... populations.¹

We mentioned migration and drift in passing, and I'm sure you all understand the rudiments of them, but we haven't yet discussed them in detail.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... on.²

As I alluded to when we first started talking about inbreeding, we can also have natural selection as a result of certain types of violations of assumption #2, e.g., sexual selection or disassortative mating. See below.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... stages.³

To keep things relatively simple we're not even going to discuss differences in fitness that may be associated with different ages. We'll assume a really simple life-cycle in which there are non-overlapping generations. So we don't need to distinguish juveniles from adults.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... selection.⁴

There are some important differences, however, and I hope we have time to discuss a couple of them.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... understand.⁵

Once you've seen what you're in for you may think I've lied about this. But if you really think I have, just ask me to illustrate some of the algebra necessary for understanding viability selection when males and females differ in fitness. That's about as simple an extension as you can imagine, and things start to get pretty complicated even then.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... this:⁶

Don't worry for the moment about how the viabilities were estimated.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... wondering⁷

Okay, ``probably'' is an overstatement. ``May be'' would have been a better guess.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

....⁸

I'm dividing by 1, in case you hadn't noticed.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... viabilities.⁹

We'll also see when we get to studying the interaction between natural selection and drift that this statement is no longer true. To understand how drift and selection interact we have to know something about absolute viabilities.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... equation.¹⁰

And you won't have noticed this and may not believe me when I tell you, but I'm not showing you every possible way to write these equations.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... learn.¹¹

But remember this definition of marginal viability anyway. You'll see it return in a few weeks when we talk about the additive effect of an allele and about Fisher's Fundamental Theorem of Natural Selection.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... fun,¹²

I'm kidding, in case you couldn't tell.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... useful¹³

If not exactly fun.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... lost.¹⁴

Strictly speaking, we need to know more than $\bar w' \ge \bar w$, but we do know the other things we need to know in this case. Trust me. Have I ever lied to you? (Don't answer that.)

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

....¹⁵

Why can I get away with this? Hint: Think about relative fitnesses.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... 1.¹⁶

Which is why I gave you the relative fitness hint in the last footnote.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

....¹⁷

Remember that the ``hats'' can mean either the estimate of an unknown paramter or an equilibrium. The context will normally make it clear which meaning applies. In this case it should be pretty obvious that I'm talking about equilibria.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... not.¹⁸

Notice that a polymorphic equilibrium doesn't even exist when selection is directional.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... equilibria.¹⁹

In fact, the marginal fitnesses are equal, i.e., $w_1=w_2$.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

....²⁰

I'm not showing the algebra that justifies this conclusion on the off chance that you may want to test your understanding by verifying it yourself.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.