Understanding the effect of predator functional response on time to extinction using stochastic models and microcosm experiments

Background/Question/Methods

Biodiversity loss has reached proportions that led to forewarnings of a sixth mass extinction event. Ecosystems are losing species at higher rates than the normal background rate measured in

fossil records. Predictions for the future are of even higher rates. Current estimates are based on a combination of theoretical studies and empirical data, and focus on single species population

dynamics. We believe that considering ecosystems at a multispecies level will bring a more accurate predictive understanding of the extinction process. Single species models can be improved

and extended to multispecies communities In this poster we present a first step in that direction. Assuming constant presence of predators, we derive a single-species stochastic birth-death

process and investigate the effect of different kinds of density-dependence in death due to predation. In particular we consider the case where predation death has a component that increases as

population numbers decrease (a functional response type II term).

Results/Conclusions

Classical results show that the mean time to extinction of a population subjected to only demographic stochasticity is exponential in the carrying capacity of the population. Using techniques

borrowed from many-particles quantum mechanics and stochastic calculus we give this dependence, in relation to different predator functional responses. We show that the presence of a non-

linear functional response alters the shape of the mean time to extinction of models in which non linearity is not included. Moreover we derive accurate approximations to describe the extinction

process and the effect of large fluctuations on the time to extinction of populations subjected to demographic stochasticity. We use predator removal experiments in microcosms with a large

generalist predator (i.e. Stentor) to test our predictions. We find that Stentor well represents the constant predator assumption. We compare the mean time to exticntion of different prey to our

models and we show that linear functional response (type I) represent our data. We then propose new experimental design to test further the effect of predation on the mean time to extinction.