The fitness of ectotherms is highly dependent on temperature, initially increasing as the environment warms then drastically declining above an optimal temperature. Fitness responses are often left skewed, suggesting that warming would have a proportionately larger impact on population survival than cooling. Temperature fluctuations are translated to population fluctuations through this nonlinear response of fitness to temperature, complicating the estimation of extinction probabilities. Using previously established temperature-dependent fecundity and mortality functions for phytoplankton populations, we investigate the influence of the mean and variance of temperature fluctuations on population extinction risk. We simulate a simple, closed population with density-dependent birth and death functions using the Gillespie algorithm. We assume a unimodal response of fecundity to temperature and an exponential increase in mortality with temperature. These relationships yield a maximum fitness at an optimal temperature (Topt) and an upper limit for survival (Tmax). We varied the mean temperature (μT) and standard deviation (σT) of fluctuations in 100 repeated simulations at each combination of μT in {Topt +- 10} and σT in {0,5} to create an extinction probability surface.
Results/Conclusions
For very low or high μT populations survive at initial densities or quickly go extinct, respectively. Very high σT yield a constant risk of extinction for all μT, while for very low σT, probability of extinction follows fecundity/mortality curve. At intermediate levels of μT and σT, extinction risk depends on the the degree of overlap between the distribution of temperatures and the fecundity/mortality curve. Increasing σT under constant μT decreases extinction risk when it causes an increase in the proportion of non-lethal temperature fluctuations. Shifting μT towards Topt under constant σT also decreases the probability of extinction. We present extinction risk surface and the pairs of μT and σT values that allow population survival. Results indicate that μT should drive selection on σT: at intermediate μT, low σT minimizes extinction but after increasing μT past a threshold, larger σT values are required to minimize extinction risk.