Pacific Institute for the Mathematical Sciences - PIMS

We analytically investigate the long-term evolution of a continuously
varying quantitative character in a diploid population that is
determined additively by a finite number of loci. The trait is under a
mixture of frequency-dependent disruptive selection induced by
intraspecific competition and frequency-independent stabilizing
selection. Moreover, the trait is restricted to a finite range by
constraints on the particular loci. Our investigations are based on
explicit analytical on the short-term dynamics under the assumption of
linkage equilibrium. We show that the population always reaches a
long-term equilibrium (LTE), i.e., an equilibrium that is resistant
against perturbations of mutations of sufficiently small effect. In
general, several LTEs can coexist. They can be calculated explicitly,
and we provide necessary and sufficient conditions for their existence.
In the case that more than one LTE exists, we exemplify numerically
that the evolutionary outcome depends crucially on the initial genetic
architecture, on the joint distribution of mutational effects across
loci, and on the particular realization of the mutation process.
Therefore, long-term evolution cannot be predicted from the ecology
alone. We further show that a partial order exists for the LTEs. The
set of LTEs has a `largest' element, an LTE, which is reached during
long-term evolution if the effects of the occurring mutant alleles are
sufficiently large.

MITACS Math Biology Seminar 2007