The Ricker map is a model of density depedence which is widely used in fisheries biology. For a high growth rate, r,  the iterated map will generate chaotic dynamcis.

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The Ricker map is often plotted as a recruitment curve. A recruitment curve expresses the size of the population at the next time step as a function of the current size. The straight line is the exact replacement line N[t]=N[t+1]. Where the replacement intersects the recruitment is known as the carrying capacity or K. For mathematical simplicity the value of K is K=1.

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The function NestList can be used to iterate the Ricker map at discrete intervals of time.

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A small change in the parameter N will lead to widely different dynamics in abundance over time.

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Created by Mathematica  (May 25, 2005)