Predicting extinction: Progress with an individual-based model of protozoan predators and prey

Despite the importance of understanding persistence, there are few direct tests of the ability of models to predict predator and prey population persistence. We tested whether an individual-based model could forecast the dynamics and time to extinction in aquatic microcosms of a protist predator and prey: predatory Didinium nasutum and bacterivorous Colpidium striatum. By addressing both persistence and dynamics, the model increases the testability of mechanisms of extinction. Population-level equations modeled the functional response and prey growth. For individual predators, we simulated time since dividing and feeding, and number of prey consumed; these influenced the timing of division and death. We tested the model by comparing simulated dynamics to data from three experiments: (1) an experiment initiated with low predator-prey ratios in 30-mL bottles; (2) an experiment similar to Experiment 1, but in which immigrant predators, prey, or both were added during the first density cycle; (3) an experiment in 30-mL bottles, initiated with various predator-prey ratios. Using only nine parameters measured in independent experiments, simulations gave satisfactory predictions of the period and amplitude of cycles of predator and prey densities, and predator and prey densities through time for Experiment 1. Adding stochasticity to the model also allowed it to reproduce observed prey and predator persistence and the proportion of replicates with prey extinctions. We used the improved model to forecast the results of Experiments 2 and 3. In Experiment 2, persistence changed with immigration. The model qualitatively reproduced these changes but underestimated their magnitude. Increasing the initial predator-prey ratio reduced persistence in Experiment 3. Simulations failed to qualitatively reproduce these results for 30-mL microcosms, unless we raised initial prey density. This study demonstrates the use of an individual-based model to help identify and test mechanisms of extinction in predator-prey interactions. The combination of individual-based and population-level formalisms can maintain both model tractability and a close working relationship between models and accessible data.