Visualizing Multivariate Selection

Abstract

Recent developments in quantitative-genetic theory have shown that natural selection can be viewed as the multivariate relationship between fitness and phenotype. This relationship can be described by a multidimensional surface depicting fitness as a function of phenotypic traits. We examine the connection between this surface and the coefficients of phenotypic selection that can be estimated by multiple regression and show how the interpretation of multivariate selection can be facilitated through the use of the method of canonical analysis. The results from this analysis can be used to visualize the surface implied by a set of selection coefficients. Such a visualization provides a compact summary of selection coefficients, can aid in the comparison of selection surfaces, and can help generate testable hypotheses as to the adaptive significance of the traits under study. Further, we discuss traditional definitions of directional, stabilizing, and disruptive selection and conclude that selection may be more usefully classified into two general modes, directional and nonlinear selection, with stabilizing and disruptive selection as special cases of nonlinear selection.

MIPoD: A Hypothesis‐Testing Framework for Microevolutionary Inference from Patterns of Divergence

“…To test this hypothesis, we need estimates of the individual selection surface, which in turn can be used to approximate the adaptive landscape. In particular, if stabilizing selection is weak, then the coefficients that describe the curvature and orientation of the individual selection surface also provide a reasonable approximation of the adaptive landscape (Lande and Arnold 1983;Phillips and Arnold 1989). Both of the approximated surfaces for garter snake data show weak curvature (i.e., small values in γ or large values in ω) and so support this assumption.…”

“…In this situation, the orientation of the direct estimate of G does not provide an explanation for the principal axes of population differentiation, and selection becomes the leading contender. Arnold et al (2001) have proposed that evolution may occur along a selective line of least resistance, the leading eigenvector of ω (ω max ), which may be visualized as a ridge on the Gaussian fitness surface (Phillips and Arnold 1989). This selective line of least resistance may or may not coincide with g max .…”

Differences in the temporal dynamics of phenotypic selection among fitness components in the wild

“…Phillips & Arnold [39] extended earlier models developed by Lande [40] to derive an equation that could be used to estimate how far a population was from its phenotypic optima for a given quantitative trait (eqn (7) in [31]). Under the assumption that a quadratic function approximates the individual fitness surface [31,39], the absolute value of the ratio of directional selection gradients to their respective quadratic gradients (jb/2gj where b are the linear selection gradients and g the quadratic selection gradients) gives an estimate of how far a population trait mean is from its optimum in phenotypic standard deviations [39]. Estes & Arnold [39] provide a lucid description of the theoretical basis for this estimate, and we refer the reader to that paper for details.…”

Biting off more than you can chew: sexual selection on the free amino acid composition of the spermatophylax in decorated crickets

“…We therefore explored the extent of nonlinear selection by conducting a canonical analysis to locate the major axes of the fitness surface [28]. The strength of linear selection along each of the eigenvectors (m i ) is given by theta (u i ) and the strength of nonlinear selection is given by their eigenvalues (l i ).…”