1339 Ecology, 79(4), 1998, pp. 1339–1356  1998 by the Ecological Society of America PLANKTON ABUNDANCE AND DYNAMICS ACROSS NUTRIENT LEVELS: TESTS OF HYPOTHESES W. W. MURDOCH, 1 R. M. NISBET, 1 E. MCCAULEY, 2 A. M. DEROOS, 3 AND W. S. C. GURNEY 4 1 Department of Biological Sciences, University of California, Santa Barbara, California 93106 USA 2 Ecology Division, Department of Biological Sciences, University of Calgary, Calgary, Alberta, Canada T2N 1N4 3 Department of Pure and Applied Ecology, University of Amsterdam, Kruislaan 320, 1098 SM Amsterdam, The Netherlands 4 Department of Statistics and Modelling Science, University of Strathclyde, Glasgow G1 1XH, Scotland Abstract. In lakes and reservoirs in which Daphnia is able to suppress the biomass of edible algae far below the level set by nutrients, the interaction is stable across the range of nutrient-poor to nutrient-rich environments. This phenomenon contradicts standard con- sumer–resource models, which predict that dynamics should become increasingly unstable with enrichment. We test four hypotheses that might account for stability at high-nutrient levels: (1) greater abundance of inedible algae with enrichment interferes with Daphnia’s feeding; (2) Daphnia’s death rate increases with enrichment; (3) Daphnia’s death rate increases with Daphnia density; (4) Daphnia’s functional response depends on Daphnia’s density. All hypotheses are rejected because they predict much higher biomass of edible algae at high-nutrient levels than is observed. Additional evidence on Daphnia death rates strengthens the case against hypotheses (2) and (3). We consider other hypotheses and conclude that three in particular would repay further investigation. (a) Inedible algae act as a nutrient ‘‘sponge,’’ reducing the effective carrying capacity for edible algae; (b) limited spatial movement can enhance stability through a metapopulation-like effect, and (c) sto- chastic variation among individuals can be stabilizing. The central problem investigated here is a general one, with implications for many consumer–resource systems. Key words: Daphnia; freshwater; models; paradox of enrichment; plankton; population dynamics. INTRODUCTION This paper concerns the following mismatch between theory and real systems. Most simple consumer–re- source (i.e., predator–prey) models predict extreme in- stability when the prey population is in a nutrient-rich environment but is suppressed far below the carrying capacity by the predator. This is sometimes called ‘‘the paradox of enrichment’’ (Rosenzweig 1971, Gilpin 1972). Instability is especially marked in Lotka-Vol- terra-type models, embodying a tension between a sta- bilizing process in the prey population (e.g., density- dependent growth) and a destabilizing process in the predator population (e.g., a time lag or a type 2 func- tional response). The result is large-amplitude cycles in which the prey is periodically suppressed by the predator to extremely low densities and then ‘‘escapes’’ to its carrying capacity before the predator catches up and suppresses it again. In contrast with theory, many real prey populations fail to show the predicted insta- bility. They are continuously suppressed by their pred- ators far below the limits set by their resources, yet show little fluctuation in density. Examples are com- mon in both natural insect populations and those under biological control (Murdoch 1994). Much of the history of predator–prey modeling can be seen as attempts to complicate models in ways that damp instability and Manuscript received 25 November 1996; revised 17 April 1997; accepted 2 June 1997. hence mimic well-regulated real populations. The list of potential complications, e.g., switching predators, aggregation, physical refuges, and spatial heteroge- neity, is extensive, even if we have few well-docu- mented demonstrations of how any one mechanism ac- tually regulates a particular population. We use the interaction between Daphnia, a fresh- water zooplankter, and its algal food supply to explore this dilemma. The Daphnia–algal system is ideal in several ways. First, planktonic communities have been viewed as likely exemplars of the paradox of enrich- ment (Rosenzweig 1971, McAllister et al. 1972). Sec- ond, Daphnia is one of the best-studied organisms in ecology at all levels from physiology to population ecology (McCauley and Murdoch 1987, McCauley et al. 1990), and we have developed a model of individual Daphnia energetics that provides a sound basis for pa- rameterizing individual-based population models (Gur- ney et al. 1990). Third, there is strong evidence that the dynamics in many field situations result from the predator–prey interaction between Daphnia and algae and not from interactions with other components of the community (McCauley and Murdoch 1987). Fourth, we have done experiments in simple mesocosms (stock tanks) that allow us to look at the system’s dynamics in the absence of many of the complications that have been offered as explanations for stability, such as pred- ators of Daphnia and spatial refuges for the prey. The dynamics in the tanks appear congruent with those seen