Abstract

Dynamic size spectrum models have been recognized as an effective way of describing how size-based interactions can give rise to the size structure of aquatic communities. They are intermediate-complexity ecological models that are solutions to partial differential equations driven by the size-dependent processes of predation, growth, mortality, and reproduction in a community of interacting species and sizes. To be useful for quantitative fisheries management these models need to be developed further in a formal statistical framework. Previous work has used time-averaged data to “calibrate” the model using optimization methods with the disadvantage of losing detailed time-series information. Using a published multispecies size spectrum model parameterized for the North Sea comprising 12 interacting fish species and a background resource, we fit the model to time-series data using a Bayesian framework for the first time. We capture the 1967–2010 period using annual estimates of fishing mortality rates as input to the model and time series of fisheries landings data to fit the model to output. We estimate 38 key parameters representing the carrying capacity of each species and background resource, as well as initial inputs of the dynamical system and errors on the model output. We then forecast the model forward to evaluate how uncertainty propagates through to population- and community-level indicators under alternative management strategies.

Highlights

  • There are a number of ecological models that can be applied to answer marine management questions (Plagányi et al 2014)

  • We describe the steps used to sample from the posterior distributions using a Markov chain Monte Carlo (MCMC) algorithm (Gelman et al 2013)

  • We experimented with ␦ t = 1, the same value used by Blanchard et al (2014), i.e., the partial differential equations (PDEs) were estimated every year, and we found that the likelihood surface was very unstable and that often made a large difference to the model output

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Summary

Introduction

There are a number of ecological models that can be applied to answer marine management questions (Plagányi et al 2014). Size spectrum models are models of intermediate complexity and are formulated around the McKendrick von Foerster partial differential equation. They are based on very simple ecological assumptions (Andersen and Pedersen 2009) about how the role of individual body size in a food web (“big individuals eat small individuals”) gives rise to community abundance (and biomass) size spectra (Hartvig et al 2011). Food for the smallest sized organisms is provided by a background community (representing phytoplankton, zooplankton, and benthos), which is modeled as an external sizestructured resource that is not driven by predation but instead follows semi-chemostat logistic growth (Andersen and Pedersen 2009; De Roos et al 2008)

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