Animated phylomorphospace projection

The so-called 'phylomorphospace' is a projection of the tree into phenotypic space for quantitative traits. Consequently, I thought it might be fun to try & animate this projection - that is, to visualize the transformation of the tree from the way it's typically projected into a phylomorphospace.

This could look something like the following:

project.phylomorphospace<-function(tree,X,nsteps=1000,sleep=0,...){
    tree<-minRotate(reorder(tree,"cladewise"),X[,2],print=FALSE)
    X<-X[tree$tip.label,]
    A<-cbind(fastAnc(tree,X[,1]),fastAnc(tree,X[,2]))
    cladogram<-tree
    cladogram$edge.length<-NULL
    mar<-par()$mar
    plotTree(cladogram,type="cladogram",nodes="centered",plot=FALSE)
    obj<-get("last_plot.phylo",envir=.PlotPhyloEnv)
    obj$xx<-obj$xx*(max(c(X[,1],A[,1]))-min(c(X[,1],A[,1])))+
        min(c(X[,1],A[,1]))
    xlim<-range(obj$xx)
    xlim[2]<-xlim[2]+max(strwidth(tree$tip.label))
    obj$yy<-(obj$yy-min(obj$yy))/(max(obj$yy)-min(obj$yy))*
        (max(c(X[,2],A[,2]))-min(c(X[,2],A[,2])))+min(c(X[,2],A[,2]))
    ylim<-range(obj$yy)
    X0<-cbind(obj$xx[1:Ntip(tree)],obj$yy[1:Ntip(tree)])
    rownames(X0)<-tree$tip.label
    A0<-cbind(obj$xx[1:tree$Nnode+Ntip(tree)],
        obj$yy[1:tree$Nnode+Ntip(tree)])
    rownames(A0)<-1:tree$Nnode+Ntip(tree)
    par(mar=mar)
    phylomorphospace(tree,X0,A0,label="horizontal",xlim=xlim,
        ylim=ylim,...)
    for(i in 1:nsteps){
        Sys.sleep(sleep)
        dev.hold()
        phylomorphospace(tree,((nsteps-i)*X0+i*X)/nsteps,
            ((nsteps-i)*A0+i*A)/nsteps,xlim=xlim,ylim=ylim,
                ...)
        dev.flush()
    }
}

And if we try it out:

library(phytools)
project.phylomorphospace(tree,X,xlab="",ylab="",
    node.size=c(0,1.2))

Kinda neat?

The .gif I generated as follows:

png(file="ppm-%04d.png",width=600,height=600,res=120)
par(mar=c(2.1,2.1,1.1,1.1))
project.phylomorphospace(tree,X,xlab="",ylab="",
    node.size=c(0,1),lwd=1,nsteps=100,fsize=0.6)
dev.off()
system("ImageMagick convert -delay 10 -loop 2 *.png 14Mar18c-post.gif")
file.remove(list.files(pattern=".png"))

Finally, here's how I simulated the tree & data:

tree<-pbtree(n=26,tip.label=LETTERS)
vcv<-matrix(c(1,-0.8,-0.8,1),2,2)
X<-sim.corrs(tree,vcv)

Some points moving around randomly in a box

For my PopGen I was thinking about writing some spatial population genetic simulations.

First I thought I'd write a little animation of things moving randomly in two dimensions. Here's what that looks like:

moving.randomly<-function(sig2=0.1,ngen=1000,sleep=0.1){
    x<-rep(1:9,9)
    y<-c()
    for(i in 1:9) y<-c(y,rep(i,9))
    n<-length(x)
    dev.hold()
    plot(x,y,xlim=c(0,10),ylim=c(0,10),pch=21,
        bg=phytools:::make.transparent("blue",0.2),cex=2)
    lines(c(0,0,10,10,0),c(0,10,10,0,0),lwd=6,
        col=phytools:::make.transparent("blue",0.2))    
    dev.flush()
    for(i in 1:ngen){
        x<-x+rnorm(n=n,sd=sqrt(sig2))
        while(!(all(x<10)&&all(x>0))){
            x[which(x<0)]<-abs(x[which(x<0)])
            x[which(x>10)]<-10-(x[which(x>10)]-10)
        }
        y<-y+rnorm(n=n,sd=sqrt(sig2))
        while(!(all(y<10)&&all(y>0))){
            y[which(y<0)]<-abs(y[which(y<0)])
            y[which(y>10)]<-10-(y[which(y>10)]-10)
        }
        dev.hold()
        plot(x,y,xlim=c(0,10),ylim=c(0,10),pch=21,
            bg=phytools:::make.transparent("blue",0.2),cex=2)
        lines(c(0,0,10,10,0),c(0,10,10,0,0),lwd=6,
            col=phytools:::make.transparent("blue",0.2))
        dev.flush()
        Sys.sleep(sleep)
    }
}

moving.randomly(sig2=0.01)

The above .gif I actually made & then subsequently embedded in the .html using ImageMagick as follows:

png(file="mr-%04d.png",width=600,height=600)
moving.randomly(sig2=0.01,sleep=0)
dev.off()
system("ImageMagick convert -delay 10 -loop 0 *.png 14Mar18b-post.gif")
file.remove(list.files(pattern=".png"))

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

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

Next, migration but no selection:

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

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

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)

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

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

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))

Cool.