Chapter 10 Bivariate response to directional selection

Figure 10. 1 Figure 10. 2

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Figure 10. 1 Response to selection as a pool shot when the G-matrix varies. The game of pool is a useful analogy for developing intuition about how two correlated traits respond to selection. The angle of the cue and and its force in hitting the ball represent, respectively, the angle and length of the vector beta (shown in black). The response of the ball to the cue stick represents the response to selection from one generation to the next, delta zbar (shown in blue). If the two traits are not genetically correlated and have the same genetic variances, the 95% confidence ellipse of the G-matrix (shown in green) is circular, and the response of the ball to the cue is exactly what we would expect from a conventional pool table. If we hit the ball at a 25 deg angle, it moves away at a 25 deg angle, a hit at 75 deg yields a 75 deg response, etc. Genetic correlation changes the behavior of the ball, but in predictable ways. Two examples are shown in the animation, one with a positive genetic correlation (rg=0.9) and one with a negative genetic correlation (rg=-0.9).

Figure 10.2 Response to selection as a pool shot, when beta varies. Even with genetic correlation (rg=0.5), as in this animation, the ball responds in the normal way if our cue is aligned with the major or the minor eigenvectors of the G-matrix. We get an especially strong response when the cue is aligned with the major eigenvector (gmax), but a much reduced response when it is aligned with the minor eigenvector (gmin). If we hit the ball at any other angle than gmin or gmax, the ball moves at an angle biased towards the direction of the major eigenvector, gmax. In other words, at any other angle, correlated responses to selection come into play so that delta zbar is not aligned with beta.