Supplementary Methods and Figures from Nonlinear averaging of thermal experience predicts population growth rates in a thermally variable environment

As thermal regimes change worldwide, projections of future population and species persistence often require estimates of how population growth rates depend on temperature. These projections rarely account for how temporal variation in temperature can systematically modify growth rates relative to projections based on constant temperatures. Here, we tested the hypothesis that time-averaged population growth rates in fluctuating thermal environments differ from growth rates in constant conditions as a consequence of Jensen's inequality, and that the thermal performance curves (TPCs) describing population growth in fluctuating environments can be predicted quantitatively based on TPCs generated in constant laboratory conditions. With experimental populations of the green alga Tetraselmis tetrahele, we show that nonlinear averaging techniques accurately predicted increased as well as decreased population growth rates in fluctuating thermal regimes relative to constant thermal regimes. We extrapolate from these results to project critical temperatures for population growth and persistence of 89 phytoplankton species in naturally variable thermal environments. These results advance our ability to predict population dynamics in the context of global change