Enhancing population stability with combined adaptive limiter control and finding the optimal harvesting-restocking balance.

Fluctuations in population size may have negative consequences (e.g., an increased risk of extinction or the occurrence of repeated outbreaks), and many management strategies are aimed at avoiding them by either only restocking or only harvesting the population. Two of these strategies are adaptive limiter control (ALC) and adaptive threshold harvesting (ATH). With ALC the population is controlled by only restocking and with ATH by only harvesting. We propose the strategy of combined adaptive limiter control (CALC) as the combination of ALC and ATH and study the potential advantages of CALC over ALC and ATH. We consider two different population models, namely a stochastic overcompensatory model and a host-pathogen-predator model. For the first model, our results show that the combination of restocking and harvesting under CALC improves the constancy stability of the managed populations when the harvesting and restocking intensities are high enough. Otherwise the effect is marginal or in rare cases negative. For the second model, we show that combining harvesting with restocking reduces the outbreak risk only if the harvesting intensity is low. For medium harvesting intensities the effect is marginal and for high harvesting intensities the risk of outbreaks is increased. In addition, we study the optimal harvesting-restocking balance by considering a proxy of the benefit obtained in terms of the reduction in the outbreak risk and the harvesting and restocking costs.