Measuring selective mortality from otoliths and similar structures: a practical guide for describing multivariate selection from cross-sectional data

Selective mortality is an important process influencing both the dynamics of marine populations and the evolution of their life histories. Despite a large and growing interest in measuring selective mortality, studies of marine species can face some serious methodological and analytical challenges. In particular, many studies of selection in marine environments use a cross- sectional approach in which fates of individuals are unknown but the distributions of trait values before and after a period of selective mortality may be compared. This approach is often used because many marine species have morphological structures (e.g. otoliths in fishes, statoliths in some invertebrates) that contain a permanent record of trait values. Although these structures often contain information on multiple, related traits, interpretation of selection measures has been limited because most studies of selection based on cross-sectional data consider selection 1 trait at a time, despite known problems with trait correlations. Here, we detail how cross-sectional data can be analyzed within a multivariate framework and provide a practical guide for conducting these types of analyses. We illustrate these methods by applying them to empirical studies of selective mortality on early life history traits in 2 species of reef fish. These examples demonstrate that analyzing selective mortality in a multivariate framework can vastly improve estimates of selection and yield new insight into how combinations of traits can interact to influence survival. Accompanying the paper are 2 R scripts that can be used to perform the calculations described here and assist with visualizing selection on multiple traits.