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ANSC*6370 QG and Animal Models
Fall 03 - Quiz 2 - Answers

1.

If $\sigma^{2}_{A} = 0.6$ and $\sigma^{2}_{D}=0.4$, then determine the following quantities:

(a)

Total genetic variance.

$$\sigma^{2}_{G} = \sigma^{2}_{A} + \sigma^{2}_{D} = 1.0$$

(b)

Covariance between parent and offspring.

$$\sigma(P,O) = 0.5 \sigma^{2}_{A} = 0.3$$

(c)

Covariance between half-sibs.

$$\sigma(HS) = 0.25 \sigma^{2}_{A} = 0.15$$

(d)

Covariance between full-sibs.

$$\sigma(FS) = 0.5 \sigma^{2}_{A} + 0.25 \sigma^{2}_{D} = 0.4$$

2.

If N=5, q_o=0.3, and $\sigma^{2}_{q_{t}} = p_{o}q_{o}[1 - (1- \frac{1}{2N})^{t}]$, then

(a)

what would be $\sigma^{2}_{q_{t}}$ after 10 generations of random matings in the small population?

$$\sigma^{2}_{q_{t}} = 0.3(0.7)[1 - (1 - 0.1)^{10}] = .1368$$

(b)

what would be the level of inbreeding in the small population after 10 generations of random matings?

F_t = [1 - (1 - 0.1)¹⁰] = 0.6513