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Two parameter bifurcation diagram with respect to mutualism strength of prey (u = v) and predator cooperation strength (α x = α z = α). Parameter values are same as those used in Fig. 1
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Positive interactions are quite common in nature but are less studied.
While positive association among species has been studied in ecological literature, how such interactions will impact the ecological dynamics when they occur within antagonist communities is not understood. Motivated by this, we studied a community module consisting of two prey...
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In this paper, we propose a stage-structured predator-prey model with migrations among patches in an n-patch environment. The net reproduction number for each patch in isolation is obtained along with the net reproduction number of the system of patches, ℛ0. Inequalities describing the relationship among these numbers are also given. Furthermore, t...
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... They are considered to be analyzed through the existing mathematical models on prey-predator dynamics, comprised of logistic growth for prey and type II functional response on them by the predators (Sarwardi et al. 2012(Sarwardi et al. , 2013Antwi-Fordjour et al. 2020). We had introduced the mutual interference as a parameter in functional response (Sha et al. 2023;Chen et al. 2013;Banerjee et al. 2020), incorporating interference competition as a parameter. As in this system, three species interaction had been considered, two predators feeding on single prey species, which calls for interspecific competition between them. ...
Several models have been proposed as an extension to the classical Holling’s disc equation to evaluate the predator and prey interactions and their applied aspect in biological control and population regulation of the target organisms. In a one prey and two predator dynamic system with mutual interference (m) as a quadratic parameter of predator density, an evaluation was made to the resultant impact on the prey. A simulation was carried out to see the extinction of prey and the stability of the system at origin, i.e., when all the three species are extinct. We assumed the data obtained for the interactions between the mosquito and the water bug predators that are common in the freshwater wetlands and involved in the population regulation. Despite the benefits to prey population due to interference competition, the expected extinction of prey is still observed. With varying magnitudes of m the declining growth curve of prey population, shifted. The equation proposed was also compared with Crowley–Martin functional response, and considerable differences were observed in selected instances when compared for the growth rate of the predators, in a species-specific manner. The stability of the system was deduced with eigenvalues of Jacobian matrix at origin to prove the extinction is stable. Our assessment supports the possible cooccurrence of the predators and mosquito prey in the wetlands with the mutual interference being one of the major factors.
... We investigate how both the population dynamics of prey and social transmission of hunting strategies can influence the evolution of cooperative hunting. Only recently have predator-prey models begun to explore the implications of cooperative behavior (Fryxell et al., 2007;Berec, 2010;Alves and Hilker, 2017;Banerjee et al., 2020) and social learning (Borofsky and Feldman, 2022b,a;Kikuchi and Simon, 2023) for population dynamics. From data and modeling of lions (Panthera leo) and wildebeests (Connochaetes taurinus), Fryxell et al. (2007) suggested that cooperative hunting by lions decreases efficiency at hunting wildebeests, although these authors did not examine how population dynamics of lions interact with those of a prey type that cannot be hunted solitarily, such as Cape buffalo (Synserus caffer; Scheel and Packer, 1991). ...
... As the strength increases, the eco-epidemiological system experiences the onset and termination of limit cycles through a pair of Hopf bifurcations. Banerjee et al. [34] studied the effect of cooperative predation on mutualistic prey communities and revealed that the interplay between prey's mutualistic association and cooperative predation can give rise to an array of multistable dynamics depending on the ecological parameters. Here, we have depicted that cooperation itself can lead to cycle disappearance and eventually extinction of infected individuals. ...
Predator foraging facilitation is well-observed in predator-prey interactions and has been explored in ecological literatures. However, the impact of such behavioral pattern on the ecological dynamics with infection in prey species is less studied. Motivated by this, we contemplate the dynamics of a predator-prey model with infection in fearful prey in presence of cooperative behavior among predators.
Our results reconfirms the destabilizing effect of infection rate and the stabilizing effect of fear factor on the system dynamics. However, under different ecological conditions the infection rate causes the eco-epidemiological system to be sensitive to initial population size and vulnerable to small perturbations, as the proposed model supports multiple stable steady states. The fear-induced eco-epidemiological model potentially exhibits various types of bistability phenomena including bistability between the infection-free equilibrium and stable coexistence equilibrium, and bistability between population cycles and infection-free equilibrium depending upon the strength of cooperation, rate of infection and birth rate of healthy prey. We also observe the phenomenon of bubbling in the intermediate range of predator's intrinsic growth rate. The model predicts a high risk of catastrophic extinction of infected individuals around the homoclinic and saddle-node bifurcations resulting from a stronger strength of cooperative hunting among predators. The ecological theories developed in this work might provide a new insight to better understand the fate of an ecosystem involving parasites.
... There are also predators such as pikes [29], tigers, sharks [2,39], and other species that hunt individually. Many researchers have discussed the benefits of group hunting, including reducing hunting risks [3], increasing hunting efficiency [7], improving the ability to search for prey [5], reducing energy consumption [4,8,33], and so on. However, group hunting comes at a price: group members must share the prey they catch. ...
In this paper, we couple population dynamics and evolutionary game theory to establish a prey–predator system in which individuals in the predator population need to choose between group hunting strategies and isolated hunting strategies. This system includes two types of delay: fitness delay and hunting delay. In the absence of delays, we discuss the stability of boundary and interior equilibria. In addition, the condition that the non-delayed system undergoes transcritical bifurcation is obtained. For the delayed system, we explore the stability of the interior equilibrium and obtain the conditions for the existence of Hopf bifurcation. The conditions for determining the direction and stability of the Hopf bifurcation and the periodic variation in the periodic solution are introduced by using the normal form theory and center manifold theory. Finally, we simulate non-delayed and delayed systems. The results indicate that when the availability of prey is high, the isolated hunting strategy is the dominant strategy. When the availability of prey is low, mixed strategies appear and the proportion of the group hunting strategy increases as the availability of prey decreases. Furthermore, large delays lead to the disappearance of the mixed hunting strategy and its replacement by pure hunting strategies.
... Figures 1 and 4 ensuring the multistable dynamics exhibited by our model points out the vulnerability of the system to small perturbations. The presence of multistability and multiple operating regimes are essential for biology such as in prey-predator commuinities, biochemical responses and generation of cell cycle oscillation [92,93]. To clarify the understanding behind the multistability, particularly at the boundaries of the basin of attraction, mathematical analysis is found to be effective. ...
Ecology and evolution are inherently linked, and studying a mathematical model that considers both holds promise of insightful discoveries related to the dynamics of cooperation. In the present article, we use the prisoner's dilemma (PD) game as a basis for long-term apprehension of the essential social dilemma related to cooperation among unrelated individuals. We upgrade the contemporary PD game with an inclusion of evolution-induced act of punishment as a third competing strategy in addition to the traditional cooperators and defectors. In a population structure, the abundance of ecologically-viable free space often regulates the reproductive opportunities of the constituents. Hence, additionally, we consider the availability of free space as an ecological footprint, thus arriving at a simple eco-evolutionary model, which displays fascinating complex dynamics. As possible outcomes, we report the individual dominance of cooperators and defectors as well as a plethora of mixed states, where different strategies coexist followed by maintaining the diversity in a socio-ecological framework. These states can either be steady or oscillating, whereby oscillations are sustained by cyclic dominance among different combinations of cooperators, defectors, and punishers. We also observe a novel route to cyclic dominance where cooperators, punishers, and defectors enter a coexistence via an inverse Hopf bifurcation that is followed by an inverse period doubling route.
... Generally, ecological theory predicts that interaction with community-level associates stabilizes or enhances mutualism fitness (Banerjee et al. 2020;Chagnon et al. 2020;Jones et al. 2009; Morris et al. 2003). However, works estimating negative (Bachelot & Lee, 2020;Ferriere et al. 2002;Mougi & Kondoh, 2014) and neutral (Arizmendi et al. 1996;Bronstein, 2001) effects also exist, showcasing a presumed role for context dependence in the diversity of species assemblages. ...
... Compared to the pollinator, NPFWs infected with nematodes spend significantly more time infected, which may lead to more detrimental effects on longevity, dispersal ability and overall fitness. This prolonged interaction between nematodes and their 'incorrect' host provides important context that has been described to benefit mutualism fitness in theoretical models(Banerjee et al. 2020;Guimarães et al. 2017;Song et al. 2020). ...
Species pairs that form mutualistic associations are also components of broader organismal community networks. These interaction networks have shaped the evolution of individual mutualisms through interspecific interactions ranging from secondarily mutualistic to intensely antagonistic. Our understanding of this complex context remains limited because characterizing the impacts of species interacting with focal mutualists is often difficult. How is the fitness of mutualists impacted by the co‐occurring interactive network of community associates?
We investigated this context using a model interaction network comprised of a fig and fig wasp mutualist, eight non‐pollinating fig wasp (NPFW) antagonists/commensals and a nematode previously believed to be associated only with the pollinator wasp mutualist.
Through repeated sampling and field observations, we characterized the ecological roles of these mutualist‐associated organisms to identify key antagonists. We then investigated how potential nematode infection of NPFWs could impact wasp survival across key life stages and, in turn, inferred how this influences the fitness of the fig–pollinator mutualists.
Unexpectedly, we found all Ficus petiolaris‐associated NPFWs to be the targets for nematode infection, with infection levels sometimes exceeding that of pollinators. Experimental data collected for the most abundant NPFW species suggest that nematode infection significantly reduces their longevity. Further, comparisons of nematode loads for emerging and successfully arriving NPFWs suggest that infection severely limits their dispersal ability.
Through these observations, we conclude that this infection could impact NPFWs more severely than either mutualistic partner, suggesting a novel role of density‐dependent facultative mutualism between figs, pollinator wasps and the nematode. This antagonist‐mediated suppression of other network antagonists may present an ecologically common mechanism through which antagonists can present net benefits for mutualists' fitness.
... Cooperation has been studied in birds (Dickinson et al., 2009;Edelman & McDonald, 2014;Kaiser et al., 2019;McDonald, 1989;Wascher et al., 2019), boars (Focardi et al., 2015), dogs (Bauer & Smuts, 2007), hyenas (East & Hofer, 2002;Gersick et al., 2015;Smale et al., 1995;Smith et al., 2015;Smith et al., 2011), mongoose (Thompson et al., 2017), non-human primates (Benenson et al., 2019;Caselli et al., 2018;de Waal & Davis, 2003;Gilby et al., 2008;Hall & Brosnan, 2017;Hrdy, 2016;Silk, 2007;Willems & van Schaik, 2017), rats (Kozma et al., 2019;Wood et al., 2016) as well as many more animals. As cooperation continues to improve in various predators, both human and non-human, there is a concern that this will lead to extinction of prey due to more efficient hunting (Banerjee et al., 2020). ...
Cooperation has been one of the most foundational aspects of human society and is frequently studied via use of “The Stag Hunt” which has been used to tease out factors which may influence cooperation. The present study is the first study to attempt to influence human cooperation by means of positive imagery. Participants included 33 males and 72 females who listened to either a 7-minute audio designed to encourage them to trust others or an audio designed to encourage them to trust themselves. Participants played 40 rounds of the Stag Hunt game. The total number of times the participant played stag was recorded. An independent-samples t-test found a significant difference in the scores for the trust others (M= 21.47, SD=3.28) and the trust self (M=19.82, SD=3.92) conditions. This suggests guided imagery tasks may influence cooperation.
... [22] have shown that in a diffusive system the hunting cooperation acts as a positive influence on the coexistence of the two population. On the other hand a different observation is drawn in [3] for a model of mutualistic prey communities with two prey species and one predator. The authors have reported that both hunting cooperation and mutualism can lead a system to destabilization. ...
Cooperative hunting is a widespread phenomenon in the predator population which promotes the predation and the coexistence of the prey-predator system. On the other hand, the Allee effect among prey may drive the system to instability. In this work, we consider a prey-predator model with Type-III functional response involving the hunting cooperation in predator and Allee effect in the growth rate of the prey population. Here our aim mainly is to demonstrate the impact of both the Allee effect and hunting cooperation on the system dynamics. Mathematically our analysis primarily focuses on the stability of coexisting equilibrium points and all possible bifurcations that the system may exhibit. We have observed transcritical bifurcation, saddle-node bifurcation, Hopf-bifurcation, Bogdanov-Takens bifurcation and SN-TC bifurcation point respectively in the course of studying the global dynamics.
... Figs. 1 and 4 ensuring the multistable dynamics exhibited by our model points out the vulnerability of the system to small perturbations. The presence of multistability and multiple operating regimes are essential for biology such as in prey-predator communities, biochemical responses and generation of cell cycle oscillation (Angeli et al., 2004;Banerjee et al., 2020). To clarify the understanding behind the multistability, particularly at the boundaries of the basin of attraction, mathematical analysis is found to be effective. ...
Ecology and evolution are inherently linked, and studying a mathematical model that considers both holds promise of insightful discoveries related to the dynamics of cooperation. In the present article, we use the prisoner’s dilemma (PD) game as a basis for long-term apprehension of the essential social dilemma related to cooperation among unrelated individuals. We upgrade the contemporary PD game with an inclusion of evolution-induced act of punishment as a third competing strategy in addition to the traditional cooperators and defectors. In a population structure, the abundance of ecologically-viable free space often regulates the reproductive opportunities of the constituents. Hence, additionally, we consider the availability of free space as an ecological footprint, thus arriving at a simple eco-evolutionary model, which displays fascinating complex dynamics. As possible outcomes, we report the individual dominance of cooperators and defectors as well as a plethora of mixed states, where different strategies coexist followed by maintaining the diversity in a socio-ecological framework. These states can either be steady or oscillating, whereby oscillations are sustained by cyclic dominance among different combinations of cooperators, defectors, and punishers. We also observe a novel route to cyclic dominance where cooperators, punishers, and defectors enter a coexistence via an inverse Hopf bifurcation that is followed by an inverse period doubling route.
... One common method that scholars use to improve our understanding of environmental phenomena is the Lotka-Volterra (or predator-prey) model -an important and popular prototype model appearing in various fields of applied mathematics -due to its descriptive power, tractability and diverse applications [2,3,4,5,6,7,8,9]. Therefore, many efforts have been made so far to propose more realistic models incorporating mutualism [10,11], parasitism [12,13], and the impact of harvesting [14,15,16,17,18,19,20]. ...
... ). Consider characteristic equation (12), then the conditions that satisfies (11) are as follows. i) For = 1, the condition is 1 > 0. ii) For = 2, the conditions are either RH conditions or (11) is satisfied for all > (2∕3). ...
... i) For = 1, the condition is 1 > 0. ii) For = 2, the conditions are either RH conditions or (11) is satisfied for all > (2∕3). iv) If ( ) > 0, 1 < 0, 2 < 0, 3 > 0, then (11) is satisfied for all 0 < < 1. v) For general , > 0, is a necessary condition for (11). ...
We first present a predator-prey model for two species and then extend the model to three species where the two predator species engage in mutualistic predation. Constant effort harvesting and the impact of by-catch issue are also incorporated. Necessary sufficient conditions for the existence and stability of positive equilibrium points are examined. It is shown that harvesting is sustainable, and the memory concept of the fractional derivative damps out oscillations in the population numbers so that the system as a whole settles on an equilibrium quicker than it would with integer time derivatives. Finally, some possible physical explanations are given for the obtained results. It is shown that the stability requires the memory concept in the model.
