Temperature-dependent fitness responses in fluctuating environments

Background/Question/Methods

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 (T_opt) and an upper limit for survival (T_max). We varied the mean temperature (μ_T) and standard deviation (σ_T) of fluctuations in 100 repeated simulations at each combination of μ_T in {T_opt +- 10} and σ_T in {0,5} to create an extinction probability surface.

Results/Conclusions

For very low or high μ_T populations survive at initial densities or quickly go extinct, respectively. Very high σ_T yield a constant risk of extinction for all μ_T, while for very low σ_T, probability of extinction follows fecundity/mortality curve. At intermediate levels of μ_T and σ_T, extinction risk depends on the the degree of overlap between the distribution of temperatures and the fecundity/mortality curve. Increasing σ_T under constant μ_T decreases extinction risk when it causes an increase in the proportion of non-lethal temperature fluctuations. Shifting μ_T towards T_opt under constant σ_T also decreases the probability of extinction. We present extinction risk surface and the pairs of μ_T and σ_T values that allow population survival. Results indicate that μ_T should drive selection on σ_T: at intermediate μ_T, low σ_T minimizes extinction but after increasing μ_T past a threshold, larger σ_T values are required to minimize extinction risk.