Verification and refinement of two species Fish Wars model

I will present joint work with Agnieszka Wiszniewska-Matyszkiel:

Verification and refinement of two species Fish Wars model.

In this paper, we investigate the model of two species Fish Wars model introduced by Fischer and Mirman (FM) in order to verify results proposed therein without complete proof. Using latest optimal control results, more general than available to FM, we prove that original results proposed as equilibria in FM are equilibria in one of the three considered cases of interactions between species. In the remaining cases, in the original model of FM, we cannot exclude unrealistic behaviour of the ecosystem, therefore proving that the proposed strategies are really equilibria, seems not possible. Besides, the original model of FM cannot deal with depletion of resources and Allee effect. Therefore, we modify the ecosystem regeneration function, to make the model closer to reality. In this model, we calculate equilibria in feedback strategies, which coincides with the results of FM on the set of sustainable states.