Convergence to stationary distributions in two-species stochastic competition models

DOI10.1007/BF00290639zbMath0717.92025OpenAlexW1978925861WikidataQ44860405 ScholiaQ44860405MaRDI QIDQ2639005

Stephen P. Ellner

Publication date: 1989

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00290639

zbMATH Keywords

sufficient conditionsirreducibilitycoexistencestochastic boundednessstrong continuityinvasibilityrandomly varying environmentconvergence to stationary distributionsnonlinear stochastic difference equationscontinuous componentslottery model with vacant spacestochastic two- species Ricker modeltwo species competing

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) (60J20) Applications of stochastic analysis (to PDEs, etc.) (60H30) Ecology (92D40)

Related Items (20)

Interacting coexistence mechanisms in annual plant communities: frequency-dependent predation and the storage effect ⋮ Persistence for stochastic difference equations: a mini-review ⋮ The age-structured lottery model ⋮ Quantifying and testing coexistence mechanisms arising from recruitment fluctuations ⋮ Age-structured population growth rates in constant and variable environments: a near equilibrium approach ⋮ Scale transition theory with special reference to species coexistence in a variable environment ⋮ Lifetime and reproduction of a marked individual in a two-species competition process ⋮ Environmental fluctuations and the maintenance of genetic diversity in age or stage-structured populations ⋮ Variation in moisture duration as a driver of coexistence by the storage effect in desert annual plants ⋮ The storage effect due to frequency-dependent predation in multispecies plant communities ⋮ General theory of competitive coexistence in spatially-varying environments. ⋮ Extinction times and size of the surviving species in a two-species competition process ⋮ Persistence in fluctuating environments ⋮ Contributions to nonstationary community theory ⋮ The storage effect due to frequency-dependent predation in multispecies plant communities ⋮ On the number of births and deaths during an extinction cycle, and the survival of a certain individual in a competition process ⋮ Coexistence, extinction, and optimal harvesting in discrete-time stochastic population models ⋮ A general theory of coexistence and extinction for stochastic ecological communities ⋮ The competitive exclusion principle in stochastic environments ⋮ Population models with environmental stochasticity

Cites Work

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• Modes of convergence of Markov chain transition probabilities
• The stabilizing effect of a random environment
• Invasibility and stochastic boundedness in monotonic competition models
• An ergodic theorem for evolution in a random environment
• Does environmental variability limit niche overlap?
• Markov Chains with Continuous Components

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