Evolutionary and ecological processes determining properties of the $\bm G$-matrix

The $\bm G$-matrix is the matrix of additive genetic variances and covariances for a vector of phenotypes. Here we apply the classical theory for the balance between selection drift and mutations to find the contributions to $\bm G$ from each locus. The fitness is approximated by a linear function of phenotypes. Fluctuations in the environment generate variation in the coefficients of the fitness function. We show that the $\bm G$-matrix can be decomposed into 4 additive components generated by selection, drift, mutations and environmental fluctuations. Selection is on average counteracted by the other three processes included in Fisher's concept of the deterioration of the environment, in accordance with Frank's approximate conservation law proposing that the response to selection at stasis on average is canceled by effects of drift and mutations. The theory illustrates that Fisher's fundamental theorem cannot be used to accumulate selection through time to describe adaption unless the..., , , # Evolutionary and ecological processes determining the properties of the $\bm G$-matrix

Steinar Engen, Department of Mathematical Sciences, Centre for Biodiversity Dynamics, NTNU, N-7491 Trondheim, Norway. Email: [[e-mail]](mailto:[e-mail])
Bernt-Erik Sæther, Department of Biology, Centre for Biodiversity Dynamics, NTNU, N-7491 Trondheim, Norway. Email: [[e-mail]](mailto:[e-mail])

We show that the additive genetic variance-covariance matrix $\bm G$ can be decomposed into 4 additive components generated by selection, drift, mutations and environmental fluctuations. Selection is on average counteracted by the other three processes included in Fisher's concept of deterioration of the environment, generating considerable changes in mean phenotypes.

The theory illustrates that neither Fisher's fundamental theorem nor Lande's classical gradient formula are sufficient for assessing adaptive changes through time unless the deterio...