An isolated population of purple dogleaf pine exists on the

An isolated population of purple dogleaf pine exists on the south side of a mountain that has recently experienced massive development for human habitation. When the housing development was initiated, a bright graduate student took the initiative and sampled the populations for later genetic study to determine the effects of drift on the population following habitat loss. Twenty years (generations) later, after the graduate student had established her own lab, the population size was calculated (N_e = 50).

Assuming that the population had remained at that size for the total 20 years, what level of heterozygosity (H) is expected if initial H was 0.80?

Same question as (a), but assume that N_e = 10.

Solution

The formula for genetic drift is--H_e=H_o(1-1/2N_e)^t, H_e=heterozygosity, H_o=initial heterozygosity, N_e=population size, t=time in years,

a)H_e= 0.80 (1-1/2 x 50)²⁰=0.80(1-1/100)²⁰ = 0.80(1-0.01)^20, , 0.80(0.99)²⁰

logH_e=log(0.80) + 20log(0.99)=-0.0969+20 x -0.00436=-0.0969-0.08729=-0.1841.

logH_e= -0.1841, H_e= antilog (-0.1841)=0.6544

Answer--Level of -Heterozygosity=H_e=0.6544.

b)level of heterozygosity=H_e=0.80(1-1/2x10)²⁰=0.80(1-1/20)²⁰=0.80(1-0.05)²⁰=0.80(0.95)²⁰

logH_e= log (0.80)+20log(0.95)=-0.0969+20 x -0.0222=-0.0969-0.445=-0.5424.

Answer--Level of heterozygosity=H_e= antilog(-0.5424)=0.286.