The Coalescent Theory And coalescent- based population genetics programs

Overview  Set up IMa run  The theory  Influence  Computer programs  IMa tutorial

Set up IMa Run  Download data file from Wiki  Open terminal  Type command: ima -i IMaEliurus -o IMaEliurus.out -q1 10 –q2 20 -m1 1 -m2 1 –n 10 -t 80 -b –L0.5 –p 45  Can vary numbers for q’s, t, & m’s

Overview  Set up IMa run  The theory  Influence  Computer programs  IMa tutorial

COALESCENT THEORY  Formalized in 1982 by Kingman in “The Coalescent”  Based on main idea of:  Retrospective model of population genetics  Dependent on ancestral population size and time since divergence

COALESCENT THEORY  Formalized in 1982 by Kingman in “The Coalescent”  Based on main idea of:  Retrospective model of population genetics  Dependent on ancestral population size and time since divergence

COALESCENT THEORY  Terms:  Coalescence: two lineages tracing back to a common ancestor at particular time  Effective Population Size (N e ): size of Wright- Fisher population; usually smaller than census  Theta, Θ: capacity of population to maintain genetic variability (=4N e μ)  Incomplete lineage sorting: failure to coalesce

COALESCENT THEORY  Terms:  Coalescence: two lineages tracing back to a common ancestor at particular time  Effective Population Size (N e ): size of Wright- Fisher population; usually smaller than census  Theta, Θ: capacity of population to maintain genetic variability (=4N e μ)  Incomplete lineage sorting: failure to coalesce

Wright Fisher Model  Describes genetic drift in finite population  Assumptions  N diploid organisms  Monoecious reproduction with infinite number of gametes  Non-overlapping generations  Random mating  No mutation  No selection

COALESCENT THEORY  Terms:  Coalescence: two lineages tracing back to a common ancestor at particular time  Effective Population Size (N e ): size of Wright- Fisher population; usually smaller than census  Theta, Θ: capacity of population to maintain genetic variability (=4N e μ)  Incomplete lineage sorting: failure to coalesce

COALESCENT THEORY  Terms:  Coalescence: two lineages tracing back to a common ancestor at particular time  Effective Population Size (N e ): size of Wright- Fisher population; usually smaller than census  Theta, Θ: capacity of population to maintain genetic variability (=4N e μ)  Incomplete lineage sorting: failure to coalesce

Incomplete Lineage Sorting Degnan & Salter (2005)

COALESCENT THEORY  Mathematical expectation of distribution of time back to coalescence  Seeks to predict amount of time elapsed between introduction of mutation and arising of particular allele/gene distribution in population

Present Past

Present Past

Present Past

Present Past

Present Past

Present Past

Present Past

Present Past

Present Past

Mathematical Representation  Θ= 4N e μ  P(Coalescent event) = 1/(2Ne)  P c (t) = (1 – (1/2N e )) t-1 (1/(2N e ))  E(t k ) = 2/(k(k-1))

Overview  Set up IMa run  The theory  Influence  Computer programs  IMa tutorial

Influence  Population Genetics  Phylogenetics  Statistical Phylogeography

Population Genetics  Theory describes the genealogical relationships among individuals in a Wright-Fisher population

Phylogenetics  Gene tree-Species tree  Predicts certain distribution of gene tree frequencies

Statistical Phylogeography  Individual gene trees contain information about past demographic events when rate of coalescence different between

Overview  Set up IMa run  The theory  Influence  Computer programs  IMa tutorial

Computer Programs  Kuhner, 2008  BEAST  GENETREE  LAMARC  MIGRATE-N  IM/IMa  IMa2

Computer Programs  Kuhner, 2008  BEAST  GENETREE  LAMARC  MIGRATE-N  IM/IMa  IMa2

Computer Programs  Kuhner, 2008  BEAST  GENETREE  LAMARC  MIGRATE-N  IM/IMa  IMa2

Computer Programs  Kuhner, 2008  BEAST  GENETREE  LAMARC  MIGRATE-N  IM/Ima  IMa2

Computer Programs  Kuhner, 2008  BEAST  GENETREE  LAMARC  MIGRATE-N  IM/IMa  IMa2

Computer Programs  Kuhner, 2008  BEAST  GENETREE  LAMARC  MIGRATE-N  IM/IMa  IMa2

Computer Programs  Coalescent Simulators  Approximate Bayesian Computation  DIY-ABC  PopABC  Simulation (Using “Pipeline” Approach)  GENOME  COAL  CoaSim

Computer Programs  Coalescent Simulators  Approximate Bayesian Computation  DIY-ABC  PopABC  Simulation (Using “Pipeline” Approach)  GENOME  COAL  CoaSim

Computer Programs  Coalescent Simulators  Approximate Bayesian Computation  DIY-ABC  PopABC  Simulation (Using “Pipeline” Approach)  GENOME  COAL  CoaSim

Computer Programs  Coalescent Simulators  Approximate Bayesian Computation  DIY-ABC  PopABC  Simulation (Using “Pipeline” Approach)  GENOME  ms  COAL  CoaSim

Computer Programs  Coalescent Simulators  Approximate Bayesian Computation  DIY-ABC  PopABC  Simulation (Using “Pipeline” Approach)  GENOME  ms  COAL  CoaSim

Computer Programs  Coalescent Simulators  Approximate Bayesian Computation  DIY-ABC  PopABC  Simulation (Using “Pipeline” Approach)  GENOME  ms  COAL  CoaSim

Computer Programs  Coalescent Simulators  Approximate Bayesian Computation  DIY-ABC  PopABC  Simulation (Using “Pipeline” Approach)  GENOME  ms  COAL  CoaSim

Overview  Set up IMa run  The theory  Influence  Computer programs  IMa tutorial

Introduction  MCMC simulation of gene genealogies  IM simulates model parameters Hey, J (2006)

Introduction cont’d  Assumptions  No other populations more closely related  Selective neutrality  No recombination within loci  Free recombination between loci  Mutation model chosen is correct  Infinite sites  Hasegawa-Kishino-Yano  Stepwise  Compound locus

Input File Example data for IM # im test data population1 population2 3 locus I ( , ) pop1_1 ACTACTGTCATGA pop2_1 AGTACTATCACGA hapstrexample J pop1_ GTAC pop1_ GTAT pop2_ GTAT strexample S ( , ) strpop11a 23 strpop11b 26 strpop21a 25 strpop21b 31

Input File Example data for IM # im test data population1 population2 3 locus I ( , ) pop1_1 ACTACTGTCATGA pop2_1 AGTACTATCACGA hapstrexample J pop1_ GTAC pop1_ GTAT pop2_ GTAT strexample S ( , ) strpop11a 23 strpop11b 26 strpop21a 25 strpop21b 31

Input File Example data for IM # im test data population1 population2 3 locus I ( , ) pop1_1 ACTACTGTCATGA pop2_1 AGTACTATCACGA hapstrexample J pop1_ GTAC pop1_ GTAT pop2_ GTAT strexample S ( , ) strpop11a 23 strpop11b 26 strpop21a 25 strpop21b 31

Command Line (terminal) Command line: ima -i IMaEliurus -o IMaEliurus.out -q1 10 –q2 20 -m1 1 -m2 1 –n 10 -t 80 -b –L10000 –p 45

Command Line (terminal) Command line: ima -i IMaEliurus -o IMaEliurus.out -q1 10 –q2 20 -m1 1 -m2 1 –n 10 -t 80 -b –L –p 45 More complex run line: ima -i IMaEliurus -o IMaEliurus.out -q1 10 -q2 10 –qA 300 –m 12 –m 23 –t 80 –n 20 –b –L 0.5 –fl –g –p 45

Important Note!  Need “IMrun” file which only says “yes” to continue indefinitely (or until it crashes or DSCR kicks the job)

Ouput File.out  MCMC information  Summary  Acceptance rates  Autocorrelation  ESS  Chain swapping

Ouput File.out  Marginal Peak  Marginal distributions  Minbin  Maxbin  HiPt  HiSmth  Mean  95lo/hi  HPD90lo/hi

Ouput File.out  ASCII  Curves  Plots

Ouput File.out.ti  No outward information  Can be used on subsequent runs when in “L mode”

How can I get a “good” run?  Conduct preliminary run  Duration?  Ideally, once run reaches stationarity and convergence  Assess autocorrelation  Use Metropolis-coupled MCMC  Run many, many times (well, at least 3)

Robustness of Coalescent  Violation to assumptions of:  Intralocus recombination  Population structure  Gene flow from unsampled populations  Linkage among loci  Divergent selection  Different model of substitution

Questions?