Parameter uncertainty of a dynamic multispecies size spectrum model

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.Résumé : Les modèles de spectres de tailles dynamiques sont reconnus comme offrant une approche efficace pour décrire comment les interactions basées sur la taille peuvent donner lieu à une structure de taille dans les communautés aquatiques. Ce sont des modèles écologiques de complexité moyenne représentant des solutions à des équations différentielles partielles déterminées par les processus dépendant de la taille que sont la prédation, la croissance, la mortalité et la reproduction dans une communauté d'espèces et de tailles interagissant entre elles. Pour être utiles dans la gestion quantitative des pêches, ces modèles doivent être approfondis dans un cadre statistique formel. Des travaux antérieurs ont fait appel à des valeurs moyennes de séries temporelles pour « étalonner » le modèle en utilisant des méthodes d'optimisation, ce qui a le désavantage d'occulter de l'information détaillée contenue dans les séries chronologiques. En utilisant un modèle publié de spectre de tailles multi-espèce paramétré pour la mer du Nord et comptant 12 espèces de poissons interagissant entre elles et les ressources de référence, nous avons calé le modèle sur des données de séries chronologiques en utilisant un cadre bayésien pour la première fois. Nous capturons la période de 1967 à 2010 en employant des estimations annuelles des taux de mortalité par pêche comme entrées au modèle et des séries chronologiques de données de débarquement de pêche pour caler le modèle sur les données de sortie. Nous estimons 38 paramètres clés représentant la capacité de charge de chaque espèce et...

The effects of seasonal processes on size spectrum dynamics

“…14 of Table 1; with species-specific fishing pressure and asymptotic sizes, these factors resulted in a similar upper limit for the number of mature individuals in the community for seasonal and nonseasonal systems. Future work on the parameter sensitivity and uncertainty (Spence et al 2016) is needed to elucidate the trade-offs in yield that result under different environmental conditions and management strategies. It is well known that fish stocks greatly fluctuate intra-annually (Horwood et al 2000), and the simulations here show that assuming a nonseasonal system means higher yield predictions than when incorporating seasonality.…”

“…Dynamic size spectrum models are increasingly being used to understand structure and dynamics of marine systems, including the effects of fishing and climate change (Blanchard et al 2012;Woodworth-Jefcoats et al 2013) and inclusion of multispecies dynamics to address questions related to fisheries (Blanchard et al 2014;Spence et al 2016). However, so far, these models have simplified reproductive processes and focused on interannual changes in plankton levels.…”

Size-based approaches to aquatic ecosystems and fisheries science: a symposium in honour of Rob Peters

“…These and other size-independent traits can be crucial for niche partitioning and the maintenance of coexistence in diverse aquatic communities (Hartvig and Andersen 2013). Stable coexistence has been achieved in multispecies size spectrum models through the addition of implicit niche partitioning and densitydependent factors, collectively represented by random matrices of feeding preferences or by stock-recruitment relationships (see the review by Andersen et al (2016b) and the studies of Spence et al (2016) and Datta and Blanchard (2016)). Nonetheless, a mechanistic inclusion of other traits can lead to important insights into the functioning of aquatic ecosystems and their responses to exploitation and would represent a natural extension of current size spectrum models.…”

“…Although size spectrum models have been parameterized for real systems before (e.g., Blanchard et al 2014), a formal statistical framework to fully explore available data and to quantify parameter and model uncertainty was lacking. Spence et al (2016) devise a Bayesian approach to estimate uncertainty from data and parameters of a size spectrum model fitted to the North Sea fish community and its multispecies fisheries and show that their more sophisticated statistical procedure greatly improved model fit over previous estimation methods.…”

A Bayesian approach for the identification of patient-specific parameters in a dialysis kinetic model

“…20,21 For example, they have been applied to estimate the inertance in a hydraulic simulator of the human circulation, 23 the parameters in a stochastic predator-prey system, 24 the thermal conductivity and the temperature profile in polymers, 25 and the aortic stiffness from non-invasive measurements. 26 More recently, Bayesian approaches have been considered for estimating the parameters that characterize the dynamics of aquatic communities, 27 and for the estimation of the mortality terms in a stage-structured demographic model. 28 However, to the best of our knowledge, they have been never applied to characterize the dynamics of plasmatic electrolytes and, more in general, they have never been applied to HD patients.…”