Modeling complex phenotypes: generalized linear models using spectrogram predictors of animal communication signals.

A major goal of evolutionary biology is to understand the dynamics of natural selection within populations. The strength and direction of selection can be described by regressing relative fitness measurements on organismal traits of ecological significance. However, many important evolutionary characteristics of organisms are complex, and have correspondingly complex relationships to fitness. Secondary sexual characteristics such as mating displays are prime examples of complex traits with important consequences for reproductive success. Typically, researchers atomize sexual traits such as mating signals into a set of measurements including pitch and duration, in order to include them in a statistical analysis. However, these researcher-defined measurements are unlikely to capture all of the relevant phenotypic variation, especially when the sources of selection are incompletely known. In order to accommodate this complexity we propose a Bayesian dimension-reduced spectrogram generalized linear model that directly incorporates representations of the entire phenotype (one-dimensional acoustic signal) into the model as a predictor while accounting for multiple sources of uncertainty. The first stage of dimension reduction is achieved by treating the spectrogram as an "image" and finding its corresponding empirical orthogonal functions. Subsequently, further dimension reduction is accomplished through model selection using stochastic search variable selection. Thus, the model we develop characterizes key aspects of the acoustic signal that influence sexual selection while alleviating the need to extract higher-level signal traits a priori. This facet of our approach is fundamental and has the potential to provide additional biological insight, as is illustrated in our analysis.