Accounting for environmental change in continuous-time stochastic population models

How phenological tracking shapes species and communities in non-stationary environments

Climate change alters the environments of all species. Predicting species responses requires understanding how species track environmental change, and how such tracking shapes communities. Growing empirical evidence suggests that how species track phenologically - how an organism shifts the timing of major biological events in response to the environment - is linked to species performance and community structure. Such research tantalizingly suggests a potential framework to predict the winners and losers of climate change, and the future communities we can expect. But developing this framework requires far greater efforts to ground empirical studies of phenological tracking in relevant ecological theory. Here we review the concept of phenological tracking in empirical studies and through the lens of coexistence theory to show why a community-level perspective is critical to accurate predictions with climate change. While much current theory for tracking ignores the importance of a multi-species context, basic community assembly theory predicts that competition will drive variation in tracking and trade-offs with other traits. We highlight how existing community assembly theory can help understand tracking in stationary and non-stationary systems. But major advances in predicting the species- and community-level consequences of climate change will require advances in theoretical and empirical studies. We outline a path forward built on greater efforts to integrate priority effects into modern coexistence theory, improved empirical estimates of multivariate environmental change, and clearly defined estimates of phenological tracking and its underlying environmental cues.

A Stochastic Model for Predicting Age and Mass at Maturity of Insects

Variation in age and mass at maturity is commonly observed in populations, even among individuals with the same genetic and environmental backgrounds. Accounting for such individual variation with a stochastic model is important for estimating optimal evolutionary strategies and for understanding potential trade-offs among life-history traits. However, most studies employ stochastic models that are either phenomenological or account for variation in only one life-history trait. We propose a model based on the developmental biology of the moth Manduca sexta that accounts for stochasticity in two key life-history traits, age and mass at maturity. The model is mechanistic, describing feeding behavior and common insect developmental processes, including the degradation of juvenile hormone prior to molting. We derive a joint probability density function for the model and explore how the distribution of age and mass at maturity is affected by different parameter values. We find that the joint distribution is generally nonnormal and highly sensitive to parameter values. In addition, our model predicts previously observed effects of temperature change and nutritional quality on the expected values of insect age and mass. Our results highlight the importance of integrating multiple sources of stochasticity into life-history models.