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 properties of the $\bm G$-matrix

The programmes are intended to produce graphs to illustrate the implications of the analytical results derived in this paper and are written in the Pascal language within the programme package Delfie 6. The are no data to be read and no external procedures, and the parameters used are part of the program code. Further information is given in the beginning of the program code for each figure.

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Figure 2

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Figure 2 is an illustration of how two stochastic effects, random genetic drift (expressed by the effective population size N_e) and environmental fluctuations in the fitness function (expressed by a factor \theta that increases with increasing environmental fluctuations), may affect the average additive genetic variance of fitness at stasis defined at the average environment, which is given by equation (4).

This program performs the computations leading to figure 2, showing for four different...