Order of events: Optimal harvest fraction in a discrete time model of a spatially structured single population protected by a marine reserve can be overestimated due to an imprecise modelling of harvest timing

摘要

The order of events in discrete time models plays an important role in the determination of the dynamics. For instance, harvest of a renewable resource can occur before or after species reproduction. In this work, we argue that a discrete time two patch dynamical model of a single population proposed in the literature is partly incorrect with respect to harvest timing. We put forward a new formulation where pre and post-reproductive harvest are precisely specified. By means of numerical bifurcation analysis employing the same parameter values of the model proposed in the literature we show that optimal harvest fractions are less than 1 while those in the referred literature are exactly 1 in the corresponding cases. These results point to an overestimation of harvest fractions in the model with incorrect harvest timing.