Interactions between temperature and nutrients determine the population dynamics of primary producers.

Global change is rapidly and fundamentally altering many of the processes regulating the flux of energy throughout ecosystems, and although researchers now understand the effect of temperature on key rates (such as aquatic primary productivity), the theoretical foundation needed to generate forecasts of biomass dynamics and extinction risk remains underdeveloped. We develop new theory that describes the interconnected effects of nutrients and temperature on phytoplankton populations and show that the thermal response of equilibrium biomass (i.e. carrying capacity) always peaks at a lower temperature than for productivity (i.e. growth rate). This mismatch is driven by differences in the thermal responses of growth, death, and per-capita impact on the nutrient pool, making our results highly general and applicable to widely used population models beyond phytoplankton. We further show that non-equilibrium dynamics depend on the pace of environmental change relative to underlying vital rates and that populations respond to variable environments differently at high versus low temperatures due to thermal asymmetries.