Hints

• Treat each maternal genotype separately, e.g., consider the numbers of $Est^FEst^F$ and $Est^FEst^S$ offspring derived from $Est^FEst^F$ mothers as a binomial sample.

      k.ff ~ dbin(ff, n.ff)
      ff <- tau*p.m + (1-tau)
  

  where k.ff is the number of $Est^FEst^F$ offspring from $Est^FEst^F$ mothers and n.ff is the sample size of progeny from $Est^FEst^F$ mothers. Treat the offspring numbers from heterozygous mothers as a multinomial sample.

      k.fs[1:3] ~ dmulti(fs[], n.fs)
      fs[1] <- tau*p.m/2 + (1-tau)/4
      fs[2] <- 1/2
      fs[3] <- tau*(1-p.m)/2 + (1-tau)/4
  

  And treat the alleles in mothers as independent so that you can estimate $p_f$ as

      n.f ~ dbin(p.f, n)
      n.f <- 2*n.ff + n.fs
      n   <- 2*(n.ff + n.fs + n.ss)
  

• Use the following priors on the parameters.

      p.m ~ dunif(0,1)
      p.f ~ dunif(0,1)
      tau ~ dunif(0,1)
      f ~ dunif(0,1)
  

• Input the data using this format.

     list(k.ff=267, n.ff=329, k.fs=c(81, 120, 44), n.fs=245, k.ss=143,
          n.ss=313)