Population variance and extinction of two competitors consuming a common resource

Background/Question/Methods

The ultimate fate of all natural populations is extinction and the risk of extinction over different time frames has important implications for understanding species coexistence and facilitating effective conservation. The relationship between extinction risk and population characteristics such as carrying capacity, average size and variance in size has been well developed for single populations, however natural populations must persist in a community context that includes competition, predation and other interactions.  We developed theoretical models to examine the relationship between extinction and population dynamics for two species competing for a limiting resource, including a stochastic version of Tilman’s resource competition model. Population trajectories were obtained numerically for parameters sets sampled from the space of birth rate, death rate, half-saturation constants, and different resource supply regimes using latin hypercube sampling. Gillespie’s direct method was used to obtain the solutions and results were tallied for analysis.

Results/Conclusions

We found that variance in population size was negatively related to the competitor’s birth rate. Because extinction is expected to become more likely as variance in size increases, it is counter-intuitive that a better competitor would decrease extinction risk. As predicted, increases in the resources entering the system cause increases in the variance in population size, making extinction more likely. Variance was also positively related to the half-saturation constant of both species, indicating that inefficient resource uptake leads to more variable population sizes, possibly due to higher levels of resources in the environment. However, the trends in variance in population size did not consistently predict observed patterns of extinction risk. Mean time to extinction did not vary with half-saturation constants and populations did not persist longer when the competitor’s birth rate was higher. Interestingly, extinction became more likely with increases in the losing competitor’s birth rate. These results indicate that inter-specific interactions have important effects on population extinction and that a mechanistic framework may be required to obtain even qualitatively correct predictions about the direction of effects.