Evolutionarily unstable fitness maxima and stable fitness minima of continuous traits

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We present models of adaptive change in continuous traits for the following situations: (1) adaptation of a single trait within a single population in which the fitness of a given individual depends on the population's mean trait value as well as its own trait value; (2) adaptation of two (or more) traits within a single population; (3) adaptation in two or more interacting species. We analyse a dynamic model of these adaptive scenarios in which the rate of change of the mean trait value is an increasing function of the fitness gradient (i.e. the rate of increase of individual fitness with the individual's trait value). Such models have been employed in evolutionary game theory and are often appropriate both for the evolution of quantitative genetic traits and for the behavioural adjustment of phenotypically plastic traits. The dynamics of the adaptation of several different ecologically important traits can result in characters that minimize individual fitness and can preclude evolution towards characters that maximize individual fitness. We discuss biological circumstances that are likely to produce such adaptive failures for situations involving foraging, predator avoidance, competition and coevolution. The results argue for greater attention to dynamical stability in models of the evolution of continuous traits.