Selection Gradients

Natural selection and sexual selection are important evolutionary processes that can shape the phenotypic distributions of natural populations and, consequently, a primary goal of evolutionary biologists is to quantify the strength and mode of selection on traits. Studying selection yields valuable information about which traits are important for a fitness-related function (e.g., changes in beak shape to improve feeding in Darwin’s finches) or how evolutionary processes caused a population to diverge into two distinct phenotypes (e.g., carnivore versus herbivore) rather than maintaining an intermediate phenotype (e.g., omnivore). A classic example was based on phenotypic traits associated with higher survival in house sparrows following a storm. Readers who are new to selection analyses are encouraged to first review the Major Books and Book Chapters section of this work for a general overview of the terminology before delving into the many advances achieved by measuring selection, and specifically the selection gradient, in natural populations. While methods to quantify the mode and total strength of selection on a trait were available since the early 1800s, another approach was needed to characterize when a trait was being directly targeted by selection. Readers are strongly recommended to have obtained a general introduction to linear algebra and regressions in order to better understand how to quantify selection on traits and how the different computational methods differ. One or more unfamiliar technical terms may be presented, and readers are encouraged to refer to the corresponding paper for a more thorough explanation of the term. Linear selection (“directional selection”) changes the mean trait value in a population through a linear function between fitness and the trait value whereas nonlinear selection involves nonlinear fitness functions that can: (1) increase trait variance when values at the tail ends of the distribution are linked to higher fitness (“disruptive selection”), (2) decrease trait variance when intermediate values relate to higher fitness (“stabilizing selection”), or (3) increase/decrease the covariance between two traits (“correlational selection”). The selection differential is a coefficient often used to estimate selection but does not partition direct versus indirect selection, whereby direct selection results in phenotypic changes that are directly related to fitness whereas indirect selection can cause a phenotypic change that is not directly related to fitness because that trait is correlated with another trait that is under direct selection. The selection gradient was then introduced to quantify the direct relationship between a phenotypic trait and fitness and originally defined as the partial derivative of (relative) fitness with respect to the mean value for a phenotypic trait. Selection gradients are also defined as the partial regression coefficients from a multiple least-squares regression where relative fitness is the response variable and phenotypic traits are the independent variables, and can be estimated with non-parametric techniques, such as path analyses or logistic regressions. In all of these contexts, the importance of selection gradients in evolutionary biology has been undeniable. Statistical analyses are, however, only as useful as the statistical models from which they were calculated and there have been substantial efforts to study the factors that could affect estimations of selection gradients. Nonlinear selection is expected to be common in nature yet attempts to quantify it has been challenging. Various methods have been applied to better capture nonlinear selection and visualize fitness surfaces and landscapes, but a consensus has yet to be reached. Moreover, estimates of selection may be affected by environmental variation, missing or skewed data, type of standardization, sampling bias, publication bias, and user error. Despite these challenges, the future of quantifying selection gradients remains a promising and fruitful endeavor. Evolutionary biology is becoming increasingly more open access to increase accessibility, enhance reproducibility, and enable future syntheses and other advancements in quantifying selection. Estimating selection gradients has become far more accessible with the advent of new computational methods that can handle a broader range of data sets and the availability of example data sets, making the present moment a particularly exciting time to measure multivariate selection on quantitative traits. In the following work, shorthand notation is provided to classify the types of selection analyzed (selection = linear, nonlinear, or linear and nonlinear) and outcome of the quadratic regression coefficients in the gamma matrix that are used to quantify nonlinear selection. Specifically, past work documented that numerous publications may have underestimated the strength of stabilizing/disruptive selection by a factor of two so it is useful to identify whether the quadratic regression coefficients for the squared traits (gamma_ii) were “doubled” (correctly multiplied by a factor of two), “not doubled,” “reviewed” (summarized from other studies), “not applicable” (not needed because nonlinear selection was not measured or another method was used to estimate the quadratic regression coefficients), “not reported” (nonlinear selection was calculated but the gamma_ii values were not displayed in the publication), or had “doubling unconfirmed” (nonlinear selection was estimated but it was unclear whether the gamma_ii values were correctly doubled).