Statistics of Mendelian segregation-A mixture model.

Abstract

Mendel's law of segregation explains why genetic variation can be maintained over time. In diploid organisms, an offspring receives one allele from each parent, not just half of the blended genetic material of the parents. Which of the two alleles is received is purely random. This stochastic process generates genetic variation among members of the same family, called Mendelian segregation variance or within-family variance. In statistics, the genetic value of a quantitative trait for an offspring follows a mixture distribution consisting of the four alleles of the two parents, guided by a Mendelian variable from each parent. The mixture model allows us to partition the total genetic variance into between-family and within-family variances. In the absence of inbreeding, the genetic variance splits half to the between-family variance and half to the within-family variance. With inbreeding, however, the between-family variance is increased at the cost of the within-family variance, leading to a net increase of the total genetic variance. This study defines multiple Mendelian variables and develops a mixture model of quantitative genetics. The phenomenon that allelic variance is maintained over time is guided by "the law of conservation of allelic variance" in biology, which is comparable to "the law of conservation of mass" in physics.