Between Population Dynamics and Adaptive Dynamics
Hans Metz
Theoretical Biology, University of Leiden, Netherlands
Abstract
I shall explore a general framework for dealing with long term biological
evolution in "realistic" ecological settings.
This framework is based on two main simplifying assumptions: (i) a
separation of the population dynamical and mutational time scales, and
(ii) clonal inheritance.
The key concept is "fitness", defined as the asymptotic average relative
rate of increase of a population in an ergodic environment (the
environment is considered given so that the individuals reproduce
independently). This makes fitness a function of two variables, the
traits of the individuals, and the nature of the environment. In the case
of a novel mutant type the latter is set by the current resident types,
so that fitness can be written as a (possibly multivalued) function of
the invader trait value, and the trait values of the resident types.
>From this vantage point I shall consider the classification of
evolutionarily singular points for one and higher dimensional trait
spaces. These points include rest points of the evolutionary trajectory
through trait space, as well as points at which this trajectory branches,
i.e., enters trait space squared.
The ideas will be illustrated with examples from various, toy and more
realistic, ecological models.
