Random Mating and the Hardy-Weinberg Law
Soon after the rediscovery of Gregor Mendel’s rules of inheritance in 1900, British mathematician Godfrey Hardy and German physician Wilhelm Weinberg published a simple mathematical treatment of the effect of sexual reproduction on the distribution of genetic variation. Both men published their ideas in 1908 and showed that there was a simple relationship between allele frequencies and genotypic frequencies in populations. An allele is simply a genetic variant of a particular gene; for example, blood type in humans is controlled by a single gene with three alleles (A, B, and O). Every individual inherits one allele for each gene from both their mother and father and has a two-allele genotype. In the simplest case with only two alleles (for example, A and a), there are three different genotypes (AA, Aa, aa). The Hardy-Weinberg predictions specify the frequencies of genotypes (combinations of two alleles) in the population: how many will have two copies of the same allele (homozygotes such as AA and aa) or copies of two different alleles (heterozygotes such as Aa).
One important assumption that underlies the Hardy-Weinberg predictions is that gametes (sperm and egg cells) unite at random to form individuals or that individuals pair randomly to produce offspring. An example of the first case is marine organisms such as oysters that release sperm and eggs into the water; zygotes (fertilized eggs) are formed when a single sperm finds a single egg. Exactly which sperm cell and which egg cell combine is expected to be unrelated to the specific allele each gamete is carrying, so the union is said to be random. In cases in which males and females form pairs and produce offspring, it is assumed that individuals find mates without reference to the particular gene under examination. In humans, people do not choose potential mates at random, but they do mate at random with respect to most genetic variation. For instance, since few people know (or care) about the blood type of potential partners, people mate at random with respect to blood-type alleles.
Inbreeding and assortative mating are violations of this basic Hardy-Weinberg assumption. For inbreeding, individuals are more likely to mate with relatives than with a randomly drawn individual (for outbreeding, the reverse is true). Assortative mating occurs when individuals make specific mate choices based on the phenotype or appearance of others. Each has somewhat different genetic consequences. When either occurs, the Hardy-Weinberg predictions are not met, and the relative proportions of homozygotes and heterozygotes are different from what is expected.
The Genetic Effects of Inbreeding
When relatives mate to produce offspring, the offspring may inherit an identical allele from each parent, because related parents share many of the same alleles, inherited from their common ancestors. The closer the genetic relationship, the more alleles two individuals will share. Inbreeding increases the number of homozygotes for a particular gene in a population because the offspring are more likely to inherit identical alleles from both parents. Inbreeding also increases the number of different genes in an individual that are homozygous. In either case, the degree of inbreeding can be measured by the level of homozygosity (the percentage or proportion of homozygotes relative to all individuals).
Inbreeding is exploited by researchers who want genetically uniform (completely homozygous) individuals for experiments: Fruit flies or mice can be made completely homozygous by repeated brother-sister matings. The increase in the frequency of homozygotes can be calculated for different degrees of inbreeding. Self-fertilization is the most extreme case of inbreeding, followed by sibling mating, and so forth. Sewall Wright
pioneered computational methods to estimate the degree of inbreeding in many different circumstances. For self-fertilization, the degree of homozygosity increases by 50 percent each generation. For repeated generation of brother-sister matings, the homozygosity increases by about 20 percent each generation.
Inbreeding Depression
Inbreeding commonly produces inbreeding depression. This is characterized by poor health, lower growth rates, reduced fertility, and increased incidence of genetic diseases. Although there are several theoretical reasons why inbreeding depression might occur, the major effects are produced by uncommon and deleterious recessive alleles. These alleles produce negative consequences for the individual when homozygous, but when they occur in a heterozygote, their negative effects are masked by the presence of the other allele. Because inbreeding increases the relative proportion of homozygotes in the population, many of these alleles are expressed, yielding reduced health and vigor. In some cases, the effects can be quite severe. For example, when researchers wish to create homozygous lines of the fruit fly
Drosophila melanogaster
by repeated brother-sister matings, 90 percent or more of the lines fail because of widespread genetic problems.
Assortative Mating
In assortative mating, the probability of particular pairings is affected by the phenotype of the individuals. In positive assortative matings, individuals are more likely to mate with others of the same phenotype, while in negative assortative mating, individuals are more likely to mate with others that are dissimilar. In both cases, the primary effect is to alter the expected genotypic frequencies in the population from those expected under the Hardy-Weinberg law. Positive assortative mating has much the same effect as inbreeding and increases the relative frequency of homozygotes. Negative assortative mating, as expected, has the opposite effect and increases the relative proportion of heterozygotes. Positive assortative mating has been demonstrated for a variety of traits in humans, including height and hair color.
Impact and Applications
The widespread, detrimental consequences of inbreeding are believed to shape many aspects of the natural history of organisms. Many plant species have mechanisms developed through natural selection to increase outbreeding and avoid inbreeding. The pollen (male gamete) may be released before the ovules (female gametes) are receptive, or there may be a genetically determined self-incompatibility to prevent self-fertilization. In most animals, self-fertilization is not possible, and there are often behavioral traits that further reduce the probability of inbreeding. In birds, males often breed near where they were born, while females disperse to new areas. In mammals, the reverse is generally true, and males disperse more widely. Humans appear to be an exception among the mammals, with a majority of cultures showing greater movement by females. These sex-biased dispersal patterns are best understood as mechanisms to prevent inbreeding.
In humans, individuals are unlikely to marry others with whom they were raised. This prevents the potentially detrimental consequences of inbreeding in matings with close relatives. This has also been demonstrated in some birds. Domestic animals and plants may become inbred if careful breeding programs are not followed. Many breeds of dogs exhibit a variety of genetic-based problems (for example, hip problems, skull and jaw deformities, and nervous temperament) that are likely caused by inbreeding. Conservation biologists who manage endangered or threatened populations must often consider inbreeding depression. In very small populations such as species maintained in captivity (zoos) or in isolated natural populations, inbreeding may be hard to avoid. Inbreeding has been blamed for a variety of health defects in cheetahs and Florida panthers.
Key Terms
allele
:
any of a number of possible genetic variants of a particular gene locus
assortative mating
:
mating that occurs when individuals make specific mate choices based on the phenotype or appearance of others
heterozygote
:
a diploid genotype that consists of two different alleles
homozygote
:
a diploid genotype that consists of two identical alleles
inbreeding
:
mating between genetically related individuals
inbreeding depression
:
a reduction in the health and vigor of inbred offspring, a common and widespread phenomenon
random mating
:
a mating system in which each male gamete (sperm) is equally likely to combine with any female gamete (egg)
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