UW Aquatic & Fishery Sciences Quantitative Seminar

Eli Holmes

NOAA Fisheries

Inferring (plankton) ecosystem dynamics with multivariate autoregressive state-space models

Diverse approaches to ecosystem modeling have been undertaken in order to understand trophic interactions and the responses of ecosystems to human extraction or perturbations. Over the last 10 years, our research group has been using vector autoregression models, similar to those used in economics and finance, to statistically infer ecosystem dynamics from long-term time-series data. These models have been used, by our group and many other researchers, to estimate the interactions between species in freshwater plankton communities and to understand how environmental drivers, like temperature or nutrient addition, affect those dynamics. In the last five years, we have been working on state-space versions of these models to allow us to apply these approaches to a wider variety of datasets, specifically to marine plankton datasets with unknown observation errors and missing data. The form of the model is a multivariate (or vector) autogressive process overlaid with an observation process. The objective is to estimate the model parameters, under appropriate constraints.

Ecological data and constraints are different in important ways from financial data and constraints, and using these models to ask ecological questions has required modification of algorithms and new model selection criteria. Specifically, ecological data are often sparse and full of missing values. Unknown observation error is pervasive and often the underlying structure of the system (for example, the number of populations or the number of effective groups in a community), is the object of inference. In this talk, I'll discuss our work on an Expectation-Maximization (EM) algorithm that allows us to fit the general class of models with linear constraints, and our R package which implements this algorithm to allow fitting of this class of model. This class includes multivariate lag-p models, models with exogenous variables, and moving average models. Model selection is a central aspect of ecological statistics, because typically different model structures support different hypotheses about the underlying ecological dynamics. I will briefly present results from a parametric bootstrap AIC we developed to deal with the bias from AIC (of AICc) for this class of models. I'll conclude with a discussion of our current research which is examining how observation error affects the estimation of interaction matrices from multi-species data using long-term plankton datasets in the English Channel as a case study.