Laboratory C - Andrew J. Crawford
Contents
1. 10 10 Growth rates negative growth implies population expansion 0 0 Number of migration matrices 0 implies no migration between demes 0 nistorical event time source sink migrants new deme size new growth rate migration matrix index 1 historical event 10000 011100 Mutation rate per generation for the whole sequence 0 0001 Number of nucleotides to simulate 10000 data type either DNA RFLP or MICROSAT If DNA we need a second term for the transition bias DNA 0 8 Gamma parameter if 0 even mutation rates if gt 0 shape parameter of the Gamma distribution 0 5 4 Second parameter is the number of discrete rate categories to simulate if zero continuous distribution Place a copy of the executable program in your folder carpeta and run this infile as explained above but perhaps do 10 30 simulations If you haven t done so already close quit FigTree before Coalescent Simulation Lab Crawford page 6 of 7 using it to open your new trees In your new true trees notice the 1 or 2 following the sample number these designate the population of origin of each sample How many of your 20 simulated trees show reciprocal monophyly of the two populations How many show paraphyly of one population with the other population monophyletic How many show polyphyly Enter your results in the third column I did 30 simulations Topolo Div time N Div time N Div time 3N Div tim2. non zero branch length among trees This length should equal 1 inferred mutational difference If you like try looking at unrooted trees using the 3 button under Layout at the top of the vertical menu on the left of the screen Which view do you prefer Notice there is not much phylogenetic information for estimating the full genealogy Many samples have identical haplotypes This situation is quite normal for a sample of haplotypes from a single population Our simulation was somewhat accurate for mtDNA in vertebrates with a mutation rate of 10E 7 per site in a population of 2N 10 000 The expected average pairwise distance among samples is 4Nu 4 5000 0 0000001 0 002 per site or 2 mutations among 1000 base pairs How does Coalescent Simulation Lab Crawford page 5 of 7 this expectation compare with the simulation Look in your file ending with gen and look at the mean and S D of number of pairwise differences In my set of 10 simulations I observed a mean of 1 28 SD 0 716 which is reasonably close to expectations HI Lineage sorting Now we will simulate a pair of diverged populations Thus not all individuals will be equivalent SIMCOAL will indicate each simulated individual by a sample number followed by a 1 for population 1 and 2 for population 2 of course Models where not all individuals are equivalent are referred to as structured coalescent models We will simulate a simple case
3. of a single ancestral population dividing into two daughter populations at some time in the past Time we will measure in numbers of generations Later we ll add migration between our two daughter populations but not yet We can use a structured coalescent model to help us visualize the process of lineage sorting and the parameters that affect this process Lineage sorting is one of the most important processes in phylogeography The process is fundamentally very simple yet at the same time difficult to understand or conceptualize SIMCOAL asks use to set time in generations but coalescent theory allows us to count the number of generations in units of N the population size since the rate of coalescence is tied to genetic drift which is determined by N We can set up 2 simulations the first will assume a time of separation N generations in the past and the second simulation will assume an older pair of populations separated 3N generations ago Prepare 2 new directories appropriately labeled perhaps 2pop_ young OUTFILES and 2pop_old OUTFILES We might raise the mutation rate a bit and or increase the length of DNA sequences just to obtain empirical gene trees mutation trees with more potential phylogenetic information The first infile might look like this Parameters for the coalescence simulation program simcoal exe 2 samples to simulate Population effective sizes number of genes 10000 10000 Samples sizes
4. as follows Parameters for the coalescence simulation program simcoal exe 1 samples to simulate Population effective sizes number of genes 10000 Samples sizes 20 Growth rates negative growth implies population expansion 0 Number of migration matrices 0 implies no migration between demes 0 nistorical event time source sink migrants new deme size new growth rate migration matrix index 0 historical events Mutation rate per generation for the whole sequence 0 0001 Number of nucleotides to simulate 1000 data type either DNA RFLP or MICROSAT If DNA we need a second term for the transition bias DNA 0 81 Gamma parameter if 0 even mutation rates if gt 0 shape parameter of the Gamma distribution 0 50 4 Second parameter is the number of discrete rate categories to simulate if zero continuous distribution Text and comments to the right of the are free to vary To prepare an infile the safest and quickest method may be to open the example file testdnal par that was distributed with the program save under a new and more descriptive name modify your new infile appropriately and save again Be sure you save the file with the ending par To keep your infiles and outfiles well organized I recommend you create a new directory carpeta with the same name as your infile followed by the text OUTFILES Place your new infile in this directory along with a copy of t
5. difference between SIMCOAL and SIMCOAL2 is that the latter allows recombination in the simulations however the former appears much easier to run Since we will not concern ourselves with recombination in today s lab we will stick to the older version SIMCOAL version 1 This program only works with the Windows operating system To visualize simulated gene trees we will use the program FigTree Software SIMCOAL for Windows 2000 Windows XP and Linux http cmpg unibe ch software simcoal FigTree for Windows OS Mac or Linux http tree bio ed ac uk software figtree Citation Schneider S Roessli D and Excoffier L 2000 Arlequin a software for population genetics data analysis User manual ver 2 000 Ver 2 000 Geneva Genetics and Biometry Lab Dept of Anthropology University of Geneva I believe this is the official citation Rozas J Sanchez DelBarrio JC Messeguer X Rozas R 2003 DnaSP DNA polymorphism analyses by the coalescent and other methods Bioinformatics 19 2496 2497 Further information Throughout this lab recall that SIMCOAL has a help page online http cempg unibe ch software simcoal Introduction Coalescent Simulation Lab Crawford page 2 of 7 GOALS Learn the basic options for coalescent simulation Observe stochastic variation in gene trees and understand its cause Understand the difference between the true genealogy of samples and a gene tree estimated from the data Understand better th
6. e 3N polosy AJC s results Your results AJC s results Your results Reciprocal monophyly 7 23 Paraphyly of 1 population 14 6 Polyphyly 9 1 Now look at the trees inferred from the mutational history Can you determine the proportion of monophyletic paraphyletic and polyphyletic trees Are these results different from the true genealogy file Why or why not Now copy your infile to the other folder e g 2pop_old OUTFILES and save under a new name Edit the age of the historical event population splitting event in forward time coalescent event in backwards time from 10 000 to 30 000 3N generations Review your resulting genealogies Tabulate the frequencies of monophyletic paraphyletic and polyphyletic genealogies Can you explain WHY you probably observed more monophyletic trees when the splitting even happened longer ago in the past If you have any non reciprocally monophyletic trees look at the ancestral lineages Do you have gt 2 lineages extending close to the root of the tree Is there any reason why you might expect more ancestral lineages extending farther back in the tree for those trees that are not reciprocally monophyletic IV Migration vs lineage sorting Lack of monophyly between two sister populations could be due to incomplete lineage sorting or it might also be due to migration In this example we will simulate 2 sister populations that diverged 5N generations in the pa
7. e process of lineage sorting Understand the causes of incomplete lineage sorting Investigate the similarities and differences in the affects of incomplete lineage sorting versus migration on genealogies Invent potential uses of coalescent simulations in testing historical models Today we will run a basic coalescent simulation using SIMCOAL We will first run simulations under a simple population model the idealized Wright Fisher population model Fisher 1922 1930 Wright 1931 In all models we will look at today we assume that there is no natural selection affecting the molecular markers of interest We further assume that all individuals are interchangable and all have an equal probability of leaving offspring Note while all individuals have an equal chance at reproducing themselves not all individuals will By random chance some will produce more some fewer some none at all This variance in reproductive success is the single source of random genetic drift in a Wright Fisher population Charlesworth 2009 Sexual selection for example would violate this assumption and would reduce the effective size Ne relative to the demographic size N In an ideal Wright Fisher population Ne is equal to N by definition For our first model we will look at the simplest case by assuming that there is no geographic population structure and population size is constant We can add population structure or population size changes later In all of toda
8. he program simcoal exe For a statistical test using simulation you should run perhaps 10 000 simulations to estimate a null distribution Today however we will just be using visual inspection of gene trees estimated from simulation so 10 30 replicate simulations would be plenty To run the program double click on the executable simcoal exe which will open the command prompt 1 Type the name of your infile but without the par suffix ending 2 Type the number of simulations to run Try 10 If the program finished correctly takes only a few seconds SIMCOAL will have created 15 new files for you 1 A numbered arp file for each simulation 10 in this case numbered 0 9 2 A batch file arb usable with the software Arlequin 3 A NEXUS file paup hopefully readable by PAUP or other phylogeny programs 4 Summary of pairwise distances and age of genealogies among simulations in a gen file 5 Tree file containing true genealogy obtained from each simulation ending with _true_trees trees 6 Tree file containing genealogy inferred from mutations added to genealogy according to our specified mutation model File ends with _mut_trees trees I Stochastic variation among gene trees Identical conditions can produce very different gene genealogies The coalescent process includes an element of chance or stochasticity Lineages coalesce at random The time between coalescent events Coa
9. lescent Simulation Lab Crawford page 4 of 7 follows an exponential distribution resulting in a sizable variance around the expected coalesence times To observe this variation select the outfile that ends with _true_trees trees and open it with the application Fig7ree We simulated 20 samples 10 times which are labeled on the right The 1 refers to the population number we simulated only 1 population Notice the scale bar at the bottom of the first tree figure and observe how it changes among trees Scroll through the 10 genealogies of 20 samples each we simulated by using the arrows in the upper menu bar above Prev Next Recall from lecture hopefully that the expected time to the final coalescence 2 lineages coalescing into 1 equals half the total expected depth of the genealogy How often do you observe this expectation In other words how often among simulations does the more ancestral half of the tree the left half in FigTree include more than two lineages Alternatively how often to you see two ancestral lineages occupying more than half the total depth of the tree In a balanced tree we would observe 50 of samples descending from each of the two ancestral lineages How often to you observe a balanced tree What s the minimum number of samples you observe descending from one of the two ancestral nodes Does the basal splitting coalescent event ever separate join 1 sample from to the other 19 sample
10. r Topicos Depto Ciencias Biol gicas UniAndes Profesor Andrew J Crawford lt andrew dna ac gt Semestre 2009 II Lab Coalescent simulation using SIMCOAL 17 septiembre 2009 Coalescent theory provides a powerful model for analyzing population genetic data In phylogeography we can use coalescent simulations to compare observed data with theoretical expectations under a given model By simulating datasets under different models we can ask which model or models are compatible with our data and which models we may be able to reject Today s lab provides us with the opportunity to observe the stochastic variation in gene trees that is inherent in the coalescent process Stochasticity comes from two ancestral processes 1 the random joining or coalescences among lineages as we look back in time and more importantly 2 the time interval between coalescent events with exponentially longer waiting times as the number of lineages drops We will observe that data simulated under even a simple population model reveals a surprising amount of variation in the topology and branch lengths of gene trees This variation among data sets under a single model illustrates the danger in over interpretation of a single inferred gene tree We will also explore the process of incomplete lineage sorting and compare it with migration as a source of paraphyly and polyphyly Today s lab will provide instructions and tips on how to run SIMCOAL The major
11. s Would you say this one sample is basal or ancestral to the other 19 Why or why not Coalescent theory predicts that the rate of coalescent events slows as the number of lineages declines Do you notice a faster rate of coalescences at the tip of the trees Are there exceptions Do you notice any polytomies in any genealogies Should we expect to observe polytomies Why or why not Notice the lengths of the tip external branches Would you expect to be able to detect even the shortest branches if you attempted to infer this true genealogy from DNA sequence data Il True genealogies vs inferred gene trees Previously we were looking at simulated true genealogies We can never know the true genealogy of a sample of DNA sequences We can only hope to estimate it from the variation among DNA sequences or other molecular markers The amount of mutations in our simulated DNA sequence datasets is determined by the mutation rate we selected and by the population size Bigger populations should have deeper genealogies and deeper trees have more total history length where mutations might be observed To observed the genealogies as estimated from the simulated mutational process close the true_trees trees file and open the file that ends with _mut_trees trees again in FigTree Flip through the 10 trees briefly You might see from 0 to 13 mutations in the genealogy How can you count mutations Note the shortest
12. sher RA 1930 The distribution of gene ratios for rare mutations Proc Roy Soc Edinb 50 205 220 Nagylaki T 1998 The expected number of heterozygous sites in a subdivided population Genetics 149 1599 1604 Wakeley J 2009 Coalescent Theory An Introduction Ben Roberts Greenwood Village Colorado Wright S 1931 Evolution in Mendelian populations Genetics 16 97 159
13. st In the absence of migration these populations are likely to be reciprocally monophyletic However in this simulation we will add a recent dispersal event from one population to the other at time W 10 generations ago During the dispersal event each member of one population has a 0 2 probability of migrating to the other population but population sizes will remain the same Modeling migration with population sizes that remain constant is referred to as conservative migration e g Nagylaki 1998 Create a new directory labeled e g 2pop MIG OUTFILES and copy the executable plus the infile par file into it Leave most of your simulation parameters the same but change the historical events as follows nistorical event time source sink migrants new deme size new growth rate migration matrix index 2 historical event 1000 010 2100 50000 011100 Coalescent Simulation Lab Crawford page 7 of 7 Run the program and examine your true genealogies as before How many of your simulated genealogies show reciprocal monophyly Paraphyly Can you detect any different in genealogies in tree shape or branch lengths between trees that were non monophyletic due to the recent dispersal event versus trees that were non monophyletic due to incomplete lineage sorting in the above exercise Can you think of a way of potentially distinguishing non monophyly due to incomplete lineage sorting versus non monophyly d
14. ue to recent dispersal or introgression Could you use SIMCOAL to do a power analysis i e explore the question of how much data you would need to distinguish between certain historical scenarios or hypotheses Most studies of incomplete lineage sorting versus introgression do not compare directly the two models rather they assume a no migration model as the null hypothesis and try to reject that For example one can estimate time and population size from the data assume these values plus the null hypothesis of no introgression in conducting coalescent simulations and then ask what is the chance of observing non monophyly in the absence of migration among the replicate simulations If non monophyly appears to be highly unlikely in the absence of migration under the simulated conditions then migration is inferred e g Buckley et al 2006 Given the flexibility of statistical testing by simulation however the student has the opportunity to create novel tests of hypotheses References Buckley TR Cordeiro M Marshall D Simon C 2006 Differentiating between hypotheses of lineage sorting and introgression in New Zealand alpine cicadas Maoricicada dugdale Systematic Biology 55 411 425 Charlesworth B 2009 Fundamental concepts in genetics Effective population size and patterns of molecular evolution and variation Nature Reviews Genetics 10 195 205 Fisher RA 1922 On the dominance ratio Proc Roy Soc Edinb 52 312 341 Fi
15. y s simulations we will assume that we are working with DNA sequence data and that we have a single gene sequence with no intragenic recombination We will further assume that our sample size n is small compared to the population size N Under this assumption we are safe in assuming that usually zero sometime 1 but never 2 coalescent events happen in a single ancestral generation This assumption simplifies the mathematics behind the model Wakeley 2009 We won t look at recombination today but those interested can try running SIMCOAL2Z later on their own time the features we need today happen to work much easier in the original SIMCOAL as far as I can tell We ll start with a single population with the following simulation parameters Number of demes 1 population Population size N 10 000 or 5 000 diploid individuals Sample size n 20 haplotypes Population growth rate 0 constant population sizes Migration 0 Historical events 0 e g population splitting dispersal expansion etc Type of molecular marker DNA DNA sequence length 1000 base pairs Mutation rate per generation per gene 0 0001 i e 1OE 7 per site Transition Transversion rate 0 66 i e transitions are twice as likely Mutation rate heterogeneity among sites 0 5 4 rate categories Coalescent Simulation Lab Crawford page 3 of 7 To implement these conditions in a coalescent simulation exercise in SIMCOAL the infile format is
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