Combining selective episodes to estimate lifetime nonlinear selection.

Studies measuring natural selection acting via different components of fitness may provide insight into such central questions in evolutionary biology as the evolution of life histories and sexual dimorphism. It is often desirable to combine estimates of selection at different episodes to understand how they interact to produce total lifetime selection. When selective episodes are sequential, total directional selection may be calculated by summing directional selection across episodes. However, it is unclear whether lifetime nonlinear (e.g., stabilizing, disruptive, or correlational) selection may be similarly calculated using estimates of quadratic selection from sequential episodes. Here, I show that lifetime quadratic selection depends not only upon the sum total of quadratic selection across episodes but also upon the pattern of directional selection across episodes. In certain cases, the effects of directional selection across episodes may cancel one another, leading to no net directional selection but strong stabilizing selection. This result suggests that true stabilizing selection may be more common than previously thought, especially when the entire life cycle is considered. The equations derived here are easily applicable to empirical data, as is illustrated both with a simulated dataset and with a reanalysis of a study of quadratic selection in dark-eyed juncos.