Patterns of natural selection

Well, all that algebra was lots of fun,¹² but what good did it do us? Not an enormous amount, except that it shows us (not surprisingly), that allele frequencies are likely to change as a result of viability selection, and it gives us a nice little formula we could plug into a computer to figure out exactly how. One of the reasons that it's useful¹³ to go through all of that algebra is that it's possible to make predictions about the consequences of natural selection simply by knowing the pattern of viaiblity differences. What do I mean by pattern? Funny you should ask (Table 1).

Table 1: Patterns of viability selection at one locus with two alleles.

Pattern	Description	Figure
Directional	$w_{11} > w_{12} > w_{22}$	Figure 1
	or
	$w_{11} < w_{12} < w_{22}$
Disruptive	$w_{11} > w_{12}$, $w_{22} > w_{12}$	Figure 2
Stabiliizing	$w_{11} < w_{12}$, $w_{22} < w_{12}$	Figure 3

Before exploring the consequences of these different patterns of natural selection, I need to introduce you to a very important result: Fisher's Fundamental Theorem of Natural Selection. We'll go through the details later when we get to quantitative genetics. For now all you need to know is that viability selection causes the mean fitness of the progeny generation to be greater than or equal to the mean fitness of the parental generation, with equality only at equilibrium, i.e.,

$$\bar w' \ge \bar w \quad .$$

How does this help us? Well, the best way to understand that is to illustrate how we can use Fisher's theorem to predict the outcome of natural selection when we know only the pattern of viability differences. Let's take each pattern in turn.