Lévy processes and stochastic von Bertalanffy models of growth, with application to fish population analysis

Tommaso Russo (1) , Paolo Baldi (2) , Antonio Parisi (3) , Giuseppe Magnifico , Stefano Mariani (4) , Stefano Cataudella (1)

1 Università degli Studi di Roma Tor Vergata [Roma] = University of Rome Tor Vergata
2 DIPMAT - Dipartimento di Matematica [Roma II]
3 Unipd - Università degli Studi di Padova = University of Padua
4 School of Biology and Environmental Science - University College of Dublin

The study of animal growth is a longstanding crucial topic of theoretical biology. In this paper we introduce a new class of stochastic growth models that enjoy two crucial properties: the growth path of an individual is monotonically increasing and the mean length at time t follows the classic von Bertalanffy model. Besides the theoretical development, the models are also tested against a large set of length-at-age data collected on Atlantic Herring (Clupea harengus): the mean lengths and variances of the cohorts were directly estimated by least squares. The results show that the use of subordinators can lead to models enjoying interesting properties, in particular able to catch some specific features often observed in fish growth data. The use of subordinators seems to allow for an increased fidelity in the description of fish growth, whilst still conforming to the general parameters of the traditional von Bertalanffy equation.

Mots clés: Individual-based models; Subordinators; Fish growth; Clupea harengus; Fisheriesc

Tommaso Russo, Paolo Baldi, Antonio Parisi, Giuseppe Magnifico, Stefano Mariani, et al.. Lévy processes and stochastic von Bertalanffy models of growth, with application to fish population analysis. Journal of Theoretical Biology, 2009, 258 (4), pp.521. ⟨10.1016/j.jtbi.2009.01.033⟩. ⟨hal-00554572⟩