Assortative mating has been suggested to result in an increase in heritability and additive genetic variance through an increase in linkage disequilibrium. The impact of assortative mating on linkage disequilibrium was explicitly examined for the two-locus model of Wright (1921) and two selective assortative mating models. For the Wright (1921) model, when the proportion of assortative mating was high, positive linkage disequilibrium was generated. However, when the proportion of assortative mating was similar to that found in some studies, the amount of linkage disequilibrium was quite low. In addition, the amount of linkage disequilibrium was independent of the level of recombination. For two selective assortative models, the amount of linkage disequilibrium was a function of the amount of recombination. For these models, the linkage disequilibrium generated was negative mainly because repulsion heterozygotes were favored over coupling heterozygotes. From these findings, the impact of assortative mating on linkage disequilibrium, and consequently heritability and additive genetic variance, appears to be small and model-specific.

Founder effects, genetic bottlenecks, and genetic drift in general can lead to low levels of genetic diversity, which can influence the persistence of populations. We examine genetic variation in two populations of desert bighorn sheep Ovis canadensis from New Mexico and Mexico to measure change over time and evaluate the impact of introducing individuals from one population into the other. Over about three generations, the amount of genetic variation in the New Mexico population increased. In contrast, over about two generations the amount of genetic variation in the Mexican population decreased by a great extent compared with an estimate from another Mexican population from which it is primarily descended. The potential reasons for these changes are discussed. In addition, although both populations have low genetic variation, introduction of Mexican rams into the New Mexico population might increase the amount of genetic variation in the New Mexico population. Overall, it appears that management to increase genetic variation might require substantial detailed monitoring and evaluation of ancestry from the different sources and fitness components.