Zusammenfassung
The evolution of quantitative characters depends on the frequencies of the alleles involved, yet these
frequencies cannot usually be measured. Previous groups have proposed an approximation to the
dynamics of quantitative traits, based on an analogy with statistical mechanics. We present a modified
version of that approach, which makes the analogy more precise and applies quite generally to describe
the evolution of allele frequencies. We calculate explicitly how the macroscopic quantities (i.e., quantities
that depend on the quantitative trait) depend on evolutionary forces, in a way that is independent of the
microscopic details. We first show that the stationary distribution of allele frequencies under drift,
selection, and mutation maximizes a certain measure of entropy, subject to constraints on the expectation
of observable quantities. We then approximate the dynamical changes in these expectations, assuming
that the distribution of allele frequencies always maximizes entropy, conditional on the expected values.
When applied to directional selection on an additive trait, this gives a very good approximation to the
evolution of the trait mean and the genetic variance, when the number of mutations per generation is
sufficiently high (4Nm . 1). We show how the method can be modified for small mutation rates (4Nm /
0). We outline how this method describes epistatic interactions as, for example, with stabilizing selection.
Nutzer