A unified measure of linear and nonlinear selection on quantitative traits

Lande and Arnold's approach to quantifying natural selection has become a standard tool in evolutionary biology due to its simplicity and generality. It treats linear and nonlinear selection in two separate frameworks, generating coefficients of selection (e.g. linear and quadratic selection gradients) that are not directly comparable. Due to this somewhat artificial division, the Lande-Arnold approach lacks an integrated measure of the strength of selection that applies across qualitatively different selection regimes (e.g. directional, stabilizing or disruptive selection). We define a unified measure of selection, the distributional selection differential (DSD), which includes both linear and nonlinear selection. The DSD quantifies total selection on a trait, regardless of the underlying selection regime. The DSD can be partitioned into a directional component, representing selection on the trait mean, and a non-directional component, representing selection on the shape of the trait distribution (e.g. variance, skew or the number of modes). When multiple traits are measured, the DSD can also be separated into direct and correlated effects, analogously to linear selection gradients. As with linear selection differentials, the DSD on a standardized trait is limited in magnitude by the opportunity for selection. The DSD is a general-purpose measure of the total strength of selection. It is particularly valuable where traditional analyses provide limited insight, such as in comparative studies where the shape of selection is variable. Partitioning the DSD into directional and non-directional selection allows biologists to assess whether selection acts consistently in one direction, or in opposing directions over different parts of the trait range.