can be performed first depending on your personal preferences The computer program Tps Dig This program is a simple means to digitalize objects If you have to download it from the internet choose Rohlf F J 2001 tpsDIG Program version 1 43 Department of Ecology and Evolutio
38. K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 The pictures are transformed to a bitmap in a program such as Adobe Photoshop to enable digitalizing with tps dig Collect the specimen you want to compare in one folder this 1s not obligatory but will help keep things organised Open MORPHOMATICA click on Specimen in the menubar and choose Insert A dialog field opens where the samples that you want to compare are selected Unbenannt Morphomatica E 7 10 x File Specimen Cluster View Deh Sg gt Specimen Cluster al Caud 9 2W 8m wd F tps al Caud Absolon f vg TPS a CcLY105M6m tps laa CcL 114m tps a CcLY15M6m tps la CcL 214m tps K la Caud Kaufmann f vg TPS sa CcL 25M6m tps Tal Caud ScharF F vg TPS a CcLY3GF10m tps a CcLY3SM6m tps laa CcLY45M6m tps aa CcLYSSM6m tps a CcLY65M6m tps laa CcLY75M6m tps laa CcL 8SM m tps laa CcLY95M6m tps laa CcRV114m tps 2 File name Files of type al Specimen Files tps med y Cancel A Coordinates NUM u To see the fit of the calculated outline select Approximation under Specimen in the menubar Unbenannt Morphomatica oj x File Specimen Cluster View Insert Delete Properties Approximation Calculate Delete Export to Image File Properties A Los E CcLY114m tps EY CcLY15M6m tps B CcLW214m tps E Col Y25M6m tps Ej CcLY3GF10m tps B CcLY35M6m tps E
39. L 1Mo41 28 tps 48 00 9 08 38 92 23 94 18 52 62 76 296 37 oo CeRVSSM6m tps 24 24 CIFL 1Mo41 29 tps 41 54 15 52 26 02 20 70 16 61 52 46 265 78 SAA d gt CIE 1 M4 20 bn 35 97 A 47 77 50 16 54 12 92 47 77 20A 7S gt Coordinates num L To export the pairwise area deviation of the whole outline select Display Differences Area total ID x Unbenannt Morphomatica 1 6 File Specimen Cluster View Insert Delete Properties EE A A O A AE A PE PERA 0 00 54 53 54 82 74 87 41 59 44 92 42 91 37 36 30 39 39 85 40 04 44 06 36 09 34 96 37 84 4 Select 54 53 0 00 34 84 41 30 22 75 45 90 31 67 35 43 28 43 27 42 23 51 19 98 37 57 21 63 28 03 2 54 82 34 84 0 00 36 67 21 84 42 30 25 58 35 37 31 74 25 75 32 72 29 28 38 91 33 50 27 95 2 Calculate M Speci A g en 74 87 41 30 36 67 0 00 42 62 74 99 56 53 65 58 55 43 50 60 55 67 47 29 68 20 54 00 55 52 5 ark as Reference IER ea ZI SSES n EIER Deg 257901 ESZES Ee 15 00 HETE 28111 051001 K NT Display Specimens A E EE Display Coordinates E rare HESSENI 25901 ae DE Display Differences gt Bie cara inca El A Area dorsal 25 75 50 60 11 29 27 13 11 67 16 07 15 84 0 00 12 25 12 36 17 94 12 78 7 46 Export to Data File CSR E E A E HERE Sal KE KEEN I BE DOS A 29 28 47 29 13 62 33 63 17 28 22 34 16 43 12 36 11 30 0 00 24 45 10 72 15 59 1 WEE 38 91 68 20 26 17 11 76 16 23 8 26 17 82 17 94 15 15 24 45 0 00 18 49 13 35 1 33 50
40. P Q is always 2 1 The area deviation cf chapter 4 2 1s a typical example for a hypermetric see also Kelly 1970 38 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 The dissimilarity index of P and O may be viewed as the ratio of the average distance between individuals of different populations to the average distance between individuals of the same population Perhaps this becomes more clear 1f the denominator of the expression defining diss P Q is written in the following form 55 P les 0 At first sight it seems that here n 2 should be replaced by n n 1 2 since this is the number of distances within the population P and analogously for Q But then the value of diss P Q would be smaller than 1 for P O which does not make sense Intuitively one might think that to a certain extent also the distances between identical individuals which are of course equal to zero should be taken into account For several purposes it will be more convenient to consider the natural logarithm of the dissimilarity index In diss P Q which yields a value in the range 0 00 instead of 1 00 The current version 1 6 of Morphomatica creates a resemblance matrix with entries representing the pairwise distances given by the area deviation Table 1 shows a resemblance matrix comparing the valves of respectively 8 specimens of the species Pseudocandona danubialis from Ada Kaleh fig 13 and Pseu
41. PHOMATICA document A new document is created every time MORPHOMATICA 1s executed This means that the document does not contain any specimen or corresponding approximation and that all program parameters are initialised with certain predefined reasonable values Alternatively the user can create a new document with the menu item File New at any time If there is already an existing document being worked with the user will be asked if he intends to save it Without saving the contents of the previous document are discarded After the creation of a new document the main program window looks as following Unbenannt Morphomatica 1 6 2 loj x File Specimen Cluster View gt Specimen amp Cluster in Open an existing Morphomatica document with the menu item File Open es You can insert specimens via the menu item Specimen Insert da To display the outline of a specimen select it in the left tree view Coordinates NUM 4 As mentioned before no specimens are contained in a new document Now you have to import specimens from an appropriate file format into the document Working with a specimen Insert a specimen into the document To insert one or more specimens from a file into the document use the menu item Specimen Insert MORPHOMATICA supports the file formats tps a file format used by DigiTPS msd files created with the program Morphosys in case that the file extension is
42. ackground very few modifications are necessary but many outlines need to be cleaned First the picture is opened and the valve righted so that the ventral contour is vertical Menubar Image Rotate Canvas Arbitrary Image Layer Select Filter View Window Help Mode L Anti aliased Adjust Duplicate Apply Image Calculations Image Size Canvas Size Rotate Canvas ropa Trim Reveal All Arbitrary Histogram Flip Horizontal Rotate Cannan x Flip vertical Tram E gon OK Angle Cow Extract litro Liquify Shft Cltri 69 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Next the scale if not there is inserted If it is necessary to use a scale from another picture open 1t and use the Rectangular Marquee tool of the toolbar on the left side of the screen to cut out 0 1 mm of the measure below left Edit Image Layer Select Filter view Wim Undo Rectangular Marquee Ctri 2 Step Forward Shft Gtr zZ Step Backward Alt Ctrl Z Fade ShrE Grr F Cut Ctrl X Gopy Merged Shrt Gtr G Paste Ctrl Paste Into Shft Ctrl Clear Fill Stroke Free Transform Ctrl T Transform Define Brush Define Pattern Define Custom Shape Purge Color Settings Shft Ctri K Preset Manager Preferences Edit Copy click the picture where you want to insert Edit P
43. also from limitations 1t performs badly when outlines are much angulated or very heterogeneous In such cases 1t seems that Elliptic Fourier analysis included in programmes like EFA Eliptic Fourier Analysis cf Rohlf 1990 or MAO Morphometrica Analysis of Outlines developed by one of us A B performs better The presentation of MORPHOMATICA 1s here offered in several contributions the mathematical part presented by W Neubauer and J Linhart the programme description sensu strictu written by W Brauneis W Neubauer A Stracke the practical description of creating tps dig files by A Strake Finally the presentation of a series of worked examples for morphometric analysis of outlines prepared by A Stracke W Neubauer L Picot and D Danielopol are intended to demonstrate the utility of MORPHOMATICA for descriptive work within two research directions comparative morphology and taxonomy 1 example morphological variability potentially related to ecological cues 2 example One should note that the information presented with MORPHOMATICA is related to the utilisation of other computer programmes too MORPHOMATICA uses the digitised information of the valve outlines captured with the programme Tps dig Rohlf 2001 We used for this programme the version 1 43 which was downloaded from the web site http life bio sunysb edu morph soft dataacq html Additionally the data obtained from the superimposition of outlines allows
44. an rocks in Kansas Paleobiology 12 290 301 14 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Siegel A F and Benson R H 1982 A robust comparison of biological shapes Biometrics 38 2 341 350 Smith L H and Bunje P M 1999 Morphologic diversity of inarticulate brachiopods through the Phanerozoic Paleobiology 25 3 396 408 Sneath P H A Trend surface analysis of transformation grids J Zool 1967 151 65 122 Stone J R 1998 Landmark Based Thin Plate Spline Relative Warp analysis of Gastropod Shells Systematic Biology 47 2 254 263 Thompson D W 1942 On growth and form Cambridge University Press Second Edition Wayne R K and O Brien S J 1986 Empirical demonstration that structural genes and morphometric variation of mandible traits are uncoupled between mouse strains Journal of Mammalogy 67 441 449 Weider L J Beaton M J and Hebert P D N 1987 Clonal diversity in high arctic populations of Daphnia pulex a polyploid apomictic complex Evolution 41 1335 1346 Wills M A 2001 Morophological disparity a primer In J M Adrian G D Edgecombe and B S Lieberman Eds Fossils Phylogeny and Form An Analytical approach Kluwer Acdemic Plenum Publishers pp 55 144 Zahn C T and Roskies R Z 1972 Fourier descriptors for plane closed curves EEE Trans Comp C 21 269 281 Zelditch M L Swiderski D L Sheets H D and Fink W L 2004
45. areletps 40 73 24 08 18 88 62 35 302 07 9281 08 705 2570 00 665 697 119 STE ER 13 7FHotarele tps 41 32 21 44 17 36 52 90 277 77 7352 29 708 36 70 00 663 95 7117 E 7FHotarele tps 6 J449 f6 tps 42 86 20 41 18 40 37 12 294 34 6662 91 707 83 0 00 664 787 124 E SFHotarele tps 14 BFHotareletps 46 65 27 31 21 60 66 07 345 67 11935 91 705 77 70 00 665 10 118 E J449 f1 tps 8 2FHotareletps 47 61 25 60 20 38 63 60 326 08 10483 60 711 52 0 00 666 097 116 D J449 2 tps 7 J449 f7tps 47 73 23 45 21 02 411 336 26 8798 72 716 18 0 00 672 15 120 E J449 3 tps 11 5FHotareletps 48 33 25 70 21 26 59 87 340 12 10565 80 704 21 70 00 660 90 7118 D 344944108 15 1FHotarele tps 52 57 25 99 21 42 6308 342 70 10808 71 708 49 0 00 669 157 118 B AE 9 FHotareletps 56 44 26 95 22 46 66 70 35931 11624 75 716 38 70 00 675 047 118 nps 10 4FHotareletps 57 12 27 33 23 05 66 08 368 78 11951 34 717 9070 00 675 557 117 El J449 6 tps 5 J449 5 tps 61 36 29 76 26 45 60 76 423 20 14169 24 71919 000 674 157 126 E J449 f7 tps E 1FHotarele tps 5 Cluster E J449 f1 tps 0 B J449 f8 tps 1 El J449 42 tps 2 E J449 f3 tps 3 B J449 14 tps 4 B J449 5 tps 5 TA AAG ima E Evaluating of pairwise differences The menu Cluster Display differences shows a comparison of each two approximating B splines of all specimens The method of calculation can be chosen before The result relies on the selected size normalization The following methods are available 61 Ber I
46. artin Gross Dan L Danielopol Werner E Piller Graz July 2008 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Contents Baltan s A Geometric Morphometrics A contribution to the study of shape variability in ostracods 3 Danielopol D L Neubauer W Baltanas A Introduction to the Computer Programme MORPHOMATICA 17 Neubauer W Linhart J Approximating and Distinguishing Ostracoda by the Use of B Splines 21 Brauneis W Neubauer W Stracke A MORPHOMATICA Programme Description 43 Stracke A From the photography to the digitalized outline suitable for MORPHOMATICA 69 Stracke A Danielopol D L Picot L Comparison of Fabaeformiscandona caudata Kaufmann and Fabaeformiscandona lozeki Absolon from the sublittoral of Lake Mondsee 75 Stracke A Danielopol D L Neubauer W Comparative study of Candona neglecta valves from the shallow and deep sites of Lake Mondsee 83 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 GEOMETRIC MORPHOMETRICS A contribution to the study of shape variability in Ostracods Angel Baltanas Department Ecologia Universidad Autonoma de Madrid Edif Biologia E 28049 Madrid E Mail angel baltanas uam es We have told each other so often and with such force and such eloquence of the uses to which the study of ostracodes has been applied that we have overlooked one startling fact almost no on
47. aste above right With the Move tool the measure 1s positioned Next all colour information is discarded Image Mode Grayscale a window asking you to first flatten opens Flatten Prior to flattening the picture and the measure are independent layers after flattening the layers are permanently joined Adobe Photoshop i Changing modes will affect layer compositing Flatten image before mode change Cancel Don t Flatten Mo de Bitmap Grayscale adjust V Duotone Duplicate Indexed Color Apply Image w EGE Color Calculations CMYK Color ET A Lab Color Image Size Multichannel Canvas Size Rotate Canvas k s G Bits Channel Crop 16 Bits Channel Trim 5 Color Table Reveal ll Assign Profile Histogram Convert to Profile Trap Extract Alk Ctri Liqguify SAPe ACtrl 70 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 All valves need to be oriented in the same way to compare the outlines right valves need to be flipped horizontally to be comparable to left valves Image Rotate Canvas Flip Horizontal Image Layer Select Filter View Window Help Mode b 7 Anti aliased Adjust V Eed O 20 IPG i 25 A Duplicate Apply Image Calculations Image Size Canvas Size Rotate Canvas 150 Erop HU CA Trim 907 CCW
48. atica nt pain E 0 x File Specimen Cluster View Deh amp amp Specimen Bil candida 10 I4m f vg TPS E candida 2 SM8m f wg TPS E candida 3 5M8m f wg TPS B candida 4 SM8m f wg TPS E neglectaS GF2m m wg TPS B protzi 3 2W8m m vg TPS amp Cluster 100 microns 381 156 NUM 4 47 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Remark If a scale is stored for a specimen in the imported file the scale labelled 100 micro meters 1s shown otherwise a scale labelled 100 pixel 1s displayed Remark Basically a rotation and translation is automatically applied to every imported specimen such that the centroid of the specimen is located in the origin of the coordinate system and that the main axes of inertia are parallel to the coordinate axes Display file information for imported specimen The file properties of a specimen can be shown with the menu entry Specimen Properties and are located within the first property page File see below left The path of the file where the specimen was imported from is displayed at the top of the dialog immediately followed by the file type Additional information of the outline is displayed as well E x x File Statistics Graphics Info File Statistics Graphics Info File of specimen Transformation Y Transform the contour points Filename Fi
49. atricii LW f Mo41 30 tps 104 65 17416 67 11 6229 609 5942 61 2 29 08 10 Limnocythere sanctipatricii LW m Mo41 28 tps 155 45 215 2 138 65 71 22 92 73 100 61 99 37 108 29 11 Limnocythere sanctipatricii LY m Mo47 26B tps 133 44 202 46 122 17 47 85 70 36 61 32 77 11 89 39 12 modified Leucocythere mirabilis LW m Mo47 29B1 tps 1133 176 43 51 2 7243 7535 4303 53 04 45 42 13 Prionocypris zenkeri TPS 117 32 132 59 94 66 166 11 166 71 152 83 167 32 130 26 14 Pseudocandona albicans TPS 137 66 100 55 116 68 175 74 196 41 163 54 191 4 137 45 22 14 lt p TMN Tabelle 141 Bereit mu a E WE os es ai 15 BS 119 ES gt l Remark Due to the structure of the algorithm for computing the area deviation of shapes where the approximating B spline changes direction cannot be calculated In this case an error message comes up and you get the entry n c for not calculable into the concerning cell As a rule such shapes occur only in faulty datasets 63 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Export specimen and cluster data The calculated data of the cluster can be exported as a text file by using the menu item Cluster Export data The contents to export depend on the selected entry in the tree view Unbenannt Morphomatica 1 6 Export to Data File Export to Image File E C kiefMlumina 130722 TP D candjinv130722 TPS 2 CandjMogb 130722 TPS E Ilyo
50. been previously selected on the basis of its biological homology Shape is a definite entity a configuration of points that keep geometric relationships among them and cannot be split into isolated items like length or height Confronted with a biological shape the morphometrician will attempt to describe it in terms of transformation from an original reference shape Although the approach proposed by Thompson was very appealing and promising it was not accompanied by any analytical procedure It was the arrival of the computer age several decades later that makes 1t possible to develop application for morphometric analysis based on Thompson s ideas feasible Bookstein 1993 Within geometric morphometrics comparisons between organic forms are addressed by collecting information concerning the location of discrete points called landmarks A set of homologous points landmarks provides information of the biological form given they are distributed homogeneously on the organism and bear some biological meaning Goodall 1983 Bookstein 1984 1986 Chapman 1990 Rohlf and Slice 1990 Schweitzer and Lohmann 1990 Reilly 1990 Bookstein 1991 1993 Reyment and Abe 1995 Foote 1995 Stone 1998 The analysis of configurations of landmarks allows the study of shape change without decomposing it into artificial variables There are several landmark based methods fig 1 and an updated review can be found in Zelditch et al 2004 Concerning ostracods there
51. better solution can be achieved if the vector C t Qi t indicating the corresponding chord length parameter of Q is perpendicular to the curve Therefore we alter the parameter t iteratively by adding a value 4 until C t Q is roughly perpendicular to the tangent C t The comparison in figure 8 shows the desired result After 6 iterations the approximating B spline curve approaches the contour data in an observable better way Figure 8a Before adjusting the parameter Figure 8b After 6 iterative steps a better approach is guaranteed To compare biological aspects of ostracoda it is sometimes useful to adjust the sizes of the standardized outlines This 1s essential for comparing e g ostracods of different age Transforming the control points of the B spline curve in such a way that the end points Po x0 0 Pn x 0 lying on the x axis get the coordinates Pp 1 0 P 1 0 is one possibility This method has one slight shortcoming The centre of gravity shifts out of the origin what can cause difficulties if the contour 1s rather anomalous or pear shaped We obtain a better solution if we use a transformation s X VaX where a is the ratio of the areas a a2 enclosed by the B spline curves dh a 9 This method keeps the centre of gravity in the origin and guarantees a better comparability 32 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 4 Distingui
52. brunnerstra e 34 A 5020 Salzburg E Mail johann linhart sbg ac at 1 Preface Biological outlines may be investigated by various mathematical models There is a well developed theory of shape Zelditch 2004 for the case of sufficiently many good landmarks For the morphometrics of outlines with few or no landmarks sometimes simple polygonal curves B zier curves have been used see for instance Loy 2000 but this may lead to polynomials of rather high degree which tend to oscillate in an undesirable way This is a well known problem in many technical applications especially in computer aided geometric design CAGD where it 1s usually overcome by the use of splines Hoschek and Lasser 1993 Farin 1990 Splines consist of several polynomial curves of low degree that smoothly fit together Two of the most widely used splines are B zier splines and B splines These are not different curves but only different representations of the same curves they may be transformed into one another Hoschek and Lasser 1993 In both cases the shape of the curve is determined by a list of geometrically meaningful control points but for B splines fewer control points are needed The name B spline was coined by Isaac Jacob Schoenberg and it is used as an abbreviation for basic spline de Boor 1978 Farin 2001 The authoritative person for the development of the theory of B spline curves and surfaces was Carl de Boor due to his researches at General Motors
53. ccording B spline 1s drawn 44 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Candoninae Exercise 2 mmd Morphomatica File Specimen Cluster View Deus E E Specimen G candida 10 I4m f wg TPS B candida 2 SM8m f vg TPS candida 3 SM8m f vg TPS candida 4 SM8m F vg TPS Ei neglectaS GF2m m vg TPS El protzi 3 ZW n m vg TPS5 Cluster E candida 10 I4m f wg TPS 0 Ez protzi 3 ZW8m m wg TPS 1 Number of Iterations 60 EES Mean Error 0 322 0 03 dorsal 0 410 0 04 ventral 100 microns Maximum Error 3 852 0 40 dorsal 2 668 0 28 ventral Las 133 Num 4 If alternatively an entry in the cluster directory of the tree view 1s selected then the approximations of all specimens contained in the cluster the associated delta vectors and the optional mean specimen outline are displayed in the cluster view n the right pane Candoninae Exercise 2 mmd Morphomatica File Specimen Cluster View Cah e Specimen G candida 10 I4m f wg TPS B candida 2 SM8m F vg TPS B candida 3 SM8m f vg TPS candida 4 SM8m f vg TPS EA neglectaS GF2m m vg TPS El protzi 3 ZW8m m wg TPS Cluster candida 10 I4m f va TPS 0 JS protzi 3 ZW8m m vg TPS 1 E candida 2 SM8m F vg TPS 2 Normalised Area DeltaVecScale 1 00 Number of Iterations 60 Coordinates NUM E A 45 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Create a new MOR
54. ch as ours a large number of points 1s generated which can contain measurement errors or computational noise In this case it is important for the curve to capture the shape of the data but not to wiggle its way through each single point Given is an array of sequenced pixels Okt k 0 which we want to approximate with a second degree B spline curve If we assign a parameter value t to each pixel Q and select the knot vector U 1uo Hal to be uniform we can set up a system of linear equations QO Cth gt Nip ty Pi 0 with 1 equations where the control points P are the n 1 unknowns The choice of the parameter values tr enormously affects the shape of the curve An adequate method provides the chordal parameterisation It assigns the parameter values t proportionally to the total length of the outline Let d be the total chord length l d K Or Oral k 1 The parameter values are given by to N wel tr tr_1 I ll u k Ge L 26 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Typically it is necessary to find a B spline curve approximating a large number of points In general the number of pixels to approximate is much higher than the number of desired control points n Hence the system of equations is overdetermined and we will not get an exact solution The best way to overcome this difficulty is to solve the system in t
55. cypris bradyi TPS 4 E Leucocythere mirabilis LY E Leucocythere mirabilis me In the upcoming dialog you have to specify a file name for the export file Export data as Speichern in Gy Sourcen D es kto D ZEN Eigene Dateien J BeBE Arbeitsplatz g 2 7 i 2 a Dateiname Candoninae Exercise 2 txt TA Ca ateityp Text Datei txt N etzwerk umd After saving this text file can be opened and further worked with e g with MS Excel or other statistical programs Example of an exported text file opened with MS Excel 64 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Ed Microsoft Excel Candoninae Exercise 2 Export Cluster txt 3 DO x WEN File Edit View Insert Format Tools Data Window Help x Dep eis A Beer E oF 00 E ut H n i D Arial a o B B I U M Specimen Info TEE e Ss SEES SSE Ss A AS eg 1 Specimen Info 3 Specimen Name Image File Locality Sex stage Identifier candida 10 ldm fyg candidal candida 2 Shiom fy candida RH candida 3 Ghim Get candida protzi 3 AWWorm m vq protzi 8 lt Mean Specimen Cluster Info 13 Specimen Name Mean Delta Max Delta Sum Delta Sum Delta Ou Mean Delta Quadrat candida 10 l m fvg 39 561 73406 349 462 46 714 044 44 119 Candida 2 hm tut 32 066 6 451 59 779 32 621 913 25 060 candida 3 him tu 35 620 65 569 054 009
56. d 13 Graz 2008 Kaesler R L 1997 Phase angles harmonic distance and the analysis of form In P E Lestrel Ed Fourier descriptors and their applications in Biology Cambridge University Press Cambridge pp 106 125 Koehl M A R 1996 When does morphology matter Annual Review of Ecology and Systematics 27 501 542 Kuhl F P and Giardina C R 1982 Elliptic Fourier features of a closed contour Computer Graphics and Image Processing 9 236 258 Legendre P and Legendre L 1998 Numerical Ecology 2 ed Development in Environmental Modelling 20 Elsevier Amsterdam pp 853 Lestrel P E 1997 Introduction and overview of Fourier descriptors In Lestrel P E Ed Fourier descriptors and their applications in Biology 4 Cambridge U P Cambridge pp 22 24 Lohman G P 1983 Eigenshape analysis of microfossils A general morphometric procedure for describing changes in shape Mathematical Geology 15 659 672 Lohmann G P and Schweitzer P N 1990 On Eigenshape Analysis In F J Rohlf and F J Bookstein Eds Proceedings of the Michigan Morphometrics Workshop Ann Arbor Michigan The University of Michigan Museum of Zoology pp 147 166 Loik M E and Noble P S 1993 Freezing tolerance and water relations of Opuntia fragilis from Canada and the United States Ecology 74 1722 1732 MacLeod N 1999 Generalizing and extending the eigenshape method of shape space visualization and analysis Paleobio
57. d carapace has a marked functional meaning it 1s the interface between the organism and its environment Benson 1981 Hence ostracod carapaces can be considered as engineering solutions a compromise between design and materials developed to match specific environmental conditions Benson 1981 Consequently it is assumed that ostracod carapace 1s subject to selection pressures i e has adaptive value At the specific level ostracod carapaces include such a number of features tubercles ribs nodes spines and are conservative enough to be used for taxonomical identification in both neontological and specially paleontological studies Carapaces however are not invariant morphological features at the specific level indeed valve shape variability has been extensively documented both within and between populations Methods for the study of shape change and variability Form and shape Form is an attribute of organisms that is made of two components size and shape Benson 1975 Bookstein 1989 Foote 1995 Baltan s et al 2000 To discern between form 4 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 and shape is not a trivial matter given that we frequently deal with information regarding shape which in fact is related to size allometry This is particularly the case when studying ontogenetic processes or in comparisons between individuals grown under different enviro
58. d curves given by Definition 4 2 A curve C t t e a b in the plane is called simply closed if it has no self intersections C t 4 Clt2 for ty ta ty te a b and the endpoints coincide C a C b Accordingly a simply closed curve C constitutes a bounded part of the plane 4 surrounded by the curve A can also be seen as the interior of C To distinguish two simply closed curves C and D with their interiors A and B we consider the area of the part of the plane which is contained in exactly one of the domains A and B and may be viewed as the area between the outlines This corresponds to the area of the symmetric difference A A B which is called the area deviation of A and B illustrated in figure 10 Figure 10 The light blue area is the area deviation of two superimposed simple closed B spline curves The area deviation offers several advantages for the use in ostracodology This common and very natural measure is demonstrative and tangible the resulting differences are in square micrometers what doubtless contributes to a better conceivability Furthermore the measure is rather inured to possible data errors and measuring faults 35 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 As mentioned above ostracods outlines feature a good characteristic for a fast computation without difficulties In general the approximating polygons are not convex but the angles between the
59. docandona eremita from Astileu fig 14 both localities in Romania The data and pictures originate from a comparative study of Iepure et al 2007 investigating the morphology of valves belonging to populations from Romania Figure 13 Lateral view of female valves belonging to the species Pseudocandona danubialis from Ada Kaleh 39 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 00 p LC A l gt gt on d 00 lt T mt N de D gt ek A Co O lt T m 0 e on ma ONE e YA Va SS e lt T m ON i N pam pa LO H mS en d Ze N Ar O I lt lt DO kh A S GA CO E zi Co A 3 dama Ei G A OM 0 A Ca el ei Ei D vi Ke DCH g Ham lt f A E rd ri E oD lt T N par A 0 OD ge O ADO E NAN Gi bt N lt T MA 6 ar fier ei 00 O 0 nm E VO D I lt T gr CO NOOO O VI ER e o Go oe CH nt g T N Cl Go Cl Gi Co Co Co gt Ekel e i neo MA VO Cl Fe Y a N O HOM ON Te 5 g CG Cl oi oi MO CH VD lt D Oo SO 7 gt ON oOo 0 Mook v AA a SE SS D NO ODM oO CH CH ci HOO E lt G va z G GO FAF 5 a se O ech N N Cl A ES 00 Co wi ast N pd 00 00 Md 00 Ka e O mm eco o nn a OW ge w eo CH eh Gi CC DON 3 e NA ech E o y tN OO OM GO OO nam gt Eir A AS A cz k o gx Lem A e Jr A E ID DNO ed Ei VO N Oo CH Co a e AA ei zi oO ya 5 8555 B a Di DD O Co A D I A ch H E
60. e basis functions are 0 outside u m Uj m 1 m 0 p The triangular scheme illustrates this fact for the basis function Nr 2 Nig Nig i i ER N 1 0 No u N 3 0 Ni 2 t is a combination of Ni o t N20 t and N3o Thus N 2 is nonzero only for t e u1 U4 Conversely in any given knot span u uj 1 at most p 1 of the N t are nonzero namely the functions NM p Nun 4 5 4 wg E Ai 3 ie a A BR O al Oo Figure 3 A curve with degree p 2 on U 0 0 0 1 6 2 6 3 6 4 6 5 6 1 1 1 moving P to Px changes the curve in the interval 2 6 5 6 25 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Moving along the curve from 0 to 1 the functions N 2 act like switches As the parameter moves past a knot one N f and the corresponding P switches off and P p 1 switches on Property 2 5 The B spline curve tangents each segment of the control polygon 2 2 Approximation to Outline Pixel Data with B Spline Curves In this section we study the construction of B spline curves that should fit a rather arbitrary set of geometric data such as pixels of an ostracod s outline following the elaborations in Hoschek and Lasser 1993 P egl 1995 Bayer et al 2002 Deuflhard and Hohmann 2002 The aim is to construct curves that do not necessarily satisfy the given data in an exact way but only approximately In some applications su
61. e sanctipe A Limnocvthere set gt Coordinates H l num di After selecting the method a matrix with the calculated values 1s printed out Unbenannt Morphomatica 1 6 beta ell ES File Specimen Cluster View Day zg 3 sone B Trajancypris clavata T Candona candida TPS Di Ilyocypris bradyi TPS DN Leucocythere kamenic ten E Leucocythere mirabilis E Leucocythere mirabilis DN Leucocythere mirabilis em B Limnocythere sanctipe wi B Limnocythere sanctipe win E Limnocythere sanctipe E Limnocythere sanctipe E modified Leucocythere win B Prionocypris zenkeri T n EY Pseudocandona albica H E Cluster DN Trajancypris clavata T DN Candona candida TPS Di Ilyocypris bradyi TPS se B Leucocythere kamenic DN Leucocythere mirabilis 3 E Leucocythere mirabilis 2 EI Limnocythere sanctipe wer B Limnocythere sanctipe GES B Limnocythere sanctipe 2 Limmocvthere a ht D gt Ready Coordinates MN 4 62 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 By clicking the right mouse button into the matrix a menu including options for processing appears Unbenannt Morphomatica 1 6 beta File Specimen Cluster View Dee E gt Specimen sone B Trajancypris clavata T EJ Candona candida TPS B Ilyocypris bradyi TPS E Leucocythere kamenic EJ Leucocythere mirabilis EJ Leucocythere mirabilis E Leucocythere mirabilis E L
62. e uses ostracodes for anything R L Kaesler 1983 Why shape Biodiversity is an issue of main concern not only for scientists but for the whole society as well Taxonomic richness is but one of the many ways we use to express biological diversity Morphological disparity the amount of shape variability within a clade is another And given that both features do not necessarily correlate Cherry et al 1979 Foote 1993a their comparison can provide further evidence about ecological and evolutionary processes involved in the production and maintenance of biodiversity Morphological disparity can be explored at a wide range of taxonomic levels Indeed there has been a growing interest in methods addressing morphological disparity in recent years Foote 1997 McGhee 1999 Ciampaglio et al 2001 Wills 2001 Zelditch et al 2004 Some classic studies concern the morphospace occupied by spiral Raup 1967 or planar branch systems McKinney 1981 aiming to understand macroevolutionary patterns at high rank taxonomic levels Studies in ecomorphology however commonly focus at lower taxonomic levels mainly closely related species seeking for correlations between morphology and ecological requirements Norberg 1994 or for the effects of competitive selective pressures assumed to occur between Dayan et al 1990 At the species level between populations disparity and its correlation with environmental conditions is used to evaluate adap
63. eir approximating B spline curves red 3 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 The distinction of ostracods using the area deviation is implemented in the current version of the program MORPHOMATICA Linhart et al 2006 and a brief documentation of the algorithm was introduced for the first time by us in Minati et al 2008 The program additionally offers the possibility to distinguish the valves by examining only the dorsal resp ventral region 5 Classification of Populations In many fields of ostracodology a comparison of whole groups or populations of ostracods is wanted and necessary In the following a measure for the dissimilarity of two populations is explained which is proposed by one of us J L It s supposed that for any two individuals a kind of distance is available So let P p p and O q 9m be two populations and d a distance defined on P U O The dissimilarity index of P and O is then defined by se ES d s P O diss P Q LE i n P i Q where s P Q K K d Pi Qk k 1 and m i n m l m s P K K d Pi Pk S O K gt d di qk Some essential properties of this dissimilarity index are l diss P 0 only depends on the distances d x y with x y e PU Q 2 diss P 0 is invariant to scaling transformations 3 diss P 0 1l1fP 0 4 If the underlying distance d is a so called hypermetric see Kelly 1970 diss
64. enson R H Chapman R E and Siegel S 1982 On the measurement of morphology and its change Paleobiology 8 4 328 339 Benson R H 1975 Morphological Stability in Ostracoda Bulletin of American Paleontology 65 13 46 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Benson R H 1976 The evolution of the ostracode Costa analyzed by Theta Rho difference Abhandlungen und Verhandlungen des Naturwissenschaftlichen Vereins in Hamburg NF 18 19 Suppl 127 139 Benson R H 1981 Form Function and architecture of ostracode shells Ann Rev Earth Planet Sc 9 59 80 Benson R H 1982 Deformations Da Vinci s concept of form and the analysis of events in evolutionary history In E Montanaro Ed Paleontology essential of historical geology Istituto di Paleontologia Universita di Modena Modena pp 241 277 Blackith R and Reyment R 1971 Multivariate Morphometrics Academic Press New York Blackith R 1965 Morphometrics In T H Waterman and H J Morowitz Eds Theoreticaland Mathematical Biology Blaisdell New York Bookstein F L 1984 Tensor biometrics for changes in cranial shape Annals of Human Biology 11 5 413 437 Bookstein F L 1986 Size and shape spaces for landmark data in two dimensions Statistical Science 1 181 242 Bookstein F L 1989 Size and shape a comment on semantics Systematic Zoology 38 173 180 Bookstein F L 1991 Morphometric too
65. er aspects of the measurements and lack any connection to the geometrical arrangement of such measurements their biological meaning or the functional processes related to the organism development Bookstein 1993 Such situation can be noticed in the first publications that use the term morphometry in its current use Blackith 1965 Blackith et al 1971 In addition traditional morphometrics has some severe limitations Lestrel 1997 a it is highly subjective b 1t does not preserve information on i e it 15 not possible to recover the original shape out of morphometric variables used distances angles and ratios and c all variables used are but a small amount of all information about shape contained in a biological object Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Aware of such circumstances several scientists Jolicoeur 1963 Burnaby 1966 Mosimann 1970 tried to put additional emphasis on the biological foundations of morphometric data Their attempt however was not successful enough The actual turnover occurs at the beginning of the 80s with the rise of the so called Geometric Morphometrics Rohlf 1990a Rohlf and Marcus 1993 Bookstein 1991 1993 Geometric Morphometrics Geometric morphometrics inspire partially at least in the work of D Arcy W Thompson 1942 who approached the study of biological shape change as distortions occurring in a cartesian coordinate system which have
66. erence of Approximating B Spline Curves with Application in Distinguishing Ostracoda Master thesis Department of Mathematics Univ of Salzburg http palstrat uni graz at morphomatica morphomatica_e htm Press W H Teukolsky S A Vetterling W T and Flannery B P 2002 Numerical recipes in C The art of scientific computing 2 ed University Press Cambridge Prossie J 1999 Programming Windows with MFC 2 ed Microsoft Press Grove City OH Rohlf F J 2001 tpsDIG Program version 1 43 Department of Ecology and Evolution State University of New York Stony Brook NY http life bio sunysb edu morph soft dataacq html 1 17 04 World Wide Web Consortium 2000 Extensible Markup Language XML 1 0 2 s ed http www w3 org TR REC xml 68 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 From the photography to the digitalized outline suitable for MORPHOMATICA Anika Stracke Heinrichstrasse 55 A 8010 Graz E Mail anika boriss yahoo com Below is presented a technique that we used successfully at the Limnological Institute in Mondsee during the last years Various amendments to this procedure can be applied For digitising the valve we first insert the microphotograph in the computer programme Adobe Photoshop as jpg file It is necessary to correct the outline of the valves with Photoshop in order to digitalize it with tps dig If the outline has a sharp edge on a clean b
67. esellschaft 44 Seiten Band 6 BOJAR A V LEIS A FRITZ H Hrsg 4 Austrian Workshop on Stable Isotopes in Environmental and Earth Sciences 38 Seiten Band 7 HUBMANN B PILLER W E RASSER M amp LATAL C eds 9 International Symposium on Fossil Cnidaria and Porifera 124 Seiten Berichte des Institutes f r Erdwissenschaften Band 8 BOJAR A V FRITZ H BOJAR H P Eds 7 Workshop of the European Society for Isotope Research 172 Seiten Band 9 HUBMANN B amp PILLER W E Hrsg Pangeo Austria 2004 Beitragskurzfassungen 436 Seiten Band 10 HUBMANN B amp PILLER W E Hrsg 75 Jahrestagung der Palaontologischen Gesellschaft Beitragskurzfassungen 146 Seiten Band 11 BOJAR A V DIETZEL M FRITZ H LEIS A Hrsg 7 Austrian Stable Isotope User Group Meeting 50 Seiten Band 12 CERNAJSEK T HUBMANN B SEIDL J VERDERBER L Hrsg 6 Wissenschaftshistorisches Symposium Geschichte der Erdwissenschaften in Osterreich 83 Seiten ISSN 1608 8166
68. ew Next insert the specimen with the menu item Cluster Insert The filename of the specimen is appended in the cluster directory of the tree view Add Specimens to Cluster m x candida 10 l4m f wg TPS Select All candida 2 SM8m f wg TPS candida 3 SM8m f wg TPS Select None candida 4 SM8m f wg TPS HOO neglecta5 GF2m m vg TPS protzi 3 Z4 Bm m g TPS Cancel Alternatively a specimen can be inserted to the cluster with a typical drag and drop operation within the tree view from the specimen directory into the cluster directory If more specimens are to be inserted into the cluster a convenient way 1s via the menu item Cluster Select At the same time you add a specimen to the cluster the corresponding cluster approximation is calculated Containing several specimens the cluster view looks like the following Candoninae Exercise 2 mmd Morphomatica File Specimen Cluster View 1O x Cee e amp Specimen E candida 10 I4m f wg TPS Ej candida 2 SM8m F vg TPS Ej candida 3 5M8m f wg TPS Ej candida 4 SM8m F vg TPS Ej neglectaS GF2m m vg TPS B protzi 3 2W8m m vg TPS amp Cluster candida 10 I4m f wg TPS 0 Ej candida 2 5M8m f wg TPS 1 Ej candida 3 5M8m f wg TPS 2 Ej protzi 3 2W8m m wg TPS 3 Normalised Area DeltavecScale 1 00 Number of iterations 6 Coordinates NUM u 55 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166
69. h a blue A next to its file name in the tree view 31 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Statistical data of the approximation The calculated approximation values are listed in MM xi Params Statistics Graphics Control points the property page Statistics too Display Iw Display mean an maxium error Mark maximum error There it is also possible to select whether the error Error Maximum error 4 240 dorsal 5 072 ventral Mean error 0 500 dorsal 0 912 ventral values are to be displayed in the specimen view or not _ Abbrechen Jbernehmer Settings for the graphical representation of the B splines As with the representation of the outline of a EEE WE x Params Statistics Graphics Control points specimen there are several options for the Spline representation of the approximating B splines which 7 Draw spine Color HA Choose color are accessible under the menu Specimen Approximation Properties After selecting this menu ren MV Draw polygon item the following options are display in the property Control points page Graphics It is possible to vary the following E Mark points Iw Index the points options Display coordinate values Draw spline If this check box is activated the control points are drawn ee Ze over the outline of the specimen It
70. he sense of minimizing the sum of the squared differences between the given set of pixels Q and the appropriate values of the B spline curve C t l l n SIC te Qll Y IS Nip te Pi Qu min k 0 k 0 0 There are manifold possibilities to get a solution for this least square problem A numerical stable computation of the minimizing problem results from the pseudo inverse matrix gathered from the singular value decomposition of the system matrix see Deuflhard and Hohmann 2002 Hogben 2007 Strang 1998 This method 1s implemented in MORPHOMATICA to approximate outlines 3 Implementation of the Formal Methods to Ostracod Outlines 3 1 Data Structure A photograph of an ostracod s valve is taken under a microscope Afterwards the so called Tps dig Rohlf 2001 saves the outline in a data set This program creates a file with the pairs of coordinates of the outlining pixels of the picture Also other information such as potential landmarks and the file name of the picture is saved in this file The illustration below schematically shows the structure of such a file 27 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 LM 0 OUTLINES 1 POINTS 1387 630 78 631 79 631 80 632 81 633 82 627 74 627 75 628 76 629 77 IMAGE J001 tif ID J001 The file describes an outline with no specified landmarks LM 0 and one contour OUTLINES 1 with 1387 pixels POINTS 1387 3
71. hoo com The programme MORPHOMATICA was initially designed and implemented by one of us W B with the mathematical framework provided by Prof Linhart Department of Mathematics University of Salzburg The functionality was strongly dependent of the requirements and suggestions of two other colleagues Dr Dan L Danielopol and Dr Angel Baltan s UAM Madrid always with the biological requirements and the desired output in mind MORPHOMATICA version 1 5 written by W B and version 1 6 expanded by W N uses the B splines algorithm adapted to ostracod outlines by Johann Linhart The mathematical background of the B splines for an approximate description of ostracod outlines is presented in Bayer et al 2002 Baltanas et al 2003 and Neubauer 2007 The program is a software application running under Microsoft Windows 98 NT 4 0 2000 XP which enables the user to apply the above described method to digitised ostracod outlines The design of the program is based on experiences made during a bachelor project at the University of Salzburg Bayer et al 2002 The software package with the same name cf Linhart et al 2006 is available at http palstrat uni graz at Working with MORPHOMATICA The following topics will be introduced Create anew MORPHOMATICA document Insert a specimen from a file and how to work with it Calculate the approximation for the outline of a specimen Combine several specimen to a cluster ca
72. imnocythere sanctipe E Limnocythere sanctipe EJ Limnocythere sanctipe E Limnocythere sanctipe EJ modified Leucocythere EJ Prionocypris zenkeri T Y Pseudocandona albica el Cluster B Trajancypris clavata T pee EI Candona candida TPS EJ Ilyocypris bradyi TPS ii fen a D H s Sort column Copy sheet Gopy column Gopy specimen Choosing the menu item Copy sheet will copy the matrix into the clipboard where the data are available for further work in other applications e g MS Excel Primer Example of an exported sheet opened with MS Excel Ed Microsoft Excel Mappei 687 Datei Bearbeiten Ansicht Einf gen Format Extras Daten Fenster Al x DEUBASRY App oer l W I gt ara u FXU gt AIS MER A BEE ELE IH 1a P 1 Trajancypris clavata TPS 7 25 10435 126 62 136 92 137 66 134 54 116 65 2 Candona candida TPS OE 0 mE ELE 223 28 210 48 218 31 155 61 3 llyocypris bradyi TPS 104 35 140 91 0110 95 1144 7955 96542 47 3 4 Leucocythere kamenicae LY m X 9 tps 126 62 207 6 110 93 0 26 51 5228 3643 81 29 5 Leucocythere mirabilis LY m Mo47 26B tps 138 92 223 28 1144 28 51 O 4741 3106 79 68 6 Leucocythere mirabilis LW m Mo47 27B tps 137 66 210 46 7955 5220 47 41 O 23 26 65 57 Leucocythere mirabilis LV m Mo47 29B1 tps 134 54 218 31 9542 36 43 31 06 23 26 0 78 8 Limnocythere sanctipatricii LW f Mo41 28 1 tps 116 65 15561 473 01 29 79 66 650 57 78 0 9 Limnocythere sanctip
73. is also possible to change the colour of the B spline there Draw polygon By selecting this entry the control polygon is drawn Mark points The control points are marked with yellow filled rectangles If the cursor is over any of those rectangles the coordinates of the corresponding control point are displayed Index the points Each control point is enumerated Display coordinate values The coordinates of each control point are written next to it 52 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Display the calculated control points coordinates Approximation The calculated control points can also be requested Params Statistics Graphics Control points via the menu item Specimen Approximation Coordinates of contol points Number Contur XCoord Coen Calculate ventral 533 402588 0 000000 ventral ventral ventral ventral ventral ventral ventral ventral dorsal dorsal dorsal dorsal dorsal dorsal dorsal dars al A MOM A UNDOD y MM A 0 OO 562 715637 425 812714 185 963806 12 260260 198 642319 445 134369 546 291382 495 985229 495 985229 470 263306 360 366547 191 792374 1 245814 190 725204 360 851959 Ana 210902 125 897392 271 462982 245 742569 227 685699 270 816071 274 088104 125 527328 0 000000 0 000000 88 893707 258 675323 348 469658 354 182220 325 287323 236 238266 q9 940170 Abbrechen bernehmen
74. l points on each half of the valve give a good result To see the coordinates of the vectors and the differences between the control points mark one valve as reference and select Display Coordinates 14 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Unbenannt Morphomatica 1 6 Mal ES File Specimen Cluster View KH Insert D Cmn en Areatotal Area dorsal Area ventral Mean Delta Square Mean Delta Max Delta Sum Delta Sun D Cup EE olon f vg TPS 0 00 0 00 0 00 0 00 0 00 0 00 0 00 E CIMR Select zwem vd f tps 54 53 18 16 36 37 26 78 22 00 71 38 351 95 El Op Calculate Mean Specimen Psolon f vg TPS 54 82 19 62 35 20 27 35 24 70 45 69 395 21 D CMR aufmann f vg TPS 74 87 23 12 51 75 34 63 29 72 78 26 475 56 BY Cm Mark as Reference charf f wg TPS 41 59 13 09 28 50 23 23 18 91 58 92 302 60 Lp asta Ee A 4m tps 44 92 18 96 25 97 20 72 18 05 39 90 288 73 Sai 6m tps 42 91 17 45 25 46 22 96 19 59 46 74 313 43 A Loz 4 v Display Coordinates 4m tps 37 36 15 74 21 62 20 79 16 53 49 53 264 45 ES El caud Display Differences gt 5M6m tps 30 39 11 79 18 60 15 46 13 31 33 06 213 00 E Caud FF 10m tps 39 85 15 59 24 26 21 29 18 43 49 07 294 83 D Caud Export to Data File M m tps 40 04 16 76 23 28 21 38 17 41 48 68 278 50 E Caud Export ta Image File M m tps 44 06 18 52 25 54 21 02 18 26 47 93 292 08 8 M m tps 36 09 16 42 19 67 17 67 15 53 32 73 248 41 5 a E 13 CcLY6SM m t
75. lculate the cluster mean and corresponding delta vectors 43 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Export specimen and cluster data for import into other applications Print specimen outlines and computational data Save a MORPHOMATICA document The User Interface of MORPHOMATICA The user interface consists of a main application window which is partitioned into two adjoining areas and several dialog objects which are displayed when additional input is required or parameters are to be manipulated In the left part of the main window the file names of the imported ostracod outlines and the associated approximations and clusters are displayed in the style of a directory tree In this tree view the user can select the file he intends to work on Unbenannt Morphomatica 1 6 Oj x File Specimen Cluster View gt Specimen amp Cluster ti Open an existing Morphomatica document with the menu item File Open a You can insert specimens via the menu item Specimen Insert a To display the outline of a specimen select it in the left tree view Coordinates MN 4 The contents of the right part of the window depend on the selected entry in the tree view If an imported ostracod outline in the specimen directory of the tree view is selected the right pane the specimen view displays its outline and 1f an approximation was calculated for the specimen the a
76. le 1 0 10708 ale most Example1 0 2 Graph2 Graph3 B Graph4 2D Stress 0 09 species sex 80 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 ck F caudata det A Kaufmann Kaufmann 1900 F lozeki male lake Mondsee det D Danielopol F lozeki female det A Absolon Absolon 1973 Further calculations such as Cluster or ANOSIM can be performed using Primer as well References Absolon A 1973 Ostracoden aus einigen Profilen sp t und postglazialer Karbonatablagerungen in Mitteleuropa Mitt Bayer Staatssamml Pal ont hist Geol 13 47 94 Kaufmann A 1900 Cyprididen und Darwinuliden aus der Schweiz Rev Suisse Zool 8 209 423 Scharf B W and Keyser D 1993 Living and subfossil Ostracoda Crustaccea from lac du Bouchet France Auvergne Doc CERLAT Mem 2 387 391 81 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 82 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Comparative study of Candona neglecta valves from the shallow and deep sites of Lake Mondsee Anika Stracke Dan L Danielopol and Walter Neubauer Heinrichstrasse 55 A 8010 Graz E Mail anika_boriss yahoo com Commission for the Stratigraphical amp Palaeontological Research of Austria Austrian Academy of Sciences c o Institute of Earth Sciences Geology amp Palaeontology University of Graz Heinrichstrasse 26 A 8010
77. letyp Thinplate Spline Specimen Area 523289 063 r Centroid Contur of specimen Number of points 935 Centroid Coord X 0 000 Y 0 000 Image file candidat 0 r Main axes Scaling factor 0 00264 First main axes x 1 001 Y 0 000 Identifier Second main axes x 0 000 Y 1 001 bernehmen Abbrechen bernehmen Abbrechen Display statistical data for specimen Mathematical parameters which are calculated from the outline defined n the specimen data file are displayed within the property page Statistics see above right As already mentioned an imported specimen s transformed to meet certain conditions The mathematical parameters for the transformation are listed below If you do not want the outline to be transformed you can deselect the check box at the top of the dialog In that case the outline is displayed using the coordinates as defined in the data file 48 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Settings for the graphical representation There are several options for the representation of the outline of a specimen To set the options for a specific specimen select 1ts name in the tree view and choose the menu item Specimen Properties After opening the property page called Graphics the following options are shown File Statistics Graphics Info r Graphics Iw Draw cen
78. logy 25 107 138 Majoran S 1990 Ontogenetic changes in the ostracod Cytherella cf ovata Roemer from the Cenomanian of Algeria J Micropal 9 37 44 Maness T R and Kaesler R L 1987 Ontogenetic changes in the carapace of Tyrrhenocythere amnicola Sars a hemicytherid ostracod Univ Kansas Paleontol Contrib 118 1 15 Marcus V and Weeks S C 1997 The effects of pond duration on the life history traits of an ephemeral pond crustacean Eulimnadia texana Hydrobiologia 359 213 21 Marcus L F 1993 Some aspects of multivariate statistics for morphometrics In L F Marcus E Bello E and A Garcia Valdecasas Eds Contributions to Morphometrics Monografias del Museo Nacional de Ciencias Naturales 8 Madrid pp 95 130 McGhee G R 1999 Theoretical Morphology Columbia University Press New York McKinney F K 1981 Planar branch systems in colonial suspension feeders Paleobiology 7 344 354 12 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 McLellan T and Endler J A 1998 The relative success of some methods for measuring the shape of complex objects Systematic Zoology 47 2 264 281 Moller A P 1994 Sexual selection and the Barn Swallow Oxford University Press Oxford Mosimann J E 1970 Size allometry Size and Shape Variables with Characterizations of the Lognormal and Generalized Gamma Distributions Journal of the American Statistical Association 65 330 930 945
79. ls for landmark data Geometry and Biology New York Cambrige University Press Bookstein F L 1993 A brief history of the morphometric synthesis In L F Marcus E Bello and A Garcia Valdecasas Eds Contributions to Morphometrics Monografias Museo Nacional de Ciencias Naturales Consejo Superior de Investigaciones Cient ficas pp 15 40 Burke C D Full W E and Gernant R E 1987 Recognition of fossil fresh water ostracodes Fourier shape analysis Lethaia 20 307 314 Burnaby T P 1966 Growth invariant discriminant functions and generalized distances Biometrics 22 1 96 110 Burstin J and Charcosset A 1997 Relationship between phenotypic and marker distances theoretical and experimental investigations Heredity 79 477 483 Chapman R E 1990 Conventional Procrustes Approaches In F J Rohlf and F L Bookstein Eds Proceedings of the Michigan Morphometrics Workshop Special Publication The Natural Museum of Natural History The Smithsonian Institution Washington D C 2 12 251 267 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Cherry L M Case S M Kunkel J G and Wilson A C 1979 Comparisons of frogs humans and chimpanzees Science 204 435 Cherry L M Case S M Kunkel J G Wyles J S and Wilson A C 1982 Body shape metrics and organismal evolution Evolution 36 5 914 933 Ciampaglio C N Kemp M and McShea D W 2001 Detecting change
80. m knot vector has referring to our application with p 2 the form m d nu 1 1 1 As an example for n 6 the basis functions of degree 2 generated by an uniform knot vector are depicted below fig 1 0 6 0 2 11 4 0 6 0 5 1 Figure 1 The nonzero second degree basis functions generated by a knot vector U 0 0 0 1 5 2 5 3 5 4 5 1 1 1 To give an introductory idea of B spline techniques we contemplate the following example Let U be a uniform knot vector as defined in the equation above p 2 and the set of control points P 1 0 20 9 1 0 2 1 3 0 5 1 0 7 1 0 1 0 5 1 1 Figure 2 shows the resulting B spline curve Bs Figure 2 B spline curve using the conditions of the example above 24 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Below a number of properties of B spline curves following mostly from the definition 2 1 are given Property 2 2 Endpoint interpolation C 0 Py and C 1 P Property 2 3 Affine invariance An affine transformation including translation rotation and scaling is applied to the curve by applying it to the control points Property 2 4 Local support Moving P changes C t only in the interval u u p 1 fig 3 This follows from the fact that N t 0 for t u U p 1 since N y is a just linear combination of N o 2 Ni p o t see definition 2 1 and those zero degre
81. measure d 1s of special interest for users from the field of biology or palaeontology since it is a tangible intelligible and easy to visualize tool The computing time is extremely short and the approximation of the outline pixel data generates a unique sequence of control points Their distances may have an explanatory power of the difference in the curves shape Nevertheless the computation of the difference of two superimposed B spline curves with the measure defined above has some shortcomings which are discussed in this section At first this distance function does not induce a metric This is easy to comprehend by imaging a B spline curve whose control points are located on a straight line 33 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 The resulting B spline curve corresponds with this line After moving one or several control points along the line our measurement d gets positive but the B spline curve is still the same line Additionally the measure d only considers the magnitude of the difference vector between two corresponding points but not the direction To comprehend the effect of shifting a control point we examine the following testing arrangement Let Po P4 be control points put on a semicircle of radius 1 in uniformly distributed angles that is Po 1 0 Pi 4 P 0 1 Ps 2 P 1 0 V2 V2 V2 V2 By selecting various vectors V with the same length V a
82. mirabilis mean speciman m tps yocypris bradyi E Leucocythere mirabilis LY Ej Leucocythere mirabilis me Ej Limnocythere sanctipatric Cluster Ej OltGrosi7 160722 TPS 1 B C kiefMlumina 130722 TP E candjinv130722 TPS 2 E CandiMo9b 130722 TPS B Ilyocypris bradyi TPS 4 Ej Leucocythere mirabilis LY E Leucocythere mirabilis me Coordinates NUM The meanings of the column headers are as follows Nr Number of specimen according to 1ts number in tree view Specimen Shorted file name of the specimen including its position inside the file if necessary Area total Is the area deviation between the given specimen and the reference specimen Area dorsal Area total applied to the dorsal region only Area ventral Area total applied to the ventral region only Sum Delta Is the sum of all Euclidian distances between control points for the given specimen and those of the reference specimen Mean Delta Is the sum of the delta lengths divided by the number of control points Max Delta Is the maximum value in the set of Euclidian distances delta length between control points for the given specimen and those of the reference specimen 60 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Sum Delta Quad Is the sum of all squared Delta Lengths e the Euclidian distances between the control points of a specimen and the corresponding homologous of the reference outline
83. n State University of New York Stony Brook NY http life b1o sunysb edu morph soft dataacq html 1 17 04 Open your picture under File Input Source File select the format you used for storing the modified picture File Modes Edit Options Help Reopen d Scanner File name Files of type ftps files Cancel 73 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Go to Options Set Scale change the size to 0 1 not EEE 5 xi Length of scale 0 1 Click one end of scale Clear x Cancel be careful to work accurately since small mistakes here will result in artificial differences in comma but point and click the beginning and end of the measure on the picture The line must be parallel to that of the scale on the picture size in MORPHOMATICA Click the outline button al to activate the tool for digitalizing the contour Place the tip of the arrow right of the valve make sure that there are no pieces of dirt between the tip of the tool and the valve and click 1t A red line marks the outline of the object as recognized by the program A 55 If the line is partially on the inside of the valve the contour was leaky and has to be corrected in Photoshop changes must be saved in Photoshop and the valve reopened in tps dig to adopt the changes Right click the mouse and choose Save as XY coords the number of points for the outline a
84. nd use the menu item Cluster Mark as reference Automatically with the selection of a specimen as cluster reference the delta vectors between this cluster reference specimen and all other specimens in the cluster are calculated and displayed The name in the cluster directory of the reference specimen 1s further marked with a blue R next to it to identify it as reference 56 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Remark If the cluster reference specimen is changed the delta vectors are automatically recalculated and actualised in the cluster view Candoninae Exercise 2 mmd Morphomatica SC u i oj x File Specimen Cluster View Deh e gt Specimen G candida 10 I4m f wg TPS E candida 2 SM8m f vg TPS B candida 3 SM8m f vg TPS B candida 4 SM8m f vg TPS E neglectaS GF2m m wg TPS Ej protzi 3 2W8m m vg TPS CES Cluster B candida 10 I4m f wg TPS O E candida 2 SM8m F vg TPS 1 E candida 3 SM8m f wg TPS 2 protzi 3 ZWw m m vg TPS 3 B lt Mean Specimen gt 4 Normalised Area DeltavecScale 2 80 Number of lterations 6 Coordinates NUM 4 Settings for the cluster approximation parameters If you need to change the parameters of the cluster select the menu item Cluster Properties You can set the parameters for the approximation of all specimens in the cluster in the upcoming dialog like before in the approximation for a single specimen App
85. nmental conditions Rohlf and Bookstein 1987 Concerning methods and techniques available for the study of shape change and variability several approaches exist but we will here concentrate in two Traditional Morphometrics and Geometric Morphometrics Traditional Morphometrics This approach also named Multivariate Morphometry Reyment 1985 Foote 1995 and Multivariate Biometry Bookstein 1993 1s an application of multivariate statistics to morphometric issues Although widely used these techniques have a main flaw they do not recognize de geometric origin of the data under scrutiny Variables used in this approach distances angles and ratios are out of context both geometrically and biologically Bookstein 1993 In other words the set of variables used in these procedures preclude the reconstruction of the original shape out of their values Such loss of information makes these methods of limited value Statistical techniques aimed to study relationships between morphological features length height weight developed well before the term biometry was coined Galton 1869 1889 Examples can be found in the works of Montbeillard Quetelet and Galton as well as n later contributions by Edgeworth Pearson Fisher and Wright The many multivariate techniques existing which have been applied to numerous sets of meristic data derived from a plethora of organisms emphasize the structure of the covariance matrix over oth
86. nst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Area total Evaluates the area between two approximating B splines Area dorsal Area total applied to the dorsal region only Area ventral Area total applied to the ventral region only Mean delta square Is the square root of the sum of all Euclidian distances between the control points of two B splines divided by the number of control points The possible methods of calculating and evaluating differences appear after choosing the menu item Unbenannt Morphomatica 1 6 beta MES File Specimen Cluster View D e NM Insert Delete Properties Select an existing Morphomatica document with the menu item File Open Galculate Mean Specimen Mark as Reference an insert specimens via the menu item Specimen Insert Display Specimens Display Coordinates Display Differences Area total Area dorsal Area ventral Mean delta quadrat splay the outline of a specimen select it in the left tree view E ane Export to Data File Ee j Export to Image File E modified Leucocythere B Prionocypris zenkeri T DN Pseudocandona albica GES Cluster em B Trajancypris clavata T E Candona candida TPS oe B Ilyocypris bradyi TPS E Leucocythere kamenic mm E Leucocythere mirabilis ve B Leucocythere mirabilis me B Limnocythere sanctipe ge B Limnocythere sanctipe 3 Limnocyther
87. o possible A to specify additional morphological data For this choose the menu item Specimen m User info Properties and in that dialog the page nfo r Source Locality Name or label Abbrechen Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Remove a specimen from a MORPHOMATICA document A specimen can be removed from the document at any time by selecting its name in the tree view and selecting the menu item Specimen Delete Alternatively pressing the Del Key deletes the selected specimen Approximate a specimen The outline of each specimen can be approximated with the B spline method described in the Mathematical background section The calculated approximation is drawn together with the outline in the specimen view Calculation of the approximation To calculate the approximation from a selected specimen select the menu item Specimen Approximation Calculate Unbenannt Morphomatica 1 6 Oj x File Specimen Cluster View C Insert Sg Zoe Properties Arc8 tps Calculate Approximation Export to Image File Export as TPS File rc5 Eps Ej Arc tps Ej Arc tps H E Cluster Properties 100 microns Coordinates NUM u 50 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Parameters for the approximation In the up coming dialog
88. opulations The example below was performed on the data produced with the setting Normalize for Area Global Test Sample statistic Global R 0 25 Significance level of sample statistic 0 1 Number of permutations 999 Random sample from a large number Number of permuted statistics greater than or equal to Global R 0 Pairwise Tests R Significance Possible Actual Number gt Groups Statistic Level Permutations Permutations Observed dr dl 0 137 147 77558760 999 16 dr sl 0 145 1 4 9657700 999 13 dr sr 0 206 0 4 818809200 999 3 dl sl 0 22 0 6 17383860 999 5 dl sr 0 51 0 1 Very large 999 0 sl sr 0 217 0 4 141120525 999 3 Result section of the Anosim analysis performed with Primer There is a rather high difference between left valves from the deep sediment compared to the right valves from the shallow sediment as compares to the other pair combinations 88 Berichte des Institutes fur Geologie und Palaontologie Band 1 HUBMANN B Hrsg Geschichte der Erdwissenschaften in Osterreich 2 Symposium Abstracts 62 Seiten Band 2 PILLER W E Hrsg AUSTROSTRAT 2000 Vortragskurzfassungen und Exkursionsfuhrer 86 Seiten Band 3 HUBMANN B Hrsg Pal ozoikumsforschung in Osterreich Workshop 73 Seiten Band 4 LATAL C amp PILLER W E EEDEN Environmental and Ecosystem Dynamics of the Eurasian Neogene 60 Seiten Band 5 HUBMANN B Hrsg 9 Jahrestagung der Osterreichischen Palaontologischen G
89. or 0 500 0 05 dorsal 0 912 0 09 ventral 100 microns Maximum Error 4 240 0 41 dorsal 5 072 0 49 ventral Coordinates num u After closing the dialog with Ok the B spline is recalculated and the new approximation 1s drawn Remark Place the mouse cursor over the yellow rectangle representing a control point 1f you want to know its coordinate values Candoninae Exercise 2 mmd Morphomatica File Specimen Cluster View Cee amp Specimen fod El candida 10 I4m f wg TPS E candida 2 SM8m f vg TPS D candida 3 SM8m f wg TPS EY candida 4 SM8m f vg TPS neglectaS GF2m m vg TPS D protzi 3 2W8m m vg TPS 2 ES Cluster E candida 10 I4m f wg TPS 0 D candida 2 SM8m f wg TPS 1 i E candida 3 SM8m f vg TPS 2 protzi 3 ZW8m m wg TPS 3 B lt Mean Specimen gt 4 v2 Number of Iterations 6 Mean Error 0 500 0 05 dorsal 0 912 0 09 ventral 100 microns Maximum Error 4 240 0 41 dorsal 5 072 0 49 ventral 360 237 MNI 4 54 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Cluster view of specimens In the cluster view the approximating B splines of all specimens in the cluster are simultaneously drawn over each other This allows an easier comparison between several specimens in interest Add a specimen to the cluster To insert a specimen from the specimen list into the cluster mark its name in specimen directory of the tree vi
90. pe variability in the non marine ostracod Heterocypris barbara Crustacea Ostracoda Yerbilimeri Geosound 35 1 11 Bachnou A Carbonnel G and Bouab B 1999 Morphom trie des Hemicytherinae Ostracodes par mod lisation math matique du profil lateral externe Application syst matique et phylog n tique C R Acad Sci Paris Sect Terre Planetes Pal ontol 328 197 202 Baltan s A Alcorlo P and Danielopol D L 2002 Morphological disparity in populations with and without sexual reproduction a case study in Eucypris virens Crustacea Ostracoda Biological Journal of the Linnean Society 75 9 19 Baltan s A Brauneis W Danielopol D L and Linhart J 2003 Morphometric methods for applied ostracodology tools for outline analysis of non marine ostracodes The Paleontological Society Papers 9 101 118 Baltanas A Namiotko T and Danielopol D L 2000a Biogeography and disparity within the genus Cryptocandona Crustacea Ostracoda Vie et Milieu 50 397 310 Baltanas A Otero M Arqueros L Rossetti G and Rossi V 2000b Ontogenetic changes in the carapace shape of the non marine ostracod Eucypris virens Jurine Hydrobiologia 419 65 72 Baltanas A and Geiger W 1998 Intraspecific morphological variability morphometry of valve outlines In K Martens Ed Sex and Parthenogenesis Evolutionary Ecology of Reproductive Modes in Non Marine Ostracods Leiden Backhuys Publishers 127 142 B
91. ppears in a window and has to be accepted an additional yellow outline appears Save as chain codes Save as radii AY Save as radii Discard outline View threshold image Refresh display Enclosed area Perimeter Cancel If the number of digitised points is suitable should be around 1000 1500 points store the information under File Save data as if not go back to Photoshop to change the Image Size and Resolution to fit your ideas 74 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Comparison of Fabaeformiscandona caudata Kaufmann and Fabaeformiscandona lozeki Absolon from the sublittoral of Lake Mondsee Anika Stracke Dan L Danielopol Laurent Picot Heinrichstrasse 55 A 8010 Graz E Mail anika boriss yahoo com Commission for the Stratigraphical amp Palaeontological Research of Austria Austrian Academy of Sciences c o Institute of Earth Sciences Geology amp Palaeontology University of Graz Heinrichstrasse 26 A 8010 Graz E Mail dan danielopol oeaw ac at Avenue des Vendeens 71 F 50400 Grandville E Mail laurent picot lavache com CAES CAC CCD 0 2mm Fabaeformiscandona caudata left valve a right valve b Fabaeformiscandona lozeki female left valve c right valve d male left valve e right valve f Above you see microphotographs representing typical specimen of the two species 75 Ber Inst Erdwiss
92. ps 34 96 14 27 20 70 17 93 14 79 43 83 236 68 i 14 CcLY7SM m tps 37 84 14 65 23 19 19 75 16 41 46 17 262 59 E CoLY2I4m tps 7 15 CcLY8SM m tps 42 03 16 11 25 92 23 66 19 17 56 80 306 71 E CeL 25M m tps 8 16 CcLY9SM6m tps 36 17 12 99 23 17 18 50 15 87 36 98 253 92 D CcL 3GF10m tps 9 17 CcLy105M6 amp m tps 40 75 17 59 23 16 21 38 17 76 52 95 284 10 DN CcLv35M m tps 10 18 CcRYil4m tps 41 19 16 39 24 80 22 72 19 19 58 72 307 10 D CcLy4sMem tps 11 19 CcRV1SM m tps 51 27 19 06 32 21 25 76 21 45 64 15 343 27 a 20 CcR 2I4m tps 43 40 16 86 26 54 25 67 21 72 62 43 347 49 g a 21 CcRV 25M m tps 32 55 13 02 19 54 18 85 15 90 41 36 254 38 22 CcR 35M m tps 39 92 17 02 22 91 23 44 19 23 62 42 307 72 CcL 7S5M m tps 14 23 CcR 45M m tps 37 05 13 10 23 95 21 01 18 04 37 78 288 58 E CcLv8sM m tps 15 24 CcR SSM m tps 41 32 17 00 24 32 22 06 18 84 51 86 301 46 E CcL 95M m tps 16 25 CcRY6SMEm tps 34 55 15 09 19 45 19 42 16 87 42 67 269 99 D CelviosMem tps 17 26 CcRY75M6m tps 44 50 13 77 30 73 21 52 18 55 46 53 296 83 CH cerviimips 18 GE Aal nel i 5378 nal enl 2917 e i m tps i i i 5 ne a 29 CIFLV114m tps 42 44 7 73 34 71 20 13 16 40 42 73 262 33 i ap CIfLY1Mo41 23 tps 45 41 12 97 32 44 20 74 17 24 51 05 275 78 CeRv2SM m tps 21 31 CIFL 1Mo41 26 tps 38 52 11 75 26 77 17 85 15 34 42 59 245 36 E CcR 3SM6m tps 22 32 CIFL 1Mo41 27 tps 45 04 14 82 30 22 22 25 18 85 57 08 301 55 E CcRV4SM6m tps 23 33 CIF
93. res Theta Rho analysis Analysis LSTRA Sneath 1967 Complexity fractal approach Curvature Zhan amp Roskies 1972 LA Eigenshape analysis Lohmann 1983 Fourier analysis Standard Fourier analysis Kaesler 4 Waters 1977 __ Biorthogonal grids Resistant Fit Theta Rho Analysis RFTRA Siegel amp Benson 1982 Elliptic Fourier analysis Kuhl amp Giardina 1932 Thin plate splines Bookstein 1989 Dual axis Fourier shape analysis Moellering amp Rayner 1981 Figure 1 Sketch of relationships between some methods in the realm of Geometric Morphometrics Course Outline Sessions in the course will offer a close view to some of the methods mentioned above together with exercises dealing with related aspects like Data Acquisition Procedures and Multivariate Analysis of Shape Descriptors Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Selected References References here included are those mentioned in the text above and many others which have not been explicitly quoted but that might be of interest for those attending the course Abe K Reyment R A Bookstein F L Honigstein A Almogi Labins A Rosenfeld A and Hermelin O 1988 Microevolution n two species of ostracods from the Santonian Cretaceous of Israel Historical Biology 1 303 322 Alcorlo P Baltanas A and Arqueros L 1999 Intra clonal sha
94. resentation with the menu item Cluster Properties The following options are shown in the property page Graphics of the property sheet Approximation x Params Graphics Printing Reference Specimen Draw reference only MV Draw mean cluster reference r Delta vectors M Draw delta vectors Iw Number vectors with specimen IDs Scaling factor for delta vectors fi 4 Abbrechen 58 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 The following options can be set Draw reference only If this option is selected only the reference specimen but together with all the delta vectors is drawn Draw mean cluster reference If the check box is activated the mean specimen is drawn Draw delta vectors Whether the delta vectors should be displayed or not Number vectors with specimen Ids The endings of the delta vectors can be marked with the number of the specimen in the cluster view corresponding to the number in the cluster directory of the tree view Scaling factor for delta vectors Use this to scale the delta vectors appropriately If two specimens are hardly different this option can be used for a better comparison Settings for the print parameters It 1s possible to change the printing settings in the property page Printing from the menu item Cluster Properties Approximation DZ D x Params Graphics Printing Pen Width Specimen Delta Vectors fi
95. roximation D n l xi Params Graphics Printing Control points Number of control points E Y Params correction Je Apply params correction Number of iteration steps E 4 Size Normalizing Don t normalize Normalize for outer control points m1 mc Normalize for area Centroid size Ubemehmen Abbrechen 97 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 The options are as follows Number of control points for upper and lower B spline Number of steps in the parameter correction the mathematical method used to improve the calculation of the approximation Apply various normalisation operations This allows for a size independent comparison of specimens o Normalize for outer control points The specimen approximations e the two B splines are transformed such that the cluster points m1 on the left side and m2 on the right side of all specimens fit together o Normalize for area The specimen approximations are transformed such that all have equal area 1000 o Normalize for centroid size The specimen approximations are transformed such that all have equal values for the centroid size of the outlines the square root of the sum of squared Euclidean distances from each contour point to the centroid divided by the number of contour points k Settings for the cluster representation It is possible to change the graphical rep
96. rphometrics and its various aspects The major part of this volume deals with an alternative geometric morphometric method newly developed in Austria mainly by specialists from the University of Salzburg Prof J Linhart and his students This method is documented herein with its mathematical background a detailed programme description and some practical examples as well and is introduced besides the workshop attendees to a broad scientific community In addition to this focus on morphometrics the workshop will also provide information on and demonstration of specific field sampling and analytical techniques for high resolution studies Such field techniques will be demonstrated in the well studied clay pit of Mataschen Styria Ecological interpretations and environmental reconstructions are based on morphological characters but are increasingly supported by and combined with analyses of the stable isotope composition of the ostracod valves preferably of a 0 and SC On the application of these geochemical techniques in ostracodology special emphasis will be placed covering different aspects from the mere analytical procedure to the influence of diagenesis on the isotopic values Dr J Boomer Birmingham Dr C Latal Graz These methodological aspects will be supplemented by contributions of most workshop participants on various ostracod and environment topics We are grateful to the Austrian Science Fund for its long year support M
97. rti M Loy A Naylor G J P and Slice D E Eds 1996 Advances in morphometrics Plenum Press New York Minati K Cabral M C Pipik R Danielopol D L Linhart J and Neubauer W 2008 Morphological variability among European populations of Vestalenula cylindrica Straub Crustacea Ostracoda Palaeogeogr Palaeoclimat Palaeoecol 264 296 305 Rohlf F J 1996 Introduction to outlines In L F Marcus M Corti A Loy G J P Naylor and D E Slice Eds Advances in morphometrics 209 210 Plenum Press New York Rohlf F J 1990 Morphometrics Ann Rev Ecol Syst 21 299 316 Rohlf F J 2001 tpsDIG Program version 1 43 Department of Ecology and Evolution State University of New York Stony Brook NY http life bio sunysb edu morph soft dataacq html 1 17 04 Sanchez Gonzalez J R Baltan s A and Danielopol D L 2004 Patterns of morphospace occupation in Recent Cypridoidea Crustacea Ostracoda Rev Esp Micropal 36 13 27 Zelditch M L Swiderski D L Sheets H D and Fink W L 2004 Geometric morphometrics for biologists a primer Elsevier Academic Press Amsterdam 20 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Approximating and Distinguishing Ostracoda by the Use of B Splines Walter Neubauer Johann Linhart Unterfeldstra e 13 10 A 5101 Bergheim E Mail mathstud gmx at Department of Mathematics University of Salzburg Hell
98. s Union Danielopol D L Baltan s A Namiotko T Geiger W Pichler M Reina M and Roidmyr G 2008 Developmental trajectories in geographically separated populations of non marine ostracods morphometric applications for palaeoecological studies Senckenbergiana lethaea 88 in print Gross M Minati K Danielopol D L and Piller W 2008 Environmental changes and diversification of Cyprideis in the Late Miocene of the Styrian Basin Lake Pannon Austria Senckenbergiana lethaea 88 in print 19 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Gu ziec A 1996 Curves and surfaces for data modeling In L F Marcus M Corti A Loy G J P Naylor and D E Slice Eds Advances in morphometrics 253 262 Plenum Press New York Hill F S 1990 Computer graphics Mc Millan Publ Co New York Iepure S Namiotko T Danielopol D L 2007 Evolutionary and taxonomic aspects within the species group Pseudocandona eremita Vejdovsky Ostracoda Candonidae Hydrobiologia 585 159 180 Iepure S Namiotko T Danielopol D L 2008 Morphological diversity and microevolutionary aspects of the lineage Cryptocandona vavra Kaufmann 1900 Ostracoda Candonidae Ann Limnol Int J Lim 44 27 42 Linhart J Brauneis W Neubauer W Danielopol D L 2006 Morphomatica Computer Program version 1 6 http palstrat uni graz at morphomatica morphomatica _e htm Marcus L F Co
99. s in morphospace occupation patterns in the fossil record characterisation and analysis of measure of disparity Paleobiology 27 695 715 Danielopol D L Ito E Wansard G Kamiya T Cronin T and Baltan s A 2002 Techniques for Collection and Study of Ostracoda In J A Holmes A R Chivas Eds The Ostracoda Applications in Quaternary Research Washington DC The American Geophysical Union pp 65 97 Dayan T Simberloff D Tchernov E and Yom Tov Y 1990 Feline canines Community wide character displacement among the small cats of Israel American Naturalist 136 39 60 Digby P G N and Kempton R A 1987 Multivariate Analysis of Ecological Communities Chapman and Hall London Dryden I L and Mardia K V 1998 Statistical Shape Analysis John Wiley and Son Chichester Elewa A M T 2004 Application of geometric morphometrics to the study of shape polymorphism in Eocene ostracodes from Egypt and Spain In Elewa A M T Ed Morphometrics Application in Biology and Paleontology Springer Verlag Berlin pp 7 28 Ferson S Rohlf F J and Koehn R K 1985 Measuring shape variation among two dimensional outlines Systematic Zoology 34 4 59 68 Fink W L 1990 Data acquisition for morphometric analysis in systematic biology In F J Rohlf and F L Bookstein Eds Proceedings of the Michigan Morphometrics Workshop The University of Michigan Museum of Zoology Ann Arbor pp 9 19 Foote
100. several parameters for the approximation can be varied It 1s possible to specify the number of control points to be calculated and the number of iterations for the parameter correction to be applied Next the approximating B splines are drawn over the outline of the specimen Additionally the control points of the upper and lower half of the B splines are Approximation 3s x Params Statistics Graphics Control points Control points Number of control points H Params correction V Apply params correction Number of iteration steps E 4 Abbrechen bernehmen displayed and enumerated as well as the corresponding control polygon The calculated values for the approximation such as the number of iterations mean and maximum approximation error of the upper and lower half are shown in the lower left corner of the specimen view Candoninae Exercise 2 mmd Morphomatica File Specimen Cluster View elm x Deus E E Specimen candida 10 I4m f wg TPS E candida 2 5M8m f wg TPS Ej candida 3 SM8m f wg TPS Ej candida 4 5M8m f wg TPS Ej neglectaS GF2m m vg TPS E protzi 3 ZW8m m wg TPS Cluster v2 Number of lterations 6 Mean Error 0 500 0 05 dorsal 0 912 0 09 ventral 100 microns Maximum Error 4 240 0 41 dorsal 5 072 0 49 ventral 214 187 NuM 4 Remark A specimen for which an approximation 1s fitted is marked wit
101. shing Outlines 4 1 Distance of the Corresponding Control Points At first sight the following concept of a distance between two B spline curves seems to be quite natural Definition 4 1 Let C D be two B spline curves with control point sequences Pn P resp Qo Q We define the distance between C and D as the square root of the sum of all squared Euclidean distances between the corresponding control points divided by the number of control points Defining the difference between two B spline curves in this way has a number of coherent reasons First of all two superimposed B spline curves are identical if their corresponding control points coincide Property 2 3 Affine invariance implies that a translation or rotation is applied to the curve by applying it to the control points Both indicate a reasonable measure A further evidence provides the attribute that the control polygon represents a kind of approximation to the B spline curve So to some extent the control points describe the shape of the curve cf Baltan s et al 2003 A further advantage of distinguishing B spline curves by using the distance of the corresponding control points arises from property 2 4 Local support A single control point takes effect just on a part of the B spline curve By measuring the Euclidean distance of two corresponding control points we should be able to determine whether the respective regions differ significantly or not Moreover our
102. ssing ostracod material and morphometric data Discussions with Prof Dr F Osterreicher Dep of Mathematics Univ of Salzburg Dr K R Clarke Plymouth Marine Laboratory were useful for the preparation of this manual The present project benefited also from the financial support offered by the Austrian Academy of Sciences and the Austrian Foundation for Scientific Research FWF Project P 17738 BO3 to D L Danielopol References Baltanas A Brauneis W Danielopol D L and Linhart J 2003 Morphometric methods for applied ostracodology tools for outline analysis of nonmarine ostracodes In L E Park and A J Smith Eds Bridging the gap trends in the ostracode biological and geological sciences Paleontol Soc Papers 9 101 118 Bayer S Brauneis W and Trischitz U 2002 Approximierende B Splines Bachelor Thesis Department of Mathematics University of Salzburg Hoschek J and Lasser D 1993 Fundamentals of Computer Aided Geometric Design A K Peters Wellesley MA Kain E and Wingo S 1998 MFC Answer Book Solutions for Effective Visual C Applications Addison Wesley Boston MA Meacham C A and T Duncan 1993 Linhart J Brauneis W Neubauer W Danielopol D L 2006 Morphomatica Computer Program version 1 6 http palstrat uni graz at morphomatica morphomatica e htm 67 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Neubauer W 2007 Measuring the Diff
103. tation to local conditions Loik and Noble 1993 and at further detail morphological variability within a population can be related to the niche concept and dynamics Pulliam 1986 or to sexual selection Meller 1994 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Finally there 1s an increasing interest in exploring the potential for shape change of a given genotype the phenotypic plasticity of morphological features as well as its adaptive value Schlichting and Pigliucci 1998 The amount of morphospace occupied by a set of clades has been used as indicator of ecological diversity Warheit et al 1999 evolutionary radiation McGhee 1999 morphological convergence in distant communities Ricklefs and Miles 1994 or selective extinctions Roy and Foote 1997 Less frequent is its use as tracer of environmental conditions or dispersal routes of groups below the species level populations clones Why Ostracods Most of the issues outlined above can be extensively addressed using ostracods Indeed this group of organisms can be labelled as ideal for a morphometric approach because of its high taxonomic richness and the diversity of habitats occupied In addition ostracods have an extensive fossil record a feature that allows the examination of shape environment relationships back into evolutionary time scale Morphometric study of ostracods mainly focuses on the analysis of carapace shape Ostraco
104. tings portrait landscape A4 or A3 format etc can be done with the menu item File Print Setup Save a MORPHOMATICA document A MORPHOMATICA document can be ees peichern unter save with the menu item File Save Speichem E Testdaten Jen Candoninae Exercise L mmd sa Candoninae Exercise 2 mmd You have to specify the desired path and file name the file is saved in a XML file format Dateiname Candoninae Evercise 2 mrnd Dateityp Filetyp Morphomatica mend M Abbrechen E If MORPHOMATICA will be closed and the current document is changed but not saved the user is informed and the document can be saved immediately Morphomatica A nderungen in Candoninae Exercise 2 mmd speichern Nein Abbrechen 66 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 The complete contents of the MORPHOMATICA document are saved in a XML file The files from which the specimens where imported are therefore no longer necessary So it s e g possible to send the XML file with the extension mmd alone per email to another user of MORPHOMATICA Remark It is also possible to extract the specimens again in the TPS file format Menu Specimen Export as TPS file Acknowledgements We are grateful to J Knoblechner Mag M Pichler Inst of Limnology Mondsee as well as to various students who worked with MORPHOMATICA during the last years and helped in the proce
105. troid Iw Draw coordinate system Draw boundingbox Draw main axes m Color Contur ET Choose color m Contur I Enumerate the points Take each n th point only 60 Iw Draw line between adjecent points bb Abbrechen Ibemehmen x It is possible to change the following options Draw centroid If the check box is activated the centroid of the specimen is marked Draw bounding box The bounding box enclosing all points of the outline of the specimen as well as the coordinates of the corner points of this rectangle are displayed Draw main axes Selects whether the main axes of inertia are drawn or not This option is useful if the outline is not transformed to normal position Draw coordinate system Option to draw the axes of the coordinate system Colour To choose the colour for the specimen Enumerate the points of contour If the option is activated then the points of the outline will be enumerated only the number of each n th point will be printed Draw line between adjacent points Given that the distance between the points of the outline is to large to form a continuous outline selecting this option will connect the points with straight line segments Additional morphological data File Statistics Graphics Info m History Not only the imported outline of a specimen can be Sex El saved in a MORPHOMATICA document it s als
106. u are now asked to give a name for the factor you are about to make the name for the factor is important if you give the samples several factors e g species and sex species sex plus individual identifier species sex plus origin etc The same factors are used for the statistical methods such as Anosim or Cluster It s possible to produce the factor lists in Excel and copy paste them into Primer paste only works with the menu or the keys and not the right mouse button this is helpful since it might speed up the process of labelling In the Factors menu you can also define a plot key plus you can move the given factors up and down which makes the legend easier to interpret To produce a MDS plot of your matrix click on Analyse and select MDS Analyse Options ANOSIM ANOSIM2 CLUSTER MYDISP RELATE 25TAGE The program asks for the number of restarts and starts calculating The more restarts you have the more reliable the results are but the longer the calculation takes ten restarts are usually sufficient The MDS will be displayed in a new window go to Graph and select Properties Choose the factor and whether you want labels and or factors displayed The graph can be rotated in order to give the best display of the data PRIMER Example1 010708 2 p lolx CH File Edit View Graph Tools Window Help Jelx De elia Sek PO amp bel 9 Example 1 010708 EE Example1 010708 Examp
107. ulting curves fit together After the standardisation this can easily be done by using the x axis as dividing line Concretely all points P x y with x gt 0 will be assigned to the dorsal region and all points with x lt 0 to the ventral region Therefore we must assume that the contour crosses the x axis 30 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 at most at two points what is usually the case for ostracods outlines fig 6 Hence there are only two pairs of consecutive points in the contour where x gt 0 and x lt 0 We pass a line through these points determine the intersection points with the x axis and add them to the contour These intersections will be the starting and end points of the approximating B spline curves Figure 6 Ostracod contour after standardisation The outlining points of the respective region get numbered consecutively clockwise and are approximated by a B spline curve of degree p 2 with a uniform knot vector and parameter value gathered by a chordal parameterisation The procedure is explained in sections 2 1 and 2 2 Figure 7 plots the contour data of an ostracod with its approximating B spline curve Figure 7 Ostracod contour approximated by a second degree B spline curve and its control polygon 31 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 However this approximation scheme does not bring an optimum result A
108. ve a thin line either going up or down that helps to position the symbols There is an imaginary plane and the samples are either in above or beneath that plane imagine balloons filled with helium above or water below the lines connect the symbols with this plane The graph can be viewed from all around to find the best view of the results Most of the valves from the deep sediment of lake Mondsee are below the plane right and left valves are grouped whereas the valves form the shallow parts of the lake are mostly within or above the plane 86 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Example 2 010708 Z E MDS Plot in 3D To open the matrix containing the data from Don t Normalize it is necessary to save the first matrix as a Primer file or close 1t to enable the program to open the same Excel workbook again In the first dialog box select sheet two as the source otherwise continue as before Copy the factor list from the first matrix and use it for the new matrix The same effect as was shown in MORPHOMATICA above s visible in the plot the variability is higher n the group of valves from the deep site BER Example2NonNorm 010708 2D Stress 0 02 e y Y 7 yo MDS plot with No Normalization 87 Ber Inst Erdwiss K F Univ Graz ISSN 1608 8166 Band 13 Graz 2008 Primer offers a randomisation test Anosim to evaluate the statistical difference between the p
109. x axis and a straight line from the origin to the vertices are in ascending order This fact makes it possible to reduce the number of computations for possible points of intersection substantially Every specimen is approximated by two open B spline curves describing two regions a dorsal and a ventral one fixed by the main axes of inertia with the minimum moment To calculate an approximative value for the enclosed area between the B spline curves of two specimen halves in the present implementation 51 points on each curve corresponding to equally spaced parameter values are computed We denote them with C for the first curve and D for the second ij 0 51 This yields a polygon with 50 line segments substituting each B spline curve with S CC denoting the segments of the first polygon and T D D 1 denoting the segments of the second To evaluate the area deviation the points of intersection of the two superimposed polygons are of importance In principle 1t would be necessary to determine the points of intersection of each segment of the first polygon with each segment of the second polygon what requires 50 x 50 2500 comparisons for each specimen half This goes beyond the scope of a tolerable computing time To accelerate the process the cotangent cot x y is assigned to every vertex C resp D For this purpose let o be the angle between the x axis and the vector OC pointing from the origin to the vertex C and y

Berichte des Institutes für Erdwissenschaften, Karl

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Berichte des Institutes f&uuml;r Erdwissenschaften, Karl

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Berichte des Institutes für Erdwissenschaften, Karl