Mathematical models of population dynamics of the kelp Laminaria religiosa, with emphasis on temperature dependence

Theoretical and numerical models were developed to investigate the effects of water temperature on the population dynamics of the kelp, Laminaria religiosa. The models describe seasonal changes in the biomass of kelp by calculation of growth and grazing rates of sea urchins, Strongylocentrotus nudus. Using the theoretical model, conditions were obtained to satisfy the statistical analysis of a relationship between water temperature and kelp harvests from a fishery census. The conditions require the negative second derivative of the growth rate with respect to temperatures, or the positive second derivative of the grazing rate. By using the numerical model, harvests of kelp were calculated for a change in water temperature over a given period. The period of a temperature change giving the maximum effects on the harvest was determined primarily by temperature dependence on the growth rate. Grazing by sea urchins had large effects on the harvest of kelp. A value of 104 was obtained for a ratio between harvests at the higher and the lower temperatures differing by ± 1∘C.