Modeling socio-economic aspects of ecosystem management and biodiversity conservation

Comparison between best-response dynamics and replicator dynamics in a social-ecological model of lake eutrophication

Social-ecological models are often used to investigate the mutual interactions between an ecological system and human behaviour at a collective level. The social system is widely represented either by the replicator dynamics or by the best-response dynamics. We investigate the consequences of choosing one or the other with the example of a social-ecological model for eutrophication in shallow lakes, where the anthropogenic discharge of pollutants into the water is determined by a behavioural model using the replicator or a best-response dynamics. We discuss a fundamental difference between the replicator dynamics and the logit formulation of the best-response dynamics. This fundamental difference results in a different number of equilibria. We show that the replicator equation is a limit case of the best-response model, when agents are assumed to behave with infinite rationality. If agents act less rationally in the model using the best-response dynamics, the correspondence with the model using the replicator dynamics decreases. Finally, we show that sustained oscillations observed in both cases may differ substantially. The replicator dynamics makes the amplitude of the limit cycle become larger and makes the system come closer to full cooperation or full defection. Thus, the dynamics along the limit cycle imply a different risk for the system to be pushed by a perturbation into a desirable or an undesirable outcome depending on the socioeconomic dynamics assumed in the model. When analyzing social-ecological models, the choice of a socioeconomic dynamics is often little justified but our results show that it may have dramatic impacts on the coupled human-environment system.

Asymmetric public goods game cooperation through pest control

Cooperation in a public goods game has been studied extensively to find the conditions for sustaining the commons, yet the effect of asymmetry between agents has been explored very little. Here we study a game theoretic model of cooperation for pest control among farmers. In our simple model, each farmer has a paddy of the same size arranged adjacently on a line. A pest outbreak occurs at an abandoned paddy at one end of the line, directly threatening the frontier farmer adjacent to it. Each farmer pays a cost of his or her choice to an agricultural collective, and the total sum held by the collective is used for pest control, with success probability increasing with the sum. Because the farmers' incentives depend on their distance from the pest outbreak, our model is an asymmetric public goods game. We derive each farmer's cost strategy at the Nash equilibrium. We find that asymmetry among farmers leads to a few unexpected outcomes. The individual costs at the equilibrium do not necessarily increase with how much the future is valued but rather show threshold behavior. Moreover, an increase in the number of farmers can sometimes paradoxically undermine pest prevention. A comparison with a symmetric public goods game model reveals that the farmer at the greatest risk pays a disproportionate amount of cost in the asymmetric game, making the use of agricultural lands less sustainable.

Biological conservation through marine protected areas in the presence of alternative stable states

This article addresses how depleted stock can be restored by creation of marine reserve and species mobility when alternative stable states persist in a marine ecosystem. To understand the role of a marine protected area, we develop a two-patch version of an originally single-patch model. In the two-patch model, we prove that some of the locally stable equilibria are not stable equilibria from an ecological viewpoint. Similarly, some unstable equilibria determined classically from the mathematical model are no longer equilibria. It is shown that increasing reserve size may produce three alternative stable states in the presence of harvesting. Dynamic solutions have a tendency to reach an upper stable state from a lower stable state when reserve size is increased, but the opposite phenomenon (i.e., shifting to a lower stable state from an upper one) never occurs. This suggests that MPAs always have a positive effect in stock conservation even when alternative stable states inherently persist in marine ecosystems.