Some population genetic models combining artificial and natural selection pressures in the presence of assortative mating.

We have attempted quantitatively through a series of assortative mating models to gain insight into the interaction between the usually antagonistic tendencies of artifical and natural selection pressures. We summarize some of the robust conclusions. In cases where natural selection is expressed only through the phenotype and acts in the opposite direction to the culling incline, then fixation of the dominant or recessive type can be achieved and which occurs depends critically on the initial composition of the population and the magnitude of the degree of culling compared to the selection coefficients. With traits determined at two loci in the case that the double heterozygote is the desired kind, the effect of selfing can only be overcome by very strong artificial selection pressures (high culling order). The degree of culling to achieve its objective can be relaxed with weakening of linkage. The relevant comparison is r2+(1-r)2less than 2(1-c) indicating the precise extent of culling needed, to prevent fixation. The relationships are more complex when natural selection forces are also involved (see Model IV).