Stochastic integral projection models for finite populations: Key population parameters and consequences for extinction risk

Background/Question/Methods

Integral projection modeling has recently arisen as a highly useful framework for demographic analyses of structured populations, when the structuring variable(s) is continuous  (e.g. body size, spatial location).  Results of integral projection models are analogous to those of matrix models, but apply to a wider range of population structures and life histories.  Here we extend this framework to include both demographic and environmental stochasticity in the population dynamics.  Demographic stochasticity acts independently among individuals at a given time and refers to the inherent randomness in individual processes of survival and reproduction.  Environmental stochasticity refers to temporal variation in the vital rates, affecting all individuals simultaneously.  Both types of stochasticity are associated with reduced long-term population growth rate and increased extinction risk. However, while the effects of environmental stochasticity are independent of population size, the effects of demographic stochasticity level off with size and are negligible for large populations. Nevertheless, many natural populations are small, especially those of conservation concern.

Results/Conclusions

By extending recent methods developed for discrete age structured models we derive the demographic and environmental variance of population growth as functions of a continuous state variable. Accordingly, we show how the total variance in population growth can be decomposed into a demographic and environmental component, depending differently on population size. Together with the expected population growth rate, the demographic and environmental variances are used to define a one-dimensional diffusion approximation of the population dynamics. The accuracy of this approximation, tested with computer simulation of given examples, demonstrates that the dynamics of this complex structured model can be described by only three population parameters, which is a main result of our study. Using examples, we demonstrate how the model can be used to evaluate extinction risk for small, continuously structured populations. Our results are especially relevant for conservation and management of small populations.