Spatially inhomogeneous population dynamics: beyond the mean field approximation

Omelyan, I. P.; Kozitsky, Yuri

doi:10.1088/1751-8121/ab2808

Cited by 15 publications

(36 citation statements)

References 59 publications

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“…In contrast, our results for this case show that both the invasion speed and the population size in the IBM are much lower than mean-field. It is possible that differences between our results and those of Omelyan and Kozitsky (2019) are due to differences between one-dimensional and two-dimensional versions of the model, or the impact of approximations inherent in the analysis based upon a moment closure approximation (Murrell et al, 2004).…”

Section: Discussionmentioning

confidence: 84%

“…The scenarios we have tested are similar to those investigated by Omelyan and Kozitsky (2019), who developed spatial moment dynamics approximation for the translationally dependent spatial stochastic logistic model in one spatial dimension. However, the solutions of Omelyan and Kozitsky (2019), particularly the speed of the invasion front, are yet to be tested against IBM simulations. Our individual-based simulations exhibit similar spatial structure to that predicted by Omelyan and Kozitsky (2019), i.e.…”

Section: Discussionmentioning

confidence: 99%

“…However, this limits the types of interactions and spatial structure that the model can support (Plank and Simpson, 2012). Omelyan and Kozitsky (2019) derived a spatial moments approximation for the translationally dependent version of the spatial stochastic logistic model in one dimension. They showed that the results differed significantly from the mean-field model, which neglects correlations among individual locations.…”

Section: Introductionmentioning

confidence: 99%

“…In this study, we investigate the dynamics of the spatial stochastic logistic model in the translationally dependent case. Similarly to Omelyan and Kozitsky (2019), we focus on the case where the population is initially confined to a subregion of the domain and subsequently invades via dispersal of individuals into previously unoccupied regions.…”

Section: Introductionmentioning

confidence: 99%

“…However, unlike Omelyan and Kozitsky (2019), we carry out individual-based simulations of the translationally dependent spatial stochastic logistic model and we work in a two-dimensional domain. We systematically investigate scenarios with different spatial scales for competition and dispersal, and compare them to predictions of the mean-field model.…”

Section: Introductionmentioning

confidence: 99%

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Small-scale spatial structure influences large-scale invasion rates

Plank

Simpson

Binny³

2019

Preprint

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Local interactions among individual members of a population can generate intricate spatial structure, which can strongly influence population dynamics. The two-way interplay between local interactions and population dynamics is well understood in the relatively simple case where the population occupies a fixed domain with a uniform average density. However, the situation where the average population density is spatially varying is less well understood. This situation includes ecologically important scenarios such as species invasions, range shifts, and moving population fronts. Here, we investigate the dynamics of the spatial stochastic logistic model in a scenario where an initially confined population subsequently invades new, previously unoccupied territory. This simple model combines densityindependent proliferation with dispersal, and density-dependent mortality via competition with other members of the population. We show that, depending on the spatial scales of dispersal and competition, either a clustered or a regular spatial structure develops over time within the invading population. In the short-range dispersal case, we observe a significant reduction in the invasion speed relative to standard predictions of the mean-field model. We conclude that mean-field models, even when they account for non-local processes such as dispersal and competition, can give misleading predictions for the speed of a moving invasion front.

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Section: Discussionmentioning

confidence: 84%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Small-scale spatial structure influences large-scale invasion rates

Plank

Simpson

Binny³

2019

Preprint

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Algorithm for numerical solutions to the kinetic equation of a spatial population dynamics model with coalescence and repulsive jumps

2020

Self Cite

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An algorithm is proposed for finding numerical solutions of a kinetic equation that describes an infinite system of point particles placed in $\mathbb {R}^{d} (d \geq 1)$ ℝ d ( d ≥ 1 ) . The particles perform random jumps with pair-wise repulsion in the course of which they can also merge. The kinetic equation is an essentially nonlinear and nonlocal integro-differential equation, which can hardly be solved analytically. The numerical algorithm which we use to solve it is based on a space-time discretization, boundary conditions, composite Simpson and trapezoidal rules, Runge-Kutta methods, and adjustable system-size schemes. We show that, for special choices of the model parameters, the solutions manifest unusual time behavior. A numerical error analysis of the obtained results is also carried out.

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Small-scale spatial structure influences large-scale invasion rates

2020

View full text Add to dashboard Cite

Local interactions among individual members of a population can generate intricate small-scale spatial structure, which can strongly influence population dynamics. The two-way interplay between local interactions and population dynamics is well understood in the relatively simple case where the population occupies a fixed domain with a uniform average density. However, the situation where the average population density is spatially varying is less well understood. This situation includes ecologically important scenarios such as species invasions, range shifts, and moving population fronts. Here, we investigate the dynamics of the spatial stochastic logistic model in a scenario where an initially confined population subsequently invades new, previously unoccupied territory. This simple model combines density-independent proliferation with dispersal, and density-dependent mortality via competition with other members of the population. We show that, depending on the spatial scales of dispersal and competition, either a clustered or a regular spatial structure develops over time within the invading population. In the short-range dispersal case, the invasion speed is significantly lower than standard predictions of the mean-field model. We conclude that mean-field models, even when they account for non-local processes such as dispersal and competition, can give misleading predictions for the speed of a moving invasion front.

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Spatially inhomogeneous population dynamics: beyond the mean field approximation

Cited by 15 publications

References 59 publications

Small-scale spatial structure influences large-scale invasion rates

Small-scale spatial structure influences large-scale invasion rates

Algorithm for numerical solutions to the kinetic equation of a spatial population dynamics model with coalescence and repulsive jumps

Small-scale spatial structure influences large-scale invasion rates

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