In lakes and reservoirs in which Daphnia is able to suppress the bioma
ss of edible algae far below the level set by nutrients, the interacti
on is stable across the range of nutrient-poor to nutrient-rich enviro
nments. 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 Da
phnia 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. Addi
tional evidence on Daphnia death rates strengthens the case against hy
potheses (2) and (3). We consider other hypotheses and conclude that t
hree in particular would repay further investigation. (a) Inedible alg
ae act as a nutrient ''sponge,'' reducing the effective carrying capac
ity for edible algae; (b) limited spatial movement can enhance stabili
ty through a metapopulation-like effect, and (c) stochastic variation
among individuals can be stabilizing. The central problem investigated
here is a general one, with implications for many consumer-resource s
ystems.