Spatial Variability Enhances Species Fitness in Stochastic Predator-Prey Interactions

Dobramysl, Ulrich; Täuber, Uwe C.

doi:10.1103/physrevlett.101.258102

Cited by 30 publications

(64 citation statements)

References 31 publications

(44 reference statements)

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“…The underlying microscopic mechanism behind these effects is the presence of lattice sites with particularly low and hence favorable reaction rates which act as prey proliferation sites. In contrast, heterogeneity in the prey reproduction and predator death rates does not significantly affect the species populations [82]. Compared with spatial heterogeneity and quenched randomness, demographic variability plays a different role: Reaction efficiencies of predators and prey, η A and η B respectively, become traits associated with individuals of both species [83] as opposed to fixed, population-based properties.…”

Section: Random Environmental Influences Versus Demographic Variabilitymentioning

confidence: 96%

Stochastic population dynamics in spatially extended predator–prey systems

Dobramysl¹,

Mobilia²,

Pleimling³

et al. 2018

J. Phys. A: Math. Theor.

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116

117

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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.

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Section: Random Environmental Influences Versus Demographic Variabilitymentioning

confidence: 96%

Stochastic population dynamics in spatially extended predator–prey systems

Dobramysl¹,

Mobilia²,

Pleimling³

et al. 2018

J. Phys. A: Math. Theor.

Self Cite

116

117

View full text Add to dashboard Cite

show abstract

“…This finding is in remarkable contrast to some already well-studied systems such as the three-species cyclic competition model, wherein spatial extension and disorder crucially help to stabilize the system [43,44]. Even though we do not allow explicit nearest-neighbor 'hopping' of particles in the lattice simulation algorithm, there still emerges effective diffusion of prey particles followed by predators.…”

Section: The Quasi-stable Three-species Coexistence Regionmentioning

confidence: 63%

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

Chen

Dobramysl

Täuber

2018

Ecological Complexity

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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.

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“…In order to construct the mean-field rate equations for the LV model (1) one assumes that the populations of both species are well-mixed and distributed homogeneously, such that one can ignore spatial and temporal correlations and fluctuations. Since the predator population decreases exponentially with rate µ, the change of the predator population has to include the term −µa(t), where a(t) denotes the time-dependent spatially averaged density of species A.…”

Section: Mean-field Rate Equationsmentioning

confidence: 99%

Environmental versus demographic variability in stochastic predator–prey models

Dobramysl¹,

Täuber²

2013

J. Stat. Mech.

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Abstract. In contrast to the neutral population cycles of the deterministic meanfield Lotka-Volterra rate equations, including spatial structure and stochastic noise in models for predator-prey interactions yields complex spatio-temporal structures associated with long-lived erratic population oscillations. Environmental variability in the form of quenched spatial randomness in the predation rates results in more localized activity patches. Population fluctuations in rare favorable regions in turn cause a remarkable increase in the asymptotic densities of both predators and prey [1]. Very intriguing features are found when variable interaction rates are affixed to individual particles rather than lattice sites. Stochastic dynamics with demographic variability in conjunction with inheritable predation efficiencies generate non-trivial time evolution for the predation rate distributions, yet with overall essentially neutral optimization Keywords:• Population dynamics (Theory)• Models for evolution (Theory)• Mutational and evolutionary processes (Theory)• Stochastic particle dynamics (Theory)

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Spatial Variability Enhances Species Fitness in Stochastic Predator-Prey Interactions

Cited by 30 publications

References 31 publications

Stochastic population dynamics in spatially extended predator–prey systems

Stochastic population dynamics in spatially extended predator–prey systems

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

Environmental versus demographic variability in stochastic predator–prey models

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