is a better way to measure fitness.
Remember relative fitness?
is a better way to measure fitness.
There are a large number of fitness components: e.g. fertility, survivorship, mating success, fecundity, etc.
Body size is so correlated with fitness components in most systems that it is often considered a fitness component itself.
The true effects of some characters may happen after the generation of the individual which carries the trait, yet nonetheless change the ultimate fitness of the genes which make up those traits. E.g., maternal care.
The response of fitness to selection is equal to the additive genetic variance for fitness. This is known as Fisher's Fundamental Theorem of Natural Selection. (named by Fisher :-).
Measuring relative fitness, the weighted selection differential for fitness is
So the response to selection is given by
By a similar derivation, the correlated response to selection on fitness for a character is given by
z is the vector of phenotypic values (i.e. {z1, z2, z3, ...} where each of these z's is the value of some character.
G is the genetic variance-covariance matrix. This means that the diagonal elements are the additive genetic variances of the different characters, and the off-diagonal elements are the additive genetic covariances of the different characters. For example, the G matrix for 2 characters X and Y is
The P matrix, similarly, is the phenotypic variance-covariance matrix.
The strength of selection on can be described for multivariate selection as well:
where the * indicates the value after selection.
Then there is a formula which describes the change in the mean from one generation to the next, analogous to R=h2 S:
The value [beta] = P-1 s is called the selection gradient. It is equivalent to the vector of partial regression coefficients of relative fitness on character states. [beta] is also known to be the least squares regression on fitness which gives the straight line that best determines the dependence of relative fitness on characters independent of the residual effects of other characters.
Two basic problems to all methods of measuring selection:
(1) There are always unmeasured characters, which may explain the true relationship of fitness and phenotype and have correlated effects on the characters studied.
(2) Fitness is hugely difficult to measure.
See nice review by Brodie et al. TREE 1995 10:313-318.
As mentioned just above, the partial regression of relative fitness on character gives a good estimate of the linear dependence of fitness on the phenotype.
This can be extended to include non-linear terms, such as stabilizing selection.
Unfortunately, while this type of analysis can be quite good at predicting short term response to selection, it is very poor at visualizing the actual relationship of the character and fitness.
Non-parametric techniques brought into evolutionary biology by our very own Dolph Schluter solve this problem. Cubic splines are a visualization technique for determining the shape of non-linear regressions. See the figures in the Brodie et al. article for good examples.
Selection for some intermediate value of the trait.
Stabilizing selection acts to reduce the phenotypic variance of the trait. it does this by increasing the canalization of the trait, as well as by reducing the genetic variance for the trait.
Canalization is the reduced sensitivity of an organism to noise from the environment.
Genetic variance can be reduced in two ways:
* By creating negative correlations of allelic effects: linkage disequilibrium.
* By changing gene frequencies to be closer to fixation.
Intermediate optima can be reached because of the tradeoffs between different fitness components.
Contrary to F+M, fitness itself can be correlated with a character as stabilizing selection. However, there are real examples of misleading selection patterns, such as the bristle example given by Kearsey and Barnes 1970.
There are a few good examples of disruptive selection. Schluter, Price and Grant 1985, cited in F+M is not one of them. Subsequent re-analysis with cubic splines find no evidence of disruptive selection.
Smith 1990, Evolution 44:832 provides a good example of disruptive selection on beak size as a function of multiple seeds available as food in African finches.
As we have discussed before, fitness components have normally:
* Low heritability
* High values for non-additive variance and environmental variance
* Actually, high additive genetic variance (when scaled by the coefficient of variation)
* High directional dominance (and therefore high inbreeding depression)
* Typically large negative correlations with other fitness components
New variance comes form mutations at a rate approximately 10-2 to 10-4 VE per generation.
VM should be equal to 2nua2, where n is the number of genes which can mutate to have effect on the trait, u is the per locus mutation rate, and a is the effect of the mutation.
We can estimate nu from mutation accumulation experiments (like Mukai 1972). For viability, nu is in the range 0.1 to 1.
This means that either the mutation rate is extremely high, or there are many loci which mutate to affect viability. (Probably the latter is true.) This explains why pleiotropy must be a pervasive element of quantitative genetic explanations.
We've seen before that the amount of genetic variation present when only mutation and drift are acting is VG=2NeVM. Therefore the total variance is 2NeVM + Ve. If we calculate the (broad-sense) heritability, and use 10-3 VE for VM, we find
So we can see using this formula that the population size need not be large at all to allow high heritability to be maintained even with drift:
There are two major models of the maintenance of variance due to a balance between mutation and stabilizing selection:
Lande (1975):
Turelli (1984):
Both require there to be unreasonably large mutation rates per locus.
So this leaves the question: what causes the high levels of genetic variance that we see for quantitative traits?
