Greed is good: from super-harvest to recovery in a stochastic predator-prey system

This paper demonstrates a predator-prey system of cod and capelin that confronts a possible scenario of prey extinction under the first-best policy in a stochastic world. We discover a novel ‘super-harvest’ phenomenon that the optimal harvest of the predator is even higher than the myopic policy, or the ‘greedy solution’, on part of the state space. This intrinsic attempt to harvest more predator to protect the prey is a critical evidence supporting the idea behind ‘greed is good’. We ban prey harvest and increase predator harvest in a designated state space area based on the optimal policy. Three heuristic recovery plans are generated following this principle. We employ stochastic simulations to analyse the probability of prey recovery and evaluate corresponding costs in terms of value loss percentage. We find that the alternative policies enhance prey recovery rates mostly around the area of 50% recovery probability under the optimal policy. When we scale up the predator harvest by 1.5, the prey recovery rate escalates for as much as 28% at a cost of 5% value loss. We establish two strategies: modest deviation from the optimal on a large area or intense measure on a small area. It seems more cost-effective to target the stock space with accuracy than to simply boost predator harvest when the aim is to achieve remarkable improvement of prey recovery probability.