Population Dynamics with Threshold Effects Give Rise to a Diverse Family of Allee Effects

Fadai, Nabil T.; Simpson, Matthew J.

doi:10.1007/s11538-020-00756-5

Cited by 22 publications

(16 citation statements)

References 51 publications

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“…As an illustrative example of the nonidentifiability of the individual-level rates, let us consider a rioter growth rate that behaves akin to logistic growth (c.f. [43,47,55]):…”

Section: A Caveat On Individual-level Parameter Identifiabilitymentioning

confidence: 99%

“…One mathematical framework that is suitable for describing such individual-level interactions is by using stochastic agent-based models, whereby individuals (agents) interact with one another according to pre-defined processes on an underlying spatial grid. Such models have found great use in cell-level dynamics [39][40][41][42], ecology [43], and epidemic modelling [44,45].…”

Section: Introductionmentioning

confidence: 99%

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Agent-based modelling of sports riots

Clements,

Fadai

2021

Preprint

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Riots originating during, or in the aftermath of, sports events can incur significant costs in damages, as well as large-scale panic and injuries. A mathematical description of sports riots is therefore sought to better understand their propagation and limit these physical and financial damages. In this work, we present an agent-based modelling framework that describes the qualitative features of populations engaging in riotous behaviour. Agents, pertaining to either a 'rioter' or a 'bystander' sub-population, move on an underlying lattice and can either be recruited or defect from their respective subpopulation. In particular, we allow these individual-level recruitment and defection processes to vary with local population density. This agent-based modelling framework provides the unifying link between multi-population stochastic models and densitydependent reaction processes. Furthermore, the continuum description of this ABM framework is shown to be a system of nonlinear reaction-diffusion equations and faithfully agrees with the average ABM behaviour from individual simulations. Finally, we determine the unique correspondence between the underlying individual-level recruitment and defection mechanisms with their population-level counterparts, providing a link between local-scale effects and macroscale rioting phenomena.

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“…As an illustrative example of the nonidentifiability of the individual-level rates, let us consider a rioter growth rate that behaves akin to logistic growth (c.f. [43,47,55]):…”

Section: A Caveat On Individual-level Parameter Identifiabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Agent-based modelling of sports riots

Clements,

Fadai

2021

Preprint

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“…Mathematical models are a useful tool for studying the complex interplay between spatio-temporal variation in the tumour micro-environment and phenotypic heterogeneity and how this interplay impacts a tumours' growth dynamics and response to treatment. The critical role of space in shaping tumour composition and/or treatment outcome has been studied in previous works, where a wide range of mathematical formalisms has been used: from discrete agent based models [7,12,19,54,62,68] to continuum models of different degree of complexity [5,23,29,34,44,75]. In particular, phenotypic-structured models have been shown to be a useful tool for understanding intra-tumour phenotypic heterogeneity [2,16,17,25,39,45,47,63,67,75].…”

Section: Introductionmentioning

confidence: 99%

“…These models comprise partial integro-differential equations in which changes in the tumour heterogeneity are mediated by proliferation, competition and epigenetic mutations. Such frameworks have been used to understand how oxygen gradients shape metabolic heterogeneity [23,75] as well as the consequences of resistance to chemotherapy [46,76].…”

Section: Introductionmentioning

confidence: 99%

Spatio-temporal modelling of phenotypic heterogeneity in tumour tissues and its impact on radiotherapy treatment

Celora¹,

Byrne²

2021

Preprint

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We present a mathematical model that describes how tumour heterogeneity evolves in a tissue slice that is oxygenated by a single blood vessel. Phenotype is identified with the stemness level of a cell, s, that determines its proliferative capacity, apoptosis propensity and response to treatment. Our study is based on numerical bifurcation analysis and dynamical simulations of a system of coupled non-local (in phenotypic "space") partial differential equations that links the phenotypic evolution of the tumour cells to local oxygen levels in the tissue. In our formulation, we consider a 1D geometry where oxygen is supplied by a blood vessel located on the domain boundary and consumed by the tumour cells as it diffuses through the tissue. For biologically relevant parameter values, the system exhibits multiple steady states; in particular, depending on the initial conditions, the tumour is either eliminated ("tumour-extinction") or it persists ("tumourinvasion"). We conclude by using the model to investigate tumour responses to radiotherapy (RT), and focus on establishing which RT strategies can eliminate the tumour. Numerical simulations reveal how phenotypic heterogeneity evolves during treatment and highlight the critical role of tissue oxygen levels on the efficacy of radiation protocols that are commonly used clinically.

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“…In this study, we focus on the strong Allee effect since we are interested in exploring threshold effects and factors that influence the Allee threshold. Initial evidence for the Allee effect came from ecological systems for various plant and animal populations [6,[9][10][11][12][13][14][15], whereas more recent studies suggest a role for the Allee effect in populations of biological cells [16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Population dynamics with spatial structure and an Allee effect

Plank

Surendran

Simpson

2020

Preprint

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Allee effects describe populations in which long-term survival is only possible if the population density is above some threshold level. A simple mathematical model of an Allee effect is one where initial densities below the threshold lead to population extinction, whereas initial densities above the threshold eventually asymptote to some positive carrying capacity density. Mean field models of population dynamics neglect spatial structure that can arise through short-range interactions, such as short-range competition and dispersal. The influence of such non mean-field effects has not been studied in the presence of an Allee effect. To address this we develop an individual-based model (IBM) that incorporates both short-range interactions and an Allee effect. To explore the role of spatial structure we derive a mathematically tractable continuum approximation of the IBM in terms of the dynamics of spatial moments. In the limit of long-range interactions where the mean-field approximation holds, our modelling framework accurately recovers the mean-field Allee threshold. We show that the Allee threshold is sensitive to spatial structure that mean-field models neglect. For example, we show that there are cases where the mean-field model predicts extinction but the population actually survives and vice versa. Through simulations we show that our new spatial moment dynamics model accurately captures the modified Allee threshold in the presence of spatial structure.

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Population Dynamics with Threshold Effects Give Rise to a Diverse Family of Allee Effects

Cited by 22 publications

References 51 publications

Agent-based modelling of sports riots

Agent-based modelling of sports riots

Spatio-temporal modelling of phenotypic heterogeneity in tumour tissues and its impact on radiotherapy treatment

Population dynamics with spatial structure and an Allee effect

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