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10-637 Animal Models
Lesson 4 Assignment
L. R. Schaeffer, March 1999

1.
Verify the following, with p+q=1:
(a)
p(1+q) = 1- q2
(b)
p3 + q3 - (p-q)2 = pq
(c)
p-q = p2 - q2
(d)
p2 + q2 = (p-q)2 + 2pq
(e)
q3 + pq2 = (1-p)2

2.
For single, autosomal locus, verify that the covariance between full-sibs is

\begin{displaymath}\sigma_{FS} = pq \alpha^2 + (pqd)^2 . \end{displaymath}

3.
Simulation problem. Assume a single locus model where the frequency of the \( \mbox{A}_1 \) allele is .26 in the large random mating population. Assume an additive model with a=1.
(a)
Generate a sample population of 20 animals from the large population and calculate the gene frequency in the sample.
(b)
Randomly mate pairs of individuals (selfing is allowed) to produce 20 offspring. Compute the gene frequency in the progeny. Compute the genetic mean and variance of the progeny.
(c)
Repeat step (b) nine (9) more times giving ten generations. Plot the change in gene frequency, mean, and variance with each generation.
(d)
Repeat steps (a), (b), and (c) nine (9) more times. Calculate the variance of p in the tenth generation over the ten replicates. Calculate the variance of the means in the tenth generation over the ten replicates. Compare to the expected variance of p. Estimate the average inbreeding coefficient in the tenth generation over replicates.


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This LaTeX document is available as postscript or asAdobe PDF.

Larry Schaeffer
1999-02-26