Question

You are studying directional selection on neck length (a quantitative trait) in a giraffe population. Below you can see data on neck length of the whole population and the breeding parents.

Neck length of all individuals in population	Neck length of breeders in population
45	90
80	80
90	75
39	95
60	60
35
95
40
75
30

(a) (4 pts) What is the selection differential? Show your calculations.

(b) (4 pts) In the offspring of the next generation you find that the average neck length is 60. Based on this and the results from (a), what was the heritability of neck length. Show your calculations.

Answer 1

Number of individuals in the initial population = 10

Sum of neck length of all individuals = 45 + 80 + 90 + 39 + 60 + 35 + 95 + 40 +75 +30 = 589

Mean of the population before selection (M) = sum of all values/ number of individuals = 589/10 = 58.9

Number of selected indiviuals = 5

Sum of the neck lengths of the selected parents = 90 + 80 + 75 + 95 + 60 = 400

Mean of selected parents (M1) = 400/5 = 80

a)

Selection differential (S) is the difference between the mean of the population after selection and mean of the population before selection

Selection differential (S) = mean of selected parents (M1) - Mean of the initial population (M)

= 80 - 58.9 = 21.1

therefore, selection differential (S) = 21.1

b)

Mean of the offspring (M2) = 60

Breeder's equation :

R = h²S

where R is the response to selection

h²= narrow sense heritability

S = selection differential

Response to selection (R) is the difference between the mean of the offspring and the mean of the initial population

Response to selection (R) = mean of offspring (M2) - mean of initial population (M)

= 60 - 58.9 = 1.1

Therefore, Response to selection (R) = 1.1

Response to selection (R) = h² * S

1.1 = h² * 21.1

h² (heritability) = 1.1/21.1 = 0.052

therefore, h² (heritability) = 0.052