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Rolf O. Peterson - One of the best experts on this subject based on the ideXlab platform.
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Predicting Prey Population Dynamics from Kill Rate, Predation Rate and Predator-Prey Ratios in three Wolf-Ungulate Systems
Intermountain Journal of Sciences, 2012Co-Authors: Mark Hebblewhite, John A. Vucetich, Doug Smith, Rolf O. PetersonAbstract:Predation rate (PR), kill rate and predator-Prey ratios are all thought to be fundamental statistics for understanding and managing predation. However, relatively little is known about how these statistics explain Prey Population dynamics. We assess these relationships across three systems where wolf–Prey dynamics have been observed for 41 years (Isle Royale), 19 years (Banff) and 12 years (Yellowstone). Theoretical simulations indicate that kill rate can be related to PR in a variety of diverse ways that depend on the nature of predator–Prey dynamics. These simulations also suggested that the ratio of predator to-Prey is a good predictor of Prey growth rate. The empirical relationships indicate that PR is not well predicted by kill rate, but is better predicted by the ratio of predator-to-Prey. Kill rate is also a poor predictor of Prey growth rate. However, PR and predator-Prey ratio’s each explained significant portions of variation in Prey growth rate for two of the three study sites. Our analyses offer two general insights. First, it remains difficult to judge whether to be more impressed by the similarities or differences among these 3 study areas. Second, our work suggests that kill rate and PR are similarly important for understanding why predation is such a complex process. We conclude with a review of potential management applications of predator-Prey ratio’s and the assumptions required to understanding Prey Population dynamics.
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predicting Prey Population dynamics from kill rate predation rate and predator Prey ratios in three wolf ungulate systems
Journal of Animal Ecology, 2011Co-Authors: John A. Vucetich, Mark Hebblewhite, Douglas W. Smith, Rolf O. PetersonAbstract:Summary 1. Predation rate (PR) and kill rate are both fundamental statistics for understanding predation. However, relatively little is known about how these statistics relate to one another and how they relate to Prey Population dynamics. We assess these relationships across three systems where wolf‐ Prey dynamics have been observed for 41 years (Isle Royale), 19 years (Banff) and 12 years (Yellowstone). 2. To provide context for this empirical assessment, we developed theoretical predictions of the relationship between kill rate and PR under a broad range of predator‐Prey models including predator-dependent, ratio-dependent andLotka-Volterradynamics. 3. The theoretical predictions indicate that kill rate can be related to PR in a variety of diverse ways (e.g. positive, negative, unrelated) that depend on the nature of predator‐Prey dynamics (e.g. structure of the functional response). These simulations also suggested that the ratio of predatorto-Prey is a good predictor of Prey growth rate. That result motivated us to assess the empirical relationship between the ratio andPrey growthrate foreachof thethree studysites. 4. The empirical relationships indicate that PR is not well predicted by kill rate, but is better predicted by the ratio of predator-to-Prey. Kill rate is also a poor predictor of Prey growth rate. However, PR and ratio of predator-to-Prey each explained significant portions of variation in Prey growthrate fortwoof thethree studysites. 5. Our analyses offer two general insights. First, Isle Royale, Banff and Yellowstone are similar insomuch as they allinclude wolves Preyingon largeungulates.However,they also differ in species diversityofpredatorandPreycommunities,exploitationbyhumansandtheroleofdispersal. Even with the benefit of our analysis, it remains difficult to judge whether to be more impressed by the similarities or differences. This difficulty nicely illustrates a fundamental property of ecological communities. Second, kill rate is the primary statistic for many traditional models of predation. However, our work suggests that kill rate and PR are similarly important for understanding why predation is such a complexprocess.
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Predicting Prey Population dynamics from kill rate, predation rate and predator–Prey ratios in three wolf‐ungulate systems
The Journal of animal ecology, 2011Co-Authors: John A. Vucetich, Mark Hebblewhite, Douglas W. Smith, Rolf O. PetersonAbstract:Summary 1. Predation rate (PR) and kill rate are both fundamental statistics for understanding predation. However, relatively little is known about how these statistics relate to one another and how they relate to Prey Population dynamics. We assess these relationships across three systems where wolf‐ Prey dynamics have been observed for 41 years (Isle Royale), 19 years (Banff) and 12 years (Yellowstone). 2. To provide context for this empirical assessment, we developed theoretical predictions of the relationship between kill rate and PR under a broad range of predator‐Prey models including predator-dependent, ratio-dependent andLotka-Volterradynamics. 3. The theoretical predictions indicate that kill rate can be related to PR in a variety of diverse ways (e.g. positive, negative, unrelated) that depend on the nature of predator‐Prey dynamics (e.g. structure of the functional response). These simulations also suggested that the ratio of predatorto-Prey is a good predictor of Prey growth rate. That result motivated us to assess the empirical relationship between the ratio andPrey growthrate foreachof thethree studysites. 4. The empirical relationships indicate that PR is not well predicted by kill rate, but is better predicted by the ratio of predator-to-Prey. Kill rate is also a poor predictor of Prey growth rate. However, PR and ratio of predator-to-Prey each explained significant portions of variation in Prey growthrate fortwoof thethree studysites. 5. Our analyses offer two general insights. First, Isle Royale, Banff and Yellowstone are similar insomuch as they allinclude wolves Preyingon largeungulates.However,they also differ in species diversityofpredatorandPreycommunities,exploitationbyhumansandtheroleofdispersal. Even with the benefit of our analysis, it remains difficult to judge whether to be more impressed by the similarities or differences. This difficulty nicely illustrates a fundamental property of ecological communities. Second, kill rate is the primary statistic for many traditional models of predation. However, our work suggests that kill rate and PR are similarly important for understanding why predation is such a complexprocess.
Joydev Chattopadhyay - One of the best experts on this subject based on the ideXlab platform.
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Backward bifurcation, oscillations and chaos in an eco-epidemiological model with fear effect
Journal of biological dynamics, 2019Co-Authors: Amar Sha, Sudip Samanta, Maia Martcheva, Joydev ChattopadhyayAbstract:This paper considers an eco-epidemiological model with disease in the Prey Population. The disease in the Prey divides the total Prey Population into two subclasses, susceptible Prey and infected Prey. The model also incorporates fear of predator that reduces the growth rate of the Prey Population. Furthermore, fear of predator lowers the activity of the Prey Population, which reduces the disease transmission. The model is well-posed with bounded solutions. It has an extinction equilibrium, susceptible Prey equilibrium, susceptible Prey-predator equilibrium, and coexistence equilibria. Conditions for local stability of equilibria are established. The model exhibits fear- induced backward bifurcation and bistability. Extensive numerical simulations show the presence of oscillations and occurrence of chaos due to fear induced lower disease transmission in the Prey Population.
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revealing the role of predator interference in a predator Prey system with disease in Prey Population
Ecological Complexity, 2015Co-Authors: Subhendu Chakraborty, B W Kooi, Barasha Biswas, Joydev ChattopadhyayAbstract:Abstract Predation on a species subjected to an infectious disease can affect both the infection level and the Population dynamics. There is an ongoing debate about the act of managing disease in natural Populations through predation. Recent theoretical and empirical evidence shows that predation on infected Populations can have both positive and negative influences on disease in Prey Populations. Here, we present a predator–Prey system where the Prey Population is subjected to an infectious disease to explore the impact of predator on disease dynamics. Specifically, we investigate how the interference among predators affects the dynamics and structure of the predator–Prey community. We perform a detailed numerical bifurcation analysis and find an unusually large variety of complex dynamics, such as, bistability, torus and chaos, in the presence of predators. We show that, depending on the strength of interference among predators, predators enhance or control disease outbreaks and Population persistence. Moreover, the presence of multistable regimes makes the system very sensitive to perturbations and facilitates a number of regime shifts. Since, the habitat structure and the choice of predators deeply influence the interference among predators, thus before applying predators to control disease in Prey Populations or applying predator control strategy for wildlife management, it is essential to carefully investigate how these predators interact with each other in that specific habitat; otherwise it may lead to ecological disaster.
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Revealing the role of predator interference in a predator–Prey system with disease in Prey Population
Ecological Complexity, 2015Co-Authors: Subhendu Chakraborty, Bob W. Kooi, Barasha Biswas, Joydev ChattopadhyayAbstract:Abstract Predation on a species subjected to an infectious disease can affect both the infection level and the Population dynamics. There is an ongoing debate about the act of managing disease in natural Populations through predation. Recent theoretical and empirical evidence shows that predation on infected Populations can have both positive and negative influences on disease in Prey Populations. Here, we present a predator–Prey system where the Prey Population is subjected to an infectious disease to explore the impact of predator on disease dynamics. Specifically, we investigate how the interference among predators affects the dynamics and structure of the predator–Prey community. We perform a detailed numerical bifurcation analysis and find an unusually large variety of complex dynamics, such as, bistability, torus and chaos, in the presence of predators. We show that, depending on the strength of interference among predators, predators enhance or control disease outbreaks and Population persistence. Moreover, the presence of multistable regimes makes the system very sensitive to perturbations and facilitates a number of regime shifts. Since, the habitat structure and the choice of predators deeply influence the interference among predators, thus before applying predators to control disease in Prey Populations or applying predator control strategy for wildlife management, it is essential to carefully investigate how these predators interact with each other in that specific habitat; otherwise it may lead to ecological disaster.
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Disease in Prey Population and body size of intermediate predator reduce the prevalence of chaos-conclusion drawn from Hastings-Powell model
Ecological Complexity, 2009Co-Authors: Krishna Pada Das, Samrat Chatterjee, Joydev ChattopadhyayAbstract:Abstract In ecology the disease in the Prey Population plays an important role in controlling the dynamical behaviour of the system. We modify Hastings and Powell’s (HP) [Hastings, A., Powell, T., 1991. Chaos in three-species food chain. Ecology 72 (3), 896–903] model by introducing disease in the Prey Population. The conditions for which the modified HP model system represents extinction, permanence or impermanence of Population are worked out. The modified model is analyzed to obtain different conditions for which the system exhibits stability around the biologically feasible equilibria. Through numerical simulations we display that the modified system enters into stable solutions depending upon the force of infection in Prey Population as well as body size of intermediate predator. Our results demonstrate that disease in Prey Population and body size of intermediate predator are the key parameters for controlling the chaotic dynamics observed in original HP model.
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infection in Prey Population may act as a biological control in ratio dependent predator Prey models
Nonlinearity, 2004Co-Authors: O Arino, El A Abdllaoui, Jilali Mikram, Joydev ChattopadhyayAbstract:A ratio-dependent predator-Prey model with infection in Prey Population is proposed and analysed. The behaviour of the system near the biological feasible equilibria is observed. The conditions for which no trajectory can reach the origin following any fixed direction or spirally are worked out. We investigate the criteria for which the system will persist. It is observed that the introduction of an infected Population in the classical ratio-dependent predator-Prey model may act as a biological control to save the Population from extinction.
Sapna Devi - One of the best experts on this subject based on the ideXlab platform.
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Effects of Prey refuge on a ratio-dependent predator–Prey model with stage-structure of Prey Population
Applied Mathematical Modelling, 2013Co-Authors: Sapna DeviAbstract:Abstract In this paper, a stage-structured predator–Prey model is proposed and analyzed to study how the type of refuges used by Prey Population influences the dynamic behavior of the model. Two types of refuges: those that protect a fixed number of Prey and those that protect a constant proportion of Prey are considered. Mathematical analyses with regard to positivity, boundedness, equilibria and their stabilities, and bifurcation are carried out. Persistence condition which brings out the useful relationship between Prey refuge parameter and maturation time delay is established. Comparing the conclusions obtained from analyzing properties of two types of refuges using by Prey, we observe that value of maturation time at which the Prey Population and hence predator Population go extinct is greater in case of refuges which protect a constant proportion of Prey.
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effects of Prey refuge on a ratio dependent predator Prey model with stage structure of Prey Population
Applied Mathematical Modelling, 2013Co-Authors: Sapna DeviAbstract:Abstract In this paper, a stage-structured predator–Prey model is proposed and analyzed to study how the type of refuges used by Prey Population influences the dynamic behavior of the model. Two types of refuges: those that protect a fixed number of Prey and those that protect a constant proportion of Prey are considered. Mathematical analyses with regard to positivity, boundedness, equilibria and their stabilities, and bifurcation are carried out. Persistence condition which brings out the useful relationship between Prey refuge parameter and maturation time delay is established. Comparing the conclusions obtained from analyzing properties of two types of refuges using by Prey, we observe that value of maturation time at which the Prey Population and hence predator Population go extinct is greater in case of refuges which protect a constant proportion of Prey.
Azhar A. Majeed - One of the best experts on this subject based on the ideXlab platform.
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The Dynamics and Analysis of Stage-Structured Predator-Prey Model Involving Disease and Refuge in Prey Population
Journal of Physics: Conference Series, 2020Co-Authors: Entsar M. Kafi, Azhar A. MajeedAbstract:Start your abstract here the objective of this paper is to study the dynamical behaviour of an eco-epidemiological system. A Prey-predator model involving infectious disease with refuge for Prey Population only, the (SI_) infectious disease is transmitted directly, within the Prey species from external sources of the environment as well as, through direct contact between susceptible and infected individuals. Linear type of incidence rate is used to describe the transmission of infectious disease. While Holling type II of functional responses are adopted to describe the predation process of the susceptible and infected predator respectively. This model is represented mathematically by the set of nonlinear differential equations. The existence, uniqueness and boundedness of the solution of this model are investigated. The local and global stability conditions of all possible equilibrium points are established. Finally, numerical simulation is used to study the global dynamics of the mode.
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The Dynamics and Analysis of Stage-Structured Predator-Prey Model With Prey Refuge and Harvesting Involving Disease in Prey Population
Communications in Mathematics and Applications, 2019Co-Authors: Azhar A. MajeedAbstract:In this paper, a mathematical model consisting of the Prey-predator model with SI infectious disease in Prey is proposed and analyzed. The model includes harvesting on the infected Prey Population, it is assume that the disease is not transmitted from Prey to predator. In addition, the disease spread by contact between susceptible individuals and infected individuals, the mature predator only can predate the susceptible and infected Prey which are outside refuge according to Lotka-Volterra type of functional response. While, the immature predator depends completely in it’s feeding on the mature predator. The existence, uniqueness and boundedness of the solution are discussed. The stability analysis of all possible equilibrium points is studied. Also, Lyapunove function is used to study the global dynamics of the model. Further, the effect of the disease, refuge and harvest on the dynamical of the system is discussed using numerical simulation.
John A. Vucetich - One of the best experts on this subject based on the ideXlab platform.
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Predicting Prey Population Dynamics from Kill Rate, Predation Rate and Predator-Prey Ratios in three Wolf-Ungulate Systems
Intermountain Journal of Sciences, 2012Co-Authors: Mark Hebblewhite, John A. Vucetich, Doug Smith, Rolf O. PetersonAbstract:Predation rate (PR), kill rate and predator-Prey ratios are all thought to be fundamental statistics for understanding and managing predation. However, relatively little is known about how these statistics explain Prey Population dynamics. We assess these relationships across three systems where wolf–Prey dynamics have been observed for 41 years (Isle Royale), 19 years (Banff) and 12 years (Yellowstone). Theoretical simulations indicate that kill rate can be related to PR in a variety of diverse ways that depend on the nature of predator–Prey dynamics. These simulations also suggested that the ratio of predator to-Prey is a good predictor of Prey growth rate. The empirical relationships indicate that PR is not well predicted by kill rate, but is better predicted by the ratio of predator-to-Prey. Kill rate is also a poor predictor of Prey growth rate. However, PR and predator-Prey ratio’s each explained significant portions of variation in Prey growth rate for two of the three study sites. Our analyses offer two general insights. First, it remains difficult to judge whether to be more impressed by the similarities or differences among these 3 study areas. Second, our work suggests that kill rate and PR are similarly important for understanding why predation is such a complex process. We conclude with a review of potential management applications of predator-Prey ratio’s and the assumptions required to understanding Prey Population dynamics.
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predicting Prey Population dynamics from kill rate predation rate and predator Prey ratios in three wolf ungulate systems
Journal of Animal Ecology, 2011Co-Authors: John A. Vucetich, Mark Hebblewhite, Douglas W. Smith, Rolf O. PetersonAbstract:Summary 1. Predation rate (PR) and kill rate are both fundamental statistics for understanding predation. However, relatively little is known about how these statistics relate to one another and how they relate to Prey Population dynamics. We assess these relationships across three systems where wolf‐ Prey dynamics have been observed for 41 years (Isle Royale), 19 years (Banff) and 12 years (Yellowstone). 2. To provide context for this empirical assessment, we developed theoretical predictions of the relationship between kill rate and PR under a broad range of predator‐Prey models including predator-dependent, ratio-dependent andLotka-Volterradynamics. 3. The theoretical predictions indicate that kill rate can be related to PR in a variety of diverse ways (e.g. positive, negative, unrelated) that depend on the nature of predator‐Prey dynamics (e.g. structure of the functional response). These simulations also suggested that the ratio of predatorto-Prey is a good predictor of Prey growth rate. That result motivated us to assess the empirical relationship between the ratio andPrey growthrate foreachof thethree studysites. 4. The empirical relationships indicate that PR is not well predicted by kill rate, but is better predicted by the ratio of predator-to-Prey. Kill rate is also a poor predictor of Prey growth rate. However, PR and ratio of predator-to-Prey each explained significant portions of variation in Prey growthrate fortwoof thethree studysites. 5. Our analyses offer two general insights. First, Isle Royale, Banff and Yellowstone are similar insomuch as they allinclude wolves Preyingon largeungulates.However,they also differ in species diversityofpredatorandPreycommunities,exploitationbyhumansandtheroleofdispersal. Even with the benefit of our analysis, it remains difficult to judge whether to be more impressed by the similarities or differences. This difficulty nicely illustrates a fundamental property of ecological communities. Second, kill rate is the primary statistic for many traditional models of predation. However, our work suggests that kill rate and PR are similarly important for understanding why predation is such a complexprocess.
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Predicting Prey Population dynamics from kill rate, predation rate and predator–Prey ratios in three wolf‐ungulate systems
The Journal of animal ecology, 2011Co-Authors: John A. Vucetich, Mark Hebblewhite, Douglas W. Smith, Rolf O. PetersonAbstract:Summary 1. Predation rate (PR) and kill rate are both fundamental statistics for understanding predation. However, relatively little is known about how these statistics relate to one another and how they relate to Prey Population dynamics. We assess these relationships across three systems where wolf‐ Prey dynamics have been observed for 41 years (Isle Royale), 19 years (Banff) and 12 years (Yellowstone). 2. To provide context for this empirical assessment, we developed theoretical predictions of the relationship between kill rate and PR under a broad range of predator‐Prey models including predator-dependent, ratio-dependent andLotka-Volterradynamics. 3. The theoretical predictions indicate that kill rate can be related to PR in a variety of diverse ways (e.g. positive, negative, unrelated) that depend on the nature of predator‐Prey dynamics (e.g. structure of the functional response). These simulations also suggested that the ratio of predatorto-Prey is a good predictor of Prey growth rate. That result motivated us to assess the empirical relationship between the ratio andPrey growthrate foreachof thethree studysites. 4. The empirical relationships indicate that PR is not well predicted by kill rate, but is better predicted by the ratio of predator-to-Prey. Kill rate is also a poor predictor of Prey growth rate. However, PR and ratio of predator-to-Prey each explained significant portions of variation in Prey growthrate fortwoof thethree studysites. 5. Our analyses offer two general insights. First, Isle Royale, Banff and Yellowstone are similar insomuch as they allinclude wolves Preyingon largeungulates.However,they also differ in species diversityofpredatorandPreycommunities,exploitationbyhumansandtheroleofdispersal. Even with the benefit of our analysis, it remains difficult to judge whether to be more impressed by the similarities or differences. This difficulty nicely illustrates a fundamental property of ecological communities. Second, kill rate is the primary statistic for many traditional models of predation. However, our work suggests that kill rate and PR are similarly important for understanding why predation is such a complexprocess.
