Impact of Fear and Habitat Complexity in a Predator-Prey System with Two Different Shaped Functional Responses: A Comparative Study

Habitat complexity or the structural complexity of habitat reduces the available space for interacting species, and subsequently, the encounter rate between the prey and predator is decreased significantly. Different experimental shreds of evidence validate that the presence of the predator strongly affects the physiological behaviour of prey individuals and dramatically reduces their reproduction rate. In this study, we investigate the interplay between the level of fear and the degree of habitat complexity in a predator-prey model with two different shaped functional responses. We, therefore, develop the functional response using the timescale separation method, and the shape of the resulting functional response depends upon the monotonous property of catch rate, gN where N is the prey biomass. Whenever gN increases strictly, a saturating functional response occurs, but for nonmonotonic gN, a dome-shaped functional response arises. For saturating case, it has been revealed that both prey and predator biomass may oscillate for lower levels of fear and a lower degree of habitat complexity. To stabilize this oscillatory behaviour to a coexistence state, we have to adequately increase the level of fear or degree of habitat complexity. However, for dome-shaped case, more complicated dynamics are observed. In this case, coexistence steady state, if exists, may be locally asymptotically stable for a lower degree of habitat complexity, but for intermediate values, the system is capable of producing multiple coexistence steady states with a bistable phenomenon between predator-free steady state and a coexistence steady state. Moreover, if the level of fear is sufficiently low, the system may experience a supercritical or/and subcritical Hopf bifurcation. In the dynamics of parametric disturbance for the degree of habitat complexity parameter, dome-shaped functional response predicts that disturbance may trap the system into a nearest attractor (either a large amplitude stable limit cycle or predator-free steady state); this can be overcome only by a larger alteration, or sometimes it is impossible to overcome (hysteresis phenomena), whereas the saturating-shaped functional response predicts a system resilience. For both the functional responses, a higher degree of habitat complexity always increases the extinction possibility of the predator, and no level of fear can compensate this biodiversity loss.