Role of Hardy-Weinberg Law in Random Mating | Genetics

In this article we will discuss about the role of Hardy-Weinberg Law in random mating of population.

Hardy-Weinberg Law is applicable only when mating is random. When genotypes do not mate at random it is called nonrandom mating, that is, individuals with certain genotypes prefer to mate with individuals of certain other genotypes. Consider for example the case of albinos having recessive genotype aa; normal individuals are AA and Aa. The frequency of a allele is 0.01, and of the normal A allele is 0.99.

When the population is at equilibrium, the frequency of AA individuals is 980 per thousand, of heterozygous carriers Aa is 19.8 in a thousand, and albinos 0.1 per thousand.

Obviously there are about 49 times more of heterozygous carriers than albinos in a sample of 1000 members of the population. Now AA and Aa individuals are both normal in appearance and mate at random. But albinos are less likely to mate with albinos or even perhaps with normals. Thus mainly Aa x Aa matings are the source of all albinos.

Inbreeding and Assortative Mating:

These are two departures from random mating. Inbreeding is a form of nonrandom mating that takes place between relatives having like genotypes. It increases the frequency of homozygotes in the population and decreases the frequency of heterozygotes. The harmful effects of inbreeding in increasing the frequency of recessive disorders in humans is under consanguineous marriages.

The closest possible degree of inbreeding is self-fertilisation which occurs in some plants such as the sweet pea. In assortative mating individuals with similar phenotypes mate more often than expected by chance.

Assortative mating causes a lesser decrease in heterozygosity than by inbreeding, but produces greater increase in phenotypic variation. Phenotypic characters like height, skin color, I.Q. and others form the basis of assortative mating in humans. The most important effect of assortative mating is to increase the variation of a trait in the population.

Inbreeding Coefficient:

The coefficient of inbreeding is the probability that an individual receives at a given locus two alleles that are identical by descent. It is a method of measuring the genetic consequences of inbreeding, namely increased frequency of homozygous genotypes. When relatives marry, they are likely to have one or more common ancestors.

If an ancestor of both mates is carrier of a harmful recessive gene, in that case, both mates who are direct descendants could also be carriers. Inbreeding gives rise to a homozygous affected child; the two alleles in such an affected child are said to be identical by descent because they originate by replication of a single allele carried by an ancestor. The probability of receiving two alleles that are identical by descent is a measure of the inbreeding coefficient and is designated by the symbol f.

In a randomly mating population with two alleles having frequency p and q, the frequency of heterozygotes is 2pq. In a population with coefficient of inbreeding f, the frequency of heterozygotes will be reduced by a fraction f of the total. One aspect of the Hardy-Weinberg Law takes inbreeding into account.

Consider 2 alleles A and a in a population with frequencies p and q such that p + q = 1. If the inbreeding coefficient of the population is f, then the frequencies of AA, Aa, and aa genotypes will be p²(1 – f) + pf, 2pq(1 – f), and q²(1 – f) + qf respectively. When there is no inbreeding, f is reduced to zero, and the proportions of genotypes attain Hardy-Weinberg equilibrium values of random mating populations.

In an imaginary situation of complete inbreeding, f = 1. However, inbreeding in humans never reaches such high values. On the average the inbreeding coefficient in humans ranges between f = 0.003 in some communities in Japan to its highest value of f= 0.02 in some states in South India such as Andhra Pradesh.

The harmful effects of inbreeding result from rare, deleterious recessive genes becoming homozygous, and also depend on the frequency of rare harmful alleles in the population, When harmful genes become homozygous in self-fertilizing plants, they are rapidly removed from the population.

Studies on the effects of inbreeding in humans have shown mental and physical defects and increased risk of death in children of first cousin marriages. Such children may or may not have a lower I.Q., growth rate and lesser capability than non-inbred children. It has been estimated that an average human being carries 3-5 genes that could produce severe mental or physical disability.

This means that a normal human being is a heterozygous carrier of 6-10 alleles which in the homozygous condition could cause death or severe mental or physical disabilities. The phenomenon is called mutational load.

Only a minority of the total number of the harmful recessive genes in a population are actually present in affected homozygotes. The majority of such genes are hidden in heterozygous, normal and healthy people who are carriers.

Inbreeding Depression and Heterosis:

Plant and animal breeders have used inbreeding for increasing homogeneity through homozygosity. It is well known that inbreeding also leads to reduction in vigour, fitness, fertility and other such attributes. This is called inbreeding depression and results from deleterious alleles becoming homozygous.

However, if independently inbred lines are crossed, the resulting hybrids show increased vigour, fitness and fertility over the parents. This is called hybrid vigour or heterosis and is much exploited in the improvement of crop plants such as maize, cotton, castor, Pennisetum and Sorghum.

Among animals, the vigour displayed by the mule, the result of a cross between a male horse and a female donkey, is a familiar example. The mule is a better beast of burden than either of its parents.