Reaction norms with bifurcations shaped by evolution.

Two versions of a model for the evolution of seasonal polyphenism investigate the evolution of reaction norm bifurcation and branching. The first version is without a specific submodel for morphological development and the second has an explicit developmental map. Version 1 is evolutionarily relatively unconstrained: (i) reaction norms are specified by matrices containing the probabilities of occurrence of environment-phenotype combinations, (ii) all conceivable reaction norm matrices are reachable through a sequence of mutations, and (iii) small as well as large mutational effects occur. This version is used to find the evolutionarily stable strategy favoured by the population ecology that is characterized by stabilizing viability selection with a cyclically fluctuating selection optimum. When the strength of selection is large and when the lag between initiation of development and selection on mature phenotype is not a multiple of half the period of the environmental cycle, a branching reaction norm evolves. In the second model version, branching reaction norms occur for certain parameter combinations of the developmental submodel, but the evolution of this pattern is often constrained. The evolutionary trajectory becomes trapped in a local selective optimum for the parameters of the developmental system. Substantial developmental noise evolves, but mutations that produce a selectively advantageous branching pattern do not occur from there.