A Modelling Investigation of Population Cycles in the Fish Rutilus rutilus

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Abstract
Two recent studies in small eutrophic lakes have revealed unusual 2-year cycles in recruitment of the fish Rutilus rutilus (L.) but the explanations offered by the investigators were different. In Alderfen Broad [England, UK], competition between young-of the-year and breeding individuals acts to reduce growth and fecundity in years following good recruitment. In Slapton Ley, good growth allows the fish to breed at a younger age (at the end of their second year of life), so that a year of good recruitment is followed 2 years later by another, when the previous prolific year-class comes to breed. The aim of this paper is to construct simulation models of the two populations and thus to check whether the two verbal models are tenable. Known features of the populations, including age at first reproduction, inter-age-class competition, fecundity and survival rates, were incorporated into the simulation models, together with reasonable values for parameters that could not be measured. The simulation models for Alderfen Broad confirmed that density-dependent loss of fecundity, operating with a time delay, could produce stable limit cycles with the observed period and amplitude. With slightly different, but still reasonable, parameter values, a perturbation to a stable population yielded a 2-year oscillation that damped out after 10-15 years. This could also be the explanation for the fish dynamics in Alderfen. The simulation models for Slapton Ley revealed that a discrete perturbation was necessary to produce a damped oscillation, with the observed period and lasting for 6-20 years, in such an age-structured population in which breeding individuals are effectively from a single age-class. This perturbation was caused by an epidermic of the cestode parasite Ligula intestinalis. Cycles are absent from both models when annual survival rate is higher than about 50%. Survival rates in Alderfen Broad (19.0%) and Slapton Ley (22.3%) are both unusually low, probably as a result of eutrophication. It is argued that cycles do not occur in most populations of R. rutilus because survival rates are typically much higher.