By Felsenstein J.
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A locus has three alleles, B , B, and b. B is completely dominant to B, and both of these are completely dominant to b. What are the frequencies of the three alleles in a random-mating population which has these phenotype frequencies: 50% B -, 30% B-, and 20% bb ? 6. In a sample of 200 individuals from a population which is expected to be at Hardy-Weinberg equilibrium for a locus with 3 alleles, the numbers of the 6 possible genotypes found are Genotype Number A1 A1 A1 A2 A1 A3 A2 A2 A2 A3 A3 A3 76 54 33 18 16 3 Calculate the gene frequencies of the three alleles, and what numbers of the six genotypes you would have expected from those frequencies.
For example, an AABB arose from two AB gametes, and an AaBB from one AB and one aB. Each sample of n diploid individuals is then exactly equivalent to a sample of 2n haploid gametes, and we can test those to see whether there is evidence for D = 0. If we cannot divide the double heterozygotes into the coupling and repulsion classes we have nine observable phenotypes, which we can regard as being arranged in a 3 × 3 table: BB Bb bb AA nAABB nAABb nAAbb Aa nAaBB nAaBb nAabb aa naaBB naaBb naabb (I-67) On seeing this arrangement, it is tempting to test linkage disequilibrium by testing independence of rows and columns in this table.
It will turn out to be easier to work in terms of the natural logarithm of the likelihood. Since the logarithm of a quantity increases as the quantity increases, the value of p which maximizes one maximizes the other. The logarithm of the likelihood is: log e L = loge C + (2nAA + nAa ) log e p + (nAa + 2naa ) loge (1 − p). (I-53) If we plot log e L as a function of p, when it reaches the maximum, the slope of the curve will be zero. Trying to find the value of p at this point, we take the derivative of (I-52) and equate it to zero: d log e L 2nAA + nAa nAa + 2naa = − = 0.
Theoretical Evolutionary Genetics by Felsenstein J.