The Coalescent Theory And coalescent- based population genetics programs

The Coalescent TheoryAnd coalescent-based population genetics programs

OverviewSet 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 100000 –L0.5 –p 45

Can vary numbers for q’s, t, & m’s


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 (Ne): size of Wright-Fisher population; usually smaller than census

Theta, Θ: capacity of population to maintain genetic variability (=4Neμ)

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











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

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Past

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Past

Present

Past

Mathematical Representation

Θ= 4Neμ

P(Coalescent event) = 1/(2Ne)

Pc(t) = (1 – (1/2Ne))t-1(1/(2Ne))

E(tk) = 2/(k(k-1))


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


The theory

Influence

Computer programs

IMa tutorial

Computer Programs Kuhner, 2008

BEAST GENETREE LAMARC MIGRATE-N IM/IMa

IMa2



IMa2



IMa2


BEAST GENETREE LAMARC MIGRATE-N IM/Ima

IMa2



IMa2



IMa2

Computer Programs Coalescent Simulators

Approximate Bayesian Computation DIY-ABC PopABC

Simulation (Using “Pipeline” Approach) GENOME COAL CoaSim









Simulation (Using “Pipeline” Approach) GENOME ms COAL CoaSim











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 FileExample data for IM

# im test data

population1 population2

3 locus1 1 1 13 I 1 0.0000000008 (0.0000000001, 0.0000000015)

pop1_1 ACTACTGTCATGA

pop2_1 AGTACTATCACGA

hapstrexample 2 1 4 J2 0.75

pop1_1 13 34 GTAC

pop1_2 12 35 GTAT

pop2_1 12 37 GTAT

strexample 2 2 1 S1 1 0.00001 (0.000001, 0.00005)

strpop11a 23 strpop11b 26

strpop21a 25

strpop21b 31


# im test data


3 locus1 1 1 13 I 1 0.0000000008 (0.0000000001, 0.0000000015)




pop1_1 13 34 GTAC

pop1_2 12 35 GTAT

pop2_1 12 37 GTAT

strexample 2 2 1 S1 1 0.00001 (0.000001, 0.00005)


strpop21a 25

strpop21b 31


# im test data


3 locus1 1 1 13 I 1 0.0000000008 (0.0000000001, 0.0000000015)




pop1_1 13 34 GTAC

pop1_2 12 35 GTAT

pop2_1 12 37 GTAT

strexample 2 2 1 S1 1 0.00001 (0.000001, 0.00005)


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 100000 –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 100000 –L100000 –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 100000 –L 0.5 –fl

–g1 0.01 –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?

Documents

The Coalescent Theory And coalescent- based population genetics programs