Evolutionary and Ecological Processes Determining the Properties of the Matrix

AbstractThe matrix is the matrix of additive genetic variances and covariances for a vector of phenotypes. Here we apply the classical theory for the balance among selection, genetic drift, and mutations to find the contributions to from each locus for populations at stasis. The fitness is approximated by a linear function of phenotypes, with coefficients affected by environmental fluctuations. We show that the matrix can be decomposed into four 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 is sufficient for assessing adaptive changes through time unless the deteriorations are corrected for. This applies for populations at stasis, but also for populations that are subject to long-term evolutionary changes. The theory also indicates several possible comparative studies for investigations of deteriorating effects. Our analyses also suggest that the factor loadings to the eigenvector of the matrix with the lowest eigenvalue will rather accurately indicate the relative contributions from different phenotype components to fitness. This is information notoriously difficult to obtain in natural populations.