Population Genetics Sherry Tamone has conducted a longterm s

Population Genetics

Sherry Tamone has conducted a long-term study of a Tanner crab population in the lab. After many years of randomly mating this isolated population, she decides to genotype some adult crabs and obtains the following genotypes at the Pncr locus (alleles: P and p). What are the allele frequencies at this locus? Does this population appear to be HW proportions (use X2 test; critical X2 value = 3.84)? If not, what is the most likely cause of this departure? (6 points) Genotype PP=Frequency, 20 Pp=Frequency, 80 pp=Frequency 15

Solution

Answer:

Hardy and Weinberg described all the possible genotypes for a gene with two alleles. The binomial expansion representing this is, p2 + 2pq + q2 = 1.0

Where,

p2 = proportion of homozygous dominant individuals (PP) = 20/115 = 0.1739

q2 = proportion of homozygous recessive individuals (pp) = 15/115 = 0.1304

2pq = proportion of heterozygotes (Pp) = 80/115 = 0.6956

a). The frequency of p allele in the population is, (P) = p2 + 1/2(2pq) = 0.1739 + ½ (0.6956) = 0.5217

b). The frequency of q allele in the population is, (p) = q2 + 1/2(2pq) = 0.1304 + ½ (0.6956) = 0.4782

The expected number of individuals with the PP genotype = 0.5217* 0.5217 = 0.2721*115 = 31.3

The expected number of individuals with the Pp genotype = 2*0.5217* 0.4782 = 0.4989 = 57.4

The expected number of individuals with the pp genotype = 0.4782*0.4782 = 0.2286 = 26.29

CHI - SQUARE (X²):

X² = (O - E)² / E

Where O = Observed frequency

E = Expected frequency

PP

20

31.3

-11.3

127.69

4.079553

Pp

80

57.4

22.6

510.76

8.898258

pp

15

26.29

-11.29

127.4641

4.848387

115

114.99

0.01

765.9141

17.8262

The calculated Chi-square value is 17.82.

The degrees of freedom, n = 3-1 = 2

The P-Value is 0.000135. The result is significant at p < 0.05.

Yes, the population is in Hardy Weinberg equilibrium.

So, we reject the null hypothesis and the population is not in H-W equilibrium. The probable cause of this departure is inbreeding.