Predator-prey System Research Articles

Dynamics of the epidemiological Predator-Prey system in advective environments.

This paper aims to establish the existence of traveling wave solutions connecting different equilibria for a spatial eco-epidemiological predator-prey system in advective environments. After applying the traveling wave coordinates, these solutions correspond to heteroclinic orbits in phase space. We investigate the existence of the traveling wave solution connecting from a boundary equilibrium to a co-existence equilibrium by using a shooting method. Different from the techniques introduced by Huang, we directly prove the convergence of the solution to a co-existence equilibrium by constructing a special bounded set. Furthermore, the Lyapunov-type function we constructed does not need the condition of bounded below. Our approach provides a different way to study the existence of traveling wave solutions about the co-existence equilibrium. The existence of traveling wave solutions between co-existence equilibria are proved by utilizing the qualitative theory and the geometric singular perturbation theory. Some other open questions of interest are also discussed in the paper.

Propagation dynamics of a three-species nonlocal dispersal predator–prey system with two weak competing aborigine preys

This paper is concerned with the propagation dynamics of a three-species nonlocal dispersal predator–prey system with two weak competing aborigine preys. Precisely, our main concern is the invading process of an alien predator into the habitat of two aborigine preys, when two preys are weak competitors in the absence of predator. This invasion process can be characterized by the spreading speed of the predator as well as the traveling wave solutions connecting the predator-free state to other states. First, by applying Schauder’s fixed point theorem with the help of two pairs of upper and lower solutions, we prove that there exists a positive number [Formula: see text], when the wave speed is large than or equals to [Formula: see text], the system admits a traveling wave solution connecting the predator-free state to the co-existence state, which indicates the occurrence of invasion-coexistence phenomenon. Then the invading speed of the predator is investigated by using the comparison argument. Our results show that (i) the weak interspecific competition between two preys will not affect the phenomenon of invasive-coexistence; (ii) the invading speed of the predator coincides with the minimal wave speed [Formula: see text].

Exploring cooperative hunting dynamics and PRCC analysis: insights from a spatio-temporal mathematical model

The proposed mathematical model explores the intricate dynamics of a predator-prey system involving prey infection and cooperative hunting of predators. The model incorporates habitat complexity, emphasizing its influence on ecological interactions. The well-posedness of the system has rigorously been examined in a temporal setting and also conducted stability analysis. The bifurcation analysis reveals the existence of several local bifurcations on the system, namely transcritical bifurcation, saddle-node bifurcation, and Hopf bifurcation. Furthermore, these investigations delineate the two-dimensional bifurcations including Bogdanov–Takens and cusp bifurcations for different parametric combinations. With suitable choices of parameter values, the proposed model exhibits diverse dynamic phenomena, including bistable and tri-stable behavior. Latin hypercube sampling is utilized to conduct uncertainty analysis on input parameters, aiming to observe their effects on population dynamics. Subsequently, Kendall’s tau and Spearman’s rank correlation coefficients are also computed to investigate the impact of these uncertainties on the population. In the later part, a spatio-temporal system is proposed with two-dimensional diffusion terms to obtain the conditions for Turing instability. Numerical simulations have been conducted to observe the emergence of spatial patterns and the impact of predator cooperation in these patterns. The study provides valuable insights into the dynamics of complex ecological systems, emphasizing the interplay of spatial and temporal factors in shaping population dynamics and predator-prey interactions.

Hopf bifurcation and patterns formation in a diffusive two prey-one predator system with fear in preys and help

Recognizing the relationship between the spatial patterns in species concentrations and ecological heterogeneity is crucial for understanding demographics and species governance in a given domain, as ecological patterning processes are believed to be imitated in real ecosystems. In this present article, we have considered a two-prey-one-predator system with Holling type-II functional response where both the preys have fear of predator and compete in the absence of predator. Additionally, we have assumed that both the prey help each other when the predator attacks them. We have incorporated self-diffusion in this system under Neumann boundary conditions. The existence and stability conditions of different equilibria are discussed. We have studied the Hopf bifurcation around positive offset and derived the stability and direction of periodic solution. We have done a series of numerical simulations to ensure our theoretical finding. Diffusion-driven instability conditions are obtained. Different instability regions and fascinating patterns, such as spots, mixtures, and stripes, are depicted. Spatiotemporal dynamics also reflects that prey populations are located in isolated areas of low population concentration with increasing level of fear, whereas an increase in handling time forms lower-density stripes. But with increasing help, prey becomes more concentrated in some stripe regions. In the Hopf-Turing region, it is observed that the diffusion coefficient of predators can stabilize the system. Overall, pattern creation in predator-prey systems can help anticipate long-term system behaviour and analyze the influence of ecological factors on system dynamics.

Complex Dynamics and Bifurcations Analysis of Discrete-Time Modified Leslie–Gower System

This work introduces a discrete modified Leslie–Gower prey–predator system with Holling type-II functional response. The persistence of the discrete model under certain conditions is discussed. The conditions assuring the existence of fixed points are derived and nonlinear dynamics of system are explored at these fixed points. It has been shown that the system exhibits transcritical bifurcation and flip bifurcation at semi-trivial fixed point under certain bifurcation values. In addition, the center manifold and bifurcation theories are employed to attain the conditions for existence of flip and Neimark–Sacker bifurcations at coexistence fixed point. The system is found to exhibit periodic solutions along with bifurcations leading to wide range of chaotic dynamics. The numerical simulations are performed to confirm the analytical analysis.

Multiple stability switches and Hopf bifurcation in an age structured prey-predator system: effects of maturation and cooperative hunting delay

Multiple stability switches and Hopf bifurcation in an age structured prey-predator system: effects of maturation and cooperative hunting delay

Dynamics of a predator–prey system with foraging facilitation and group defense

Foraging facilitation and group defense are widespread phenomena in population ecosystem, which promote and prevent the predation in opposite processes respectively. In this work, a predator–prey system with foraging facilitation among predators and group defense in prey is proposed and investigated. To demonstrate the impact of both the foraging facilitation and the group defense on the system dynamics, the analysis primarily focuses on the qualitative properties of equilibria and possible bifurcations that the system may exhibit. It is shown that there are various non-hyperbolic equilibria for various parameter values such as the saddle–node, the weak focus of multiplicity at most three and the nilpotent cusp of codimension at most two as well as the system exhibits numerous kinds of bifurcation phenomena as the parameter values vary including the saddle–node bifurcation, the transcritical bifurcation, the pitchfork bifurcation, the Hopf bifurcation, the homoclinic bifurcation and the Bogdanov–Takens bifurcation. The results reveal that both foraging facilitation and group defense mechanisms play an important role in enriching the dynamics of predator–prey system and promoting the balance and diversity of ecosystem.

Dynamical behavior of a discrete-time predator–prey system incorporating prey refuge and fear effect

This paper explores the effects of fear and refuge in a discrete-time two species predator–prey model. The fraction of prey that seeks refuge is assumed to be proportional to the amount of predators. The local stability of the corresponding fixed points is analyzed. The conditions of flip bifurcation and Neimark–Sacker bifurcation at the positive fixed point are described. The sufficient conditions for the positive fixed point to be globally asymptotically stable are derived in this article. Utilization of hybrid control strategy stabilizes the system’s chaotic nature. Finally, the paper supports the theoretical analysis with a numerical simulation that demonstrates the intricate nature of the system. It is observed that both fear effect and prey refuge can destabilize or stabilize the system depending on the value of handling time. Also, fear effect can restore stability in the system that exhibits chaos due to a high prey growth rate.

Analytical solutions and physical interpretation of a predator–prey system with Allee effect using fractional derivative operators

This study investigates the dynamics of a predator–prey system by incorporating the Allee effect. The exact analytical solutions of the system are explored using the generalized exponential function method and the Bäcklund transformation approach. The system is discussed using Conformable, M-truncated, and Beta time fractional derivative operators to provide a physical interpretation. The effects of these derivative operators on the solutions are demonstrated through various 2D and 3D graphical simulations. Furthermore, the impacts of physical parameters on the model are analysed, providing valuable insights into the dynamics of Predator–prey systems with the Allee effect. Our obtained solutions differ from those in the literature, owing to the methodologies employed and the choice of differential operators utilized. Nevertheless, we believe that the comparisons presented for the differential operators are effective and beneficial.

Multiple Bifurcations and Chaos Control in a Coupled Network of Discrete Fractional Order Predator–Prey System

Multiple Bifurcations and Chaos Control in a Coupled Network of Discrete Fractional Order Predator–Prey System

Geographic variation in evolutionary rescue under climate change in a crop pest-predator system.

Species distribution models (SDMs) are often built upon the "niche conservatism" assumption, such that they ignore the possibility of "evolutionary rescue" and may underestimate species' future range limits under climate change. We select aphids and ladybirds as model species and develop an eco-evolutionary model to explore evolutionary rescue in a predator-prey system under climate change. We model the adaptive change of species' thermal performances, accounting for biotic interactions. Our study suggests that, without considering evolutionary adaptation, the warming climate will result in a reduction in aphid populations and the extinction of ladybirds in large parts of the United States. However, when incorporating evolutionary adaptation into the model, aphids can adapt to climate change, whereas ladybirds demonstrate geographic variation in their evolutionary rescue potential. Specifically, ladybirds in southern regions are more likely to be rescued than those in the north. In certain northern regions, ladybirds do not avoid extinction due to severe warming trends and seasonality of the climate. While higher warming trends do prompt stronger evolutionary changes in phenotype, they also lead to reduced aphid population abundance such that ecology constrains ladybird population growth. Higher seasonality induces an ecological effect by limiting the length of reproductive season, thereby reducing the capacity for evolutionary rescue. Together, these findings reveal the complex interplay between ecological and evolutionary dynamics in the context of evolutionary adaptation to climate change.

Counteractive effects of predator invasion and habitat destruction on predator-prey systems.

Alien species invasion and habitat destruction are among the primary threats to native animal communities, particularly for native predator-prey systems. However, when predator invasion and habitat destruction co-occur, it remains unclear whether their respective threats to native systems compensate each other or accumulate, as well as how these effects respond to the different characteristics of predator invasion and habitat destruction. In this study, we developed a spatially explicit simulation model with one prey species and one predator species and exposed it to invasive predators and habitat destruction with different properties. The results revealed the following insights: (1) Habitat destruction can compensate threats to native predator-prey systems from global predator invasion only when native predators possess predation capability similar to those of the invaders. In other scenarios, cumulative effects arise from predator invasion and habitat destruction. (2) Low levels of habitat destruction occurring at a faster rate, in conjunction with a substantial number of global invasive predators being present, can better compensate their respective threats to native predator-prey systems than the other scenarios. These findings provide valuable insights into situations where habitat destruction and alien species invasion coincide. They raise the question of whether we can leverage the interaction between them to reduce threats to biodiversity.

The relationship between clustering and networked Turing patterns.

Networked Turing patterns often manifest as groups of nodes distributed on either side of the homogeneous equilibrium, exhibiting high and low density. These pattern formations are significantly influenced by network topological characteristics, such as the average degree. However, the impact of clustering on them remains inadequately understood. Here, we investigate the relationship between clustering and networked Turing patterns using classical prey-predator models. Our findings reveal that when nodes of high and low density are completely distributed on both sides of the homogeneous equilibrium, there is a linear decay in Turing patterns as global clustering coefficients increase, given a fixed node size and average degree; otherwise, this linear decay may not always hold due to the presence of high-density nodes considered as low-density nodes. This discovery provides a qualitative assessment of how clustering coefficients impact the formation of Turing patterns and may contribute to understanding why using refuges in ecosystems could enhance the stability of prey-predator systems. The results link network topological structures with the stability of prey-predator systems, offering new insights into predicting and controlling pattern formations in real-world systems from a network perspective.

Local-manifold-distance-based regression: an estimation method for quantifying dynamic biological interactions with empirical time series.

Quantifying species interactions based on empirical observations is crucial for ecological studies. Advancements in nonlinear time-series analyses, particularly S-maps, are promising for high-dimensional and non-equilibrium ecosystems. S-maps sequentially perform a local linear model fitting to the time evolution of neighbouring points on the reconstructed attractor manifold, and the coefficients can approximate the Jacobian elements corresponding to interaction effects. However, despite that the advantages in nonlinear forecasting with noise-contaminated data, these methodologies have a limitation in the Jacobian estimation accuracy owing to non-equidistantly stretched local manifolds in the state space. Herein, we therefore introduced a local manifold distance (LMD) concept, a non-equidistant measure based on the multi-faceted state dependency. By integrating LMD with advanced computation techniques, we presented a robust and efficient analytical method, LMD-based regression (LMDr). To validate its advantages in prediction and Jacobian estimation, we analysed synthetic time series of model ecosystems with different noise levels and applied it to an experimental protozoan predator-prey system with established biological information. The robustness to noise was the highest for LMDr, which also showed a better correspondence to expected predator-prey interactions in the protozoan system. Thus, LMDr can be applied to study complex ecological networks under dynamic conditions.

Fifth-order A(α)-stable block hybrid adams-moulton method for solutions of predator-prey and Lorenz Systems

Problems associated with nonlinearity in predator-prey and chaotic nature embedded in Lorenz system place a significant challenge on numerical methods for their solutions. Some numerical methods may become unstable as step size increases. In this study, a fifth-order A(alpha )-stable (alpha = 89.90 ) k-step block hybrid Adams-Moulton method (BHAMM) was derived incorporating 16/9 as an off-step interpolation point using multistep collocation and matrix inversion technique. Choice of the off-step point of the BHAMM was in the upper part of interval of interpolation points. It was shown that the derived block method was consistent and zero-stable hence a convergent block method. Numerical simulations of predator-prey and Lorenz systems with the newly derived k=3 BHAMM indicated that it was adequate and compared well with Matlab ode23s.

Traumatism of Grey Wolf (<i>Canis Lupus</i>, Canidae, Carnivora) Skulls in the Center of the European Part of Russia

A total of 297 wolf skulls from the collection of the Central Forest State Biosphere Reserve were studied for the presence of injuries. Of these, 129 (43.4 ± 2.9%) skulls had traumas of various origins or a deformed sagittal crest. Aside from the sagittal crest, the rate of traumas was 32.3 ± 2.7%. Based on the causes of origin, the traumas were divided into three groups: those received when hunting moose, as a result of aggressive intraspecific contacts, and accidental. Complicated fractures of dental crowns predominate among accidental traumas. Moose hunting traumas and intraspecific aggression are more common in subadult wolves than in adults, this being explicable by the elimination of injured animals. The incidence of accidental traumas, on the other hand, was increased with age. The level of traumas serves as a population characteristic indicating tension in the predator-prey system and the degree of intraspecific aggression.

Avoiding visitors to a protected area increases predation risk for the endangered mountain gazelle

Abstract People's recreational activities in nature are essential to promote wildlife conservation. The interplay between humans and the environment is complex, as the presence of humans may impact wildlife both directly and by altering species interactions. Thus, conservation management in protected areas where people frequently interact with wildlife is challenging. We investigated the combined impact of different recreational activities of varying intensity, along with environmental and temporal factors, on the activity of the endangered mountain gazelle (Gazella gazella) and its predator, the golden Jackal (Canis aureus) in Ramat Hanadiv Nature Park—a protected area in northern Israel. We placed 109 camera traps in gazelles' activity centres over 5 years. We analysed the activity patterns of both species and how these patterns were affected by visitor activity. We found that gazelles became more nocturnal in areas with higher visitor activity, which led to greater overlap in their activity periods with golden Jackals. Both species were less active when there were more visitors in the park, but jackals were more attracted to disturbed areas, while gazelles avoided them. Furthermore, we found that gazelles' activity was primarily affected by visitor activity compared to environmental factors, study year or predator activity. Policy implications. We show direct and indirect effects of visitors on a predator–prey system and highlight the importance of understanding these impacts to manage protected areas and support human–wildlife coexistence. Read the free Plain Language Summary for this article on the Journal blog.

Bottom-up effects drive the dynamic of an Antarctic seabird predator-prey system.

Understanding how populations respond to variability in environmental conditions and interspecific interactions is one of the biggest challenges of population ecology, particularly in the context of global change. Although many studies have investigated population responses to climate change, very few have explicitly integrated interspecific relationships when studying these responses. In this study, we aimed to understand the combined effects of interspecific interactions and environmental conditions on the demographic parameters of a prey-predator system of three sympatric seabird populations breeding in Antarctica: the south polar skua (Catharacta maccormicki) and its two main preys during the breeding season, the Adélie penguin (Pygoscelis adeliae) and the emperor penguin (Aptenodytes forsteri). We built a two-species integrated population model (IPM) with 31 years of capture-recapture and count data and provided a framework that made it possible to estimate the demographic parameters and abundance of a predator-prey system in a context where capture-recapture data were not available for one species. Our results showed that predator-prey interactions and local environmental conditions differentially affected south polar skuas depending on their breeding state of the previous year. Concerning prey-predator relationships, the number of Adélie penguin breeding pairs showed a positive effect on south polar skua survival and breeding probability, and the number of emperor penguin dead chicks showed a positive effect on the breeding success of south polar skuas. In contrast, there was no evidence for an effect of the number of south polar skuas on the demography of Adélie penguins. We also found an important impact of sea ice conditions on both the dynamics of south polar skuas and Adélie penguins. Our results suggest that this prey-predator system is mostly driven by bottom-up processes and local environmental conditions.

Food quantity and quality modulates inducible defenses in a common predator–prey system

AbstractZooplankton displays different inducible defenses against invertebrate and vertebrate predators. The response pattern to gape‐limited invertebrate predators involves increased somatic growth and offspring body size but delayed maturity and reduced offspring numbers. In contrast to this general pattern, the freshwater model organism Daphnia magna has been reported to exhibit a different response when encountering the gape‐limited tadpole shrimp Triops cancriformis. Under laboratory conditions, D. magna showed increased somatic growth, earlier maturation, and an increase in both offspring number and size. We propose here that the discrepancy between the previously observed and the theory‐based response patterns against invertebrate predators is due to differences in food availability in the applied laboratory settings and assessed whether the defensive response of D. magna against T. cancriformis is modulated differently by food quantity and quality. We found a strong impact of food quantity and quality on the defense response of D. magna to T. cancriformis kairomones. The prey seem to be able to overcome trade‐offs between morphological defense traits and reproductive traits, but distinctly between high food quantity and high food quality. Thereby, reproductive traits were preferred over morphological defenses. Furthermore, the removal of particles from the T. cancriformis‐conditioned water caused a defense pattern in D. magna that was consistent with the general response pattern known from other invertebrate predators, thus explaining the described discrepancy to previous studies with T. cancriformis. Our study highlights the importance of assessing food‐related effects on predator–prey interactions to understand trophic relationships and food web processes.

Bifurcation Analysis and Spatiotemporal Dynamics in a Diffusive Predator–Prey System Incorporating a Holling Type II Functional Response

This study aims to investigate a diffusive predator–prey system incorporating additional food for predators, prey refuge, fear effect, and its carry-over effects. For the temporal model, the well-posedness and persistence of the system have been discussed. We investigated the existence and the stability behavior of the various equilibria. Furthermore, we explored the bifurcations of codimension-1 including transcritical, saddle-node, and Hopf, concerning the crucial parameters. The system also presents codimension-2 bifurcations such as Bogdanov–Takens and cusp bifurcation along with the global homoclinic bifurcation. We observed the bubbling phenomena, which illustrate the fluctuations in the amplitudes of the periodic oscillations. For the spatiotemporal system, we established the non-negativity and boundedness of the solutions. We derived the conditions for the diffusion-driven instabilities in a confined region with Neumann boundary conditions. Extensive numerical simulations have been conducted to depict the various stationary patterns in Turing space. It is observed that incorporating cross-diffusion divides the bi-parametric plane into various sub-regions and dynamic patterns are analyzed in these different regions. The intricate spatiotemporal dynamics exhibited by prey–predator interactions are crucial for unraveling the intricacies within ecological systems.