# Genetics Question - heritability?

A Wagga breeder uses natural mating in a closed stud consisting of 750 breeding cows (age structure is given in attached image).

He is interested in improving milk yield via direct selection for the trait. The heritability (h2) and standard deviation (σp) of milk yield is 0.6 and 500 Kg respectively. Assuming a weaning rate of 0.8 and no mortality, calculate:

What are the selected proportions of males and females? (1 mark)

What is the overall generation interval? (1 mark)

What is the expected response to selection per generation? (1 mark)

What is the expected response per year? (1 mark)

What is the effective population size? (1 mark)

What is the rate of inbreeding after 20 years? (1 mark)

If the weaning rate increased to 1 (i.e. 100% weaning with no mortality), would the expected response to selection (both per year and per generation) increase, decrease or remain the same and why? (1 mark) Relevance

1) Proportion of males and females 3/150 = 1:50

2) Overall generation intervals :

Lmale = 2.5 years

LFemale = 4 years

Lgen = (2.5 + 4)/2 = 3.25 years

3) expected response:

Rgen = (imale + ifemale)/2 σph²

Rgen = (0.0013 + 0.2)/2 x 500 x 0.6

= 30.2 kg

4) Ryear =[(imale + ifemale)/(imale + ifemale)] σph²

= [(0.0013 + 0.2)x 500 x 0.6]/(2.5 + 4)

= 9.29kg

5) Effective population size

Nε = (4 x Nm x Nf)/( Nm + Nf)

= (4 x 6 x 750)/(6 + 750)

= 23.81 ≈ 24

Δf =1/(2Nε)= 1/48

6) Rgen and Ryear values will show increase because of increasing value of imale, i.e.,

imale =3/750 = .004 [ 0.0013 < .004 ]