A beginner's guide to adaptive dynamics
Volume 63 / 2003
Abstract
The aim of these notes is to illustrate, largely by way of
examples, how standard ecological models can be put into an
evolutionary perspective in order to gain insight in the role of
natural selection in shaping life history characteristics. We
limit ourselves to phenotypic evolution under clonal reproduction
(that is, we simply ignore the importance of genes and sex). Another
basic assumption is that mutation occurs on a time scale which is
long relative to the time scale of convergence to an ecological
attractor.
We begin by illustrating the idea of interaction via environmental
variables through the example of competition for substrate in the
chemostat. In this context we explain the trait/strategy
substitution sequence, capturing how successful invaders/mutants
outcompete the resident and then become the new resident. We also
introduce the PIP, the pairwise invasibility plot, as a convenient
graphical tool to study the adaptive dynamics of a one-dimensional
trait.
We high-light the pessimization principle: if the environmental
condition is one-dimensional, mutation and natural selection
inevitably lead to deterioration/Verelendung. We illuminate the
Tragedy of the Commons as well as evolutionary suicide and, while
we're about it, adaptive dynamics as an added feature to a
bifurcation diagram (with, possibly, AD-induced branch switching).
Then we rewrite the invasion exponent as a function of resident and
invader trait, define the selection gradient and turn to the core of
the theory: the classification of singular points (where the
selection gradient vanishes) in terms of ESS, CSS, mutual
invasibility, converging – and diverging dimorphisms and branching
points. An extensive collection of allied examples focuses on the
timing of reproduction of semelparous organisms. We show how to
analyse steady states of structured population models, how fitness
measures relate to the dimension of the environmental condition and
to the specific form of density dependence and we establish the
central role of the ideal free distribution (i.e., the principle of
indifference). We also describe the “resident strikes back"
phenomenon. In the final section we very concisely sketch the wider
perspective, alternative theories and the agenda of AD.
An almost identical earlier version of these notes appeared in:
Summer School on Mathematical Biology,
A. Margheri, C. Rebelo, F. Zanolin (eds.),
CIM, Lisboa, Portugal, 2002.
