Statistical inference for a multivariate diffusion model of an ecological time series

Diffusion processes are natural modelling frameworks for many stochastic phenomena. However since inference for nonlinear diffusion models is difficult, the diffusion models used within the ecological literature are predominantly linear thus ignoring the more complex forces that many populations and environments are subject to. We suggest a parameter estimation procedure that is computationally efficient and valid for a wide class of diffusion models. This includes diffusions that are nonlinear and/or multivariate. The procedure is used to fit a diffusion model to a time series with three variables: the plankton abundances for both Pseudo-nitzschia australis and Prorocentrum micans in addition to the surface water temperature. Pseudo-nitzschia australis are shown to achieve maximal growth with a water temperature in the region of 7.8-16.0 degrees C. The corresponding optimum temperature region for Prorocentrum micans is 12.5-24.5 degrees C with the dinoflagellate appearing to be less sensitive to sub-optimal temperatures. Both species are governed by r-type strategies and are subject to regulated growth. Though Prorocentrum micans are known to feed on diatoms, we are unable to find evidence of feeding on Pseudo-nitzschia australis. We thus demonstrate that by fitting a diffusion model to an ecological dataset, one may learn much about the factors that affect the ecosystem. A good understanding of these factors is vital in order to manage an ecosystem appropriately.