Marginal fitnesses

In case you haven't already noticed, there's almost always more than one way to write an equation.¹⁰ They're all mathematically equivalent, but they emphasize different things. In this case, it can be instructive to look at the difference in allele frequencies from one generation to the next, $\Delta p$:

$$\begin{eqnarray*} \Delta p &=& p' - p \\ &=& \frac{w_{11}p^2 + w_{12}pq}{\bar w... ... \bar w)}{\bar w} \\ &=& \frac{p(w_1 - \bar w)}{\bar w} \quad , \end{eqnarray*}$$

where $w_1$ is the marginal fitness of allele $A_1$. To explain why it's called a marginal fitness, I'd have to teach you some probability theory that you probably don't want to learn.¹¹ Fortunately, all you really need to know is that it corresponds to the probability that a randomly chosen $A_1$ allele in a newly formed zygote will survive into a reproductive adult.

Why do we care? Because it provides some (obvious) intuition on how allele frequencies will change from one generation to the next. If $w_1 > \bar w$, i.e., if the chances of a zygote carrying an $A_1$ allele of surviving to make an adult are greater than the chances of a randomly chosen zygote, then $A_1$ will increase in frequency. If $w_1 < \bar w$, $A_1$ will decrease in frequency. Only if $p=0$, $p=1$, or $w_1=\bar w$ will the allele frequency not change from one generation to the next.