In a sample from a grasshopper population, you find four alleles at a particular

Question

In a sample from a grasshopper population, you find four alleles at a particular locus. The frequencies of A1, A2, A3, and A4 are p1= 0.50, p2=0.30, p3=0.15, and 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?

Explanation / Answer

A1, A2, A3, and A4 are p1= 0.50, p2=0.30, p3=0.15, and p4=0.05 (A1+A2+A3+A4)2 ------------A12+A22+A32+A42 +2A1A2+2A1A3+2A1A3+2A2A3+2A2A4+2A3A4 A1A1=0.50 X0.50=0.250 A2A2=0.30 X0.30=0.09 A3A3=0.15X0.15=0.0225 A4A4=0.05X0.05=0.00225 2A1A2=2X0.50X0.30=0.3000 2A1A3=2X0.50X0.15=0.1500 2A1A3=2X0.50X0.15=0.15 2A2A3=2X0.30X0.15=0.09 2A2A4=2X0.30X0.05=0.0300 2A3A4=2X0.15X0.05=0.0150

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