Math Insight

Hint

Use an underscore to indicate a subscript. For example type R_1 for $R_1$ and m_(t+1) for $m_{t+1}$

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Hint

Your original R code should look something like this:

     # growth rate
     R = 1.04

     # simulation time
     tmax = 100

     # initial conditions
     ms = 900

     # iterate the model
     for(t in 0:(tmax-1)) { 
          ms[t+2] = R*ms[t+1] 
     } 

     # plot the results
     plot(0:tmax, ms, xlab="time", ylab="population size")

To simulate two populations, you'll need define two growth rates R_1 and R_2, as well as a second state variable ns. Update the loop where iterate the model to update both ms and ns based on R_1 and R_2.

To plot lines for population 1, population 2, and the total population on the same graph, first put all your data in one matrix:

     nplot = matrix(c(ms,ns,ms+ns),nr=3,byrow=T)

You can use matplot to plot the matrix, with a command such as the following.

  matplot(0:tmax, t(nplot),
        type = "l", # specify line
        lty = 1:3, #specify life types
        col=c("blue","red","black"), # specify colors
        xlab="time", ylab="population size"   # add x and y labels
) 

With several lines on one figure, it is helpful to add a legend. Here you'll need to specify the legend location, the text labels, and finally which line styles and colors to use, e.g.:

     legend("topleft",legend = c("pop 1","pop 2","total"),
          lty = 1:3, #specify life types
          col=c("blue","red","black") # specify colors
     )

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