Effects of the probability of a predator catching prey on predator-prey system stability

한국응용곤충학회 2011 Journal of Asia-Pacific Entomology Vol. No.

To understand the effect of the probability of a predator catching prey, <TEX>$P_{catch}$</TEX>, on the stability of the predator-prey system, a spatially explicit lattice model consisting of predators, prey, and grass was constructed. The predators and prey randomly move on the lattice space, and the grass grows according to its growth probability. When a predator encounters prey, the predator eats the prey in accordance with the probability <TEX>$P_{catch}$</TEX>. When a prey encounters grass, the prey eats the grass. The predator and prey give birth to offspring according to a birth probability after eating prey or grass, respectively. When a predator or prey is initially introduced or newly born, its health state is set at a high given value. This health state decreases by one with every time step. When the state of an animal decreases to less than zero, the individual dies and is removed from the system. Population densities for predator and prey fluctuated significantly according to <TEX>$P_{catch}$</TEX>. System stability was characterized by the standard deviation <TEX>${\phi}$</TEX> of the fluctuation. The simulation results showed that <TEX>${\phi}$</TEX> for predators increased with an increase of <TEX>$P_{catch}$</TEX>; <TEX>${\phi}$</TEX> for prey reached a maximum at <TEX>$P_{catch}$</TEX>=0.4; and <TEX>${\phi}$</TEX> for grass fluctuated little regardless of <TEX>$P_{catch}$</TEX>. These results were due to the tradeoff between <TEX>$P_{catch}$</TEX> and the predator-prey encounter rate, which represents the degree of interaction between predator and prey and the average population density, respectively.

Effects of the probability of a predator catching prey on predator–prey system stability

이상희 한국응용곤충학회 2011 Journal of Asia-Pacific Entomology Vol.14 No.2

To understand the effect of the probability of a predator catching prey, Pcatch, on the stability of the predator–prey system, a spatially explicit lattice model consisting of predators, prey, and grass was constructed. The predators and prey randomly move on the lattice space, and the grass grows according to its growth probability. When a predator encounters prey, the predator eats the prey in accordance with the probability P_(catch_. When a prey encounters grass, the prey eats the grass. The predator and prey give birth to offspring according to a birth probability after eating prey or grass, respectively. When a predator or prey is initially introduced or newly born, its health state is set at a high given value. This health state decreases by one with every time step. When the state of an animal decreases to less than zero, the individual dies and is removed from the system. Population densities for predator and prey fluctuated significantly according to P_(catch). System stability was characterized by the standard deviation ϕ of the fluctuation. The simulation results showed that ϕ for predators increased with an increase of Pcatch; ϕ for prey reached a maximum at P_(catch)=0.4; and ϕ for grass fluctuated little regardless of P_(catch). These results were due to the tradeoff between P_(catch) and the predator–prey encounter rate, which represents the degree of interaction between predator and prey and the average population density, respectively.

Effects of the Prey Refuge Distribution on a Predator-Prey System

Sang-Hee Lee,Ohsung Kwon,송학수 한국물리학회 2016 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.68 No.6

The existence of prey refuges in a predator-prey system is known to be strongly related to the ecosystem’s stability. In this study, we explored how the prey refuge distribution affects the predator-prey system. To do so, we constructed a spatial lattice model to simulate an integrative predator (wolf) - prey (rabbit) - plant (grass) relationship. When a wolf (rabbit) encountered a rabbit (grass), the wolf (rabbit) tended to move to the rabbit (grass) for foraging while the rabbit tended to escape from the wolf. These behaviors were mathematically described by the degrees of willingness for hunting (H) and escaping (E). Initially, n refuges for prey were heterogeneously distributed in the lattice space. The heterogeneity was characterized as variable A. Higher values of A equate to higher aggregation in the refuge. We investigated the mean population density for different values of H, E, and A. To simply characterize the refuge distribution effect, we built an H-E grid map containing the population density for each species. Then, we counted the number of grids, N, with a population density 0.25. Simulation results showed that an appropriate value of A positively affected prey survival while values of A were too high had a negative effect on prey survival. The results were explained by using the trade-off between the staying time of the prey in the refuge and the cluster size of the refuge.

Effects of Hunting and Escaping Strategy of Predator and Prey on the Ecosystem

Sang-Hee Lee,Jung-Hee Cho 한국응용곤충학회 2013 한국응용곤충학회 학술대회논문집 Vol.2013 No.04

Understanding the predator-prey dynamics is essential to comprehend the ecosystem resilience and stability because ecosystems consist of dynamically interacting subsystems with predator-prey relationship. The relationship is likely to be of the predator and prey hunting-escaping strategy. Thus, to better understand the ecosystems, we should comprehend how the hunting and the escaping strategy affect the ecosystems. To do so, we constructed a spatially explicit lattice model to simulate the integrative predator-prey-plant relationships. When an individual simultaneously encounters its predator and/or prey, the individual should take priority between the two strategies. When the hunting (or escaping) strategy takes priority, we call it hunting preferred strategy, HPS, (or escaping preferred strategy, EPS). Each strategy was characterized by the willingness for each strategy. The degree of willingness was represented as H (for hunting) and E (for escaping). Higher value of H (or E) means stronger willingness for hunting (or escaping). We investigated the population density of each species for different values of H and E for HPS and EPS. The main conclusion that emerges from this study was that HPS plays a positive role in the ecosystem stability. In addition, we briefly discussed the development of the present model to be used to understand the predator-prey interaction in specific species.

Existence of non-constant positive solution of a diffusive modified Leslie-Gower prey-predator system with prey infection and Beddington DeAngelis functional response

Dawit Melese 한국전산응용수학회 2022 Journal of applied mathematics & informatics Vol.40 No.3

In this paper, a diffusive predator-prey system with Beddington DeAngelis functional response and the modified Leslie-Gower type predator dynamics when a prey population is infected is considered. The predator is assumed to predate both the susceptible prey and infected prey following the Beddington-DeAngelis functional response and Holling type II functional response, respectively. The predator follows the modified Leslie-Gower predator dynamics. Both the prey, susceptible and infected, and predator are assumed to be distributed in-homogeneous in space. A reaction-diffusion equation with Neumann boundary conditions is considered to capture the dynamics of the prey and predator population. The global attractor and persistence properties of the system are studied. The priori estimates of the non-constant positive steady state of the system are obtained. The existence of non-constant positive steady state of the system is investigated by the use of Leray-Schauder Theorem. The existence of non-constant positive steady state of the system, with large diffusivity, guarantees for the occurrence of interesting Turing patterns.

“Hidden” Warning Coloration: Predators Learn to aVoid Distasteful Prey with Hidden Conspicuous Display

Chang Ku Kang,Hyun Joon Cho,Sang im Lee,Piotr G. Jablonski 한국응용곤충학회 2013 한국응용곤충학회 학술대회논문집 Vol.2013 No.04

Defended (distasteful or toxic) prey are often characterized by conspicuous coloration and this phenomenon is called "aposematism". The main advantage of aposematism is that it promotes faster learning by predators to avoid the prey. Some defended prey species use a different strategy; they remain cryptic in the normal state, but display conspicuous aposematic signal (which is normally hidden) in response to a predator's approach/attack. This anti-predator strategy of a defended prey has not been well studied yet although it can theoretically give the benefits of both camouflage and aposematism. Here, we investigated the effectiveness of this ‘hidden-aposematic signal’ as a warning signal. Using wild tits (Parus minor) as predator and novel artificial prey models (which mimics wings of insects), we tested whether hidden conspicuous signal of a defended prey enhances the avoidance learning rate of predators and how does it compare with the typical conspicuous/non-conspicuous signal. We found that hidden conspicuous signal indeed enhances the avoidance learning rate of predators in comparison with the non-conspicuous signal. However the overall learning rate by predators to avoid the defended prey was slower than for the normal conspicuous signal. Our results suggest that the prey with hidden-aposematic signals could enjoy both the benefits camouflage and the benefits of aposematism that are however lower than benefits from a typical aposematic signal. We, for the first time, highlight the functional aspect of a unique, but yet largely ignored, defensive coloration of prey.

Effects of Predator and Prey Hunting and Escape Strategies on Ecosystem Dynamics

Jung-Hee Cho,이상희 한국물리학회 2014 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.64 No.5

Understanding of an ecosystem’s resilience and stability requires an understanding of predatorpreydynamics because ecosystems consist of dynamical interacting subsystems that includepredator-prey relationships. These relationships are closely related to the hunting-escaping strategiesemployed by the predator and prey. Therefore, understanding the effects of hunting andescaping strategies on ecosystems will lead to a better understanding of those systems. To thisend, we constructed a spatially explicit lattice model to simulate integrative predator-prey-plantrelationships. When an individual simultaneously encounters its predator and prey, either huntingor escaping should take priority. Hunting priority is referred to as a hunting preferred strategy(HPS), while escape priority is referred to as an escape preferred strategy (EPS). These strategiesare associated with some degree of willingness to either hunt (H) or escape (E). In our model, thewillingness of an individual to hunt or escape increased with increasing value of H or E, respectivelywe investigated changes in the predicted population densities for predator, prey, and plant specieswith changes in the values of H and E. Simulation results indicated that HPS positively contributedto ecosystem stability because those individuals that employed HPS had a greater chanceof reproduction than those that employed EPS. In addition, we briefly discuss the development ofour model as a tool for understanding behavioral strategies in specific predator-prey interactions.

Life traits and predatory potential of Antilochus coqueberti (Fab.) (Heteroptera: Pyrrhocoridae) against Dysdercus koenigii Fab.

K. Sahayaraj,S. Merin Fernandez 한국응용곤충학회 2017 Journal of Asia-Pacific Entomology Vol.20 No.4

The red cotton bug, Dysdercus koenigii Fab., and its specialized predator Antilochus coquebertii (Fab.), are among the most abundant insects in Asian cotton agro-ecosystems. To gauge the potential of using A. coquebertii to control D. koenigii in cotton, we tested the role of feeding on cotton leaves in development of the predator, prey stage preference and characterized the functional response of the predator to prey density under laboratory conditions. Antilochus coquebertii exhibited an active hunting strategy indicative of using both olfactory and visual orientation. Immature stages of the predator successfully developed and reproduced when offered D. koenigii or cotton leaves with D. koenigii. However, A. coquebertii nymphs failed to develop past the third instar when feeding on cotton leaves alone. The food regime did not significantly affect body size of the predator. Mated male and female adults live long when fed with D. koenigii. Total number of prey consumed by an adult predator during 15-days observation reveals not much deviation when offered D. koenigii or cotton leaves with D. koenigii. The adults of A. coquebertii killed a maximum of six D. koenigii adults per day, and were preying on D. koenigii populations in a density dependent manner (showed a type II functional response). We argue that A. coquebertii has considerable potential for the biological control of the red cotton bug D. koenigii.

Effects of perturbation on the predator–prey system in a heterogeneous landscape

이상희,전태수 한국응용곤충학회 2012 Journal of Asia-Pacific Entomology Vol.15 No.1

Environmental perturbations occur in ecosystems as the result of disturbance, which is closely related to ecosystem stability and resilience. To understand how perturbations can affect ecosystems, we constructed a spatially explicit lattice model to simulate the integrative predator–prey–grass relationships. In this model,a predator (or prey) gives birth to offspring, according to a specific birth probability, when it is able to feed on prey (or grass). When a predator or prey animal was initially introduced or newly born, its health state was set at a given high value. This state decreased by 1 with each time step. When the state of an animal decreased to zero, the animal was considered dead and was removed from the system. In this model, the perturbation was defined as the sudden death of some portion of the population. The heterogeneous landscape was characterized by a parameter, H, which controlled the degree of heterogeneity. When H≥0.6,the predator population size was positively influenced by the perturbation. However, the perturbation had little effect upon the population sizes of prey or grass, regardless of the value of H.

Hopf Bifurcation Properties of Holling Type Predator-prey Systems

심성아 한국수학교육학회 2008 純粹 및 應用數學 Vol.15 No.3

There have been many experimental and observational evidences which indicate the predator response to prey density needs not always monotone increasing as in the classical predator-prey models in population dynamics. Holling type functional response depicts situations in which sufficiently large number of the prey species increases their ability to defend or disguise themselves from the predator. In this paper we investigated the stability and instability property for a Holling type predator-prey system of a generalized form. Hopf type bifurcation properties of the non-diffusive system and the diffusion effects on instability and bifurcation values are studied.