Individual variability in dispersal and invasion speed

Morris, Aled; Börger, Luca; Crooks, Elaine

doi:10.48550/arxiv.1612.06768

Cited by 3 publications

(4 citation statements)

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“…Just after the submission of this paper, a paper by Moris et al [41] submitted concurrently and devoted to the analytical confirmation of Elliott and Cornell's numerical observations was brought to our attention. By applying's successfully Wang's framework, they obtained the existence of traveling waves as well as the spreading speed for the Cauchy problem.…”

Section: General Definition Of Multidimensional Kpp Nonlinearitymentioning

confidence: 99%

Non-cooperative Fisher–KPP systems: traveling waves and long-time behavior

Girardin

2017

Nonlinearity

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The solution to a problem left open in the original paper [1] and solved afterwards is presented. Additionally, a few conflicting notations and a typo are corrected. Extinction in the critical caseThe critical case λ PF (L) = 0, for which extinction still occurs, was unsolved at the time of writing [1]. It was solved later on thanks to a hint of Adrian Lam, who pointed out that the argument used to establish the upper estimates of [1, theorem 1.2] can actually be used again to solve the extinction case.Consequently, [1, theorem 1.3] should be corrected as follows. The conjecture following [1, theorem 1.3] and the discussion in [1, section 4.1.1] can now safely be ignored. Theorem (Extinction or persistence dichotomy).1. Assume λ PF (L) < 0. Then all bounded nonnegative classical solutions of (E KPP ) set in (0, +∞) × R converge asymptotically in time, exponentially fast, and uniformly in space to 0. 2. Assume λ PF (L) > 0. Then there exists ν > 0 such that all bounded positive classical solutions u of (E KPP ) set in (0, +∞) × R satisfy, for all bounded intervals I ⊂ R,ν1 N,1 .

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Section: General Definition Of Multidimensional Kpp Nonlinearitymentioning

confidence: 99%

Non-cooperative Fisher–KPP systems: traveling waves and long-time behavior

Girardin

2017

Nonlinearity

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“…It turns also out that c * ∞ coincides with the asymptotic speed of propagation of another system, recently studied in [10], describing the evolution of two densities that represent two parts of a population with different phenotypes. Such subpopulations are assumed to compete between each other, and to diffuse and grow each with its own rate.…”

Section: Introductionmentioning

confidence: 74%

“…Such subpopulations are assumed to compete between each other, and to diffuse and grow each with its own rate. A difference with (1.1) is that in [10] the two densities share the same environment and can mutate from one type to the other. The rates of mutation play the role of the exchange coefficients that in our system allow each of the densities to pass to the adjacent domain.…”

Section: Introductionmentioning

confidence: 99%

Coupled reaction-diffusion equations on adjacent domains

Berestycki,

Rossi,

Tellini

2019

Preprint

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We consider a reaction-diffusion system for two densities lying in adjacent domains of R N . We treat two configurations: either a cylinder and its complement, or two halfspaces. Diffusion and reaction heterogeneities for the two densities are considered, and an exchange occurs through the separating boundary.We study the long-time behavior of the solution, and, when it converges to a positive steady state, we prove the existence of an asymptotic speed of propagation in some specific directions. Moreover, we determine how such a speed qualitatively depends with respect to several parameters appearing in the model.In the case N = 2, we compare such properties to those studied in [6-9] for a model with a line representing a road of fast diffusion at the boundary of a half-plane, which can be seen as a singular limit of the problem studied here.

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“…This idea was already discussed in [10]. It has been used to study how dispersal polymorphism can affect the spreading speed of biological invasions [11,31]. Some very strong and interesting results on traveling waves, spreading speeds, and dynamics for Fisher-KPP models with switching or mutation are presented in [15,16,17].…”

Section: Introductionmentioning

confidence: 99%

Populations with individual variation in dispersal in heterogeneous environments: Dynamics and competition with simply diffusing populations

Cantrell

Cosner

2020

Sci. China Math.

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We consider a model for a population in a heterogeneous environment, with logistic-type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior has been observed in some natural systems. We study how environmental heterogeneity and the rates of switching and diffusion affect the persistence of the population. The reaction-diffusion systems in the models can be cooperative at some population densities and competitive at others. The results extend our previous work on similar models in homogeneous environments. We also consider competition between two populations that are ecologically identical, but where one population diffuses at a fixed rate and the other switches between two different diffusion rates. The motivation for that is to gain insight into when switching might be advantageous versus diffusing at a fixed rate. This is a variation on the classical results for ecologically identical competitors with differing fixed diffusion rates, where it is well known that "the slower diffuser wins".

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Individual variability in dispersal and invasion speed

Cited by 3 publications

References 0 publications

Non-cooperative Fisher–KPP systems: traveling waves and long-time behavior

Non-cooperative Fisher–KPP systems: traveling waves and long-time behavior

Coupled reaction-diffusion equations on adjacent domains

Populations with individual variation in dispersal in heterogeneous environments: Dynamics and competition with simply diffusing populations

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