Cooperation In Hunting Research Articles

A diffusive predator-prey system with hunting cooperation in predators and prey-taxis: II stationary pattern formation

This paper is a continuation of the study conducted by Ko and Ryu (2024) [5], which introduces and analyzes a generalized predator-prey reaction-diffusion system incorporating (repulsive) prey-taxis and a hunting cooperation effect in predators, under homogeneous Neumann boundary conditions. In the study, the existence and uniqueness of global and classical solutions for the time- and space-dependent system are analytically examined. Furthermore, the study examines the local and global stability and convergence rate at the constant predator-extinction and coexistence states. In our paper, we analyze the stationary system corresponding to the system in [5], with a specific focus on examining the existence and nonexistence of positive and nonconstant solutions. The nonexistence occurs when the diffusion rate of prey is sufficiently high. On the other hand, the existence occurs when the prey-tactic rate is sufficiently high, indicating a strong repulsive prey-taxis, and the diffusion rate of prey is sufficiently low. For this investigation, we separately employ the energy method and the Leray-Schauder degree theory.

Prey group defense and hunting cooperation among generalist-predators induce complex dynamics: a mathematical study.

Group defense in prey and hunting cooperation in predators are two important ecological phenomena and can occur concurrently. In this article, we consider cooperative hunting in generalist predators and group defense in prey under a mathematical framework to comprehend the enormous diversity the model could capture. To do so, we consider a modified Holling-Tanner model where we implement Holling type IV functional response to characterize grazing pattern of predators where prey species exhibit group defense. Additionally, we allow a modification in the attack rate of predators to quantify the hunting cooperation among them. The model admits three boundary equilibria and up to three coexistence equilibrium points. The geometry of the nontrivial prey and predator nullclines and thus the number of coexistence equilibria primarily depends on a specific threshold of the availability of alternative food for predators. We use linear stability analysis to determine the types of hyperbolic equilibrium points and characterize the non-hyperbolic equilibrium points through normal form and center manifold theory. Change in the model parameters leading to the occurrences of a series of local bifurcations from non-hyperbolic equilibrium points, namely, transcritical, saddle-node, Hopf, cusp and Bogdanov-Takens bifurcation; there are also occurrences of global bifurcations such as homoclinic bifurcation and saddle-node bifurcation of limit cycles. We observe two interesting closed 'bubble' form induced by global bifurcations due to change in the strength of hunting cooperation and the availability of alternative food for predators. A three dimensional bifurcation diagram, concerning the original system parameters, captures how the alternation in model formulation induces gradual changes in the bifurcation scenarios. Our model highlights the stabilizing effects of group or gregarious behaviour in both prey and predator, hence supporting the predator-herbivore regulation hypothesis. Additionally, our model highlights the occurrence of "saltatory equilibria" in ecological systems and capture the dynamics observed for lion-herbivore interactions.

A stochastic predator–prey eco-epidemiological model with hunting cooperation

Cooperative hunting can increase the predator’s hunting ability. In this work, we study a stochastic eco-epidemiological predator–prey model incorporating hunting cooperation. By constructing appropriate auxiliary functions, we establish a sufficient criterion for the existence of a unique ergodic stationary distribution. The findings imply that cooperative hunting has a significant effect on the density of infected predators when the epidemic is protracted.

Spatio-Temporal Steady-State Analysis in a Prey-Predator Model with Saturated Hunting Cooperation and Chemotaxis

Spatio-Temporal Steady-State Analysis in a Prey-Predator Model with Saturated Hunting Cooperation and Chemotaxis

Dynamics Behavior of a Predatorg-Prey Diffusion Model Incorporating Hunting Cooperation and Predator-Taxis

In this paper, we consider a predator-prey diffusion model incorporating hunting cooperation and predator-taxis. Firstly, we establish the global existence of a classical solution for the model in any spatial dimension. Secondly, we analyze the stability/instability caused by predator-taxis, and we observe that predator-taxis play a key role in inducing stability changes. Specifically, if the positive equilibrium is stable for the corresponding reaction-diffusion model, the attractive predator-taxis can further stabilize the system, while the repulsive predator-taxis may lead to a change in spatial stability, if the positive equilibrium is unstable for the corresponding reaction-diffusion model, the attractive predator-taxis makes the model remain unstable, while the repulsive predator-taxis has a stabilizing effect. Finally, numerical simulations are employed to validate the obtained results.

IMPACT OF HUNTING COOPERATION AND FEAR EFFECT IN A GENERALIST PREDATOR–PREY MODEL

Predator foraging facilitation or hunting cooperation and the antipredator behavior of prey are essential mechanisms in evolutionary biology and ecology and may strongly influence the predator–prey dynamics. In a real-world scenario, this behavioral tendency is well documented, but less is known about how it could affect the dynamics between predator and prey. Here, we investigate the impact of the fear of predator on prey and the hunting cooperation in predator on the predator–prey dynamics, where the predator is assumed to be of generalist type. We observe that without fear, even with the high level of hunting cooperation, both populations may coexist, though the increasing level of hunting cooperation reduces the prey density at coexistence equilibrium. Moreover, increasing level of fear also destabilizes the system with and without hunting cooperation. Further, in the presence of hunting cooperation and fear effect, the model shows three different types of bistability phenomena: bistability between two coexisting equilibria, bistability between coexisting equilibria and prey-free equilibrium, and bistability between stable limit cycle and coexisting equilibria. In addition, saddle-node, Hopf, transcritical bifurcation of codimension one, Bautin (generalized Hopf), Bogdanov–Takens, and cusp bifurcation of codimension two are observed.

Dyadic inter-group cooperation in shotgun hunting activities in a Congo Basin village.

Understanding the dynamics of inter-group cooperation in human adaptation has been the subject of recent empirical and theoretical studies in evolutionary anthropology, beginning to fill gaps in our knowledge of how interactions across political, economic and social domains can - and often do - lead to stable, large-scale cooperation. Here we investigate dyadic intergroup cooperation in shotgun hunting in the Republic of the Congo. In the Congo Basin, inter-group cooperation between foragers and farmers is at the centre of an exchange system maintained by traditional norms and institutions such as fictive kinship. Here, we focused on what factors predict cooperative shotgun hunting exchanges between BaYaka and Yambe. We conducted structured interviews with 48 BaYaka hunters and 18 Yambe men who organise hunts in a village along the Motaba River. We used Bayesian multilevel regression models to investigate the influence of Yambe and BaYaka attributes on probability of dyadic cooperation. We found that BaYaka men's reputations as skilled hunters and their family size each predicted cooperation in shotgun hunting, whereas there was no effect of Yambe attributes (status, wealth, family size). We discuss the results in terms of evolutionary models of men as hunters and inter-group cooperation, as well as biodiversity conservation implications.

BIFURCATION ANALYSIS OF A MODIFIED LESLIE–GOWER PREDATOR–PREY MODEL WITH HUNTING COOPERATION AND FAVORABLE ADDITIONAL FOOD FOR PREDATOR

In this paper, we consider a modified Lasslie–Gower-type predator–prey model with the effect of hunting cooperation and favorable additional food for predator. We establish the conditions of positivity, boundedness, and permanence of solutions of the proposed model. Along with the trivial, predator free, prey free equilibrium points the system contains at most two coexistence equilibrium points. The system experiences the transcritical, saddle-node, Hopf, cusp, Bautin, and Bogdanov–Takens bifurcation depending on the model parameters. All the theoretical analyses are verified using numerical simulations. It is numerically established that the cooperation and extra food have high impact on the model dynamics.

Effects of prey refuge and predator cooperation on a predator–prey system

ABSTRACT We develop and investigate a discrete-time predator–prey model with cooperative hunting among predators and a spatial prey refuge. The system can exhibit two positive equilibria if the magnitude of cooperation is large and the maximal reproduction number of predators is less than one. In such a scenario, the predator population may exhibit a strong Allee effect, and therefore the predator may survive if its density is above the threshold. When the positive equilibrium is unique, we prove that hunting cooperation can destabilize the equilibrium through a Neimark–Sacker bifurcation. Numerical findings indicate that a high degree of predator hunting cooperation can help rescue the predator population if the proportion of prey refuge is large, while hunting cooperation becomes destabilizing when the proportion of refuge is small. Despite hunting cooperation's destabilizing effect, it can facilitate predator persistence, particularly with a large proportion of prey refuge. Furthermore, there exists a wide parameter space where the predator–prey interaction may exhibit chaotic behaviour.

Dynamical behaviour of an intraguild predator–prey model with prey refuge and hunting cooperation

ABSTRACT An intraguild predator–prey model including prey refuge and hunting cooperation is investigated in this paper. First, for the corresponding ordinary differential equation model, the existence and stability of all equilibria are given, and the existence of Hopf bifurcation, direction and stability of bifurcating periodic solutions are investigated. Then, for partial differential equation model, the diffusion-driven Turing instability is obtained. What is more, the existence and non-existence of the non-constant positive steady state of the reaction–diffusion model are established by the Leray–Schauder degree theory and some priori estimates. Next, some numerical simulations are performed to support analytical results. The results showed that prey refuge can change the stability of model and even have a stabilizing effect on this model, meanwhile the hunting cooperation can make such model without diffusion unstable, but make such model with diffusion stable. Lastly, a brief conclusion is concluded in the last section.

Bifurcation in a delayed predator–prey model with Holling type IV functional response incorporating hunting cooperation and fear effect

Bifurcation in a delayed predator–prey model with Holling type IV functional response incorporating hunting cooperation and fear effect

Qualitative analysis for a diffusive predator-prey model with hunting cooperation and holling type III functional response

The Spatio-temporal pattern induced by self-diffusion of a predator-prey model with Boiling type III functional response that incorporates the hunting cooperation between predators has been investigated in this paper. For the local model without structure, the stability of non-negative equilibria with or without collaborative hunting in predators is studied. For the Spatio-temporal model, we analyze the effect of hunting cooperation term on diffusion-driven Turing instability of the homogeneous positive equilibria. To get an idea about patterns formation near the Turing bifurcation, we derive and give a detailed study of the amplitude equation using the multiple-scale analysis. Our result shows that hunting cooperation plays a crucial role in determining the stability and the Turing bifurcation of the model, which is in sharp contrast to the case without cooperation in hunting. Furthermore, some numerical simulations are illustrated to visualize the complex dynamic behavior of the model.

Promotion of cooperation mechanism on the stability of delay-induced host-generalist parasitoid model

Hunting cooperation widely exists in biological systems, which increases the possibility of the encounter between prey and predator populations. It is worth noting that predators are often divided into specialists and generalists. The research on considering cooperation mechanism in the specialist predator–prey model has received extensive attention. However, there is few attentions on the generalist predator–prey model. In this paper, we consider the classical delay-induced host-generalist parasitoid model to determine the impact of such a cooperation mechanism. Specifically, the existence and stability of the equilibria are studied without considering the delay factor. It is clearly proved that the system without delay is a stable system, where the cooperation mechanism will not cause instability. Further, to explore the potential role of the cooperation mechanism in the delay-induced system, we emphasize the dynamical variation induced by delay. We, therefore, investigate the underlying bifurcation properties under different cases, where the direction of Hopf bifurcation and stability of the periodic solutions are determined by the normal form theory and the center manifold theorem. Interestingly, a series of dynamical changes occur in the population, including periodic oscillation, irregular oscillation, and chaotic attractor when the double delays are introduced in both populations. Then through the numerical experiments, we examine the impacts of cooperation levels on the dynamic properties. Hence, it is conclusive that the cooperation mechanism will inhibit the generation of complex phenomena in the host-generalist parasitoid system, thereby promoting the stability of the biological system. The present study puts insights into the mechanism of predator cooperation in a more straightforward and practical manner.

Dynamics of a Leslie-Gower predator-prey system with hunting cooperation and prey harvesting

<p style='text-indent:20px;'>In this paper, we study the dynamics of a Leslie-Gower predator-prey system with hunting cooperation among predator population and constant-rate harvesting for prey population. It is shown that there are a weak focus of multiplicity up to three and a cusp of codimension at most two for various parameter values, and the system exhibits two saddle-node bifurcations, a Bogdanov-Takens bifurcation of codimension two and a Hopf bifurcation as the bifurcation parameters vary. The results developed in this article reveal far more complex dynamics compared to the Leslie-Gower system and show how the prey harvesting and the hunting cooperation affect the dynamics of the system. In particular, there exist some critical values of prey harvesting and hunting cooperation such that the predator and prey populations are at risk of extinction if the intensities of harvesting and hunting cooperation are greater than these critical values. Moreover, numerical simulations are presented to illustrate our theoretical results.</p>

A delay nonautonomous model for the impacts of fear and refuge in a three species food chain model with hunting cooperation

In this article, we study the dynamics of a three species food chain model for a predator–prey system with hunting cooperation in predators; due to fear of predation risk, prey population shows anti-predator behavior. Fear of middle-predator affects the growth rate of prey and the fear of top-predator reduces the predation of middle-predator on prey species. The prey and middle-predator are assumed to take refuge against predation. Numerical results confirm the stabilizing role of refuge whereas hunting cooperation destroys stability and induces limit cycle oscillations. We find that the fear of middle-predator on prey has tendency to stabilize the system while the fear of top-predator on middle-predator creates instability in the system. Further, time delays are considered in the processes of taking refuges and hunting cooperations. Delay in hunting cooperations creates multiple stability switches in the system. Furthermore, seasonal forcing of parameters related to refuges and hunting cooperations depicts a more realistic scenario. We investigate the behaviors of seasonally forced system in the absence as well as presence of time delays. The seasonally forced system exhibits different types of periodic solutions. Complex bursting patterns are observed due to periodicity in refuge of middle-predator (cooperation of top-predator).

Cooperation and opportunism in Galapagos sea lion hunting for shoaling fish.

For predators, cooperation can decrease the cost of hunting and potentially augment the benefits. It can also make prey accessible that a single predator could not catch. The degree of cooperation varies substantially and may range from common attraction to a productive food source to true cooperation involving communication and complementary action by the individuals involved. We here describe cooperative hunting of Galapagos sea lions (Zalophus wollebaeki) for Amberstripe scad (Decapterus muroadsi), a schooling, fast swimming semipelagic fish. A group of 6–10 sea lions, usually females only, drove scad over at least 600–800 m from open water into a cove where, in successful hunts, they drove them ashore. Frequently, these “core hunters” were joined toward the final stages of the hunt by another set of opportunistic sea lions from a local colony at that beach. The “core hunters” did not belong to that colony and apparently were together coming toward the area specifically for the scad hunt. Based on the observation of 40 such hunts from 2016 to 2020, it became evident that the females performed complementary actions in driving the scad toward the cove. No specialization of roles in the hunt was observed. All “core hunters” and also opportunistically joining sea lions from the cove shared the scad by randomly picking up a few of the 25–300 (mean 100) stranded fish as did scrounging brown pelicans. In one of these hunts, four individual sea lions were observed to consume 7–8 fish each in 25 s. We conclude that the core hunters must communicate about a goal that is not present to achieve joint hunting but presently cannot say how they do so. This is a surprising achievement for a species that usually hunts singly and in which joint hunting plays no known role in the evolution of its sociality.

Role of Allee effect in prey and hunting cooperation in a generalist predator

Cooperation is a very common phenomenon in the predator population. It can also be considered as one kind of Allee effect. By cooperation, we mean that the consumption rate per predator is dependent on the density of the predator. Despite a few recent studies the study of such systems is rare in the literature. It is well known from previous studies that incorporation of Allee effect in prey population enables the models to address many complex dynamical features. On the other hand, the dynamics of a generalist predator in a prey–predator system is also a very important area of research on populations. In this work, we concentrate on a model where Allee effect is incorporated in the prey growth in the presence of hunting cooperation in a generalist predator to observe how the Allee effect and the hunting cooperation affect the dynamics. Here we mainly study the stability and bifurcation of the system and hence describe the global dynamics to see how the Allee effect in prey and hunting cooperation affect the system dynamics.

COMPETITION AND COOPERATION ON PREDATION: BIFURCATION THEORY OF MUTUALISM

In this paper, we investigate two predator–prey models which take into consideration hunting cooperation (i.e., mutualism) between two different predators and within one predator species, respectively. Local and global dynamics are obtained for the model systems. By a detailed bifurcation analysis, we investigate the dependence of predation dynamics on mutualism (cooperative predation). From our study, we prove that mutualism may enhance the survival of mutualist predators in a severe condition and break the competitive exclusion principle. We further provide quantitative information about how the cooperative predation (mutualism) may (i) establish multiple stability switches on the positive equilibrium; (ii) generate backward bifurcation on equilibria; (iii) induce supercritical or subcritical Hopf bifurcations; and (iv) establish bi-stability phenomenon between the predator-free equilibrium and a positive equilibrium (or a limit cycle).

Traveling waves in cooperative predation: relaxation of sublinearity

In this paper, we investigate traveling wave solutions of a diffusive predator-prey model which takes into consideration hunting cooperation. Sublinearity condition is violated for the function of cooperative predation. When the basic reproduction number for the diffusion-free model is greater than one, we find a critical wave speed below which no positive traveling wave solution shall exist. On the other hand, if the wave speed exceeds this critical value, we prove the existence of a positive traveling wave solution connecting the predator-free equilibrium to the unique positive equilibrium under a technical assumption of weak cooperative predation. The key idea of the proof contains two major steps: (i) we construct a suitable pentahedron and find inside it a trajectory connecting the predator-free equilibrium; and (ii) we construct a suitable Lyapunov function and use LaSalle invariance principle to prove that the trajectory also connects the positive equilibrium. In the end of this paper, we propose five open problems related to traveling wave solutions in cooperative predation.

Bifurcations and organized structures in a predator-prey model with hunting cooperation

Abstract We report new organized structures in bi-parameter space for a nonlinear discrete predator-prey model with hunting cooperation. The intrinsic hunting cooperation among predator populations alters the dynamical behaviors of the model significantly. Especially, the stable periodic organized structures, viz. the Arnold tongues and shrimp-shaped structures in quasi-periodic and chaotic regimes exist near the boundary of Neimark-Sacker bifurcation for moderate values of the hunting cooperation parameter. Interestingly, these regular structures lead to different period-adding sequences. The transition to chaos via period-bubbling cascade near the inner boundaries of the shrimp-shaped structures is obtained. Shrimp structures maintain the universality of period 3-times self-similarity. Also, the coexistence of multiple periodic cycles and chaotic attractors with fractal basin boundaries are found owing to the hunting cooperation among the predators.