For over a century, ecologists have pursued the task of characterizing species’ population dynamics via mathematical equations derived from first principles. This pursuit has yielded foundational models, such as Verhulst’s logistic growth and the Lotka-Volterra predator-prey equations, as well as untold numbers of more detailed models that vary widely across the spectrum of mechanistic to phenomenological. But what if ecologists could look to data and machine learning for assistance? Would these same equations come to light, or would novel equation forms to describe the population and community dynamics emerge? Here, we applied a form of machine learning known as symbolic regression to the 30+ year, biannually monitored time series of kelp and urchin abundances of San Nicolas Island, CA. We thereby infer the Pareto front of human interpretable single-species equations that best describe kelp dynamics over increasing levels of equation complexity. Comparing the mathematical forms and dynamical predictions of these best-performing equations to those of existing models in the ecological literature reveals both congruence and differences that strengthen our understanding of kelp forest ecosystems and offer new hypotheses for the processes that underlie their dynamics.