A unified measure of linear and nonlinear selection on quantitative traits

Abstract

Summary 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.

Phenotypic Selection on Flower Color and Floral Display Size by Three Bee Species

“…Besides using regression analyses, we also examined the distributional selection gradient on the floral traits ( Henshaw and Zemel, 2017 ). This measures total selection on a trait and can be broken down into a directional component (dD) illustrating selection on a trait mean and a non-directional component (dN) that reflects selection on the shape of the trait distribution.…”

Sexual selection on male body size, genital length and heterozygosity: Consistency across habitats and social settings

“…Significance values were obtained from the same model except that the relative number of offspring sired was power transformed to account for its non‐normal distribution and pool identity was treated as a random effect to avoid pseudoreplication. We estimated non‐directional selection on each trait using the recently developed method of Henshaw and Zemel (), which quantifies the total strength of non‐directional selection of any kind (e.g. stabilizing or disruptive selection: Brodie, Moore, & Janzen, ).…”

Heritability of the extra-pair mating behaviour of the pied flycatcher in Western Siberia

“…At some point, the time allocated to find extra-pair females may lead to both a loss of within-pair paternity and a decrease in parental care for within-pair offspring. The emergence of such a trade-off can be considered by modification of the selection differential: the linear selection differential can be replaced by the quadratic selection differential (for details, please, refer to Henshaw & Zemel (2017) ). At the same time, the forces driving extra-pair reproduction by socially monogamous females are less clear because EPC is not associated with an increase of a female’s immediate reproductive success since female’s EPC does not necessarily increase fecundity.…”