Associate Professor Oregon State University Corvallis, Oregon, United States
Populations embedded in complex ecosystems are influenced by numerous factors and feedbacks that render their dynamics challenging to understand without mathematical models. Kelp forests typify such ecosystems and hold immense cultural, ecological, and economic value, with the importance of understanding their dynamics becoming ever more crucial due to the dramatic changes kelp forests are exhibiting around the world. Many kelp species, including the best-studied species, giant kelp (Macrocystis pyrifera), exhibit annual and multi-year oscillations in abundance. Most kelp-forest population models are therefore derived to capture deterministic mechanisms of stable limit cycles, including logistic growth and the time-lagged feedback between kelp and grazers, competitors, or facilitating species. Here, rather than derive such models from first principles, we apply a form of machine learning known as symbolic regression to learn the governing equations of a persistently cyclical population of giant kelp directly from time-series data. The data come from a site located off San Nicolas Island, CA, USA that has been biannually monitored for the past 38 years. Using symbolic regression and Takens' theorem to encapsulate the multi-dimensionality of kelp dynamics, we evolve equations towards the Pareto front of human-interpretable, single-species equations that best describe kelp dynamics over varying levels of equation complexity. Comparing the mathematical forms and local stability properties of these best-performing equations reveals a fundamental contrast to existing models of kelp-forest dynamics: the persistence of kelp population cycles is driven not by long-term deterministic mechanisms but is instead a consequence of their near local instability and the effects of external perturbations that keep kelp populations in persistently transient regimes of recovery.
