Multivariate Autoregressive Processes for Estimating the Covariance of Time-Varying Pre-Recruit Productivity

The maximum reproductive rate is a parameter of central
importance to population ecology and resource management. It determines,
amongst others, the intrinsic rate of population growth, productivity,
overfishing limits and reference points. Traditional approaches to stock
recruitment relationships don't allow for inter-annual variation in the
maximum reproductive rate. Allowing for such stochastic variation
provides an opportunity to track changes in productivity. We extend
previous foundational single-stock applications to the multivariate
case, where the covariance structure of the trends in productivity
across taxa and geographic regions is also of interest. The formulation,
estimation, and interpretation of the covariance of the states, is
presented. Example applications within species across their range and
across species within systems in the North Atlantic are presented. These
indicate substantial temporal changes in productivity with an underlying
tendency of declining reproductive rates conserved within some species.
We conclude that time-varying parameter techniques provide a useful
framework that integrates across many dimensions of environmental change
affecting recruitment dynamics. Such an approach may be an attractive
method for incorporating environmental change into stock assessments.