Pacific Institute for the Mathematical Sciences - PIMS

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.

MITACS Math Biology Seminar 2007