Phenotypic memory drives population growth and extinction risk in a noisy environment.

Random environmental fluctuations pose major threats to wild populations. As patterns of environmental noise are themselves altered by global change, there is a growing need to identify general mechanisms underlying their effects on population dynamics. This notably requires understanding and predicting population responses to the colour of environmental noise, in other words its temporal autocorrelation pattern. Here, we show experimentally that environmental autocorrelation has a large influence on population dynamics and extinction rates, which can be predicted accurately provided that a memory of past environment is accounted for. We exposed nearly 1,000 lines of the microalgae Dunaliella salina to randomly fluctuating salinity, with autocorrelation ranging from negative to highly positive. We found lower population growth, and twice as many extinctions, under lower autocorrelation. These responses closely matched predictions based on a tolerance curve with environmental memory, showing that non-genetic inheritance can be a major driver of population dynamics in randomly fluctuating environments.