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Inbreeding
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Inbreeding comes about in two ways: (1) the systematic choice of relatives as mates and (2) the subdivision of a population into small subunits, leaving individuals little choice but to mate with relatives. We will concentrate on inbreeding as the systematic choice of relatives as mates. The consequences of both are similar.
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An inbred individual is one whose parents are related that is, there is common ancestry in the family tree. The extent of inbreeding thus depends on the degree of common ancestry that the parents of an inbred individual share. When mates share ancestral genes, each may pass on copies of the same ancestral allele to their offspring. An inbred individual can then carry identical copies of a single ancestral allele. In other words, an in-
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The Hardy-Weinberg equilibrium is based on the assumption of random mating. Deviations from random mating come about when phenotypic resemblance or re-
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IV. Quantitative and Evolutionary Genetics
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19. Population Genetics: The Hardy Weinberg Equilibrium and Mating Systems
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Nonrandom Mating
dividual of aa genotype is homozygous and, if it is possible that the a allele from each parent is a length of DNA originally copied from a common ancestor, the aa individual is said to be inbred. The rst observable effect of inbreeding is the expression of hidden recessives. In human beings, each individual carries, on the average, about four lethalequivalent alleles, alleles that kill when paired to form a homozygous genotype (box 19.1). In many, and probably most, human societies, zygotes are generally heterozygous for these lethal alleles because of a cultural pattern of outbreeding, mating with nonrelatives. Rarely does an outbred zygote receive the same recessive lethal from each parent. Dominance acts to mask the expression of deleterious recessive alleles. But, in the process of inbreeding, when the zygote may receive copies of the same ancestral allele from each parent, there is a substantial increase in the probability that a deleterious allele will pair to form a homozygous genotype ( g. 19.2). Inbreeding can result in spontaneous abortions (miscarriages), fetal deaths, and congenital deformities. In many species, however, inbreeding even self-fertilization occurs normally. These species usually do not have the problem with lethal equivalents that species that normally outbreed do. Through time, species that normally inbreed have had these deleterious alleles mostly eliminated, presumably by natural selection. Inbreeding has even been used successfully for arti cial selection in livestock and crop plants. From our previous discussion, you can see that there are two types of homozygosity allozygosity, in which two alleles are alike but unrelated (not copies of the same ancestral allele) and autozygosity, in which two alleles have identity by descent (i.e., are copies of the same ancestral allele). An inbreeding coef cient, F, can be de ned as the probability of autozygosity, or the probability that the two alleles in an individual at a given locus are identical by descent. This coef cient can range from zero, at which point there is no inbreeding, to one, at which point it is certain an individual is autozygous.
Homozygosity by descent of copies of the same ancestral allele, a. The individual at the bottom of the pedigree is inbred with the aa genotype.
Increased Homozygosity from Inbreeding
What are the effects of inbreeding on the HardyWeinberg equilibrium Let us for a moment return to the gene pool concept to produce zygotes. Assume that an allele drawn from this gene pool is of the A type, drawn with a probability of p. On the second draw, the probability of autozygosity, that is, of drawing a copy of the same allele A, is F, the inbreeding coef cient.Thus the probability of an autozygous AA individual is pF. On the second draw, however, with probability (1 F ), either the A or a allele can be drawn, with probabilities of p2(1 F ) and pq(1 F ), respectively. Note that a second A allele produces a homozygote that is not inbred
(allozygous). If the rst allele drawn was an a allele, with probability q, then the probability of drawing the same allele (copy of the same ancestral allele) is F, and thus the probability of autozygosity is qF. However, the probability of drawing an a or A allele that does not contribute to inbreeding is (1 F ) and, therefore, the probability of an aa or Aa genotype is q2(1 F ) and pq(1 F ), respectively. These calculations are summarized in table 19.5, a summary of the genotypic proportions in a population with inbreeding. Several points emerge from table 19.5. First, when the inbreeding coef cient is zero (completely random mating), the table reduces to Hardy-Weinberg proportions. Second, compared with Hardy-Weinberg proportions, inbreeding increases the proportion of homozygotes in the population (identity by descent implies homozygosity). With complete inbreeding (F 1), only homozygotes will occur in the population. How does inbreeding affect allelic frequencies Recall that an allelic frequency is calculated as the frequency of homozygotes for one allele plus half the frequency of the heterozygotes. Here we let pn 1 be the frequency of the A allele after one generation of inbreeding: pn
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