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number of NN total number (1 2)f(MN )
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Thus, allelic frequencies can be calculated as the frequency of homozygotes, plus half the frequency of heterozygotes, as follows: p f(M ) 0.57 q f(N ) 0.05 or q 1 p 1 0.76 0.24 f(MM ) (1 2)0.38 f(NN ) (1 2)0.38 (1 2)f(MN ) 0.76 (1 2) f(MN ) 0.24
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Tamarin: Principles of Genetics, Seventh Edition
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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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Hardy-Weinberg Equilibrium
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the next generation. Thus genotypic, but not allelic, frequencies change under nonrandom mating.
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Large Population Size
Even when an extremely large number of gametes is produced in each generation, each successive generation is the result of a sampling of a relatively small portion of the gametes of the previous generation. A sample may not be an accurate representation of a population, especially if the sample is small. Thus, the second assumption of the Hardy-Weinberg equilibrium is that the population is in nitely large. A large population produces a large sample of successful gametes. The larger the sample, the greater the probability that the allelic frequencies of the offspring will accurately represent the allelic frequencies in the parental population. When populations are small or when alleles are rare, changes in allelic frequencies take place due to chance alone. These changes are referred to as random genetic drift, or just genetic drift.
relatively small population can still closely approximate Hardy-Weinberg equilibrium. In other words, minor deviations from the other assumptions can still result in a good t to the equilibrium; only major deviations can be detected statistically. Second, the Hardy-Weinberg equilibrium is extremely resilient to change because, regardless of the perturbation, the equilibrium is usually reestablished after only one generation of random mating. The new equilibrium will be, however, at the new allelic frequencies the Hardy-Weinberg equilibrium does not return to previous allelic values.
Proof of Hardy-Weinberg Equilibrium
The three properties of the Hardy-Weinberg equilibrium are that (1) allelic frequencies do not change from generation to generation, (2) allelic frequencies determine genotypic frequencies, and (3) the equilibrium is achieved in one generation of random mating. We will concentrate for a moment on the second property. In a population of individuals segregating the A and a alleles at the A locus, each individual will be one of three genotypes: AA, Aa, or aa. If p f(A) and q f(a), then we can predict the genotypic frequencies in the next generation. If all the assumptions of the Hardy-Weinberg equilibrium are met, the three genotypes should occur in the population in the same frequencies at which gametes would be randomly drawn in pairs from a gene pool. A gene pool is de ned as all of the alleles available among the reproductive members of a population from which gametes can be drawn. Thus, f(AA) f(Aa) f(aa) (p (p (q p) q) q) p2 (q q
No Mutation or Migration
Allelic and genotypic frequencies may change through the loss or addition of alleles through mutation or migration (immigration or emigration) of individuals from or into a population.The third and fourth assumptions of the HardyWeinberg equilibrium are that neither mutation nor migration causes such allelic loss or addition in the population.
No Natural Selection
The nal assumption necessary to the Hardy-Weinberg equilibrium is that no individual will have a reproductive advantage over another individual because of its genotype. In other words, no natural selection is occurring. (Arti cial selection, as practiced by animal and plant breeders, will also perturb the Hardy-Weinberg equilibrium of captive populations.) In summary, the Hardy-Weinberg equilibrium holds (is exactly true) for an in nitely large, randomly mating population in which mutation, migration, and natural selection do not occur. In view of these assumptions, it seems that such an equilibrium would never be characteristic of natural populations. However, this is not the case. Hardy-Weinberg equilibrium is approximated in natural populations for two major reasons. First, the consequences of violating some of the assumptions, such as no mutation or in nitely large population size, are small. Mutation rates, for example, are on the order of one change per locus per generation per 106 gametes. Thus, there is virtually no measurable effect of mutation in a single generation. In addition, populations do not have to be in nitely large to act as if they were. As we will see, a
demonstrates the second property of the HardyWeinberg equilibrium ( g. 19.1).
Gene pool concept of zygote formation. Males and females have the same frequencies of the two alleles: f (A) p and f (a) q. After one generation of random mating, the three genotypes, AA, Aa, and aa, have the frequencies of p2, 2pq, and q2, respectively.
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