Stochastic animal population dynamics

While ecological systems display a dizzying array structures, diversity, and robustness, our ability to understand these properties is limited by our inability to characterize all the factors driving our study systems. These limitations place strong constraints on our ability to understand how animal populations embedded in complex ecological systems are able to persist and the factors that contribute to that persistence.

Stochastic modeling approaches have filled this gap by allowing scientists and mathematicians to account for the uncertainty generated by the unmeasured components of our system. A key insight behind stochastic modeling approaches is that the focus becomes on modeling the ensemble properties of the system, rather than trying to explain all of factors that drive variation in animal birth rates and survival. These model give bounds on future population forecasts and have yielded a number of key properties that have used understand to ecological systems. A natural assumption behind these laws is that increases in the variability of fecundity and survival rates map to increases in the population variability. However, there are cases where increases in the variability of these rates can actually lead to more stable populations. We are exploring this emergent property, called stochastic stabilization, by developing the mathematical foundations to explain this paradox and develop an conduct empirical analyses to demonstrate the effect in nature.