User Manual
Contents
1. Checked option links crossing patches are Unchecked option links crossing patches are removed kept Save real path checked box links are saved as paths representing the actual route of the link between two patches unchecked box links are saved in topological form only In this case display of links with the realistic view is unavailable This is recommended for graphs with very many links e g a non thresholded complete graph so as to limit the use of memory Unless paths are saved intra patch distances cannot be included in the computation of metrics 2 3 2 Distance or link impedance Distances are calculated from edge to edge between patches Two main types of distance are available Euclidean distances and least cost distances Euclidean distance links are defined in Euclidean distances distance as the crow flies between patches meaning the matrix is considered to be uniform Least cost distance links are defined in cost distances Matrix heterogeneity is taken into account by assigning a resistance value friction to each landscape category The user can activate this option in either of two ways 1 either by specifying different costs for the landscape map categories in the table 2 or from an external raster file tif or rst in which each pixel has a resistance value The use of least cost distance provides two types of impedance using the same paths cumulative cost impedanc2. Flux F Formula Meaning Global level LASG For the entire graph sum of potential dispersions from all patches ry Yaf eet i 1 j 1 j i Local level us For the focal patch i sum of capacity of patches other than i and F gt af e7 tij weighted according to their minimum distance to the focal patch i 4 through the graph This sum is an indicator of the potential Jai dispersion from the patch i or conversely to the patch i Values Values depend on the definition of a If a represents an area F expresses an area Minimum value 0 Maximum value Total area of habitat Comment The path used in the graph is the one that maximizes e i e the one that minimizes the distance d or the cost between the patches i and j This metric is called Area Weighted Flux AWF in some publications However in Graphab a is more general because it represents patch capacity which may be their area or some other criterion chosen by the user Similarly the weighting is variable depending on the 6 parameter In CS22 AWF is calculated only from patches directly connected to the focal patch while Graphab takes into account indirectly connected patches References Urban and Keitt 2001 Saura and Torn 2009 Folt te et al 2012a Probability of Connectivity PC Formula Meaning Global level For the entire graph sum of products of capacity of all pairs of 1 n n patches weighted by their interaction probability divid
3. X 1083605 834 Y 2348697 529 The user must load a file of presence points and specify the name of the set of presence pseudo absence points t Several o be created parameters must be defined to randomly sample absence points Cell size of the grid in meters to define the size of cells from which absence points will be potentially sampled The update grid button can be used to display the grid according to the selected cell size Minimum distance between points this function reduces the effects of spatial autocorrelation by specifying a minimum distance in meters to be observed between the generated absence points and between these points and presence points Type of distance the unit of the minimum distance between points depends on the type of the distance used in the link set selected 18 Keep only one existing point by cell this option checked box retains only one presence point in each cell thereby reducing the effects of spatial autocorrelation 6 4 Species distribution model If a set of presence absence points has been defined the software can use the connectivity metrics calculated from a graph as predictors in a species distribution model from the Analysis Species distribution model menu Such modeling is possible even if points are not located in habitat patches by means of a spatial extrapolation of the values of metrics The logistic regression model is a based on minimizing the AIC criterio
4. 0 Maximum value 1 Reference Pascual Hortal and Saura 2006 28 Area metrics Mean Size of the Components MSC Formula Meaning Global level 1 nG For the entire graph mean of the component capacities MSC D acy nc k 1 Values Minimum value minimum capacity Maximum value SLC Size of the Largest Component SLC Formula Meaning Global level SLC max ac For the entire graph largest capacity of components Values Minimum value minimum capacity Maximum value maximum capacity Class Coincidence Probability CCP Formula Meaning Global level ue ac 2 For the entire graph probability that two points randomly placed CCP 7 on the graph belong to the same component D1 acy k 1 Values Minimum value minimum capacity as many components as patches and regular capacities Maximum value sum of capacities only one component Reference Pascual Hortal and Saura 2006 Expected Cluster Size ECS Formula Meaning Global level 1 NE For the entire graph size of a component ECS ac ac Xk Ak k 1 Values Minimum value minimum capacity as many components as patches and regular capacities Maximum value sum of capacities only one component Reference O Brien et al 2006 29 Topological metrics Harary Index H Formula Meaning Global level LL 1 Sum
5. 9 1 Details of metric calculations sseesssosessssssssosssssoessseoosessooseseosssssccsessossessossessooseseesseseos 25 9 2 Referenti Sarnia a a 33 1 Introduction 1 1 About Graphab Graphab is a software application for modeling ecological networks using landscape graphs It is composed of four modules for constructing graphs including loading initial landscape data and identifying patches and links Euclidean distances or least cost paths computing connectivity metrics from graphs integrating graph based connectivity metrics into species distribution models visual and cartographic interfacing 1 1 1 Authors Graphab has been developed by Gilles Vuidel and Jean Christophe Folt te at Th MA laboratory University of Franche Comt CNRS Funding has been provided by the French Ministry of Ecology Energy Sustainable Development and the Sea ITTECOP Program The Graphab logo was designed by Gachwell 1 1 2 Terms of use Graphab is distributed free of charge for non commercial use Users must cite the following reference in their publications Folt te J C Clauzel C Vuidel G 2012 A software tool dedicated to the modelling of landscape networks Environmental Modelling amp Software 38 316 327 For any other use the prior consent of Th ma laboratory is required Send applications to graphab univ fcomte fr 1 2 System requirements Graphab runs on any computer supporting Java 1 6
6. Each graph in a project can be used to compute different connectivity metrics The details of how they are computed and references are listed in the Annex Computations are made at several levels corresponding to major sections in the Metrics menu table 1 Metrics Global metrics describe the entire graph Metrics Component metrics describe connectivity within each component or sub graph Metrics Local metrics describe the connectivity of each graph element node or link Metrics Delta metrics also describe each graph element but using a specific computing method Using the removal method remove nodes or remove links the relative importance of each graph element is assessed by computing the rate of variation in the global metric induced by each removal The result of a delta metric is at a local level but by reference to the global level After selecting one of these four computing methods three families of metrics are available in the new window weighted metrics are based on criteria of distance and patch capacity They have to adjusted to suit the reference species These metrics involve computing paths in a graph via Dijkstra s algorithm After selecting one of these metrics the user must specify the desired adjustment area metrics are based primarily on the area criterion If capacity corresponds to a criterion other than patch area these metrics can be computed and they are expressed in the unit of the cri
7. J C Clauzel C Vuidel G 2012b A software tool dedicated to the modelling of landscape networks Environmental Modelling and Software 38 316 327 O Brien D Manseau M Fall A Fortin M J 2006 Testing the importance of spatial configuration of winter habitat for woodland caribou An application of graph theory Biological Conservation 130 70 83 Minor E S Urban D L 2008 A graph theory framework for evaluating landscape connectivity and conservation planning Conservation Biology 22 297 307 Pascual Hortal L Saura S 2006 Comparison and development of new graph based landscape connectivity indices towards the priorization of habitat patches and corridors for conservation Landscape Ecology 21 959 967 Rayfield B Fortin M J Fall A 2011 Connectivity for conservation a framework to classify network measures Ecology 92 847 858 Ricotta C Stanisci A Avena G C Blasi C 2000 Quantifying the network connectivity of landscape mosaics a graph theoretical approach Community Ecology 1 1 89 94 Saura S Pascual Hortal L 2007 A new habitat availability index to integrate connectivity in landscape conservation planning Comparison with existing indices and application to a case study Landscape and Urban Planning 83 91 103 Saura S Torn J 2009 ConeforSensinode 2 2 A software package for quantifying the importance of habitat patches for landscape connectivity Environmental Modelling and Software 24
8. OS graphab User Manual Summary 1 Introduction sesisssiteccsenseeieck Se ebccdenatuauad sanei scene sveces Ei RAET Eaa da sdecdesseweess OR i aTa 4 1 1 ADOUt Gra pha sscs iss ices cctesescsssscccssssweddccesedcssstueeassscadecsccsvedsdeesusececotseesscosesacsscesssddsvsesscsssssssss 4 1 2 System requirements i 6 scidscss cc cecs cessed sciececdessetccdsdessaceesssesedsdcosucedscosdedsscssusassccesssddensssscesedssess 4 1 3 Installing the software and launching a Project ccssssscccsssssccccsssssccesssscccesssssceesssssceenenss 4 2 Starting a Graphab Project ccssscccsssccrsscccsccccnssccccsscccnssccasssccssssccssssccssssscescsscsscsaassess 5 2 1 Mdentif ying a project aissis cee cecvescsbescdce suds deccossscdeesusaccccasssecocsesacecsesssddsesesscssstassss 5 2 2 Importing landscape maps and defining NOAES ssssscccssssccccssssscccenssceccecssssceanssceseaeenes 6 2 3 Cheating MNK SOE ceis a aa SE E ENS cccueuecessaddoc eseunsedseescucesseensecedeecduasste 7 BE Creating Graphs siiisiniririreiieren inse p ia E EEEE EEEE TE SE EEEE ETE E A EE SEa 9 4 Pateh capacity er ianea ea aae aaa e ais nei a Eroa era Taa Saa iSO 10 4 1 Capacity as a function of the neighborhood sssssessssossssssssseoossssoossssoosessoossssoosesecsseseos 10 4 2 Capacity defined from external data ssscccssssccccssssccccsssccccenssseccecssseccansssecsanssssseeesnss 11 5 Calculating connectivity metrics 0
9. absence of any connection between two nodes is noted NaN This matrix is saved in the project file in text format named graph name odmatrix txt 7 2 Object properties The properties of link sets graph elements nodes links and components and point data are available by right clicking on each of them The Style menu includes the display parameters for objects color line width label symbol size for nodes only Objects can be represented in the same way single symbol or according to some attribute A discretization method can be applied to classify objects according to the values of the selected attribute By default the legend of objects is displayed in the table of contents It can be masked by unchecking the Legend button The Export menu can be used to export objects to a shapefile shp or a text file txt The Statistic menu displays the distribution of the values of one or more attributes scatter plot values of two attributes are plotted on a two dimensional graph histogram the bar chart of the values of an attribute is generated It is also possible to display the values of a given object by selecting it with the white arrow After selection the values of attributes are displayed in a new right hand column named feature properties This column can be closed by clicking on the Properties menu in the top bar 22 Graphab 1 1 T Ql N A P 17 vayers Properties Add layer Export
10. it is often useful to connect these elements with external data Graphab allows graph data to interact with a points data set 6 1 Importing points sets Point data can be imported via the Data Import point set menu These data may contain several attributes but only binary attributes presence absence are taken into account in certain procedures see 6 3 Species distribution model import point set Point file a_graphab AbcZE3_V3_base Exo jeu_point1 shp ID Id v x M Available Selection IdPatch presence lt Remove Add all gt gt lt lt Remove all OK Cancel The imported file may be either in shapefile format shp or in table format csv For files in table format the user must specify the columns corresponding to identifiers and to the XY coordinates of points in the table The attributes to be considered must be selected from the list of attributes available If point data do not contain an absence attribute they cannot be used in species distribution models If the user wants to set up a species distribution model a set of pseudo absence points can be generated by the Data Generate random point menu 6 2 Inter point distance matrix Point data imported to Graphab can be used to calculate the inter point distance matrix by right clicking on the name of the point data Several types of distance are available 17 Raster based distance distance calculated in raster mode for a given lin
11. or later PC under Linux Windows Mac etc However when dealing with very large datasets the amount of RAM memory in the computer will limit the maximum number of nodes and links that can be processed in a single run with Graphab In addition for some complex metrics processing power CPU will determine the speed of computing For details see section 8 below and the journal article cited above 1 3 Installing the software and launching a project Graphab can be downloaded from http thema univ fcomte fr productions graphab Download and install Java 1 6 java com If you have a 64 bit operating system it is best to install the 64 bit version of Java Download and unzip graphab zip Launch GraphAB jar After launching GraphAB jar the File menu provides access to four sections File New project to create a new project in which all data and results are saved automatically File Open project to open an existing project File Preferences to change certain software parameters English French maximum amount of memory to use number of processors to use It is recommended to adjust the amount of memory and number of processors to suit your computer see section 8 File Log window to display the event log 2 Starting a Graphab project New projects are created from the File New project menu The user must complete a series of windows to identify the project import a landscape map and create
12. view P ad 8 Feature properties gt Point sets ue 5 f v 7803 7329 7 bapaan ID1 7803 seed L 2 7329 Dist 1046 854736328125 amp nodes DistM 3835 340546095176 amp Edges BCs_d1000_p0 05_beta1_Gri ie C_lcomponents BC_d1_p0 05_beta1_Graph gt Graph1 BC_d2_p0 05_beta1_Graph v Link sets BC_d3_p0 05_beta1_Graph 4 50 100 BC_d4_p0 05_beta1_Graph iet BC_d5_p0 05_beta1_Graph Voronoi links Patch Landscape map tg ate X 883255 615 Y 2264938 833 8 Processing capabilities and limitations Graph based methods provide an efficient modeling framework but they can raise a question of computing capacity Two specific points have received particular attention in Graphab 1 calculation of link sets 2 calculation of connectivity metrics All these computations have been optimized by parallelization This development mode improves computational efficiency by using a multi processor architecture a quad core processor being theoretically four times faster than a single core processor In the journal publication Folt te J C Clauzel C Vuidel G 2012 A software tool dedicated to the modelling of landscape networks Environmental Modelling amp Software 38 316 327 several tests were conducted to measure the computational capacity of Graphab 1 0 in different configurations Three configurations were compared for these tests 1 one core 3 Go RAM corresponding to a current
13. 00scsccceossssccccsssscecccssssccccssssccccessssscsesssssssccssssessoees 12 5 1 Metrics family and computing level sssssscccssssccccssssccccesssccccessseccecssseccenssssesansseseeenss 12 5 2 Parameters Of Weighted MEtriCS sscessssssccsssssccccesssscecessssccesssseceesesssceacssssceanseseeansnss 13 5 3 Calculating batch Mm eCtrics c siciccccccecscdcccssecesscecescceccesecccceseeccdecssscecsdsesccsesecsecsvecddbensesensossts 14 5 4 Interpolating Metrics viccssicccssceccosscessddccsescccecsscescges cesecsccussd dcteusescscssedsccsecesecssexssddcsonsescuce ses 16 6 Connecting graphs and point AALA cccsecccrssccrssscccsscccsssccssssccssscccssseccsscnsasscsscssccees 17 6 1 Importing points sets seisis anssen e i a 17 6 2 Inter point distance matrix sesssssessssossssoossssoossssoosessoossssosssssoossssoosessoosessossssscosessessess 17 6 3 Generating random points sssesssssessssossssoosessoossssoosessoosessosssssoesessoossssoosssssssssseosessesese 18 6 4 Species distribution model ssesssssessssosssesosessoossssoosessoessssossessossessoosessoosessoosesscosessoesese 19 7s DISPIGY APEE A A EATE E E A TE 21 7 1 Graph PrOPerties seses a a a a i 21 2 2 Object properties ens ESE E EENS OS EAEAN SEEN N OES 22 8 Processing capabilities and limitations scccceesssccccssssssccccssssccccssssccccecsssscsccsssscecoees 23 O ANNEXES niaaa ea aaa aa raaa ae aaa EAr aa aaao oa e aaan aaa 25
14. 135 139 Saura S Rubio L 2010 A common currency for the different ways in which patches and links can contribute to habitat availability and connectivity in the landscape Ecography 33 523 537 Urban D L Keitt T H 2001 Landscape connectivity a graph theoretic approach Ecology 82 1205 1218 33
15. 957322735539907 log p d d 1 000 gt Min oj p 0 05 L Max 21 107 594 B 1i Increment 1 include intra patch distance anaa Cancel Graphs are defined following three criteria selected by users min smallest threshold used for the first graph in the series By default this minimum is 0O corresponding to the total absence of links max maximum threshold used for the final graph in the series By default this maximum corresponds to the maximum distance or to the link number of the selected link set increment distance value added between each new graph Once the calculation is completed the software opens a new window displaying the curve of the selected metric versus the threshold distance The values of this curve can be saved with the Export button by selecting text format 5 3 2 Batch parameter The Metrics Batch parameter menu is used to calculate a series of metrics from a given graph This procedure applies to the weighted metrics only It is divided into two entries local metrics or global metrics Batch parameter for local metrics A local weighted metric is calculated in series according to the variation of one of its parameters The user must select the graph the metric and the parameter to be varied The variation of computation is defined by min minimum value of the parameter max maximum value of the parameter increment interval value between two metric computations Once the cal
16. AN to each other over the possible total i i j IN ICIN 1 4 JEN Values Minimum value 0 Maximum value 1 Comment Si N lt 1 7 CC 0 Reference Ricotta et al 2000 Closeness Centrality CCe Formula Meaning Local level 1 nk Mean distance from the patch i to all other patches of its component k ce dy p nm 14 j 1 j i Values Minimum value 0 Maximum value 00 Comment Sing 1 gt CCe 0 Reference Freeman 1979 31 Eccentricity Ec Formula Meaning Local level Maximum distance from the patch i to another patch of its Ec max dj component k j Values Minimum value 0 Maximum value 00 Reference Urban and Keitt 2001 Connectivity correlation CCor Formula Meaning Local level IN 2 Ratio between the degree of the node i and the degree of its CCor k neighboring patches j Z jen N Values Minimum value 0 Maximum value N Comment Si N 0 gt CCor 0 Reference Minor and Urban 2008 32 9 2 References Bodin O Saura S 2010 Ranking individual habitat patches as connectivity providers Integrating network analysis and patch removal experiments Ecological Modelling 221 2393 2405 Folt te J C Clauzel C Tournant P Vuidel G 2012a Integrating graph based connectivity metrics into species distribution models Landscape Ecology 27 557 569 Folt te
17. F Constant 1 3558473054645068 Capacity 33 1155923384945 Add patch variable Cell size 100 Name Extrapol1 Add raster variable Remove In the new window which opens the user finds the model parameters as described previously The cell size of the grid in meters indicates the level of spatial accuracy of the extrapolation This parameter has a significant consequence on the computing time required to obtain the result The result is saved as a raster layer in tif format and is displayed in the main window 7 Display 7 1 Graph properties Properties of a graph are available by right clicking on the name of the graph Two ways for viewing graphs are available The topologic view displays a simplified view of the graph in which nodes are represented by dots and links by straight lines between centroids The realistic view displays habitat patches according to their actual boundaries and links are represented by least cost paths between two patches 21 Topologic view Realistic view The Remove button can be used to remove the graph selected Properties displays the parameters used in constructing the graph graph name graph type with the possible threshold used and the number of links The OD Matrix Origin Destination Matrix button creates a table with the distance between each pair of nodes for the given graph The unit of distance depends on the type of distance used in the graph The
18. a link set Each project is associated with a single landscape map but may contain several link sets After the start phase the project is the medium for creating multiple graphs and for computing connectivity metrics 2 1 Identifying a project In the first window the user must enter a project name and specify the folder in which it is to be created New project Project name Project1 Path home gvuidel Bureau Project1 am Cancel Prev Next 2 2 Importing landscape maps and defining nodes The second window is for importing the landscape map It must be a raster file tif rst in which the value of each pixel corresponds to a category land cover or other classification New project Landscape map home gvuidel data_graphab extrait tif 27 No data 12 v Habitat patch code 1 v Minimum patch area o ha Patch connexity 4 connexity 8 connexity amp simplify patch for planar graph Cancel Prev Next Finish If the raster format is tif without a Geotiff extension the file must be associated with a world file for geolocation tfw structured as follows Example 10 Pixel size in the X direction 0 Rotation about X axis 0 Rotation about Y axis 10 Pixel size in the Y direction 821755 X coordinate of the center of the upper left pixel 2342995 Y coordinate of the center of the upper left pixel If the raster format is rst the file must be associated with a geo
19. al patch i each path is Values Values depend on the configuration They correspond to a weight of potential transit Minimum value 0 Maximum value square of the total area of habitat Comment With an adjustment of a 0 and 6 0 uniform weighting of paths the BC index is the same as that used in other types of graphs An adjustment of a 1 and 6 0 gives paths a weight proportional to the product of the capacities of the patches that they connect whatever their distance In Folt te et al 2012a 2012b the BCI index was proposed so as to give greater weight to paths exceeding a given criterion e g dispersal distance But tests showed that this index was strongly correlated with the weighted BC adjusted with 6 0 In Bodin and Saura 2010 the BC is the weighted BC with d equal to the dispersal distance as e 4 0 05 and f 1 Reference Bodin and Saura 2010 Folt te et al 2012b Integral Index of Connectivity IIC Formula Meaning Global level Component level For the entire graph product of patch capacities divided by the number of links between them the sum is divided by the square of n n 1 ai IIC gt ud the area of the study zone A2 1 nlij IIC is built like the PC index but using the inverse of a topological i 1 j 1 distance rather than a negative exponential function of the Delta distance based on the link impedance Values Minimum value
20. culation is completed the patches and in some cases the links of the graph are characterized by a series of additional metrics 15 Batch parameter for global metrics For a given graph a global weighted metric is calculated in series according to the variation of one of its parameters As previously this variation is defined between a minimum value min a maximum value max and with an interval increment The procedure ends with the opening of a new window displaying the curve of the selected metric versus the parameter Table 2 summarizes possible metrics calculations Family Connectivity metrics Code Patch Intra Parameters Batch Batch capacity patch graph parameter distance a 6 Flux F x x x x x x 8 Probability of connectivity PC x x x x x 7 Flow Probability of connectivity FPC x x x x E Fractions of delta Probability of dPC x x x x connectivity o Betweenness centrality index BC x x x x x z Integral index of connectivity IIC x x Mean size of the components MSC x x amp Size of the largest component SLC x x o Class coincidence probability CCP x x lt E Expected cluster size ECS x x Node Degree Dg a Clustering coefficient cc Closeness centrality CCe x Eccentricity Ec Xx E Connectivity correlation CCor 3 Number of components NC x 2 Graph diameter GD x x z Harary Index H x Table 2 Possible connectivity metrics calculations 5 4 Interpolating metric
21. d 2 Go 24 9 Annexes 9 1 Details of metric calculations Summary table of metrics in Graphab 1 1 Family Connectivity metrics Code Computing level Delta Global Component Local metrics Weighted Flux F x x x metrics Probability of connectivity PC x x Flow Probability of connectivity FPC x Fractions of delta Probability of dPC connectivity Betweenness centrality index BC x Integral index of connectivity IIC x x Area metrics Mean size of the components MSC x Size of the largest component SLC x Class coincidence probability CCP x Expected cluster size ECS x Topological Node Degree Dg x metrics Clustering coefficient cc x Closeness centrality CCe x Eccentricity Ec x Connectivity correlation CCor x Number of components NC x Graph diameter GD x x Harary Index H x x Mathematical terms used Terms Meaning n Number of patches nc Number of components Nk Number of patches in the component k N All patches close to the patch i di Capacity of the patch i generally the surface area aCk Capacity of the component k sum of the capacity of the patches composing k A Area of the study zone dij Distance between the patches i and j generally the least cost distance between them e72tij Probability of movement between the patches i and j a Brake on movement distance B Exponent to weight more or less capacity 25 Weighted metrics
22. desktop computer 2 four cores 6 Go RAM corresponding to a workstation and 3 20 cores 15 Go RAM corresponding to a server The landscape map used was a grid of 14000 18000 pixels 252 millions of pixels representing the landscape elements of the region of Franche Comt France at a spatial resolution of 10 m The landscape map contained 22 634 habitat patches Topology Distance Current desktop Workstation Server Euclidean 1927s 32 min 516s 8 min 133s 2 min Complete f Least cost 19252s 5h 21 min 4301s 1h 11 min 1037s 17 min Euclidean 43s 12s 2 6s Planar Least cost 1080s 18 min 295s 5 min 82s 1 min Table 3 Computation times seconds required for calculating several link sets 23 In version 1 1 computation times for calculating metrics with intra patch distances have been optimized The difference in computation times with or without intra patch distances is now negligible The memory used by the software plays an important role If there is not enough RAM computation will be slower or may fail QutOfMemoryError or GC Overhead message The File Preferences Memory menu can be used to adjust the memory allocated to Graphab If you have a 32 bit version of Java Graphab will be limited to about 2 Go 2000 Mo of memory If your computer has more than 2 Go of RAM memory it is highly recommended you install the 64 bit version of Java to use the available memory beyon
23. e is equal to the sum of the costs of all the pixels along the path path length impedance is equal to the metric length of the path For each link created its metric distance and its cost unit distance are saved and available in link properties see section 6 2 3 Creating graphs A Graphab project may entail the creation of several graphs Each graph is created from a given link set either the link set defined in the initial project or a new link set defined from the Graph Create link set menu Graphs are created from the Graph Create graph menu Create graph Name Graph_1000 Link set 1 50 100 v Type Thresholded graph max dist 1 000 lt Non thresholded graph Minimum spanning tree include intra patch distance for metrics OK Cancel First the new graph must be named The user must select one of the link sets created in step 2 2 and then select the type of graph Thresholded graph the selected links are less than or equal to the selected threshold distance Non thresholded graph all links between patches are validated regardless of length Minimum spanning tree graph connecting all the patches in which the total weight of links is minimal For a thresholded graph the unit of the threshold distance depends on the type of distance used in creating the link set If the link set is created using Euclidean distances the threshold distance of the graph is in meters If the link set
24. ed by the ad f the area of the study zone This ratio is the equivalent to PC af afe adij square o Component level A2 t j the probability that two points randomly placed in the study area i 1 j 1 are connected Delta Values Values correspond to a probability Minimum value 0 Maximum value 1 Comment For each pair of patches the path of the graph used is the one that maximizes e 4 i e the one that minimizes the distance d or the cost between the patches i and j In CS22 the weighting of capacities is set to 1 in Graphab it can be modified If a does not represent patch area the result is no longer a probability Reference Saura and Pascual Hortal 2007 26 Flow Probability of Connectivity FPC Formula Meaning Local level 1 ile Sum of products of the focal patch capacity with all the other FPC af ae enti patches weighted by their interaction probability and divided by A r rid the square of the area of the study zone j Values Minimum value 0 Maximum value 1 Comment For each pair of patches the path of the graph used is one that maximizes e i e one that minimizes the distance d or the cost between the patches i and j This metric is just the local contribution of a patch in the PC index since PC FPC It is the equivalent of the dPCfiux index not divided by the global value of PC However the FPC metric is obtained more quickly than dP Cuy because it is n
25. ighting is based on an exponential function 13 where p is the probability of movement between two patches d the distance between these patches and aa parameter defining the rate of decline in probability as distance increases As it is not easy to determine the value of the parameter Graphab calculates it from the other two parameters Users must specify the distance corresponding to a certain value of probability e g the maximum dispersal distance of species corresponding to a small value of p 0 05 or 0 01 the average dispersal distance of species corresponding to a median value of p 0 5 The value of a is automatically obtained from the formula a log p d In the case of a thresholded graph it is assumed that the distance d used in the setting is consistent with the distance used for the graph thresholding 5 2 2 Beta parameter The metrics F PC FPC and BC are controlled by the 6 parameter This parameter is the exponent applied to patch capacity It adjusts the relative balance between the weight of distances and the weight of patch capacity in the weighting of metrics Taking the example of the metric F in local computation whose generic form is F Ya e724 a value of 8 0 means that the patch capacity plays no part in the weighting a value of 8 1 means that the patch capacity acts linearly in the weighting a value of 8 2 means that the patch capacity is squared in the weighting a va
26. is created using cost distances the threshold distance of the graph is given as a cumulative cost An approximation of the distance metric DistM expressed as a cumulative cost Dist can be obtained by displaying the scatter plot of the link set see section 6 2 and using the regression line Dist intercept slope x DistM to perform the conversion Scatter plot DistM Dist 800 slope 0 105570 750 intercept 85178 700 C a o lt m Dist o 500 1 000 1 500 2 000 2500 3 000 3 500 4 000 4 500 5 000 5 500 6 000 6 500 7 000 7 500 DistM Include intra patch distances for metrics option if the box is checked the computation of metrics includes the distances between and across patches recommended If the box is unchecked only the distances between but not across patches are taken into account To perform a multiscale analysis it is often necessary to create a series of graphs in which increasing thresholds are defined Users can create this series manually But if the objective is to analyze the behavior of a metric according to the threshold the Metrics Batch graphs menu can be used see section 5 3 4 Patch capacity The capacity of a patch reflects its intrinsic quality as an indicator of its demographic potential A patch with a high capacity can accommodate a large population and vice versa Capacity is included directly in the calculation of some area connectivity metrics and weighted connectivi
27. istance depends on the type of distance used in creating the link set Euclidean or cost distance Codes included the user may select one or more landscape categories other than the habitat category to be included in calculating capacity The cost weight option introduces a weighting with distance to the patch through a negative exponential function In this way the areas selected have greater weight if they are close to the patch and vice versa The capacity values calculated replace the patch area for all subsequent computations But users can return to the initial parameter via the Data Calculate patch capacity menu and by selecting patch area 4 2 Capacity defined from external data The Data Import patch capacity menu allows a data table csv to be imported describing all the patches of the project and containing capacity values defined in advance by the user The patch identifiers in the table must be the same as the patch identifiers in the Graphab project The capacity values in the imported table replace patch area values for all subsequent computations after importing But users can restore the initial parameter via the Data Calculate patch capacity menu and by selecting patch area 11 Import patch capacity Capacity file home gvuidel data_graphab AbcZE amp Patch id Id v Capacity Capacity v Cancel 5 Calculating connectivity metrics 5 1 Metrics family and computing level
28. k set Depending on the selected link set it may be Euclidean distance cumulative cost distance or length of a least cost path In the latter two cases calculation includes costs assigned to the landscape map categories as defined when creating the link set The result is a distance matrix which is independent of the graph this matrix corresponds to the calculation provided by the Geographic information Systems Graph based distance distance calculated according the shortest path in a reference graph The type of distance is the same as that used in creating the link set of the reference graph At both ends of a given path the calculation includes the distance between each point and the nearest patch Depending on the choice made when creating the graph the calculation may or may not include intra patch distances 6 3 Generating random points The Data Generate random points menu can be used to generate a set of pseudo absence points based on a set of presence points Graphab 1 1 7 Q N P X4 Layers Properties Add layer Export view v AbcZE3_V3 gt Graphs v Link sets 1 50 100 test Points aphab AbcZE3_V3_base Exo d1 shp 2 Voronoi lir amp patch Cellsize 20 00 Update grid Landscape map Grid Presences 11 Absences 25 2 0000 Minimal distance between points 9 000 1 5000 e 3 Keep only one existing point by cell 1 0000 Linkset 1 50 100 v Name pointset1 Generate Close
29. lue of 8 0 5 means that the square root of the patch capacity features in the weighting a value of 8 1 means that the patch capacity acts in an inversely proportional way in the weighting In addition to these few examples any weighting values are possible 5 3 Calculating batch metrics Every metric compatible with the global level can be calculated following the variation of the scale of distances This variation may concern either graph thresholding 5 3 1 or metric adjustment 5 3 2 The type of distance used for thresholding depends on the type of distance used in creating the link set Euclidean least cost distance or least cost path 5 3 1 Batch graph The Metrics Batch graph menu allows a series of thresholded graphs to be created from a given link set and a metric to be calculated for each graph at global level The thresholds of successive graphs are increasingly defined in either of two ways distance a fixed increment of distance is defined between successive graphs The metric values are therefore calculated in regular intervals of threshold distance number of links a fixed number of links is defined between successive graphs This number of links is automatically converted into distance used to threshold the graph These threshold distances may be unevenly spread 14 Batch graph Link set 1 50 100 v Metric Flux F v Distance threshold distance Parameters number of links a 0 0029
30. n Point set jeu_point1 Formule presence 1 35585 33 1156 Cap Standard 12109 7 Capacity Target variable presence v Likelihood ratio 16 7442 p 4 27719e 05 Graph Graph 500 r2 McFadden 0 245761 AIC 53 3879 Distance weighting a 0059914645471079815 a log p d 4 b d 500 ja P 0 05 i Variable Coef Std coef Capacity 33 1156 12109 7 _ Multi connection Predictive variable Capacity Add patch variable BCs_d1000_p0 05_beta1_Grapl cabbie Remove Find best model Fitmodel Extrapolate Diff Exporttable Close First the user must specify the set of point data to use the target variable in the predictive model the reference graph for the use of connectivity metrics 6 4 1 Weighting for extrapolating metrics to points The values of metrics are calculated for any point by a spatial interpolation This interpolation is based on values being weighted by a decreasing function from patch edges weight of 1 The weight decreases as the same negative exponential function as the one used for weighted metrics see section 5 2 1 the adjustment is therefore identical The user selects a distance d corresponding to a certain probability p and the software deduces the value of the a parameter In principle this adjustment must be consistent with the choice of reference graph or of any weighted metrics included in the model using the same value of d 19 The Mul
31. of the inverse of the number of links between all pairs of H gt gt patches 4 nlij Component level i 1 j 1 j i Values Minimum value minimum capacity as many components as patches and regular capacities Maximum value sum of capacities only one component Comment For pairs of patches not connected by a path we have nl 00 Reference Ricotta et al 2000 Graph Diameter GD Formula Meaning Global level GD max dij Greatest distance between two patches of the graph ij Component level Delta GD max Ec l Values Minimum value 0 Maximum value 00 Comment When the nodes i and j are not related dij 0 This metric is the global version of the metric Ec Reference Urban and Keitt 2001 Number of Components NC Formula Meaning Global level Number of components of the graph NC nc Values Minimum value 1 Maximum value n Reference Urban and Keitt 2001 30 Node Degree Dg Formula Meaning Local level Number of the patches close to the patch i Dgi N l Values Minimum value 0 Maximum value n Comment There is an equivalence between the node degree and the number of nearest patches because graphs are not oriented and do not contain any loops Reference Freeman 1979 Clustering Coefficient CC Formula Meaning Local level 1 Ratio of the number of nodes close to i which are neighbors CC N
32. ot calculated on the basis of patch removal delta mode Fractions of delta Probability of Connectivity APC dPCarea dPCux APCconnector Formula Meaning Delta PC PCi Rate of variation between the value of PC index and the value of dPC pp PC corresponding to the removal of the patch i The value of dPC is decomposed into three parts APCorea is the variation induced by the area lost after removal dPC dPC dPC dPC cae area flux t connector _ APC is the variation induced by the loss of interaction between 26 the patch i and other patches a APCconnector iS the variation induced by the modification of paths dP Corea A2PC connecting other patches and initially routed through i aPC FPC flux PC Values Minimum value 0 Maximum value 1 Comment In CS22 the weighting of capacities is set to 1 in Graphab it can be modified If a does not represent patch area the result is no longer a probability and dPCarea does not express a loss of area but a loss of capacity Reference Saura and Rubio 2010 27 Betweenness Centrality index BC Formula Meaning Local level weighted by the product of the capacities of the patches j k connected and of their interaction probability Pik represents all the patches crossed by the shortest path between j k E 1 n k lt j i E Pik the patches j and k BCG gt af abe ek Sum of the shortest paths through the foc
33. referencing file rdc generated by Idrisi software The units of the image coordinate system must be meters If not the areal and distance units will be incorrect The image can be reprojected in a metric projection UTM Lambert93 using GIS software No data pixel value representing the absence of data in the raster file Habitat patch code pixel value assigned to the habitat category used to define habitat patches Minimum patch area minimum area in hectares for a habitat patch to become a graph node Patch connexity 4 connexity a habitat patch consists of the central pixel with its four neighbors if they are of the same value 8 connexity a habitat patch consists of the central pixel with its eight neighbors if they are of the same value Simplify patch for planar graph checking the box accelerates the creation of a planar graph simplifying the polygonal boundaries of patches This simplification process is not deterministic and so creating two planar graphs for one and the same landscape map may result in slightly different polygon edges Consequently this box should not to be checked when planar graphs are to be compared 2 3 Creating link sets The third window is for creating a link set for which several parameters must be selected topology and link weighting Creating a link set is the final step in starting a Graphab project However users may create new link sets within the same project via the Graph
34. s The Analysis Metric interpolation menu is used to create raster layers from local metrics calculated at patch level This transformation is based on a specific spatial interpolation which assigns connectivity values of patches to each cell of a grid using a decreasing weighting function from the patch edge weight of 1 Overall the farther cells are away from the graph the lower their connectivity values The weighting is a negative exponential function as p e for which the user selects a distance d corresponding to a certain probability p and the software deduces the value of the a parameter In theory this adjustment must be consistent with the choice of reference graph or of any weighted metrics using the same value of d The Multi connection option allows several patches to be included in the calculation of metrics at the point level The calculation is based on a weighted mean of values of all patches in the vicinity of the points up to the specified Maximum distance The distance used in these calculations depends on the reference graph If it is based on least cost distance the spatial interpolation uses the same distance and not Euclidean distance 16 The metric interpolation is used automatically in calculating species distribution models see 6 3 Species distribution model 6 Connecting graphs and point data The main part of the software is for graph construction and computation of connectivity metrics But
35. s Create link set menu Name Linkset1 Topology Planar D Complete ignore links crossing patch Distance Euclidean Cost from landscape map Code Cost Impedance 50 p 1 cumulative cost 1 50 50 100 50 50 Path length 10 0 INO Un BW iN Cost from raster file cancel Lok 2 3 1 Link topology Two topologies are available planar only links that form a minimal planar graph are considered This topology is set up through Voronoi polygons around each habitat patch These polygons are defined from the edges of patches in Euclidean distance complete all the links between patches are potentially taken into account Max distance this option specifies a threshold distance for the complete topology Links that exceed this distance are no longer created This limits the number of links created and so accelerates the creation of the link set Ignore links crossing patch this default option means that a link between two patches A and C in the figure below which crosses an intermediate patch B is not created It is recommended for calculating the betweenness centrality metric BC to take into account how often a patch lies on the shortest path between all pairs of patches in the graph If the option is unchecked a link is created between two patches A and C crossing an intermediate patch representing the complete true distance between A and C
36. terion used topological metrics are derived from graph theory and they do not require adjustment Whichever the selected level the user must first specify the graph on which the calculation will be made and then select the connectivity metric 12 Family Connectivity metrics Code Computing level Delta Global Component Local metrics Weighted Flux F x x x metrics Probability of connectivity PC x x x Flow Probability of connectivity FPC x Fractions of delta Probability of dPC x connectivity Betweenness centrality index BC x Integral index of connectivity IIC x x x Area metrics Mean size of the components MSC x Size of the largest component SLC x Class coincidence probability CCP x Expected cluster size ECS x Topological Node Degree Dg x metrics Clustering coefficient cc x Closeness centrality CCe x Eccentricity Ec x Connectivity correlation CCor x Number of components Cut x Graph diameter NC x Harary Index GD x x x Node Degree H x x x Table 1 Connectivity metrics and computing level 5 2 Parameters of weighted metrics Graph Graph 500 v Metric Probability of Connectivity PC v Parameters a 0 0059914645471079815 log p d d 500 p 0 05 2 B 16 LOK Cancel 5 2 1 Alpha parameter Several metrics include a weighting in their calculation which converts the distance between patches into the probability of movement These metrics are F PC FPC and BC The we
37. ti connection option allows several patches to be included in calculating metrics at points Calculation is based on the weighted mean of values of all patches surrounding points up to the specified Maximum distance Details of this weighting are given in Foltete et al 2012a 6 4 2 Estimating the model The selection of a graph to perform the model displays all available connectivity metrics among predictive variables Metrics from another graph can be added by clicking on the Add patch variable button External variables can also be added by clicking on the Add external variable button Once the predictor variables have been selected the Fit model button can be used to calculate the coefficients of the logistic regression The results are displayed on the right hand side of the window The Find best model option tests all possible combinations of variables and selects the one that minimizes the AIC criterion 6 4 3 Using the model A predictive model which is considered to be valid can be used in several ways The Export table button can be used to export a table csv format with all statistical variables involved in the regression The Extrapolate button provides an estimation of the probability of the species presence in all cells of a grid 20 Extrapolation Link set 1 50 100 Distance weighting a 0059914645471079815 a log p d d 500 p 0 05 Multi connection Predictive variables Variable Coe
38. ty metrics see section 5 When the project is first created the patch capacity is equal by default to the patch area in m However users may replace area by any other quality indicator In some cases species presence is related not to patch size but to the area of other types of land cover around the patch For example the presence of amphibians in a breeding pond does not depend on the pond size but on the amount of terrestrial habitat surrounding the pond 4 1 Capacity as a function of the neighborhood The Data Calculate patch capacity menu can be used to define patch capacity as a function of the neighborhood composition and to calculate it directly from Graphab 10 Calc patch capacity Patch area default Neighborhood area Cost 1 50 100 v Codes included Max cost 100 1 Cost weight 3 Users must define three parameters type of distance maximum distance landscape categories Cost This is the spatial metric Euclidean or cost distance corresponding to one link set available in the project The use of costs in this procedure amounts to defining an anisotropic neighborhood around patches which may differ greatly from a buffer function For consistency it is recommended to use the same type of distance as was used in creating the links of the graph For a link set created with Euclidean distance the user must select all costs 1 Max cost Like the graph threshold distance the unit of this maximum d
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