Nonlinear dynamics and intermittency in a long term copepod time series

François G Schmitt (1, 2) , Juan Carlos Molinero (3) , Sylvie Zongo Brizard (2)

1 Ecosystèmes Littoraux et Cotiers
2 LOG - Laboratoire d’Océanologie et de Géosciences (LOG) - UMR 8187
3 CARRTEL - Centre Alpin de Recherche sur les Réseaux Trophiques et Ecosystèmes Limniques

We consider the nonlinear dynamics of a long-term copepod (small crustaceans) time series sampled weekly in the Mediterranean sea from 1967 to 1992. Such population dynamics display a high variability that we consider here in an interdisciplinary study, using tools borrowed from the field of statistical physics. We analyse the extreme events of male and female abundances, and of the total population, and show that they both have heavy tailed probability density functions (pdf). We provide hyperbolic fits of the form $p(x)\sim 1/x^{\mu+1}$, and estimate the value fo $\mu$ using Hill's estimator. We then study the ratio of male to female abundances, compared to the female abundances. Using conditional probability density functions and conditional averages, we show that this ratio is independent of the female density, when the latter is larger than a given threshold. This property is very useful for modelisation. We also consider the product of male to female abundances, which can be ecologically related to the encounters. We show that this product is extremely intermittent, and link its pdf to the female pdf.

Mots clés: Biological time series; Extreme events; Intermittency; Nonlinear dynamics

Domaines: Analyse de données, Statistiques et Probabilités [physics.data-an]; Biodiversité et Ecologie

François G Schmitt, Juan Carlos Molinero, Sylvie Zongo Brizard. Nonlinear dynamics and intermittency in a long term copepod time series. Communications in Nonlinear Science and Numerical Simulation, 2008, 13 (2), pp.407-415. ⟨10.1016/j.cnsns.2006.04.005⟩. ⟨hal-00264838⟩