ArticleScientific reports2017
Co-operation, Competition and Crowding: A Discrete Framework Linking Allee Kinetics, Nonlinear Diffusion, Shocks and Sharp-Fronted Travelling Waves.
Article in Scientific reports, 2017. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 14 papers.
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14 citing papers in PubMed.
- Modelling collective invasion with reaction-diffusion equations: When does domain curvature matter?Applied mathematics letters · 2025Article
- Discrete and continuous mathematical models of sharp-fronted collective cell migration and invasion.Royal Society open science · 2024Article
- Scaling relations for auxin waves.Journal of mathematical biology · 2022Article
- Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework.Proceedings. Mathematical, physical, and engineering sciences · 2022Article
- Learning differential equation models from stochastic agent-based model simulations.Journal of the Royal Society, Interface · 2021Article
- Travelling wave solutions in a negative nonlinear diffusion-reaction model.Journal of mathematical biology · 2020Article
- Population dynamics with spatial structure and an Allee effect.Proceedings. Mathematical, physical, and engineering sciences · 2020Article
- Unpacking the Allee effect: determining individual-level mechanisms that drive global population dynamics.Proceedings. Mathematical, physical, and engineering sciences · 2020Article
- Population Dynamics with Threshold Effects Give Rise to a Diverse Family of Allee Effects.Bulletin of mathematical biology · 2020Article
- Predicting population extinction in lattice-based birth-death-movement models.Proceedings. Mathematical, physical, and engineering sciences · 2020Article
- From a discrete model of chemotaxis with volume-filling to a generalized Patlak-Keller-Segel model.Proceedings. Mathematical, physical, and engineering sciences · 2020Article
- Bridging the gap between individual-based and continuum models of growing cell populations.Journal of mathematical biology · 2020Article
- Modelling collective cell migration: neural crest as a model paradigm.Journal of mathematical biology · 2020Article
- Spatial structure arising from chase-escape interactions with crowding.Scientific reports · 2019Article
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4 authors.
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Abstract
Invasion processes are ubiquitous throughout cell biology and ecology. During invasion, individuals can become isolated from the bulk population and behave differently. We present a discrete, exclusion-based description of the birth, death and movement of individuals. The model distinguishes between individuals that are part of, or are isolated from, the bulk population by imposing different rates of birth, death and movement. This enables the simulation of various co-operative or competitive mechanisms, where there is either a positive or negative benefit associated with being part of the bulk population, respectively. The mean-field approximation of the discrete process gives rise to 22 different classes of partial differential equation, which can include Allee kinetics and nonlinear diffusion. Here we examine the ability of each class of partial differential equation to support travelling wave solutions and interpret the long time behaviour in terms of the individual-level parameters. For the first time we show that the strong Allee effect and nonlinear diffusion can result in shock-fronted travelling waves. We also demonstrate how differences in group and individual motility rates can influence the persistence of a population and provide conditions for the successful invasion of a population.
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