Multivariate autoregressive (MAR) modeling has been used extensively to study freshwater plankton communities in order to infer the inter-species interactions, the dominant environmental drivers and the system stability and resilience.  MAR modeling is well-grounded on theory concerning population and community dynamics and comparative properties of communities, such as resistance to disturbance, resilience, and return time after disturbance, are easily calculated in terms of the stability properties of the matrix of species interaction strengths.  As part of a larger and ongoing project, we are extending this statistical framework in order to use it to study the community dynamics and environmental drivers of marine plankton.  Our research addresses four technical barriers that hinder widespread application of MAR modeling for studying community dynamics of marine plankton – observation error, lower temporal autocorrelaton due to infrequent sampling, multiple spatially-distributed sampling locations, and uncertainty concerning the level of model complexity supported by the data.   

Results/Conclusions

In this poster, we introduce MAR state-space models (MARSS) for analysis of multivariate time-series data with substantial observation error and multiple observation time series per hidden states (the species abundances).  We show how these models can be fit by maximum-likelihood (via a EM algorithm, REML, or data-cloning) or Bayesian approaches.  We found that while the MARSS models can be fit robustly, the likelihood surface for the critical B matrix (the species interaction matrix) has ridge-like features which can make inference and estimation problematic.  We show how spatial replicates can be modeled using block-diagonal matrices and thus fit using the identical algorithms (and code) used for the single replicate case.  The use of spatial replicates mitigates the problem with poor estimation of the species interaction matrix.  Finally, we introduce an algorithm for MARSS model selection using AIC based on a parametric bootstrap.  The standard AIC metric has a strong small-sample bias leading to selection of overly complex MARSS models.  This parametrically bootstrapped AIC metric is asymptotically unbiased – although rather computationally intensive.  In summary, MAR state-space models provide a rigorous framework for analysis of multivariate time-series data and for study of hidden multivariate random walks.  Although computationally intensive, we have reduced this barrier by developing an R package for fitting of MAR state-space models.