Habitat complexity, dispersal and metapopulations: Macroscopic study of a predator–prey system

A semilinear parabolic predator–prey system with time delay and habitat complexity effect

Based on the research on the predator–prey model with Holling type response function, a delayed predator–prey system with diffusion term and habitat complexity effect is established, and the effects of time delay and diffusion on dynamical behavior of the system are studied. First, taking habitat complexity as the parameter, the dynamical properties of the system without time delay are studied. By eigenvalue analysis, the sufficient conditions for locally asymptotic stability of the positive equilibrium and globally asymptotic stability of the boundary equilibrium are given, the existence conditions of Hopf bifurcation induced by diffusion term are discussed. In an appropriate range, diffusion makes a family of spatially homogeneous and inhomogeneous periodic solutions bifurcate from the positive equilibrium. Second, taking production delay as the bifurcation parameter, the existence conditions of Hopf bifurcation are given, the method to determine the bifurcation direction and the stability of bifurcating periodic solutions is given by using the center manifold theory and normal form method. Finally, the biological interpretations of the results are given, and some numerical simulations are given to verify the theoretical analysis results.

Dynamics of a stochastic Holling II predator-prey model with Lévy jumps and habitat complexity

This paper investigates a stochastic Holling II predator-prey model with Lévy jumps and habit complexity. It is first proved that the established model admits a unique global positive solution by employing the Lyapunov technique, and the stochastic ultimate boundedness of this positive solution is also obtained. Sufficient conditions are established for the extinction and persistence of this solution. Moreover, some numerical simulations are carried out to support the obtained results.

Diffusion-induced regular and chaotic patterns in a ratio-dependent predator-prey model with fear factor and prey refuge

Population distribution of interacting species in a large scale natural system is heterogeneous and subject to change for various reasons. Here, we explore how behavioral modification in prey species due to fear of predator and mutual interference between predators can create different spatiotemporal patterns in population distribution. We show that the fear factor and diffusion in a ratio-dependent predator-prey model may show more complex dynamics than observed earlier. It is shown that when prey diffusivity is low, prey remains concentrated at different patches throughout the domain. However, prey density becomes low at the patches as they disperse at a higher rate. Mixed and stripe patterns are observed during the transition from a hot spot pattern at the lower prey diffusivity to a cold spot pattern at its higher value. Pattern transition is, however, completely opposite if the antipredator behavior is gradually increased. Our simulation results reveal that the spatiotemporal chaotic pattern may also be observed in the Hopf-Turing region of instability provided prey shows a higher level of antipredator behavior. The chaotic pattern of the Hopf-Turing region may be shifted to a spot type pattern of the Turing region depending on the refuge level of the habitat.

HOW DO PARTIALLY HIDING BEHAVIOR AND COMPLETELY HIDING BEHAVIOR IMPACT INTERACTING POPULATIONS?

As the two main behaviors of prey populations in ecological systems, the partially hiding behavior (PHB) and the completely hiding behavior (CHB) play a significant role in determining the dynamics of predator–prey models. This work examines to the dynamical consequences of predator–prey systems with the PHB and the CHB. Previous research has independently studied the two behaviors, and the general conclusions are that the two behaviors can have positive and/or negative impacts on the considered population models. However, to our knowledge, no study has combined and compared the two behaviors in studying the dynamical consequences of predation interactions. Motivated by this, we investigated the dynamical consequences induced by the PHB and the CHB. From a mathematical point of view, the dynamical behaviors are studied and the corresponding sufficient conditions are given. Our findings are general and some published models are special cases of ours. From an ecological point of view, we find that the size of the ecological regions is mainly determined by the two behaviors, and which one is ecologically beneficial for the health coexistence of the interacting populations are primarily determined by the functional response and the attack coefficient of predators. Moreover, we conclude that the evolutionary and optimal choices of prey behavior (PHB or CHB) depend on the predators attack coefficient (large or small attack coefficient) and the resource level (abundant or pool resource level).

A GENERALIZED PREDATOR–PREY SYSTEM WITH HABITAT COMPLEXITY

This paper presents a generalized predator–prey system and considers the effect of habitat complexity on the dynamical consequences. The results show that habitat complexity has a major impact on the dynamical consequences of the considered system. On the one hand, habitat complexity has a stabilizing impact under certain conditions. A numerical simulation in our study and in experiments conducted in the published studies elaborate on this stabilizing effect. On the other hand, the most interesting and open issue is that a destabilizing effect of habitat complexity is found theoretically. All results are explained and illustrated from the ecological viewpoint.