Predator Populations Research Articles

Mathematical modeling and bifurcation analysis of a delayed eco-epidemiological model with disease in predator and linear harvesting

ABSTRACT This study proposes a three-dimensional prey-predator model with disease in predators, including the time delay due to the gestation of the predator population. The positive invariance of the solutions and the existence of equilibria in the proposed system have been explained. We also analyse the local stability of all feasible equilibrium points for the delayed and non-delayed systems. Additionally, the system’s Hopf bifurcation with regard to several parameters has been investigated. Further, the existence of periodic solutions through Hopf bifurcation is shown with respect to time delay, and it is also shown that time delay is crucial in order to control the dynamics of the system. Explicit formulas are presented to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solution using the normal form theory and the centre manifold theorem. The outcome of the theoretical investigation is ultimately validated through numerical simulation.

Perceptions and reality in fisher coexistence with aquatic predators in the Peruvian Amazon

AbstractHumans and large aquatic predators compete for fish and negative interactions are widely reported as ‘human–wildlife conflicts’. When aquatic predators are perceived to damage fisheries or fishing equipment, lethal control can occur. The perceptions and reality of damage are infrequently compared, but this relationship is key to determining how negative outcomes can be mitigated. We examine coexistence between people and six large aquatic piscivores (two caiman, two dolphins, two otters) in Amazonian Peru. We determine the extent of damage to fishing equipment caused by each species and compare this to the amount of damage perceived by fishers. Giant otter populations have recently recovered in some areas, so we expected different perceptions relating to experiences with otters. We trained fishers to complete fishing registers (n = 278, 1173 h of fishing) to record damage to nets by wildlife. We interviewed 302 people from three sites to determine perceptions of damage by predators, and attitudes towards giant otters. Rates of damage to nets reflected the presence and populations of different aquatic predators at each site, but when present, dolphins and caimans damaged nets more than otters, which rarely damaged nets. People living where giant otters had recently recovered perceived higher relative levels of damage to nets by them and had more negative attitudes about them, compared to people from areas where giant otters had been present for longer, aquatic predators were more abundant, and community resource management was longer‐established. Better knowledge and more experience with a species may lead to more accurate perceptions of damage and increased tolerance. Where humans and animals compete for natural resources, conflict mitigation rarely includes better resource management. If tolerance of predators is greater where predators are common, and resources have not been overexploited, resource management may yield greater gains for stakeholders than other commonly prescribed forms of mitigation.

Dietary experience alters predatory behavior of two ladybird species on tomato potato psyllid.

The tomato potato psyllid, Bactericera cockerelli, is an invasive pest in Australia, which can cause severe economic loss in the production of Solanaceous crops. As an invasive pest, B. cockerelli may also modify biotic interactions in Australian agricultural and native ecosystems. Resident generalist predators in an area may have the ability to utilize invasive pest species as prey but this will depend on their specific predatory behavior. The extent to which generalist predators learn from their previous dietary experience (i.e., whether they have used a particular species as prey before) and how this impacts subsequent prey choice will influence predator and prey population dynamics after invasion. In this study, one nonnative resident ladybird, Hippodamia variegata, and one native ladybird, Coccinella transversalis, were investigated. Dietary experience with B. cockerelli as a prey species significantly increased preference for the psyllid in a short term (6 h) Petri dish study where a choice of prey was given. Greater suppression of B. cockerelli populations by experienced ladybirds was also observed on glasshouse grown tomato plants. This was presumably due to altered prey recognition by experience. The result of this study suggest the potential to improve the impact of biological control agents on invasive pests by providing early life experience consuming the target species. It may prove valuable for developing improved augmentative release strategies for ladybirds to manage specific insect pest species.

Stability, bifurcation, and control: Modeling interaction of the predator-prey system with Alles effect

In this study, we investigate the resilience and bifurcation properties of a discrete-time predator-prey model incorporating an Allee effect, the transfer of prey to predator energy, and a necessary threshold for prey consumption prior to predator reproduction. The discrete-time formulation involves iteratively adjusting the predator and prey populations at distinct time steps. The model encompasses equations that depict the fluctuations in population sizes, considering processes like breeding, predation, death, and the influence of the Allee effects. The investigation results indicate that the system's boundary equilibrium goes through a period-doubling bifurcation. Moreover, when the system is in close proximity to the exclusive positive equilibrium influenced by the prey-predator population, it exhibits Neimark-Sacker bifurcations. It's worth noting that our observations suggest that the predator population might approach extinction or achieve a stable equilibrium when chaotic dynamics appear in the prey population. The validity of this phenomenon is confirmed using the Lyapunov exponents calculation, which verifies the range of diverse dynamic behaviors. The outcomes and analysis of this research offer intriguing insights in both mathematical and biological realms. Implementing methods for chaos control could be beneficial in stabilizing or mitigating the occurrence of chaotic dynamics. Additionally, the theoretical results are supported by numerical simulations, phase portraits, bifurcation diagrams, graphs depicting chaos control, and maximum Lyapunov exponent graphs.

Dynamics of a generalist predator–prey system with harvesting and hunting cooperation in deterministic/stochastic environment

In this investigation, we explore a predator–prey system characterized by generalist predators exhibiting cooperative behavior during hunting, subject to nonlinear harvesting rate. Employing a Beverton–Holt type functional response to capture the impact of additional food sources on predator growth, our numerical findings affirm the destabilizing influence of hunting cooperation, excessive predation, and supplementary food sources. Conversely, the system demonstrates stabilization in response to increased prey species growth. We unveil the occurrence of both forward and backward bifurcations in the system due to the predator growth attributed to additional food sources, contingent on the degree of hunting cooperation. To broaden the scope, we extend our proposed model to its stochastic counterpart, introducing environmental white noises. Our numerical results anticipate that higher intensities of white noises lead to fluctuations of greater amplitude, while smaller intensities exhibit a more modest impact. Additionally, we elucidate the dynamics of prey and predator populations through histogram plots. The theoretical and numerical insights derived from this study provide a deeper understanding of the intricate dynamics within predator–prey systems of ecological communities, emphasizing the significance of additional food sources for cooperative predators subject to harvesting in both constant and fluctuating environments.

Taxis-Driven Pattern Formation in Tri-Trophic Food Chain Model with Omnivory

The spatiotemporal dynamics of a three-component model of a food web are considered. The model describes the interactions between populations of resources, prey, and predators that consume both species. It assumes that the predator responds to the spatial change in the resource and prey densities by occupying areas where species density is higher (prey-taxis) and that the prey population avoids areas with a high predator density (predator-taxis). This work studies the conditions for the taxis-driven instability leading to the emergence of stationary patterns resulting from Turing instability and autowaves caused by wave instability. The existence of nonconstant positive steady states for the system is assessed through a rigorous bifurcation analysis. Meanwhile, the conditions for the existence of both types of instabilities are obtained by linear stability analysis. It is shown that the presence of cross-diffusion in the system supports the formation of spatially heterogeneous patterns. For low values of the resource-tactic and predator-tactic coefficients, Turing and wave instabilities coexist. The system undergoes only Turing instability for high levels of these parameters.

KONTROL OPTIMAL MODEL LESLIE-GOWER DENGAN PEMANENAN PADA POPULASI PREDATOR DAN PERLINDUNGAN PADA PREY

This paper studied the Leslie-Gower predator-prey model with the effects of prey refuge and linear harvesting on predator populations. Prey populations grow as a logistic model when there is no interaction with predators. The predator population is assumed to have economic value. Analysis of Bionomic and Harvesting Control have been studied further. The results showed that the protective effect of prey had an effect on harvesting activity in the population so that it affected profits in predatory harvests. Simulation of several calculations is given to purchase the analysis results

The Pelagic Species Trait Database, an open data resource to support trait-based ocean research

Trait-based frameworks are increasingly used for predicting how ecological communities respond to ongoing global change. As species range shifts result in novel encounters between predators and prey, identifying prey ‘guilds’, based on a suite of shared traits, can distill complex species interactions, and aid in predicting food web dynamics. To support advances in trait-based research in open-ocean systems, we present the Pelagic Species Trait Database, an extensive resource documenting functional traits of 529 pelagic fish and invertebrate species in a single, open-source repository. We synthesized literature sources and online resources, conducted morphometric analysis of species images, as well as laboratory analyses of trawl-captured specimens to collate traits describing 1) habitat use and behavior, 2) morphology, 3) nutritional quality, and 4) population status information. Species in the dataset primarily inhabit the California Current system and broader NE Pacific Ocean, but also includes pelagic species known to be consumed by top ocean predators from other ocean basins. The aim of this dataset is to enhance the use of trait-based approaches in marine ecosystems and for predator populations worldwide.

Dynamical behaviors of stochastic eco‐epidemic predator–prey model with Allee effect in prey and Lévy jump

In this paper, the dynamical behaviors of a stochastic eco‐epidemic predator–prey model with Lévy jump and Allee effect for prey population are investigated. First, the existence and uniqueness of the global positive solution are built. Then, the long‐term behaviors of the prey and predator populations are obtained. Furthermore, we demonstrate the stochastic ultimate boundedness of all species and the ergodic stationary distribution without Lévy jump. Finally, numerical examples are provided to support the theoretical analysis results.

Virome of Australia's most endangered parrot in captivity evidenced of harboring hitherto unknown viruses.

The impact of circulating viruses on the critically endangered, orange-bellied parrot (OBP) population can be devastating. The OBP already faces numerous threats to its survival in the wild, including habitat loss, predation, and small population impacts. Conservation of the wild OBP population is heavily reliant on supplementation using OBPs from a managed captive breeding program. These birds may act as a source for introduction of a novel disease agent to the wild population that may affect survival and reproduction. It is, therefore, essential to monitor and assess the health of OBPs and take appropriate measures to prevent and control the spread of viral infections. This requires knowledge of the existing virome to identify novel and emerging viruses and support development of appropriate measures to manage associated risk. By monitoring and protecting these animals from emerging viral diseases, we can help ensure their ongoing survival and preserve the biodiversity of our planet.

Demographic response of osprey within the lower Chesapeake Bay to fluctuations in menhaden stock

Forage fish support the largest fisheries in the world and play a vital role in marine food webs by transferring energy from plankton to consumers within higher trophic levels. Growing commercial demand for these species and concern for the impact of over harvest on predator populations has driven a paradigm shift in management objectives from maximizing economic return to the establishment of ecosystem-based limits on harvest rates. How well current harvest policy supports noncommercial species like piscivorous birds remains poorly understood. We investigated the relationship between osprey breeding performance within the lower Chesapeake Bay and a menhaden stock index during a period (1974-2021) when the menhaden index fluctuated over 35-fold. Reproductive rate (young/pair/year), brood provisioning (fish/10-h) and the proportion of menhaden in the diet all declined during the study period. Indicators of food stress including brood reduction and nest failure increased during the study period. The population transitioned from reproductive surplus (demographic source) to reproductive deficit (demographic sink). A significant relationship between reproductive rate and the menhaden index suggests that osprey population viability requires that the menhaden stock be restored to 1980s levels. Current ecological reference points based on the food requirements of predatory fish are unlikely to protect the osprey population. We suggest the establishment of menhaden or reproductive thresholds designed to allow osprey to meet demographic targets (1.15 young/pair/year).

Dynamics caused by the mean-reverting Ornstein–Uhlenbeck process in a stochastic predator–prey model with stage structure

There are many species that go through different life stages in nature, they have different ecological characteristics in different stages, besides, stochastic variation exists in the natural environment. Based on this biological phenomenon, we develop and investigate dynamics in a predator–prey system with stage structure and the mean-reverting Ornstein–Uhlenbeck processes. We prove that this system satisfies the existence and uniqueness of globally positive equilibrium. The sufficient conditions for the existence of a stationary Markov process in stochastic system are attained. We deal with explicit expression and the existence of density function of the system which make a great contribution to biological intrinsic essence for the system. In addition, the sufficient criteria for extinction of the predator populations is derived. Finally, numerical simulations are furnished to illustrate the analysis results.

Effect of weather parameters on pink bollworm damage and population of predators in Bt cotton in Central India

Effect of weather parameters on pink bollworm damage and population of predators in Bt cotton in Central India

Mathematical analysis of a predator-prey system with shared resource, climatic effects, and neural network insight

This research paper introduces a predator-prey system in which both organisms depend on a common sustenance source. In order to establish environmental dynamics that are more plausible, we integrated climatic effects on the predator population by implementing a sigmoidal function. The objective is to study the impact of climate on the population dynamics of interacting species by employing mathematical tools like stability analysis and Artificial Neural Networks. By employing meticulous mathematical analysis, we were able to ascertain the equilibrium points of the system and examine their stability on a global scale. Our investigation covered both diffusive and non-diffusive models, providing insight into the unique dynamical characteristics of each. Moreover, in order to leverage the capabilities of modern computational methods, a neural network strategy was implemented to analyses the system's complexities in greater detail. In conclusion, exhaustive diagrams were used to meticulously illustrate the effect of varying parameters, thereby providing invaluable insights into the behavior of the system under various conditions.

Direction and stability of Hopf bifurcation in an eco-epidemic model with disease in prey and predator gestation delay using Crowley-Martin functional response

<p>In this work, we have studied an eco-epidemic model using the Crowley-Martin functional response that includes disease in prey and gestation delay in the predator population. The model possesses three equilibria, namely the disease-free, Predator-free, and the interior equilibrium point. In addition, we examined the stability of the equilibrium points varying the infection rate and time delay parameter. Detailed analysis of Hopf bifurcation of the interior equilibrium point contains two situations: with delay and without delay. Moreover, we have studied the direction of the Hopf bifurcation and the stability of periodic solutions utilizing normal form theory and the center manifold theorem. It is emphasized that Hopf bifurcation occurs when the time delay exceeds the critical value and that the critical value of the delay is strongly impacted by the infection rate in prey. A detailed numerical simulation is provided to verify the analytical results.</p>

Hopf bifurcation and hybrid control of a delayed diffusive semi-ratio-dependent predator-prey model

<p>A delayed diffusive predator-prey system with nonmonotonic functional response subject to Neumann boundary conditions is introduced in this paper. First, we analyze the associated characteristic equation to research the conditions for local stability of the positive equilibrium point and the occurrence of Turing instability induced by diffusion in the absence of delay. Second, we provide conditions for the existence of Hopf bifurcation driven by time delay. By utilizing the normal theory and center manifold theorem, we derive explicit formulas for Hopf bifurcation properties such as direction and stability from the positive equilibrium. Third, a hybrid controller is added to the system. By judiciously adjusting the control parameters, we effectively enhance the stability domain of the system, resulting in a modification of the position of the Hopf bifurcation periodic solutions. Numerical simulations demonstrate the presence of rich dynamical phenomena within the system. Moreover, sensitivity analysis was conducted using Latin hypercube sampling (LHS)/partial rank correlation coefficient (PRCC) to explore the impact of parameter variations on the output of prey and predator populations.</p>

Stability analysis of fuzzy differential equation for prey–predator system underZ-number fuzzy and granular differentiability concept

The stability analysis is one of the basic problems in the field of system, prey–predator, production inventory control, signal processing etc. The goal of stability analysis for prey–predator and production inventory control model is to determine the region of the different variables and parameters at which the system is stable or unstable. This paper explores an uncertain prey–predator model where both prey and predator populations are fuzzy variables. Also we have considered all the prey–predator parameters of the system are imprecise. This fuzzy prey–predator model is converted to an equivalent crisp model using granular differentiability approach. The condition of local stability is obtained mathematically by analysis the eigenvalues of characteristic equation. And also we introduced a production inventory model as a case study of fuzzy dynamical system to illustrate the efficiency of the result and practical aspects.

Analysis of Predator–Prey Model With Inclusion of Temperature Variability in Prey Refugees

One of the central concerns in ecology is assessing the impact of environmental changes, such as global temperature shifts, on the dynamic interactions between predators and prey across diverse ecosystems. This study explores the relationship between prey and predator populations in the context of climate‐induced temperature changes. Utilizing linearization and the Lyapunov approach, we analyze the local and global stability of the system’s equilibrium points. Applying Sotomayor’s theorem, we further investigate the local bifurcation of the fixed points. Additionally, the persistence of the model system is studied. The ecological models developed in this research aim to explore the stability of these predator–prey systems and provide insights to prevent the decline of endangered species. Numerical simulations are conducted to study the impact of environmental changes on the proposed models. The simulation results indicate that the temperature dependence of the predator–prey population dynamics is directly proportional to the size of the reserved habitat area for the prey when the temperature is high. These findings suggest that the preservation of sufficient habitat reserves plays a crucial role in promoting the long‐term survival of species and stabilizing their ecological interactions.

A predator-prey fractional model with disease in the prey species.

In this paper, we study a generalized eco-epidemiological model of fractional order for the predator-prey type in the presence of an infectious disease in the prey. The proposed model considers that the disease infects the prey, causing them to be divided into two classes, susceptible prey and infected prey, with different density-dependent predation rates between the two classes. We propose logistic growth in both the prey and predator populations, and we also propose that the predators have alternative food sources (i.e., they do not feed exclusively on these prey). The model is evaluated from the perspective of the global and local generalized derivatives by using the generalized Caputo derivative and the generalized conformable derivative. The existence, uniqueness, non-negativity, and boundedness of the solutions of fractional order systems are demonstrated for the classical Caputo derivative. In addition, we study the stability of the equilibrium points of the model and the asymptotic behavior of its solution by using the Routh-Hurwitz stability criteria and the Matignon condition. Numerical simulations of the system are presented for both approaches (the classical Caputo derivative and the conformable Khalil derivative), and the results are compared with those obtained from the model with integro-differential equations. Finally, it is shown numerically that the introduction of a predator population in a susceptible-infectious system can help to control the spread of an infectious disease in the susceptible and infected prey population.

Stability Analysis of Prey-Predator Model Migration with Holling Type-III Response Function in The Presence of Competition and Toxicity

In this paper, we propose and investigate a prey-predator model with two zones contaminated with heavy metal toxicity, especially copper (Cu), which enter the reservation zone and the unreserved zone in the aquatic environment. The dynamics of the prey population in the ecosystem can migrate from the reservation zone to the unreserved zone or vice versa, while predators are assumed to look for prey in the unreserved zone. The dynamic behavior of the population is expressed as a system of differential equations based on food intake capacity and other factors. We introduce a predator population with a Holling type III predation response function, coupled with inter-specific competition among prey due to overlapping diets and assuming the prey is contaminated with copper metal toxicity. The presence of a positive equilibrium point, namely the interior equilibrium point, is analyzed and investigated for its stability using the Routh-Hurwitz stability test. Numerical simulations are carried out to verify the results of the analysis and dynamics of the system solution. The results of the analysis of the interior equilibrium point T3 in each case is a stable point. This indicates a change in the balance of prey populations and predator populations.