Turing instability in a diffusive predator-prey model with multiple Allee effect and herd behavior

Diffusion-driven instability and bifurcation analysis are studied in a predator-prey model with herd behavior and quadratic mortality by incorporating multiple Allee effect into prey species. The existence and stability of the equilibria of the system are studied. And bifurcation behaviors of the system without diffusion are shown. The sufficient and necessary conditions for Turing instability occurring are obtained. And the stability and the direction of Hopf and steady state bifurcations are explored by using the normal form method. Furthermore, some numerical simulations are presented to support our theoretical analysis. We found that too large diffusion rate of prey prevents Turing instability from emerging. Finally, we summarize our findings in the conclusion

Dynamics of a diffusive predator–prey model with herd behavior

This paper is devoted to considering a diffusive predator–prey model with Leslie–Gower term and herd behavior subject to the homogeneous Neumann boundary conditions. Concretely, by choosing the proper bifurcation parameter, the local stability of constant equilibria of this model without diffusion and the existence of Hopf bifurcation are investigated by analyzing the distribution of the eigenvalues. Furthermore, the explicit formula for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are also derived by applying the normal form theory. Next, we show the stability of positive constant equilibrium, the existence and stability of periodic solutions near positive constant equilibrium for the diffusive model. Finally, some numerical simulations are carried out to support the analytical results

Modeling the herd prey response to individualistic predators attacks

In this paper, we consider predators hunting on prey gathered in groups and in such way exhibiting the possibility of reducing the predators pressure. To model this feature, however, we depart from the Holling type II (HTII) response function, in that we assume that a sufficiently large set of prey could respond to individualistic attacks and therefore induce the predator to renounce. The basic idea is described at first in a simple two-populations predator-prey system. It is then expanded considering the generalist predators to deal with two prey. In the first case, both are gathered in herds, and in the second one, one of the two instead behaves individualistically. The net outcome is an enhanced survival for the prey with respect to both the herding cases without and with predators feeding satiation (i.e., using the HTII response)

Trade-Offs Between Predation Risk and Forage Differ Between Migrant Strategies in a Migratory Ungulate

Trade-offs between predation risk and forage fundamentally drive resource selection by animals. Among migratory ungulates, trade-offs can occur at large spatial scales through migration, which allows an escape\u27\u27 from predation, but trade-offs can also occur at finer spatial scales. Previous authors suggest that ungulates will avoid predation risk at the largest scale, although few studies have examined multi-scale trade-offs to test for the relative benefits of risk avoidance across scales. Building on previously developed spatial models of forage and wolf predation risk, we tested for trade-offs at the broad landscape scale and at a finer, within-home-range scale for migratory and non-migratory resident elk (Cervus elaphus) during summer in the Canadian Rockies in Banff National Park (BNP) and adjacent Alberta, Canada. Migration reduced exposure to wolf predation risk by 70% relative to residents at the landscape scale; at the fine scale, migrants used areas that were, on average, 6% higher in forage digestibility. In contrast, by forgoing migration, resident elk were exposed to higher predation risk, but they reduced predation risk at fine scales to only 15% higher than migrants by using areas close to human activity, which wolves avoided. Thus, residents paid for trying to avoid predation risk with lower forage quality. Residents may have been able to compensate, however, by using areas of abundant forage close to human activity where they may have been able to forage more selectively while avoiding predation risk. Human activity effectively decoupled the positive correlation between high forage quality and wolf predation, providing an effective alternate strategy for residents, similar to recent findings in other systems. Although ungulates appear capable of balancing risk and forage at different spatial scales, risk avoidance at large landscape scales may be more effective in the absence of human-caused refugia from predation

Stability and Hopf Bifurcation in a Delayed Predator-Prey System with Herd Behavior

A special predator-prey system is investigated in which the prey population exhibits herd behavior in order to provide a self-defense against predators, while the predator is intermediate and its population shows individualistic behavior. Considering the fact that there always exists a time delay in the conversion of the biomass of prey to that of predator in this system, we obtain a delayed predator-prey model with square root functional response and quadratic mortality. For this model, we mainly investigate the stability of positive equilibrium and the existence of Hopf bifurcation by choosing the time delay as a bifurcation parameter

Spatio-Temporal Recruitment Dynamics Of Mountain-Dwelling Caribou In The Yukon Territory, Canada

Thesis (Ph.D.) University of Alaska Fairbanks, 2010Understanding processes and mechanisms resulting in observed ecological patterns is critical information for biologists charged with effectively managing and conserving wildlife populations. In many areas across North America woodland caribou (Rangifer tarandus caribou Gmelin) populations are declining, as are caribou and reindeer populations globally. Why these declines are occurring is a key research question of biologists and managers. I investigated factors influencing recruitment of mountain-dwelling woodland caribou using long-term time series from ten herds (populations) in the Yukon Territory, Canada (Yukon). Recruitment was indexed by the calf:cow ratio observed during the fall breeding season using data collected during aerial monitoring surveys. I first examined the seasonal effects of the Pacific Decadal Oscillation (PDO), on observed recruitment in these herds. The PDO was positively related to recruitment and had its strongest effect during the winter preceding birth and immediately before calving. These results indicate that female body condition, and hence conception rates, were not affecting observed recruitment patterns. Rather, parturition and/or early calf survival were the most likely vital rates affecting the number of calves being recruited into the breeding population. I next examined the interacting effect of large-scale climate (PDO) and predation [wolf (Canis lupus L.) density] on recruitment in the Finlayson herd of east-central Yukon. A large-scale wolf control program in the 1980s allowed me to assess recruitment over a range of wolf densities and climatic conditions. The effect of the PDO immediately before calving was negligible when wolf numbers were significantly reduced indicating the climatic effect was modified by wolf density. Additionally, as springtime climate improved (i.e. increasing PDO) the difference in recruitment between years with and without wolf removals was reduced