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10637 Animal Models
Lesson 4 Assignment
L. R. Schaeffer, March 1999
 1.
 Verify the following, with p+q=1:
 (a)

p(1+q) = 1 q^{2}
 (b)

p^{3} + q^{3}  (pq)^{2} = pq
 (c)

pq = p^{2}  q^{2}
 (d)

p^{2} + q^{2} = (pq)^{2} + 2pq
 (e)

q^{3} + pq^{2} = (1p)^{2}
 2.
 For single, autosomal locus, verify that the covariance between
fullsibs is
 3.
 Simulation problem. Assume a single locus model where the
frequency of the
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.
This LaTeX document is available as postscript or asAdobe PDF.
Larry Schaeffer
19990226