2. A biologist wanted to know more about this population of capybaras and discovered that 70% of the females (N = 40) and 40% of the males cannot breed (although the causes were not determined). Recall from question 1 that there are 104 total capybaras in the population, and assume a polygynous mating system.
a) Calculate the effective population size
The formula to calculate
effective population size is: Ne = 4 * M * F / (M + F). HOWEVER,
the number of
males and females (M and F) only includes breeding individuals.
We know from the question
that there are 40 total females. However, 70% of these females do not breed,
meaning that only 30% of these 40 females breed. Therefore, the number of
breeding females (F) = 40 * 0.3 = 12.
Because there is a total of
104 individuals in our population, of which 40 are female, we know that there
are 64 total males in the population. However, 40% of these males do not breed,
meaning that 60% of males breed. Therefore, the number of breeding males (M) =
64 * .6 = 38
Plugging values for M and F
into our formula for effective population size, we get:
Ne = 4 * 38 *12
/ (38 + 12) = 36.48
b) How would assuming a monogynous
mating structure influence your calculations in part a?
Because each female mates
with one male, the total number of breeding individuals (M or F) can be no
larger than the minimum number of either males or females, whichever number is
smallest. Therefore, for this population of capybaras, M and F would both be
equal to 12.
c) Calculate the loss of heterozygosity per generation
The loss of H from one
generation to the next = 1 / 2Ne
We know from question 1b
that Ne is approximately 36, therefore:
The loss of H from one
generation to the next = 1 / 2 * 36 = 0.014
d) Calculate the percent heterozygosity remaining after 7 generations
Because we are calculating
the percent heterozygosity lost, we start with 100% heterozygosity (H0
= 1).
Ht = H0
(1- 1 / 2Ne)t
H7 = 1 (1 - 1 /
2 * 36)7
H7 = 0.9867
= 0.986 * 0.986 * 0.986 * 0.986 * 0.986 * 0.986 * 0.986