More hints on Problem #2

As promised yesterday in class, I'm providing a few more hints that should help you solve Problem #2. Everyone I've talked with is on the right track, but there are some details that aren't quite as obvious as I thought they were.

Hint #1: Think about the genotype proportions in the initial populations (i.e., the 100:900 or 900:100 ratio of AA:BB) as giving you information about the allele frequency in newly formed zygotes. Estimate the frequency of A from that sample, remembering that (a) the frequency of A is equal to the frequency of AA (since there aren't any heterozygotes) and (b) you have two categories in which you're trying to estimate the frequency, so the number of AAs will be a binomial sample from the total.

Hint #2: Look back at the notes on estimating viability selection. You'll notice that to get relative viabilities you only need the genotype frequencies in zygotes and adults. You should be able to calculate the genotype frequencies in zygotes from the frequency of A in the base popNulation (see Hint #1).

Hint #3: To estimate the genotype frequencies after selection, you'll need to estimate the frequencies from a multinomial sample. Specifically,

n.a[1:3} ~ dmulti(x.a[], N.a)
N.a <- sum(n.a[])

# priors

y.a[1] ~ dexp(1)

y.a[2] ~ dexp(2)

y.a[3] ~ desp(3)

x.a[1] ~ y.a[1]/sum(y.a[])

x.a[2] ~ y.a[2]/sum(y.a[])

x.a[3] ~ y.a[3]/sum(y.a[])

where

n.a[]

x.a[]