Modelling the feeding rate of the sea urchin Strongylocentrotus nudus (A. Agassiz) on kelp

Abstract

This paper presents mathematical models for estimating the amount of kelp eaten by sea urchins Strongylocentrotus nudus (A. Agassiz) using five data sets available from four different research groups or persons who have performed laboratory feeding experiments. These experiments used as food large brown algae, Laminaria spp., Eisenia bicyclis Setchell and Undaria pinnatifida Suringar, which commonly occur in the S. nudus habitats. Non linear regression analysis using three data sets from the experiments with Laminaria fed is carried out to estimate model parameters. Two models are presented for estimating the daily feeding rate. The first model is described as a function of water temperature and test diameter, and the second model is given by multiplying the first model by a seasonal factor that is expressed as a function of day of the year. On the basis of Akaike's information criterion, the second model is selected as a better model for the data given. The model selected predicts that the feeding rate is proportional to the 2.1 power of test diameter; begins to increase at 1 °C and reach a maximum at 10 °C, beyond which it decreases and finally ceases at 28 °C; varying sinusoidally with season by more than 30% of the rate predicted only from temperature and the test diameter. Analysis of the deviations between observed and predicted feeding rates shows that the predicted rates are in good agreement with the observed ones over all factors, on average. Application of the model to feeding rates on kelp species other than Laminaria suggests that the model may also give a reasonably good estimate for the feeding rate for Eisenia bicyclis, but may give a substantial underestimate for Undaria pinnatifida. More detailed analyses of model parameters indicate that the exponent of the feeding rate on test diameter may differ seasonally from the estimate of the model, probably due to reproductive activity. In addition, the analyses suggest that actual feeding rates may change with season, before or after the predicted ones. Despite the presence of unexpected seasonal fluctuations in daily feeding rate, the amount of annual feeding per animal is proportional to about the 2.1 power of test diameter with a very high correlation. The result suggests that daily feeding rates vary with a size-dependent limit in the amount of annual feeding.