#This function plots dynamics and lines using Levins's equation together
metapop_plot = function(imi,ext,ini,alfa,dim,nostep, animation) {

# imi - immigration rate
# ext - extinction rate
# ini - proportion of habitats initially occupied (0 - one individual in the centre)
# alfa - shape constant for the rescue effect (if == 0 -> standard Levins's equation)
# dim - number of rows of cells (dim^2 is the number of habitats)
# nostep - number of simulation steps
#animation - whether to animate


  x=seq(0,1,by=0.01);
  plot(x,imi*x*(1-x),lwd=2,type="l",col="blue",xlab="Proportion of habitats occupied", ylab="Immigration or extinction per step");
  lines(x,(ext*x)/(1+alfa*ext*x),lwd=2,col="green");
  stp = max(imi*x*(1-x))/10



  y=metapop(imi,ext,ini,alfa,dim,0, 0,nostep);
  xx = seq(stp,stp+(nostep-1)*stp/(nostep),by=stp/(nostep));

  if (animation > 0) {
    for (i in 1:(nostep-1)) {
      points(y[i],xx[i],col="red",pch=20,type="p");
      Sys.sleep(0.2);
    }
  } 
  else
    points(y,xx,col="red",pch=20,type="p");
}