Spontaneous emergence of spatial patterns in a predator-prey model

Carneiro, M. V.; Charret, I. C.

doi:10.1103/physreve.76.061902

Cited by 11 publications

(6 citation statements)

References 24 publications

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“…We considered an individual-based predator–prey dynamic ecosystem that performed on a square lattice of linear size L with periodic spatial boundary conditions [ 3 , 4 , 8 , 9 , 13 ]. Each site can be either covered by a predator

, a prey

or empty

.…”

Section: Modelmentioning

confidence: 99%

“…However, the adaptation and evolution of organisms to the environment is unpredictable due to the sophisticated changes and the lengthy processes, but fortunately, we can make meaningful estimates of those processes by some means [ 1 , 2 ]. Monte Carlo simulation algorithm is one of the most important method to study the temporal and spatial characteristics of large-scale ecosystem [ 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 ]. Compared with the traditional population dynamics algorithm, the Monte Carlo simulation in two-dimensional space can reveal more details and spatio-temporal characteristics.…”

Section: Introductionmentioning

confidence: 99%

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Deep-Reinforcement Learning-Based Co-Evolution in a Predator–Prey System

Wang

Cheng

Wang

2019

Entropy

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Understanding or estimating the co-evolution processes is critical in ecology, but very challenging. Traditional methods are difficult to deal with the complex processes of evolution and to predict their consequences on nature. In this paper, we use the deep-reinforcement learning algorithms to endow the organism with learning ability, and simulate their evolution process by using the Monte Carlo simulation algorithm in a large-scale ecosystem. The combination of the two algorithms allows organisms to use experiences to determine their behavior through interaction with that environment, and to pass on experience to their offspring. Our research showed that the predators' reinforcement learning ability contributed to the stability of the ecosystem and helped predators obtain a more reasonable behavior pattern of coexistence with its prey. The reinforcement learning effect of prey on its own population was not as good as that of predators and increased the risk of extinction of predators. The inconsistent learning periods and speed of prey and predators aggravated that risk. The co-evolution of the two species had resulted in fewer numbers of their populations due to their potentially antagonistic evolutionary networks. If the learnable predators and prey invade an ecosystem at the same time, prey had an advantage. Thus, the proposed model illustrates the influence of learning mechanism on a predator-prey ecosystem and demonstrates the feasibility of predicting the behavior evolution in a predator-prey ecosystem using AI approaches.

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, a prey

or empty

.…”

Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Deep-Reinforcement Learning-Based Co-Evolution in a Predator–Prey System

Wang

Cheng

Wang

2019

Entropy

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“…Theoretical studies of the dynamics of these systems show a very rich behavior, like the existence of phase transitions from mixed to segregated states [4][5][6]; the spontaneous emergence of spatial patterns [3,7,8]; complexity [9,10]. Noise-induced effects are also frequently studied.…”

Section: Introductionmentioning

confidence: 99%

Ecological competition and the role of an apex predator

Camargo-Gamboa

Huerta-Quintanilla

Rodríguez-Achach

2010

Physica A: Statistical Mechanics and its Applications

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“…To interpret these difficult cases, models based on individuals are increasingly applied to biology [9]. Various individual-based schemes have been proposed [10][11][12][13][14][15][16][17][18][19][20][21]. For simulation studies, lattice models or patch-panel models are often adopted to introduce the migration of animals [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

A New Stochastic Individual-Based Model for Pattern Formation and its Application to Predator–Prey Systems

2008

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Reaction-diffusion theory has played a very important role in the study of pattern formation in biology. However, a group of individuals is described by a single state variable representing population density in reaction-diffusion models, and interaction between individuals can be included only phenomenologically. In this paper, we propose a new scheme that seamlessly combines individual-based models with elements of reaction-diffusion theory and apply it to predator-prey systems as a test of our scheme. In the model, starvation periods and the time to reproductive maturity are modeled for individual predators. Similarly, the life cycle and time to reproductive maturity of an individual prey are modeled. Furthermore, both predators and prey migrate through a two-dimensional space. To include animal migration in the model, we use a relationship between the diffusion and the random numbers generated according to a two-dimensional bivariate normal distribution. Despite the simplicity of this model, our scheme successfully produces logistic patterns and oscillations in the population size of both predator and prey. The peak for the predator population oscillation lags slightly behind the prey peak. The simplicity of this scheme will aid additional study of spatially distributed negative-feedback systems.

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Spontaneous emergence of spatial patterns in a predator-prey model

Cited by 11 publications

References 24 publications

Deep-Reinforcement Learning-Based Co-Evolution in a Predator–Prey System

Deep-Reinforcement Learning-Based Co-Evolution in a Predator–Prey System

Ecological competition and the role of an apex predator

A New Stochastic Individual-Based Model for Pattern Formation and its Application to Predator–Prey Systems

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