Simple Models and Variation in Plankton Densities Among Lakes

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Abstract
To explore the idea that the dynamics of the zooplankter Daphnia and its algal food supply can be accounted for by simple predator-prey models, we tested the ability of such models to predict how the average densities change along a gradient of nutrient enrichment. Total algal carrying capacity is known to increase from nutrient-poor to nutrient-rich lakes. Here we show that this is true also for edible algae alone. We also provide evidence that the realized per capita growth rate of edible algae increases with trophy (trend 1). A synthesis of laboratory and field data suggests two other trends associated with increasing nutrient status: (2) Daphnia's attack rate decreases in response to increasing concentrations of inedible algae; and (3) its death rate increases in response to greater predation pressure. In models of the Lotka-Volterra type, either trend 2 or a combination of trends 1 and 3 leads to the prediction that the abundance of both Daphnia and their algal prey should increase along a nutrient gradient in natural habitats where inedible algae and predators of Daphnia both occur. In contrast, where these features are missing, the original "paradox of enrichment" prediction is expected: Daphnia density should increase but algal density should not. Our analysis of more than 30 study-years of data from natural lakes confirmed the first of these predictions; results from outdoor artificial habitats, lacking inedible algae and predators of Daphnia, confirmed the second. We cannot evaluate the relative importance of the two mechanisms competing to explain the result from natural habitats, but our analyses suggest new observations and experiments that could test these mechanisms. These results are consistent with our general hypothesis that the dynamics of the Daphnia-algae interaction can be explained by simple predator-prey models. In particular, they support two assumptions: (1) other species in the system can be modeled simply as part of the environment of the predator-prey interaction; and (2) variation in the dynamics from one habitat to another results from merely quantitative differences in parameter values and does not require us to postulate qualitative, or "structural," changes among habitats.