This article appears in the following ICES Journal of Marine Science issue: Herring: linking biology, ecology, and status of populations in the context of changing environments [View the issue table of contents]
Progress in modelling herring populations: an individual-based model of growth
1 Laboratory of Experimental Ecology and Aquaculture, Department of Biology, Faculty of Science, University of Rome "Tor Vergata", Via della Ricerca Scientifica 1, Rome 00133, Italy
2 School of Biology and Environmental Science, University College Dublin, Belfield, Dublin 4, Ireland
3 Department of Mathematics, Faculty of Science, University of Rome "Tor Vergata", Via della Ricerca Scientifica 1, Rome 00133, Italy
4 Department of Financial Economics and Quantitative Methods, Faculty of Economics, University of Rome "Tor Vergata", Via Columbia 2, Rome 00133, Italy
5 National Research Council of Italy (CNR), Piazzale Aldo Moro 7, Rome 00185, Italy
6 Section of Ecosystem and Population Dynamics, National Institute of Aquatic Resources, Technical University of Denmark, DK-2920 Charlottenlund, Denmark
Correspondence to T. Russo: tel: +39 06 7259 5974; fax: +39 06 7259 5965; e-mail: tommaso.russo{at}uniroma2.it
Russo, T., Mariani, S., Baldi, P., Parisi, A., Magnifico, G., Clausen, L. W., and Cataudella, S. 2009. Progress in modelling herring populations: an individual-based model of growth. – ICES Journal of Marine Science, 66: 1718–1725.Stock assessment may gain from taking into account individual variations in growth, because size is a key predictor of survival and reproduction. In trying to understand patterns in empirical observations, a major challenge is to model the changes in the size distribution of a cohort with age. We introduce an individual-based growth model that is founded on the use of a stochastic class of processes called subordinators. This modelling approach has several desirable features, because it (i) can take account of both individual and environmental sources of random variations, (ii) has the property of letting size increase monotonically, and (iii) ensures that the mean size-at-age follows the widely accepted von Bertalanffy equation. The parameterization of the model is tested on two Atlantic herring (Clupea harengus) datasets collected from the stocks of North Sea autumn spawners (ICES Divisions IVa, IVb, and IVc) and western Baltic spring spawners (ICES Subarea III). The size distributions obtained from the subordinator model largely match the observed size distributions, suggesting that this approach might be successfully implemented to support the assessment of commercial fish stocks, such as when modelling of size variability is required.
Keywords: Clupea harengus, individual-based model, stochastic variation, subordinator, von Bertalanffy growth equation
Received 29 August 2008; accepted 1 April 2009; advance access publication 1 January 2009.