Introduction

Being able to make predictions with known (or estimated) viabilities, doesn't do us a heck of a lot of good unless we can figure out what those viabilities are. Fortunately, figuring them out isn't too hard to do. If we know the number of individuals of each genotype before selection, it's really easy as a matter of fact. Consider that our data looks like this:

Genotype	$A_1A_1$	$A_1A_2$	$A_2A_2$
Number in zygotes	$n_{11}^{(z)}$	$n_{12}^{(z)}$	$n_{22}^{(z)}$
Viability	$w_{11}$	$w_{12}$	$w_{22}$
Number in adults	$n_{11}^{(a)} = w_{11}n_{11}^{(z)}$	$n_{12}^{(a)} = w_{12}n_{12}^{(z)}$	$n_{22}^{(a)} = w_{22}n_{22}^{(z)}$

In other words, estimating the absolute viability simply consists of estimating the probability that an individuals of each genotype that survive from zygote to adult. The maximum-likelihood estimate is, of course, just what you would probably guess:

$$w_{ij} = \frac{n_{ij}^{(a)}}{n_{ij}^{(z)}} \quad ,$$

Since $w_{ij}$ is a probability and the outcome is binary (survive or die), you should be able to guess what kind of likelihood relates the observed data to the unseen parameter, namely, a binomial likelihood. In WinBUGS notation:¹

   n.11.adult ~ dbin(w.11, n.11)
   n.12.adult ~ dbin(w.12, n.11)
   n.22.adult ~ dbin(w.22, n.11)