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This can be interpreted to mean that about 6.25% of individual I s loci are autozygous, or that there is a 6.25% chance of autozygosity at any one of I s loci. The inbreeding coef cient of the offspring of siblings ( g. 19.5) can also be calculated, assuming that A and B are not themselves inbred (FA and FB are zero), as FI 2(1 2)3 0.25
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It is also possible to de ne the inbreeding coef cient, F, of a population as the relative reduction in heterozygosity in the population due to inbreeding. In an individual, F is the probability of autozygosity; it represents an increase in homozygosity, which is therefore a decrease in heterozygosity. In a population, it also represents the reduction in heterozygosity. From the de nition, we can calculate the population F as follows: F (2pq H) 2pq
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Conversion of a sib-mating pedigree to a path diagram. Individual I is inbred.
where H is the actual proportion of heterozygotes in a population, and 2pq is the expected proportion of het-
Tamarin: Principles of Genetics, Seventh Edition
IV. Quantitative and Evolutionary Genetics
19. Population Genetics: The Hardy Weinberg Equilibrium and Mating Systems
The McGraw Hill Companies, 2001
Nonrandom Mating
erozygotes based on Hardy-Weinberg proportions. This equation reduces to F 1 H 2pq (19.2)
This equation shows that when H 2pq, F is zero, meaning that there is no decrease in heterozygotes and therefore, apparently, no inbreeding. When there are no heterozygotes, F 1. This could be the case in a completely inbred population for example, a selffertilizing plant species.
As an example of an intermediate case, take the sample of one hundred individuals segregating the A1 and A2 alleles at the A locus: A1A1, fty-four; A1A2, thirty-two; and A2A2, fourteen. In this example, p 0.7, q 0.3, and H 0.32. Since 2pq 0.42, H/2pq 0.32/0.42 0.76, and F 1 0.76, or 0.24. Thus, the inbreeding coef cient of this population is 0.24; there is a 24% reduction in heterozygotes, due presumably to inbreeding.
E E F
I Pedigree
I Path diagram
Paths A B A B
I (1) Figure 19.6
I (2)
I (3)
I (4)
I (5)
I (6)
Pedigree and path diagram of two generations of sib matings. The six paths involving the 0.05. The paths involve common ancestors in two generations. potential for autozygosity are shown. FA
Tamarin: Principles of Genetics, Seventh Edition
IV. Quantitative and Evolutionary Genetics
19. Population Genetics: The Hardy Weinberg Equilibrium and Mating Systems
The McGraw Hill Companies, 2001
Nineteen
Population Genetics: The Hardy-Weinberg Equilibrium and Mating Systems
S U M M A R Y
STUDY OBJECTIVE 1: To understand the concept of population-level genetic processes 553 554 In a large, randomly mating population of sexually reproducing diploid organisms, not subject to the in uences of mutation, migration, or selection, an equilibrium will be achieved for an autosomal locus with two alleles. STUDY OBJECTIVE 2: To learn the assumptions and naSTUDY OBJECTIVE 4: To analyze the process and consequences of nonrandom mating in diploid populations 560 565 Random mating is required for the Hardy-Weinberg equilibrium to hold. Deviations from random mating fall into two categories, depending on whether phenotypic resemblance or relatedness is involved in mate choice. Phenotypic resemblance is the basis for assortative and disassortative mating, in which individuals choose similar or dissimilar mates, respectively. Assortative mating causes increased homozygosity only among loci controlling the traits that in uence mate choice. There are no changes in allelic frequencies. Similarly, disassortative mating causes increased heterozygosity without changing allelic frequencies. Mating among relatives, or inbreeding, is represented by F, the inbreeding coef cient, which measures the probability of autozygosity (homozygosity by descent). It can be calculated from pedigrees by using the formula
ture of the Hardy-Weinberg equilibrium and its extensions 554 557
The Hardy-Weinberg equilibrium predicts that (1) allelic frequencies ( p, q) will not change from generation to generation; (2) genotypes will occur according to the binomial distribution p2 f(AA), 2pq f(Aa), and q2 f(aa); and (3) if perturbed, equilibrium will reestablish itself in just one generation of random mating. STUDY OBJECTIVE 3: To test whether a population is in
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