Biological power laws and Darwin's principle.

Assuming that the repertoire of responses by living systems to perturbation gives a measure of their Darwinian fitness in a rapidly fluctuating environment, those that fulfill allometries (power laws) are described by means of catastrophes, whose variables and parameters are smooth functions of biological attributes. Using empirical allometries from a given system as input, a method is proposed to construct its associated catastrophe, allowing specific predictions on its susceptibility to perturbation and related properties, based on general results from catastrophe theory. The method is discussed within the macroecological context, and an example is provided by applying it to ecological systems that satisfy the self-thinning rule.

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