Work in progress: The evolution of phenotype determination and an attempt to classify simple life-history models

In this talk I will present two pieces of work in progress. In the first half of the talk I will speak about the evolution of phenotype determining mechanisms. Many heterogeneous environments favour different phenotypes in different places or at different times. Phenotypic diversity can either result from genetic diversity of from a single genotype capable of producing different phenotypes. A single genotype might produce different phenotypes for example in response to an environmental cue (phenotypic plasticity), through a randomization mechanism (bet-hedging), or through a combination of the two. A large part of the existing theoretical literature attempts to give conditions under which one of these specific mechanisms is favoured over a phenotypically monomorphic population. However, in many circumstances different evolutionary responses are favoured simultaneously and the real question becomes which of these different responses might evolve first and possibly pre-empt any selection driving one of the alternative responses. I will address this question by presenting some preliminary results derived from a model designed to study evolution in a temporarily heterogeneous environment.

In the second half of the talk I will present a classification of the evolutionary dynamics for a class of simple life-history models. The aim of this classification is to find principles governing the evolutionary dynamics that are valid beyond a single specific model. The family of models considered is characterized by discrete time population dynamics, density-dependent population growth, by the assumption that individuals can occur in two states, and that two evolving traits are coupled by a trade-off. Individual models differ in the choice of traits that are presumed to be evolving and in the way population regulation is incorporated. I classify models according to curvature properties of the fitness landscape and whether the evolutionary dynamics can be analysed by means of an optimization criterion. The first classification allows me to infer whether trait combinations that are characterized by a zero fitness gradient are susceptible to invasion by similar trait combinations. The second classification distinguishes models where evolutionary change is frequency-independent from models that give rise to frequency dependence. I will conclude by summarizing some general patterns emerging from this analysis.