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The Hardy-Weinberg equilibrium can also be extended to consider several loci at the same time in the same population. This situation deserves mention because the whole genome is likely involved in evolutionary processes and we must, eventually, consider simultaneous allelic changes in all loci segregating alleles in an organism. (Even with a high-speed computer, simultaneous consideration of many loci is a bit far off in the future.) When two loci, A and B, on the same chromosome are in equilibrium with each other, the combinations of alleles on a chromosome in a gamete follow the product rule of probability. Consider the A locus with alleles A and a and the B locus with alleles B and b, respectively, with allelic frequencies pA and qA for A and a, respectively, and pB and qB for B and b, respectively. Given completely random circumstances, the chromosome with the A and B alleles should occur at the frequency pA pB. This is referred to as linkage equilibrium. When alleles of different loci are not in equilibrium (i.e., not randomly distributed in gametes), the condition is referred to as linkage disequilibrium. The approach to linkage equilibrium is gradual and is a function of the recombination distance between the two loci. For example, let s start with a population out of equilibrium so that all chromosomes are AB (70%) or ab (30%). Then pA 0.7, qA 0.3, pB 0.7, and qB 0.3. We expect the Ab chromosome to occur 0.7 0.3 0.21, or 21% of the time. The frequency of the Ab chromosome is zero. Assume the map distance between the two loci is 0.1; in other words, 10% of chromatids in gametes are recombinant. Initially, we consider that each locus is in Hardy-Weinberg proportions, or the frequency of AB/AB individuals 0.49 (0.7 0.7); the frequency of ab/ab individuals is 0.09 (0.3 0.3); and the frequency of AB/ab individuals is 0.42 (2 0.7 0.3).
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From table 19.4, we see that blood type A plus blood type O include only the genotypes I AI A, I Ai, and ii. If the population is in Hardy-Weinberg proportions, these together should be ( p r)2, in which p2 f(I AI A), 2pr f(I Ai), and r2 f(ii): (p r)2 (199 231) 500 0.860
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Then, taking the square root of each side p and p 0.927 r 0.927 0.680 0.247 r 0.860 0.927
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Table 19.4 ABO Blood-Type Distribution in 500
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Blood Type A B AB O Total Genotype I AI A or I Ai I BI B or I Bi I AI B ii Number 199 53 17 231 500
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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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The McGraw Hill Companies, 2001
Nineteen
Population Genetics: The Hardy-Weinberg Equilibrium and Mating Systems
After one generation of random mating, gametes will be as follows: from AB/AB individuals (49%): only AB gametes, 49% of total from ab/ab individuals (9%): only ab gametes, 9% of total from AB/ab individuals (42%): AB gametes, 18.9% of total (0.45 0.42) ab gametes, 18.9% of total (0.45 0.42) Ab gametes, 2.1% of total (0.05 0.42) aB gametes, 2.1% of total (0.05 0.42) (The values of 18.9% and 2.1% for the dihybrids result from the fact that since map distance is 0.1, 10% of gametes will be recombinant, split equally between the two recombinant classes 5% and 5%. Ninety percent will be parental, split equally between the two parental classes 45% and 45%. Each of these numbers must be multiplied by 0.42 because the dihybrid makes up 42% of the total number of individuals.) Although we expect 21% of the chromosomes to be of the Ab type, only 2.1%, 10% of the expected, appear in the gene pool after one generation of random mating. You can see that linkage equilibrium is achieved at a rate dependent on the map distance between loci. Unlinked genes, appearing 50 map units apart, also gradually approach linkage equilibrium. Although we will not derive these extensions here, we note two others. If the frequencies of alleles at an autosomal locus differ in the two sexes, it takes two generations of random mating to achieve equilibrium. In the rst generation, the allelic frequencies in the two sexes are averaged so that each sex now has the same allelic frequencies. Genotypic frequencies then come into Hardy-Weinberg proportions in the second generation. However, if the allelic frequencies differ in the two sexes for a sex-linked locus, Hardy-Weinberg proportions are established only gradually. The reasoning is straightforward. Females, with an X chromosome from each parent, average the allelic frequencies from the previous generation. However, males, who get their X chromosomes from their mothers, have the allelic frequencies of the females in the previous generation. Hence, the allelic frequencies are not the same in the two sexes after one generation of random mating, and equilibrium is achieved slowly.
latedness in uences mate choice. When phenotypic resemblance in uences mate choice, either assortative or disassortative mating occurs, depending on whether individuals choose mates on the basis of similarity or dissimilarity, respectively. For example, in human beings, assortative mating occurs for height short men tend to marry short women, and tall men tend to marry tall women. When relatedness in uences mate choice, either inbreeding or outbreeding occurs, depending on whether mates are more or less related than two randomly chosen individuals from the population. An example of inbreeding in human beings is marriage between rst cousins. Both types of nonrandom mating (assortative-disassortative mating and inbreeding-outbreeding) have the same qualitative effects on the Hardy-Weinberg equilibrium: assortative mating and inbreeding increase homozygosity without changing allelic frequencies, whereas disassortative mating and outbreeding increase heterozygosity without changing allelic frequencies. Two differences are apparent, however, between the effects of phenotypic resemblance and relatedness on mate choice. First, assortative or disassortative mating disturbs the Hardy-Weinberg equilibrium only when the phenotype and genotype are closely related. That is, if assortative mating occurs for a nongenetic trait, then the Hardy-Weinberg equilibrium will not be distorted. Inbreeding and outbreeding affect the genome directly. A second difference between the two types of mating is that the effects of inbreeding or outbreeding are felt across the whole genome, whereas the disturbances to the equilibrium caused by assortative and disassortative mating occur only for the particular trait being considered (and for closely linked loci). Given the similarities in the consequences of the two types of matings, we will concentrate our discussion on inbreeding.