Environmental versus demographic variability in stochastic predator–prey models

Dobramysl, Ulrich; Täuber, Uwe C.

doi:10.1088/1742-5468/2013/10/p10001

Cited by 4 publications

(15 citation statements)

References 35 publications

(75 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, individuals are assigned their efficiencies at birth, drawn from a truncated Gaussian distribution centered around the parent's value of η. The ensuing coupled population and evolutionary dynamics of this system leads to an intriguing optimization of the efficiency distributions, shown in figure 10, which can also be approximated using an adapted multi-quasi-species mean-field approach [51]. Interestingly, the net effect on population densities of the evolutionary efficiency optimization is actually essentially neutral.…”

Section: Random Environmental Influences Versus Demographic Variabilitymentioning

confidence: 99%

Stochastic population dynamics in spatially extended predator–prey systems

Dobramysl¹,

Mobilia²,

Pleimling³

et al. 2018

J. Phys. A: Math. Theor.

124

117

View full text Add to dashboard Cite

Abstract. Spatially extended population dynamics models that incorporate demographic noise serve as case studies for the crucial role of fluctuations and correlations in biological systems. Numerical and analytic tools from non-equilibrium statistical physics capture the stochastic kinetics of these complex interacting manyparticle systems beyond rate equation approximations. Including spatial structure and stochastic noise in models for predator-prey competition invalidates the neutral Lotka-Volterra population cycles. Stochastic models yield long-lived erratic oscillations stemming from a resonant amplification mechanism. Spatially extended predator-prey systems display noise-stabilized activity fronts that generate persistent correlations. Fluctuation-induced renormalizations of the oscillation parameters can be analyzed perturbatively via a Doi-Peliti field theory mapping of the master equation; related tools allow detailed characterization of extinction pathways. The critical steadystate and non-equilibrium relaxation dynamics at the predator extinction threshold are governed by the directed percolation universality class. Spatial predation rate variability results in more localized clusters, enhancing both competing species' population densities. Affixing variable interaction rates to individual particles and allowing for trait inheritance subject to mutations induces fast evolutionary dynamics for the rate distributions. Stochastic spatial variants of three-species competition with 'rock-paper-scissors' interactions metaphorically describe cyclic dominance. These models illustrate intimate connections between population dynamics and evolutionary game theory, underscore the role of fluctuations to drive populations toward extinction, and demonstrate how space can support species diversity. Two-dimensional cyclic three-species May-Leonard models are characterized by the emergence of spiraling patterns whose properties are elucidated by a mapping onto a complex GinzburgLandau equation. Multiple-species extensions to general 'food networks' can be classified on the mean-field level, providing both fundamental understanding of ensuing cooperativity and profound insight into the rich spatio-temporal features and coarsening kinetics in the corresponding spatially extended systems. Novel space-time Stochastic population dynamics in spatially extended predator-prey systems 2 patterns emerge as a result of the formation of competing alliances; e.g., coarsening domains that each incorporate rock-paper-scissors competition games.

show abstract

Section: Random Environmental Influences Versus Demographic Variabilitymentioning

confidence: 99%

Stochastic population dynamics in spatially extended predator–prey systems

Dobramysl¹,

Mobilia²,

Pleimling³

et al. 2018

J. Phys. A: Math. Theor.

124

117

View full text Add to dashboard Cite

show abstract

“…External fluctuations in evolutionary games have been previously introduced by adding extrinsic noise to continuous model parameters [ 30 ], or by letting strategy space itself vary in time [ 31 ]. Environmental variability has also been the subject of investigation in predator–prey models [ 32 , 33 ].…”

Section: Introductionmentioning

confidence: 99%

Fixation in finite populations evolving in fluctuating environments

Ashcroft

Altrock

Galla

2014

J. R. Soc. Interface.

104

View full text Add to dashboard Cite

The environment in which a population evolves can have a crucial impact on selection. We study evolutionary dynamics in finite populations of fixed size in a changing environment. The population dynamics are driven by birth and death events. The rates of these events may vary in time depending on the state of the environment, which follows an independent Markov process. We develop a general theory for the fixation probability of a mutant in a population of wild-types, and for mean unconditional and conditional fixation times. We apply our theory to evolutionary games for which the payoff structure varies in time. The mutant can exploit the environmental noise; a dynamic environment that switches between two states can lead to a probability of fixation that is higher than in any of the individual environmental states. We provide an intuitive interpretation of this surprising effect. We also investigate stationary distributions when mutations are present in the dynamics. In this regime, we find two approximations of the stationary measure. One works well for rapid switching, the other for slowly fluctuating environments.

show abstract

“…with such demographic variability [31,37]. In that case, the system arrived at a final steady state with stable stationary positive species abundances.…”

Section: Model Descriptionmentioning

confidence: 98%

“…In the binned version, we may use the discretized form f ij = f (η i , η j ). Similarly, we have a reproduction probability function g ij for predator species B and h ij for the prey C. Finally, we assign the arithmetic mean λ ik = (η i + η k )/2 to set the effective predation interaction rate of predator i with prey k [31,37].…”

Section: Quasi-species Mean-field Equations and Numerical Solutionmentioning

confidence: 99%

Evolutionary dynamics and competition stabilize three-species predator–prey communities

Chen

Dobramysl

Täuber

2018

Ecological Complexity

View full text Add to dashboard Cite

We perform individual-based Monte Carlo simulations in a community consisting of two predator species competing for a single prey species, with the purpose of studying biodiversity stabilization in this simple model system. Predators are characterized with predation efficiency and death rates, to which Darwinian evolutionary adaptation is introduced. Competition for limited prey abundance drives the populations' optimization with respect to predation efficiency and death rates. We study the influence of various ecological elements on the final state, finding that both indirect competition and evolutionary adaptation are insufficient to yield a stable ecosystem. However, stable three-species coexistence is observed when direct interaction between the two predator species is implemented.

show abstract

Environmental versus demographic variability in stochastic predator–prey models

Cited by 4 publications

References 35 publications

Stochastic population dynamics in spatially extended predator–prey systems

Stochastic population dynamics in spatially extended predator–prey systems

Fixation in finite populations evolving in fluctuating environments

Evolutionary dynamics and competition stabilize three-species predator–prey communities

Contact Info

Product

Resources

About