Predator–prey dynamics in environments rich and poor in nutrients

STABLE predator–prey models with a tension between the stabilizing effect of prey density-dependence and the destabilizing effect of predators generally become unstable when the nutrient environment of the prey is enriched1–3. This 'paradox of enrichment' occurs in a wide range of models incorporating realistic features4–6. Enriched models quickly produce cycles with enormous amplitude and increased periods2,3,6–8. In real systems, however, there have been few tests for 'paradox' behaviour, and the few results are equivocal9–12. We have now tested for paradox behaviour in populations of the freshwater zooplankter Daphnia and their algal prey. In lakes and ponds these populations show both stable and cyclic dynamics13,14 caused by the interaction between the populations. The cycles are not driven by external forces14,15, but do not seem to be of the paradox-of-enrichment type: their amplitude is small, their period (equal to a Daphnia generation) is short, and there is good evidence that they are caused by the developmental delay of Daphnia14,15. Stage-structured models of the Daphnia–algae interaction indicate that such single-generation 'time-lag' cycles occur in the progression of instability from stable equilibrium to paradox cycles6,7, and that this progression may be driven by increasing nutrient levels7. We show here, however, that enrichment does not lead to paradox cycles, either in field or experimental Daphnia–algae systems. We suggest that concomitant changes in the predator–prey interaction accompanying enrichment could account for the absence of paradox behaviour.