Complex dynamics on hardy-weinberg equilibrium with mutation: a mathematical model

Marcos Teixeira Godinho, Sara Dalia Barbosa


This paper shows that a small modification of the Hardy-Weinberg law will lead to a completely different equilibrium. This new equilibrium is chaotic, in a mathematical sense. It is well known that dynamic difference or differential equation models, which are characterized by nonlinearity, can present chaotic properties over nontrivial ranges of values of their parameters. Chaotic orbit, besides its deterministic behavior, is undistinguishable from a random process, or rather, a process perturbed by a random shock. Despite its complexity, in a certain range, the model is stable, presenting a rich variety of behavior. The key point is that we do not need to attribute to a random walk or statistical model or to a drift as an external force to act upon the population.

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