Abstract
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, g N where N is the prey biomass. Whenever g N increases strictly, a saturating functional response occurs, but for nonmonotonic g N , 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.
Highlights
In ecology, food is one of the basic substances essential for maintaining life and growth of a species
Eoretical ecologists and evolutionary biologists have clarified that the presence of predator may affect the physiological behaviour of prey species to such an extent that it can be more effective in reducing prey biomass than direct predation [29, 30]
We have derived a functional response based on timescale separation arguments, which includes the catch rate, g(N), and depending upon the monotonic property of g(N), various functional responses emerge
Summary
Food is one of the basic substances essential for maintaining life and growth of a species. Most of the previous studies have considered that for high level of fear or larger predator biomass, fear function may affect the reproduction of prey to such an extent that the number of offspring decreases to zero This is not the real scenario observed in various experimental evidences. In this model, instead of using a particular functional response, a general response function has been employed whose graphical shape depends on the monotonic property of the catch rate.
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