Brownian Motion GIF with R and ImageMagick

 # First, we simulate continuous trait evolution by adding in each iteration    # a random number from a normal distribution with mean equal to 0 and standard    # deviation equal to 1. We simulate a total of 4 processes, to obtain at first    # two species and a specieation event at the middle of the simulation, obtaining    # a total of 3 species at the end.    df1<- data.frame(0,0)    names(df1)<- c("Y","X")    y<-0    for (g in 1:750){    df1[g,2] <- g    df1[g,1] <- y    y <- y + rnorm(1,0,1)    }    #plot(df1$X,df1$Y, ylim=c(-100,100), xlim=c(0,1500), cex=0)    #lines(df1$X,df1$Y, col="red")    df2<- data.frame(0,0)    names(df2)<- c("Y","X")    y<-0    for (g in 1:1500){     df2[g,2] <- g     df2[g,1] <- y     y <- y + rnorm(1,0,1)    }    #lines(df2$X,df2$Y, col="blue")    df3<- data.frame(750,df1[750,1])    names(df3)<- c("Y","X")    y<-df1[750,1]    for (g in 750:1500){     df3[g-749,2] <- g     df3[g-749,1] <- y     y <- y + rnorm(1,0,1)    }    #lines(df3$X,df3$Y, col="green")    df4<- data.frame(750,df1[750,1])    names(df4)<- c("Y","X")    y<-df1[750,1]    for (g in 750:1500){     df4[g-749,2] <- g     df4[g-749,1] <- y     y <- y + rnorm(1,0,1)    }    #lines(df4$X,df4$Y, col="orange")   

 # Now, we have to plot each simmulation lapse and store them in our computer.    # I added some code to make lighter the gif (plotting just odd generations) and     # to add a label at the speciation time. Note that, since Brownan Model is a     # stocasthic process, my simulation will be different from yours.    # You should adjust labels or repeat the simulation process if you don't     # like the shape of your plot.    parp<-rep(0:1, times=7, each= 15)    parp<- c(parp, rep(0, 600))    for (q in 1:750){     if ( q %% 2 == 1) {     id <- sprintf("%04d", q+749)     png(paste("bm",id,".png", sep=""), width=900, height=570, units="px",        pointsize=18)     par(omd = c(.05, 1, .05, 1))     plot(df1$X,df1$Y, ylim=c(-70,70), xlim=c(0,1500), cex=0,         main=paste("Brownian motion model \n generation=", 749 + q) ,         xlab="generations", ylab="trait value", font.lab=2, cex.lab=1.5 )    lines(df1$X,df1$Y, col="red", lwd=4)    lines(df2$X[1:(q+749)],df2$Y[1:(q+749)], col="blue", lwd=4)    lines(df3$X[1:q],df3$Y[1:q], col="green", lwd=4)    lines(df4$X[1:q],df4$Y[1:q], col="orange", lwd=4)    if (parp[q]==0)    text(750, 65,labels="speciation event", cex= 1.5, col="black", font=2)    if (parp[q]==0)    arrows(750, 60, 750, 35, length = 0.20, angle = 30, lwd = 3)    dev.off()    }    }   

 Now, you just have to use ImageMagick to put all the PNG files together in a GIF using a command like this in a terminal:

 convert -delay 10 *.png bm.gif   

Et voilà!