An overview of where we're headed

Woltereck's ideas force us to realize that when we see a phenotypic difference between two individuals in a population there are three possible explanations for that difference:

1. The individuals have different genotypes.

2. The individuals developed in different environments.

3. The individuals have different genotypes and they developed in different environments.

This leads us naturally to think that phenotypic variation consists of two separable components, namely genotypic and environmental components.¹ Putting that into an equation

$$\mbox{Var}(P) = \mbox{Var}(G) + \mbox{Var}(E) \quad ,$$

where $\mbox{Var}(P)$ is the phenotypic variance, $\mbox{Var}(G)$ is the genetic variance, and $\mbox{Var}(E)$ is the environmental variance.² As we'll see in just a moment, we can also partition the genetic variance into components, the additive genetic variance, $\mbox{Var}(A)$, and the dominance variance, $\mbox{Var}(D)$.

There's a surprisingly subtle and important insight buried in that very simple equation: Because the expression of a quantitative trait is a result both of genes involved in that trait's expression and the environment in which it is expressed, it doesn't make sense to say of a particular individual's phenotype that genes are more important than environment in determining it. You wouldn't have a phenotype without both. What we might be able to say is that when we look at some population of organisms some fraction of the phenotypic differences among them is due to differences in the genes they carry and that some fraction is due to differences in the environment they have experienced.³

It's often useful to talk about how much of the phenotypic variance is a result of additive genetic variance or of genetic variance.

$$h^2_n = \frac{\mbox{Var}(A)}{\mbox{Var}(P)}$$

is what's known as the narrow-sense heritability. It's the proportion of phenotypic variance that's attributable to differences among individuals in their additive genotype,⁴ much as $F_{st}$ can be thought of as the proportion of genotypic diversity that attributable to differences among populations. Similarly,

$$h^2_b = \frac{\mbox{Var}(G)}{\mbox{Var}(P)}$$

is the broad-sense heritability. It's the proportion of phenotypic variance that's attributable to differences among individuals in their genotype. It is not, repeat NOT, a measure of how important genes are in determining phenotype. Every individuals phenotype is determined both by its genes and by its phenotype. It measures how much of the difference among individuals is attributable to differences in their genes.⁵ Why bother to make the distinction? Because, as we'll see, it's only the additive genetic variance that responds to natural selection. In fact,

$$R = h^2_nS \quad ,$$

where $R$ is the response to selection and $S$ is the selective differential.

As you'll see in the coming weeks, there's a lot of stuff hidden behind these simple equations, including a lot of assumptions. But quantitative genetics is very useful. Its principles have been widely applied in plant and animal breeding for almost a century, and they have been increasingly applied in evolutionary investigations in the last thirty years. Nonetheless, it's useful to remember that quantitative genetics is a lot like a bikini. What it reveals is interesting, but what it conceals is crucial.