###Discrete-time Ornstein-Uhlenbeck model of trait evolution. There are seven arguments needed for the
# simulation. They are the number of species (NumSP), the number of time steps (nsteps), the standard 
#deviation (SD –which controls the spread), the strength of selection (alph –which when zero is a Brownian 
#motion model), the trait optimum (theta), line colour (colr) and line width (wid). 

##by Marc Cadotte
##Oct 2010


OUM<-function(NumSp,nsteps,SD=1,alph=0.5,theta=100,colr="red",wid=1.2){
	
	plot(0,0,ylim=c(-100,100),xlim=c(0,nsteps),type="n",
		ylab="Trait value",xlab="Time")

	x<-c(0:nsteps)
	
	for (i in 1:NumSp){
		
		devs<-rnorm(nsteps,sd=SD)
		
		for (i in 1:nsteps) { 
			x[i+1] <- x[i] + alph*(theta-x[i]) + devs[i] 
			lines(i:(i+1), x[i:(i+1)], col=colr,lwd=wid) 
			} 

		}
	}