Lecture 48: Quantitative Genetics III. Response to Selection

(version: 20 July 1999)

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Response to Selection

R = h² S

R = change in population mean (from one generation to the next)
S = Mean selected parents - population mean

S is called the Selection differential

Example

If height in reproducing parents is 75 inches, while the population average is 65,

S = 75-65 = 10
R = h²* 10
The new mean becomes 65 + h²*10

What happens when selection occurs only on one sex?

R = (h²/2) S

For example, suppose we are selecting for height in corn, and only let tall individuals become pollinated.

Here, there is no selection on the parents producing the pollens, only those receiving it.

Thus, the heritability of height is 0.5 and we only let plants 12 inches over the mean hieght become pollinated, the expected increase in height is (0.5/2)(12) = 3 inches.

Fisher's Fundamental Theorem

Fisher showed that the rate of selection response is proportional to the additive genetic variance in fitness.

Corollary: At equilibrium, additive variance in fitness is zero.

We can see this by recalling that the marginal fitness of an allele (say A), W_A equals the average effect of that allele on fitness. Likewise, the variance of average effects is just the additive variance. If all alleles have the same marginal fitness, there is no change in allele frequencies. Likewise, there is no additive variance as all the average effects (here the marginal finesses) are identical.

Example

Suppose the genotypes AA : Aa : aa have fitnesses 1: 1+s : 1. This is overdominant selection with an equilibrium allele frequnecy of freq(A) = 1/2.

What happens to the heritability of fitness?

Thus, at the equilibrium value the heritability equals zero.

What happens to the genetic variances?

Note that p = 1/2 corresponds to a stable equilibrium point, but that the total genetic variance is largest at this point. It is only the ADDITIVE variance that is zero. This is one reason we worry so much about what fraction of the genetic variance is additive.

Fisher's Fundamental Theorem applies to FITNESS, not the other characters.

Suppose the genotypes AA : Aa : aa have average heights of z = 15: 20: 25, but that selection acts on height, with

W(z) = 1- 0.01 (z -20)² This is an example of stabilizing selection

Heritability (and additive genetic variance) in height is maximized at p = 1/2, but heritability in FITNESS is zero at this value (as the fitnesses are 0.75: 1 : 0.75).

Fitness surfaces, W(z)

The Fitness surface, W(z) maps character values z into fitnesses. We have seen an example with stabilizing selection above. Fitness surfaces can also show directional selection and disruptive selection.

The local geometry of the fitness surfaces informs us as to what type of selection the character is experiencing.

Fitness surfaces can be complex, showing regions of stabilizing selection, regions of directional selection, and regions of distributive selection.

Selection tends to act in such as way as to increase the fitness of the population, so that characters evolve to increase fitness.

Long- term selection response

Our expression R = h²S predicts the single-generation response to selection. What happens after multiple generations of selection?

The rate of response eventually declines and approaches an apparent selection limit as allele frequency changes cause the additive variance in fitness to approach zero.

Note that the heritability can actually increase before it starts to decline.

Does the selection response really grind to such a halt? Yes for the short-term. Further response occurs as new variation is generated by mutation.