Question

Extend the HW principle to apply to three alleles/locus within a population (A, a, a’) Answer these questions: 1.How many genotypes are possible 2. Extend the binomial theory to develop an equation to predict the expected frequencies of all possible genotypes for any given allele frequency? 3.Would this equation make predictions similar to the HW predictions? 4.If the frequencies of the three alleles are A = 0.5, a = 0.45, and a’ =0.05 5.What are the frequencies of the three genotypes. 6.IF the population was composed of 11,580 individuals How many of them would be predicted to be homozygous for the a’ allele? How many of them would be predicted to be heterozygous for any combination of alleles?

Answer 1

HW principle extended to 3 alleles within a population (A,a,a')

1. Number of genotypes possible are: AA, Aa, Aa', aa, aa', a'a'

total number of genotypes is 6

2. Binomial theory

A= frequency of allele A

a=frequency of allele a

a'=frequency of allele a'

equation is (A+a+a')²=1

A²+a²+a'²+2Aa+2aa'+2a'A = 1

3. Yes, this equation makes prediction similar to HW prediction.

4. Frequency of allele A= 0.5

Frequency of allele a= 0.45

Frequency of allele a'=0.05

5. Frequency of 3 genotypes AA, Aa, aa

I) A² * total number of individuals = Frequency of AA

(0.5)² * 11,580 = 2,895 = Frequency of AA

II) 2Aa * Total number of individuals = Frequency of Aa

(2*0.5*0.45) * 11,580 = 20,844

III) a² * total number of individuals = Frequency of aa

(0.45)² * 11,580 = 2,345

6. total number of individuals homozygous for allele a' are

a'² * 11,580 = (0.05)² * 11,580 = 29

total number of heterozygous individuals are

Aa = ( 2 * 0.5 * 0.45) * 11,580 = 5,211

Aa' = ( 2 * 0.5 * 0.05) * 11,580 = 579

aa' = ( 2 * 0.45 * 0.05) * 11,580 = 521