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Adaptive dynamics is a widely used framework for modeling long-term evolutionof continuous phenotypes. It is based on invasion fitness functions, whichdetermine selection gradients and the canonical equation of adaptive dynamics.Even though the derivation of the adaptive dynamics from a given invasionfitness function is general and model-independent, the derivation of theinvasion fitness function itself requires specification of an underlyingecological model. Therefore, evolutionary insights gained from adaptivedynamics models are generally model-dependent. Logistic models for symmetric,frequency-dependent competition are widely used in this context. Such modelshave the property that the selection gradients derived from them are gradientsof scalar functions, which reflects a certain gradient property of thecorresponding invasion fitness function. We show that any adaptive dynamicsmodel that is based on an invasion fitness functions with this gradientproperty can be transformed into a generalized symmetric competition model.This provides a precise delineation of the generality of results derived fromcompetition models. Roughly speaking, to understand the adaptive dynamics ofthe class of models satisfying a certain gradient condition, one only needs acomplete understanding of the adaptive dynamics of symmetric,frequency-dependent competition. We show how this result can be applied tonumber of basic issues in evolutionary theory.

Symmetric competition as a general model for single-species adaptive dynamics