How to model marine reserves?

The safeguarding of resources is one of the principal subjects of halieutics studies. Among the solutions proposed to avert the disappearance of species, the setting in place of preservation (no take) reserves is often mentioned. Most work on this subject, theoretical as well as applied, was undertaken in recent years. In this paper, we seek to compare two different models presented in existing literature by highlighting their underlying assumptions. Both models were derived from what is often referred to as the “model of Schaefer–Clark” (reference to the work of the last author on Mathematical Bioeconomics: Clark [C.W. Clark, Mathematical Bioecomics: The Optimal Management of Renewable Resources, 2nd ed., John Wiley and Sons, New-York, 1990]). We show that various variations of this model lead to properties that can be very different.