Selection on Multiple Traits

The immediate change produced by selection depends both on the effect on fitness of the traits under study and on the phenotypic correlations between the various traits. Lande and Arnold (1983) showed how correlations can be accounted for when we measure selection on quantitative traits. To understand their method, we consider a simple example involving two traits. Suppose that one trait influences fitness directly—in other words, it is under direct selection. In contrast, the second trait has no influence on fitness—that is, it is neutral. For example, body size might have a direct effect on chance of survival, but another trait, such as tail length, might have no effect. In Figure WN19.1, imagine an adaptive landscape that slopes uphill from left to right; the vertical dashed lines show contours of fitness. If the two traits vary independently of each other, then selection on one of them will not affect the other. However, if they are correlated, then selection on one will also increase the other. (Body size might be correlated with tail length, say, so that if individuals survive better because they are larger, survivors will also have larger tails.) In Figure WN19.1, the black ellipses represent the distribution of the traits in the population before selection and the blue ellipses the distribution in the population after selection. Fitness is only directly influenced by one of the traits, and so the selection gradient runs horizontally from left to right (dashed arrow). However, both traits increase after selection, because they are correlated with each other. The change in the population mean caused by selection is known as the selection differential (p. 477) and is represented by the solid (blue) arrow.

The selection gradient β can easily be estimated from the observed selection differential S provided the variances of the traits and their correlations with each other are known, In fact, the selection gradient for each trait is just the coefficient of a regression of fitness on that trait. We continue with the example, introduced in Chapter 17, of the Galápagos finches, Geospiza fortis, on the island of Daphne Major. During 1977, a severe drought reduced the availability of seeds and most of the birds died. Small seeds were eaten first and so, as the drought continued, birds needed to crack the larger seeds that remained. In Chapter 17, we only examined changes in beak depth. In fact, several other traits were measured, and all increased substantially and significantly (Table WN19.1). However, the selection gradients on each trait showed that selection acted primarily to favor heavier birds and deeper beaks; there was no evidence that selection acted on beak length, which may have increased only because it was correlated with the selected traits. As always, the differences in survival might have been caused by unknown and unmeasured traits. However, independent evidence that birds with deeper beaks could crack larger seeds supported the straightforward interpretation that they could therefore survive better.

Here, we have only considered the immediate change in phenotype due to selection within one generation. When we ask how this selection will affect the composition of the population in the next generation, we must take into account genetic correlations (p. 480). If two traits are genetically correlated and one of them increases as a result of selection, then both traits will increase in the next generation. This effect on changes from one generation to the next is distinct from the effects of selection within a generation, discussed here. One depends on genetic correlations, the other on phenotypic correlations.