Persistence in multilayer ecological network consisting of harvested patches

Complex network theory yields a powerful approach to solve the difficulties arising in a major section of ecological systems, prey-predator interaction being one among them. A large variety of ecological systems have been successfully investigated employing the theory of complex networks, and one of the most significant advancements in this theory is the emerging field of multilayer networks. The field of multilayer networks provides a natural framework to accommodate multiple layers of complexities emerging in ecosystems. In this article, we consider prey-predator patches communicating among themselves while being connected by distinct small-world dispersal topologies in two layers of the network. We scrutinize the robustness of the multilayer ecological network sustaining gradually over harvested patches. We thoroughly report the consequences of introducing asymmetries in both interlayer and intralayer dispersal strengths as well as the network topologies on the global persistence of species in the network. Besides numerical simulation, we analytically derive the critical point up to which the network can sustain species in the network. Apart from the results on a purely multiplex framework, we validate our claims for multilayer formalism in which the patches of the layers are different. Interestingly, we observe that due to the interaction between the two layers, species are recovered in the layer that we assume to be extinct initially. Moreover, we find similar results while considering two completely different prey-predator systems, which eventually attests that the outcomes are not model specific.