Finding analytical approximations for discrete, stochastic, individual-based models of ecology

DOI10.1016/j.mbs.2023.109084arXiv2301.08094WikidataQ125099825 ScholiaQ125099825MaRDI QIDQ6063828

Linnéa Gyllingberg, David J. T. Sumpter, Åke Brännström

Publication date: 12 December 2023

Published in: Mathematical Biosciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2301.08094

zbMATH Keywords

approximationdifference equationsspatial correlationsspatial ecologyindividual-based modelsite-based model

Mathematics Subject Classification ID

Input-output approaches in control theory (93D25) Ecology (92D40) Applications of difference equations (39A60)

Cites Work

• Coupled map lattice approximations for spatially explicit individual-based models of ecology
• Individual-based competition between species with spatial correlation and aggregation
• Bottom-up derivation of discrete-time population models with the Allee effect
• From local interactions to population dynamics in site-based models of ecology
• On the derivation of reaction-diffusion equations as limit dynamics of systems of moderately interacting stochastic processes
• Does migration stabilize local population dynamics? Analysis of a discrete metapopulation model
• The importance of being discrete (and spatial)
• Using moment equations to understand stochastically driven spatial pattern formation in ecological systems
• Spatial moment description of birth-death-movement processes incorporating the effects of crowding and obstacles
• Spatially implicit plankton population models: transient spatial variability
• On moment closures for population dynamics in continuous space
• Moment approximation of individual-based models. Application to the study of the spatial dynamics of phytoplankton populations
• Bottom-up derivation of population models for competition involving multiple resources
• Propagation of chaos in neural fields
• Individual-based chaos: extensions of the discrete logistic model
• Aggregation, Blowup, and Collapse: The ABC's of Taxis in Reinforced Random Walks
• Stochastic Spatial Models
• How Reaction-Diffusion PDEs Approximate the Large-Population Limit of Stochastic Particle Models
• Mean Field Limits of Particle-Based Stochastic Reaction-Diffusion Models
• Spatially inhomogeneous population dynamics: beyond the mean field approximation
• Probabilistic Foundations of Spatial Mean-Field Models in Ecology and Applications

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