Selection acts on relative viability

Let's stare at the selection equation for awhile and see what it means.

$$p' = \frac{w_{11}p^2 + w_{12}pq}{\bar w} \quad .$$ (1)

Suppose, for example, that we were to divide the numerator and denominator of (1) by $w_{11}$.⁸ We'd then have

$$p' = \frac{p^2 + (w_{12}/w_{11})pq}{(\bar w/w_{11})} \quad .$$ (2)

Why did I bother to do that? Well, notice that we start with the same allele frequency, $p$, in the parental generation in both equations and that we end up with the same allele frequency in the offspring generation, $p'$, in both equations, but the fitnesses are different:

	Fitnesses
Equation	$A_1A_1$	$A_1A_2$	$A_2A_2$
1	$w_{11}$	$w_{12}$	$w_{22}$
2	1	$w_{12}/w_{11}$	$w_{22}/w_{11}$

I could have, of course, divided the numerator and denominator by $w_{12}$ or $w_{22}$ intead and ended up with yet other sets of fitnesses that produce exactly the same change in allele frequency. This illustrates the following general principle:

The consequences of natural selection (in an infinite population) depend only on the relative magnitude of fitnesses, not on their absolute magnitude.

That means, for example, that in order to predict the outcome of viability selection, we don't have to know the probability that each genotype will survive, their absolute viabilities. We only need to know the probability that each genotype will survive relative to the probability that other genotypes will survive, their relative viabilities. As we'll see later, it's sometimes easier to estimate the relative viabilities than to estimate absolute viabilities.⁹