Life history variation and environmental fluctuations jointly shape extinction risk of a population
For many species, life history processes and individual fitness are highly dependent on temperature. Temporal fluctuations in temperature can promote coexistence, prolong persistence times, and alter the overall species composition in a community. These effects are mediated by the thermal response of individual fitness to temperature. In this study we investigate how a population's extinction risk is altered by its environment: the mean and variance of temperature fluctuations. We also ask how intraspecific trait variation changes the relationship between the mean and variance of the environment and the risk of extinction. We approximate a set of ordinary differential equations with a Gillespie algorithm where waiting times between birth, death, and fluctuation events are Exponentially distributed. We use thermal response curves to model the effects of temperature on life history processes. We introduce trait variation by allowing individuals to differ in a single parameter: the thermal optimum which follows a Normal distribution. Individual's traits are not heritable but are instead stochastic outcomes of a single distribution, leading to standing variation within a population.
We find that population extinction risk is nonlinearly dependent on the mean and variance of the environment. This relationship is asymmetric; population can tolerate higher variation at temperatures below its thermal optimum. At the extreme edges of the species' niche, small amounts of variation in the environment decrease extinction risk. Intraspecific variation in the thermal response of life history processes buffers against extinction risk, leading to longer persistence times for populations in environments with mean temperatures around and just above its thermal optimum regardless of the variation present. Small amounts of intraspecific variation can have non-trivial impacts on extinction risk, especially in small populations.