Thursday, March 8, 2018

Simulating migration, natural selection, & genetic drift in R

I just added another function to my evolutionary genetics teaching R package, PopGen to simulate the simultaneous actions of migration, natural selection, & genetic drift.

Here is what the function code looks like:

msd<-function(p0=c(0.5,0.5),Ne=c(100,100),
    w=list(c(1,1,1),c(1,1,1)),m=c(0.01,0.01),ngen=400,
    colors=c("red","blue"),...){
    if(hasArg(show.legend)) show.legend=list(...)$show.legend
    else show.legend<-TRUE
    w<-lapply(w,function(w) (w/max(w))[3:1])
    gametes<-lapply(Ne,function(Ne) rep(0,2*Ne))
    gametes<-mapply(function(p0,g,N){
        g[1:round(p0*2*N)]<-1
        g},p0=p0,g=gametes,N=Ne,SIMPLIFY=FALSE)
    p<-lapply(gametes,mean)
    for(i in 1:ngen){
        genotypes<-lapply(gametes,function(x) matrix(sample(x),
            length(x)/2,2))
        migrants<-mapply(function(N,m) which(runif(N)<=m),N=Ne,
            m=m,SIMPLIFY=FALSE)
        for(j in 1:length(genotypes)){
            to<-if(j==1) 2 else 1
            genotypes[[to]]<-rbind(genotypes[[to]],
                genotypes[[j]][migrants[[j]],])
        }
        for(j in 1:length(genotypes)){
            if(length(migrants[[j]])>0)
                genotypes[[j]]<-genotypes[[j]][-migrants[[j]],]
        }
        fitness<-mapply(function(x,w) w[rowSums(x)+1],x=genotypes,
            w=w,SIMPLIFY=FALSE)
        selected<-mapply(function(prob,N,Ne) 
            cbind(sample(N,Ne,prob=prob,replace=TRUE),
            sample(N,Ne,prob=prob,replace=TRUE)),prob=fitness,
            N=sapply(genotypes,nrow),Ne=Ne,SIMPLIFY=FALSE)
        copy<-lapply(Ne,function(Ne)
            matrix(sample(1:2,2*Ne,replace=TRUE),Ne,2))
        gametes<-mapply(function(g,s,c) c(diag(g[s[,1],][,c[,1]]),
            diag(g[s[,2],][,c[,2]])),
            g=genotypes,s=selected,c=copy,SIMPLIFY=FALSE)
        for(j in 1:2) p[[j]][i+1]<-mean(gametes[[j]])
    }
    plot(0:ngen,p[[1]],type="l",col=colors[1],lwd=2,ylim=c(0,1),
        xlab="time (generations)",ylab="f(A)")
    lines(x=0:ngen,y=p[[2]],col=colors[2],lwd=2)
    if(show.legend) legend(x="topright",legend=1:2,lty=1,col=colors,
        lwd=2,bg=make.transparent("white",0.8))
    invisible(p)
}

in which the function name, msd, stands for migration, selection, & drift. It is a relatively simple modification of another function, drift.selection, but in which individuals are swapped from one population to another at some rate. It's pretty flexible in that, for instance, we simulate things like asymmetric migration rates between populations (the function argument m should contain emigration rates), differing effective population sizes, and different genotypic selection between populations.

Here are a few of examples of how it might be used.

First, load package:

library(PopGen)
packageVersion("PopGen")
## [1] '0.9.1'

Now, genetic drift absent migration between populations:

msd(m=c(0,0),Ne=c(200,200),ngen=500) ## with NO migration

plot of chunk unnamed-chunk-3

msd(m=c(0,0),Ne=c(200,200),ngen=500)

plot of chunk unnamed-chunk-3

Next, migration but no selection:

Ne<-c(200,200)
msd(m=1/Ne,Ne=Ne,ngen=500) ## relatively low migration

plot of chunk unnamed-chunk-4

msd(m=10/Ne,Ne=Ne,ngen=500) ## relatively high migration

plot of chunk unnamed-chunk-4

Now we're ready to introduce divergent natural selection between populations.

First, for reference, absent migration:

msd(p0=c(0.25,0.75),Ne=Ne,w=list(c(1,0.95,0.9),c(0.9,0.95,1)),
    m=c(0,0),ngen=500)

plot of chunk unnamed-chunk-5

Next, with some or a lot of migration:

msd(p0=c(0.25,0.75),Ne=Ne,w=list(c(1,0.95,0.9),c(0.9,0.95,1)),
    m=1/Ne,ngen=500) ## some migration

plot of chunk unnamed-chunk-6

msd(p0=c(0.25,0.75),Ne=Ne,w=list(c(1,0.95,0.9),c(0.9,0.95,1)),
    m=10/Ne,ngen=500) ## lots of migration

plot of chunk unnamed-chunk-6

Finally, what happens when one population is much larger than the other?

msd(p0=c(0.25,0.75),Ne=c(100,1000),w=list(c(1,0.95,0.9),c(0.9,0.95,1)),
    m=1/500,ngen=500,show.legend=F)
legend(x="topright",legend=c(expression(paste(N[e],"= 100")),
    expression(paste(N[e],"= 1,000"))),lty=1,col=c("red","blue"), 
    lwd=2,bg=phytools::make.transparent("white", 0.8))

plot of chunk unnamed-chunk-7

Cool.

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