Developmental thresholds and the evolution of reaction norms for age and size at life-history transitions.

It is quite common in studies of life-history plasticity to find a negative relationship between the age at which various life-history transitions occur and the growth conditions under which individuals develop. In particular, high growth typically results in earlier transitions, often at a larger size. Here, we use a relatively general optimization model for age and size at life-history transitions to argue that current life-history theory cannot adequately explain these results. Specifically, most such theory requires key assumptions that are unlikely to be generally met. This suggests that some important component of the biology of many organisms must be missing from many of the models in life-history theory. We suggest that this missing component might be the phenomenon of developmental thresholds. There are at least two different types of developmental thresholds possible, and we incorporate these into our general optimality model to demonstrate how they can cause a negative relationship between growth conditions and age at a transition. If developmental thresholds are common throughout taxa, then this might explain the empirical results. Our model formulation and analysis also formalizes the popular Wilbur-Collins hypothesis for age and size at metamorphosis in amphibians. The results demonstrate that optimal combinations of age and size, and the slope of the reaction norm connecting them, depend on the existence and type of threshold assumed. Our results also provide an evolutionary framework that can be used to view the data and many of the proximate submodels derived from the Wilbur-Collins hypothesis.