Mating and offspring frequencies under partial outcrossing in a structured population

This paper gives a model of a structured population with respect to an autosomal locus with two alleles. The population reproduces in discrete and non-overlapping generations. The population is assumed to be in equilibrium in that exactly the same distribution of genotypic proportions is reproduced in each generation. The population is subdivided into 'localities' which are characterized by the local gene frequencies. Within each locality the genotypic proportions may depart from Hardy-Weinberg proportions and the same fixation index applies to all localities. The system departs from reality by assuming that the frequency of the first allele follows the beta distribution. However, this enables a convenient way to derive the mating frequencies of parents so that equilibrium is maintained. Wright's F-statistics are applied to characterize the population as a whole. The system is extended to permit an arbitrary level of outbreeding.

On extending the Hardy-Weinberg law

This paper gives a general mating system for an autosomal locus with two alleles. The population reproduces in discrete and non-overlapping generations. The parental population, the same in both sexes, is arbitrary as is that of the offspring and the gene frequencies of the parents are maintained in the offspring. The system encompasses a number of special cases including the random mating model of Weinberg and Hardy. Thus it demonstrates, in the most general way possible, how genetic variation can be conserved in an indefinitely large population without invoking random mating or balancing selection. An important feature is that it provides a mating system which identifies when mating does and does not produce Hardy-Weinberg proportions among offspring.

Stages in the evolution of the Hardy-Weinberg law

The Hardy-Weinberg law has been used widely for about one hundred years with little question as to the foundations laid down by its originators. The basic assumption of random mating, that is choice of mates by a process akin to that of a lottery, was shown to produce genotypic proportions following the "binomial-square" rule, the so-called Hardy-Weinberg proportions (HWP). It has been assumed by many that random mating was the only way of pairing genes capable of producing HWP. However it has been shown that HWP can be obtained and maintained by non-random mating. The steps along the way to this revelation and some implications are reviewed.

The Hardy-Weinberg principle

Hardy-Weinberg genotypic proportions can be maintained in a population under non-random mating. A compact formula gives the proportions of mating pair types. These are illustrated by some simple examples.

The coefficient of common identity

No presente trabalho introduzimos um coeficiente probabilístico capaz de medir o grau de parentesco de dois indivíduos em relaçäo a um loco autossômico. Esse coeficiente, denominado coeficiente de origem comum, pode ser usado para determinar-se a probabilidade de que um gene manifestado por um caso índice esteja presente num outro membro qualquer da família. No presente trabalho discutimos também o uso näo muito apropriado que vem sendo feito do coeficiente de parentesco introduzido por Wright