Mutual information reveals variation in temperature-dependent sex determination in response to environmental fluctuation, lifespan and selection

Quantifying the degree to which sex determination depends on the environment can yield insight into the evolution, ecological dynamics, and functional aspects of sex determination. In temperature-dependent sex determination (TSD), theory often predicts a complete dependence of sex on temperature, with a switch-like reaction norm. However, empirical data suggest more shallow relationships between sex and temperature. Here, we demonstrate the usefulness of an index, mutual information (MI), to reflect the degree of temperature dependence in sex. MI depends on both the shape of a reaction norm and the natural temperature variation, thus providing a measure of TSD that is ecologically dependent. We demonstrate that increased lifespan and decreased environmental fluctuation predict reaction norms with high MI (switch-like). However, mutation and weaker selection on sex-specific performance reduce average MI in a population, suggesting that mutation-selection balance can resolve some of the conflict between theoretical predictions of individual-based optimality and population-based empirical results. The MI index allows clear comparison of TSD across life histories and habitats and reveals functional similarities between reaction norms that may appear different. The model provides testable predictions for TSD across populations, namely that MI should increase with lifespan and decrease with historical environmental fluctuations.