MATHEMATICAL-MODELS OF POPULATION-DYNAMICS OF THE KELP LAMINARIA-RELIGIOSA, WITH EMPHASIS ON TEMPERATURE-DEPENDENCE

Theoretical and numerical models were developed to investigate the eff ects of water temperature on the population dynamics of the kelp, Lami naria religiosa. The models describe seasonal changes in the biomass o f kelp by calculation of growth and grazing rates oi sea urchins, Stro ngylocentrotus nudus. Using the theoretical model, conditions were obt ained to satisfy the statistical analysis of a relationship between wa ter temperature and kelp harvests from a fishery census. The condition s require the negative second derivative Of the growth rate with respe ct to temperatures, or the positive second derivative oi the grazing r ate. By using the numerical model, harvests of kelp were calculated fo r a change in water temperature over a given period. The period oi a t emperature change giving the maximum effects an the harvest was determ ined primarily by temperature dependence on the growth rate. Grazing b y sea urchins had large effects on the harvest of kelp. A value of 10( 4) was obtained for a ratio between harvests at the higher and the low er temperatures differing by +/- 1 degrees C.