Abstract
We apply the method of contraction, familiar in statistical mechanics applications, to reduce the Fisher equation describing population growth and dispersal in the space-time domain to an equation in the time domain. The resulting equation is identical to the well-known logistic equation with an additional correction term that depends on the global solution to the Fisher equation. This equation provides a possible basis for explaining why logistic dynamics has not always described experimental data and also for then formulating models that generalize the logistic equation.
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