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Hi there!

Last Monday we celebrated a “Scientific Marathon” at Royal Botanic Garden in Madrid, a kind of mini-conference to talk about our research. I was talking about the relation between fungal spore size and environmental variables such as temperature and precipitation. To make my presentation more friendly, I created a GIF to explain the Brownian Motion model. In evolutionary biology, we can use this model to simulate the random variation of a continuous trait through time. Under this model, we can notice how closer species tend to maintain closer trait values due to shared evolutionary history. You have a lot of information about Brownian Motion models in evolutionary biology everywhere!
Here I will show you how I built a GIF to explain Brownian Motion in my talk using 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!