Exploring the dynamics of a Holling–Tanner model with cannibalism in both predator and prey population

2018 ◽  
Vol 11 (01) ◽  
pp. 1850010 ◽  
Author(s):  
Aladeen Al Basheer ◽  
Rana D. Parshad ◽  
Emmanuel Quansah ◽  
Shengbin Yu ◽  
Ranjit Kumar Upadhyay
Keyword(s):  
Prey Species ◽  
Joint Effect ◽  
Prey Population ◽  
Life History Trait ◽  
Spatially Explicit ◽  
Spatially Explicit Model ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Invasive Species Control ◽  
Predator Cannibalism

Cannibalism is an intriguing life history trait, that has been considered primarily in the predator, in predator–prey population models. Recent experimental evidence shows that prey cannibalism can have a significant impact on predator–prey population dynamics in natural communities. Motivated by these experimental results, we investigate a ratio-dependent Holling–Tanner model, where cannibalism occurs simultaneously in both the predator and prey species. We show that depending on parameters, whilst prey or predator cannibalism acting alone leads to instability, their joint effect can actually stabilize the unstable interior equilibrium. Furthermore, in the spatially explicit model, we find that depending on parameters, prey and predator cannibalism acting jointly can cause spatial patterns to form, while not so acting individually. We discuss ecological consequences of these findings in light of food chain dynamics, invasive species control and climate change.

scholarly journals A spatial theory for characterizing predator–multiprey interactions in heterogeneous landscapes

2015 ◽  
Vol 282 (1812) ◽  
pp. 20150973 ◽  
Author(s):  
Daniel Fortin ◽  
Pietro-Luciano Buono ◽  
Oswald J. Schmitz ◽  
Nicolas Courbin ◽  
Chrystel Losier ◽  
...  
Keyword(s):  
Prey Species ◽  
Landscape Heterogeneity ◽  
Spatially Explicit ◽  
Human Disturbances ◽  
Predator Prey ◽  
Heterogeneous Landscapes ◽  
Empirically Supported ◽  
Predator Interactions ◽  
Predator Prey Models ◽  
Species Specific

Trophic interactions in multiprey systems can be largely determined by prey distributions. Yet, classic predator–prey models assume spatially homogeneous interactions between predators and prey. We developed a spatially informed theory that predicts how habitat heterogeneity alters the landscape-scale distribution of mortality risk of prey from predation, and hence the nature of predator interactions in multiprey systems. The theoretical model is a spatially explicit, multiprey functional response in which species-specific advection–diffusion models account for the response of individual prey to habitat edges. The model demonstrates that distinct responses of alternative prey species can alter the consequences of conspecific aggregation, from increasing safety to increasing predation risk. Observations of threatened boreal caribou, moose and grey wolf interacting over 378 181 km 2 of human-managed boreal forest support this principle. This empirically supported theory demonstrates how distinct responses of apparent competitors to landscape heterogeneity, including to human disturbances, can reverse density dependence in fitness correlates.

A mathematical study of a predator–prey model with disease circulating in the both populations

2015 ◽  
Vol 08 (02) ◽  
pp. 1550015 ◽  
Author(s):  
Krishna Pada Das ◽  
J. Chattopadhyay
Keyword(s):  
Equilibrium Point ◽  
Prey Population ◽  
Global Dynamics ◽  
Predator Population ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Force Of Infection ◽  
Predator Prey Model ◽  
High Infection ◽  
Infected Prey

Disease in ecological systems plays an important role. In the present investigation we propose and analyze a predator–prey mathematical model in which both species are affected by infectious disease. The parasite is transmitted directly (by contact) within the prey population and indirectly (by consumption of infected prey) within the predator population. We derive biologically feasible and insightful quantities in terms of ecological as well as epidemiological reproduction numbers that allow us to describe the dynamics of the proposed system. Our observations indicate that predator–prey system is stable without disease but high infection rate drive the predator population toward extinction. We also observe that predation of vulnerable infected prey makes the disease to eradicate into the community composition of the model system. Local stability analysis of the interior equilibrium point near the disease-free equilibrium point is worked out. To study the global dynamics of the system, numerical simulations are performed. Our simulation results show that for higher values of the force of infection in the prey population the predator population goes to extinction. Our numerical analysis reveals that predation rates specially on susceptible prey population and recovery of infective predator play crucial role for preventing the extinction of the susceptible predator and disease propagation.

Time-delayed predator–prey interaction with the benefit of antipredation response in presence of refuge

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Sudeshna Mondal ◽  
Guruprasad Samanta
Keyword(s):  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Prey Population ◽  
Predator Prey ◽  
Terrestrial Vertebrates ◽  
Interior Equilibrium ◽  
Predator Prey Model ◽  
Refuge Area ◽  
Prey Interaction ◽  
Transcritical Bifurcations

AbstractA field experiment on terrestrial vertebrates observes that direct predation on predator–prey interaction can not only affect the population dynamics but the indirect effect of predator’s fear (felt by prey) through chemical and/or vocal cues may also reduce the reproduction of prey and change their life history. In this work, we have described a predator–prey model with Holling type II functional response incorporating prey refuge. Irrespective of being considering either a constant number of prey being refuged or a proportion of the prey population being refuged, a different growth rate and different carrying capacity for the prey population in the refuge area are considered. The total prey population is divided into two subclasses: (i) prey x in the refuge area and (ii) prey y in the predatory area. We have taken the migration of the prey population from refuge area to predatory area. Also, we have considered a benefit from the antipredation response of the prey population y in presence of cost of fear. Feasible equilibrium points of the proposed system are derived, and the dynamical behavior of the system around equilibria is investigated. Birth rate of prey in predatory region has been regarded as bifurcation parameter to examine the occurrence of Hopf bifurcation in the neighborhood of the interior equilibrium point. Moreover, the conditions for occurrence of transcritical bifurcations have been determined. Further, we have incorporated discrete-type gestational delay on the system to make it more realistic. The dynamical behavior of the delayed system is analyzed. Finally, some numerical simulations are given to verify the analytical results.

scholarly journals Density Dependent Delayed Migration for Rosenzweig-Macaurther Model with Holling Type II Predator Functional Response

2019 ◽  
pp. 1-12
Author(s):  
Samuel B. Apima ◽  
George O. Lawi ◽  
Nthiiri J. Kagendo
Keyword(s):  
Time Delay ◽  
Prey Species ◽  
Prey Population ◽  
Population Increase ◽  
Logistic Growth ◽  
Natural Habitats ◽  
Predator Prey ◽  
Density Dependent ◽  
Predator Prey Model ◽  
Predator Prey Models

The model describing the interaction between the predator and prey species is referred to as a predator-prey model. The migration of these species from one patch to another may not be instantaneous. This may be due to barriers such as a swollen river or a busy infrastructure through the natural habitat. Recent predator-prey models have either incorporated a logistic growth for the prey population or a time delay in migration of the two species. Predator-prey models with logistic growth that integrate time delays in density-dependent migration of both species have been given little attention. A Rosenzweig-MacAurther model with density-dependent migration and time delay in the migration of both species is developed and analyzed in this study. The Analysis of the model when the prey migration rate is greater than or equal to the prey growth rate, the two species will coexist, otherwise, at least one species will become extinct. A longer delay slows down the rate at which the predator and prey population increase or decrease, thus aecting the population density of these species. The prey migration due to the predator density does not greatly affect the prey density and existence compared to the other factors that cause the prey to migrate. These factors include human activities in the natural habitats like logging and natural causes like bad climatic conditions, limited food resources and overpopulation of the prey species in a patch among others.

scholarly journals Mathematical study on a dynamical predator-prey model with constant prey harvesting and proportional harvesting in predator

2021 ◽  
Author(s):  
Md Golam Mortuja ◽  
Mithilesh Kumar Chaube ◽  
Santosh Kumar
Keyword(s):  
Handling Time ◽  
Maximum Sustainable Yield ◽  
Prey Population ◽  
Sustainable Yield ◽  
Mathematical Study ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Predator Prey Model ◽  
Prey Model ◽  
Herd Behaviour

Abstract A dynamical predator-prey model with constant prey harvesting, proportional harvesting in predator has been studied. The square root func- tional response also has been incorporated in the system to describe the prey herd behaviour, assuming the average handling time is zero. The existence and the local stability of equilibria of the system have been discussed. It is examined that, two types of bifurcation occur in the system. The two types of bifurcations have been analyzed, and it has been found by analyzing the saddle-node bifurcation that, there is a maximum sustainable yield. It is ob- served that if harvesting rate is greater than the maximum sustainable yield, the prey population abolish from the system and then extinction of the preda- tor population happen. But if harvesting rate is lesser than the maximum sustainable yield, the extinction of the prey population can not be possible. By analyzing the Hopf bifurcation, it is obtained that, there exists an unstable limit cycle around the interior equilibrium point. Several numerical simulations are performed to check the results.

scholarly journals A predator-prey model with disease in prey

2013 ◽  
Vol 18 (2) ◽  
pp. 191-209 ◽  
Author(s):  
Md. Sabiar Rahman ◽  
Santabrata Chakravarty
Keyword(s):  
Hopf Bifurcation ◽  
Prey Species ◽  
Dynamical Behaviour ◽  
Point Of View ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Predator Prey Model ◽  
Prey Model ◽  
Predator Interactions ◽  
Disease In Prey

. The present investigation deals with the disease in the prey population having significant role in curbing the dynamical behaviour of the system of prey-predator interactions from both ecological and mathematical point of view. The predator-prey model introduced by Cosner et al. [1] has been wisely modified in the present work based on the biological point of considerations. Here one introduces the disease which may spread among the prey species only. Following the formulation of the model, all the equilibria are systematically analyzed and the existence of a Hopf bifurcation at the interior equilibrium has been duly carried out through their graphical representations with appropriate discussion in order to validate the applicability of the system under consideration

The population dynamics of bite-sized predators: prey dependence, territoriality, and mobility

2018 ◽  
Author(s):  
Xavier Lambin
Keyword(s):  
Prey Species ◽  
Top Down ◽  
Predator Prey ◽  
Biological Barrier ◽  
Reciprocal Interactions ◽  
Demographic Rates ◽  
Risk Of Predation ◽  
Increased Risk ◽  
Rodent Prey ◽  
Small Mustelids

The dependency of mustelid demographic rates on prey abundance has the potential to cause a strong coupling between predator-prey populations. Data on mustelid dynamics show that such strong reciprocal interactions only materialise in some restricted conditions. Bite-size mustelid predators searching for scarce, depleted prey expose themselves to increased risk of predation by larger predators of small mammal that are themselves searching for similar prey species. As voles or muskrats become scarcer, weasels and mink searching for prey over larger areas become increasingly exposed to intra-guild predation, unless they operate in a habitat refuge such as the sub-nivean space. Where larger predators are sufficiently abundant or exert year-round predation pressure on small mustelids, their impact on mustelids may impose biological barrier to dispersal that are sufficient to weaken the coupling between small mustelids and their rodent prey, and thus impose a degree of top down limitation on mustelids.

scholarly journals The Influence of Fear Effect to a Discrete-Time Predator-Prey System with Predator Has Other Food Resource

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 865
Author(s):  
Jialin Chen ◽  
Xiaqing He ◽  
Fengde Chen
Keyword(s):  
Discrete Time ◽  
Food Resource ◽  
Sufficient Conditions ◽  
Iteration Scheme ◽  
Predator Species ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Fear Effect ◽  
Prey System ◽  
Trivial Equilibrium

A discrete-time predator–prey system incorporating fear effect of the prey with the predator has other food resource is proposed in this paper. The trivial equilibrium and the predator free equilibrium are both unstable. A set of sufficient conditions for the global attractivity of prey free equilibrium and interior equilibrium are established by using iteration scheme and the comparison principle of difference equations. Our study shows that due to the fear of predation, the prey species will be driven to extinction while the predator species tends to be stable since it has other food resource, i.e., the prey free equilibrium may be globally stable under some suitable conditions. Numeric simulations are provided to illustrate the feasibility of the main results.

Three-dimensional predator–prey interactions: a computer simulation of bird flocks and aircraft

1986 ◽  
Vol 64 (11) ◽  
pp. 2624-2633 ◽  
Author(s):  
Peter F. Major ◽  
Lawrence M. Dill ◽  
David M. Eaves
Keyword(s):  
Computer Simulation ◽  
Prey Species ◽  
Three Dimensional ◽  
Aircraft Engine ◽  
Aquatic Environments ◽  
Aircraft Engines ◽  
Predator Prey ◽  
Simulation Techniques ◽  
Computer Simulation Techniques ◽  
Individual Prey

Three-dimensional interactions between grouped aerial predators (frontal discs of aircraft engines), either linearly arrayed or clustered, and flocks of small birds were studied using interactive computer simulation techniques. Each predator modelled was orders of magnitude larger than an individual prey, but the prey flock was larger than each predator. Expected numbers of individual prey captured from flocks were determined for various predator speeds and trajectories, flock–predator initial distances and angles, and flock sizes, shapes, densities, trajectories, and speeds. Generally, larger predators and clustered predators caught more prey. The simulation techniques employed in this study may also prove useful in studies of predator–prey interactions between schools or swarms of small aquatic prey species and their much larger vertebrate predators, such as mysticete cetaceans.The study also provides a method to study problems associated with turbine aircraft engine damage caused by the ingestion of small flocking birds, as well as net sampling of organisms in open aquatic environments.

scholarly journals On a Periodic Predator-Prey System with Holling III Functional Response and Stage Structure for Prey

2010 ◽  
Vol 2010 ◽  
pp. 1-12
Author(s):  
Xiangzeng Kong ◽  
Zhiqin Chen ◽  
Li Xu ◽  
Wensheng Yang
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Necessary Conditions ◽  
Stage Structure ◽  
Predator Prey ◽  
Prey System ◽  
Sufficient And Necessary Conditions ◽  
Holling Iii Functional Response

We propose and study the permanence of the following periodic Holling III predator-prey system with stage structure for prey and both two predators which consume immature prey. Sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained.

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