A quantitative test of the size efficiency hypothesis by means of a physiologically structured model

According to the size-efficiency hypothesis (SEH) larger bodied cladocerans are better competitors for food than small bodied species. In environments with fish, however, the higher losses of the large bodied species due to size-selective predation may shift the balance in favor of the small bodied species. Here we present a theoretical framework for the analysis of the competitive abilities of zooplankton species that takes both competition and predation into account in one coherent analysis. By applying the conceptually well-understood framework of physiologically structured population models we were able to predict the relative difference in predation rates necessary to cause a shift in dominance of the large-bodied species (Daphnia pulicaria) to the small-bodied species (D. galeata). These predictions depend only on seven easily interpretable parameters per species: size at birth, size at maturity and maximum size, age at maturity, maximal clutch size, egg development time and finally the half-saturation constant for food. The critical equilibrium mortality of D. pulicaria was 0.16 d1 at food concentrations close to the critical food concentration of D. galeata, i.e. D. pulicaria will win the competition as long as its mortality rate is below 0.16 d1. At higher food concentrations the differential mortality curve (plotting equilibrium mortalities of both species against each other) approached a linear function with a slope of one and an intercept equal to the difference in maximal population birth rates. The prediction of critical predation rates was independent of the ingestion rate of the cladocerans and the algal carrying capacity and food regeneration rate of the environment although the mechanism works through competition for a shared algal food resource. We interpret these findings in terms of the relative predation risk large and small-bodied cladocerans will face in various freshwater ecosystems.