Discrete Population Growth with Stochastic Effects
by Mike Martin

On this page, you can investigate the behavior of the discrete growth model given by

bt+1 = r bt

when r takes on random values within δ-units from its central value.  More precisely, r is a random variable uniformly distributed in that interval.  The user must input the central r-value (denoted by r), the value of δ, the initial population bo, and the number of generations N.  The per-capita reproduction rate is not allowed to go below zero.  The output is in the form of two graphs.  The first graph consists of the discrete points superimposed on a plot of the solution without stochastic effects.  The second plot is the same as the first but on a semi-log scale.

Enter in the value of the parameters r, δ, b0, and N, then press the "Plot" button.

r =  

δ =  

b0 =  

N =  


References:

MathWorld's Exponential Growth

Wikipedia's Exponential Growth