Genetic Variance and Covariance under Positive Assortative Mating

Abstract

The effect of positive assertative mating on genetic variance and covariance has been studied under varying conditions of dominance. The study deals separately with the situations (i) one locus segregating and (ii) any number of loci segregating; assuming in each case, arbitrary gene frequencies. With one locus segregating, the effect of repeated positive assortative mating has also been dealth with giving general results for a population subject to this type of mating for ‘n’ generations. The consequences, if two loci segregating are linked have also been worked out assuming half as gene frequencies in each case. The effect of selection combined with positive assortative mating when one locus is segregating with arbitrary gene frequencies has also been investigated.

With one locus segregating and when dominance is not operating, it is found that while the positive assortative mating does not effect the mean value it increases the total genetic variance in such a way that the within family variance is halved. When dominance is operating, the mean value, however, depends on ‘p’ the frequence of dominant allelomorph and decreases or increases from generation to generation according a ‘p’ is less than or greater than0.3. The covariance between family means and parental mean values in successive generations is also affected only when ‘p’ is greater than 0.3.

With any number of loci segregating, provided the genes involved are independent in action and distribution, it has been found that the contribution of each of the genes involved to the means, variances and covariance depends only on the dominance situation characteristic of that gene, being unaffected by the dominance situation of the other genes and further that these contributions are simply additive. The contribution is also similar in form if two genes are exhibiting the same type of dominance.

In the absence of dominance, the effect of positive assortative mating combined with selection against recessives is found to increase the genetic variability but the increase is much less than would be obtained if selection is dropped. In the present of dominance in positive direction, however, it is found that the effect of positive assortative mating with selection against recessives is to increase the mean value, but to decrease the total genetic variability to a considerable extent.