Species interactions are the basis of highly complex dynamical systems that form food webs where the predator-prey relationship is essential in maintaining the equilibrium between different species as critical effects can be drag down by unbalanced predator-prey relationships. The dynamics of predator-prey systems is also driven by environmental stochasticity, and the degree of correlation in the environmental noise can affect the dynamics of interacting predators and prey. We define a model where the predator and prey interact through a behavioral functional response and are both affected by climate. Simultaneous climate effects on predator and prey are set with correlated environmental noises. The predator-prey system is harvested by using a proportional threshold harvesting strategy for which only a given fraction of the difference between the estimate and the threshold is harvested if the population estimate is larger than the threshold. We study the dynamics of the predators and prey population when affected by different degrees of correlation in the environmental noises and the probability distribution of the mean and variance of the yield as a function of different levels of harvest, prey population fluctuations, and climate effects. We analyze the probability distribution of the mean and variance of the yield when harvesting different trophic levels either separately or simultaneously.
Results/Conclusions
The predators and prey fluctuate in opposite way when the environmental noises are oppositely correlated. The effect is higher when environmental stochasticity increases and predators and prey are desynchronized when the environmental noises are negatively correlated. We show that the level of environmental stochasticity affects harvest thresholds. Optimal yield remains constant when the environmental stochasticity is low while prey fluctuations affect harvest thresholds when environmental stochasticity is high. Correlation in environmental noises affects the variance of the yield, which is lower when the environmental noises are negatively correlated. Our study aims to find out optimal harvesting strategies for interacting predator and prey affected by climate effects by keeping an equilibrium between both predators and prey and open a way for joining harvest and conservation of different interacting species.