Some models of genetic selection

This paper begins with a description of the classical theory of viability selection in which probabilities that individuals of various genotypes survive are in proportions that do not change with time and are independent of population structure. Salient features of viability selection with one and two loci are reviewed. This theory is intimately connected with the usual theory of mass selection in quantitative genetics. It is well known that the mean of the relative viabilities does not necessarily increase if there is viability selection at more than one locus. It also turns out that if there is selection for fecundity with one locus, the mean fecundity may steadily decrease or oscillate rather than increase. This and the fact that a Hardy-Weinberg structure may no longer exist at any stage of life may have a bearing on predicting progress from artificial selection on reproductive characters. Classical viability selection theory does not completely describe natural selection. Other possibilities are discussed. Among these is the density and frequency dependent selection induced when the population lives in a limited habitat. Implications in quantitative genetics are discussed.