Management of Eutrophication for Lakes Subject to Potentially Irreversible Change

We analyzed management policies for ecosystems subject to alternate states, thresholds, and irreversible changes. We focused on the problem of lake eutrophication by excessive phosphorus (P) input. Eutrophic lakes may be classified, with respect to their response to reduced P input alone, as reversible (recovery is immediate and proportional to the reduction in P input), hysteretic (recovery requires extreme reductions in P input for a period of time), or irreversible (recovery cannot be accomplished by reducing P input alone). A model with one state variable and one control variable describes the responses of lake trophic state to changes in P input and other management interventions. Activities that generate P input to the lake are assumed to create profits, while the value of ecosystem services provided by the lake declines at high P levels. We then calculated P input policies that maximize the discounted net benefits from polluting activities and ecosystem services. If “optimality” is defined as maximizing this discounted criterion, then analyses based on deterministic lake dynamics usually lead to higher P input rates than analyses that assume various kinds of variability (e.g., inputs are affected by stochastic factors such as weather, policy is implemented with lags, or parameters of the limnological model are uncertain). In reality, all of these complications occur. Therefore, if maximum economic benefit is the goal of lake management, P input targets should be reduced below levels derived from traditional deterministic models. This pattern may apply to other situations where diffuse pollution causes nonlinear changes in ecosystem state, such as the greenhouse effect or acid deposition.