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mgarr mgarr
wrote...
9 years ago
 In a sample from a different population of this grasshopper species, you find four alleles at this locus. The frequencies of A1, A2, A3, and A4 are p1 = 0.50, p2 = 0.30, p3 = 0.15, p4 = 0.05. Assuming Hardy-Weinberg equilibrium, calculate the expected proportion of each of the ten possible genotypes (e.g., that of A2A3 should be 0.09). Show that heterozygotes, of all kinds, should constitute 63.9 percent of the population. In a sample of 100 specimens, how many would you expect to be heterozygous for allele A4? How many would you expect to be homozygous A4A4?

I know how to use the HW equation to figure out 2 different alleles like A1A1, A1A2, A2A2, but im lost on how to do the above problems since it's talking about 4 alleles
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wrote...
Educator
9 years ago
Homozygote frequencies are equal to the square of allele frequency, and heterozygote frequencies are equal to two times the product of the allele frequencies of each allele present in the heterozygote of interest.
Proportion A1A1 = 0.50*0.50 = 0.25
Proportion A2A2 = 0.30*0.30 = 0.09
Proportion A3A3 = 0.15*0.15 = 0.0225
Proportion A4A4 = 0.05*0.05 = 0.0025
Proportion A1A2 = 2*0.50*0.30 = 0.3
Proportion A1A3 = 2*0.50*0.15 = 0.15
Proportion A1A4 = 2*0.50*0.05 = 0.05
Proportion A2A3 = 2*0.30*0.15 = 0.09
Proportion A2A4 = 2*0.30*0.05 = 0.03
Proportion A3A4 = 2*0.15*0.05 = 0.015
Summing up the last six genotype frequencies above gives us the total proportion that is heterozygous. This is equal to 0.635. The value given in the textbook differs from this exact proportion due to rounding error. The expected number of heterozygotes containing the A4 allele can be found by summing expected frequencies for each heterozygous genotype that contains an A4 allele and then multiplying by the sample size. In a sample of 100 specimens we would expect 9 or 10 to be heterozygous for the A4 allele (0.095). We would not expect to find any A4A4 homozygotes in a sample of 100 specimens (as the expected genotype frequency is only 0.0025).
mgarr Author
wrote...
9 years ago
so i figured it out I just needed to use the formula
(pxp)+2pq+2pr+2ps+(qxq)+2qr+2qs+(rxr)+2rs+(sxs) = 1
wrote...
Educator
9 years ago
Thanks for the update.
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