Population dispersal and Allee effect

Wang, Wendi

doi:10.1007/s11587-016-0273-0

Cited by 12 publications

(5 citation statements)

References 33 publications

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“…This is of particular relevance when the local dynamics include a strong Allee effect. However, Allee effects were considered mostly in models for spatially structured populations in continuous time (Gruntfest et al 1997;Amarasekare 1998;Gyllenberg et al 1999;Kang and Lanchier 2011;Wang 2016;Johnson and Hastings 2018). One important result from these models is the rescue effect, where a subpopulation that falls under the Allee threshold is rescued from extinction by migration from another location (Brown and Kodric-Brown 1977).…”

Section: Introductionmentioning

confidence: 99%

Multiple Attractors and Long Transients in Spatially Structured Populations with an Allee Effect

et al. 2020

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We present a discrete-time model of a spatially structured population and explore the effects of coupling when the local dynamics contain a strong Allee effect and overcompensation. While an isolated population can exhibit only bistability and essential extinction, a spatially structured population can exhibit numerous coexisting attractors. We identify mechanisms and parameter ranges that can protect the spatially structured population from essential extinction, whereas it is inevitable in the local system. In the case of weak coupling, a state where one subpopulation density lies above and the other one below the Allee threshold can prevent essential extinction. Strong coupling, on the other hand, enables both populations to persist above the Allee threshold when dynamics are (approximately) out of phase. In both cases, attractors have fractal basin boundaries. Outside of these parameter ranges, dispersal was not found to prevent essential extinction. We also demonstrate how spatial structure can lead to long transients of persistence before the population goes extinct.

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Section: Introductionmentioning

confidence: 99%

Multiple Attractors and Long Transients in Spatially Structured Populations with an Allee Effect

et al. 2020

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“…One can get the positive equilibrium E in (u * , v * ) = (5, 4.598), which is locally asymptotically stable for model (2) without delay since H (u * ) ≈ −0.00062 < 0 by Lemma 2. For the delayed model (3), by (25), the critical delay values are computed as follows:…”

Section: At the Positive Equilibrium E Inmentioning

confidence: 99%

“…See, for example [2,12,[17][18][19][20][21][22][23]. The models with a component Allee effect, of a type similar to (1), was first mentioned by Kostitizin [24] and applied in [2,11,[25][26][27][28][29][30][31][32] .…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a Predator–Prey Model with the Additive Predation in Prey

Bai

Zhang

2022

Mathematics

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In this paper, we consider a predator–prey model, in which the prey’s growth is affected by the additive predation of its potential predators. Due to the additive predation term in prey, the model may exhibit the cases of the strong Allee effect, weak Allee effect and no Allee effect. In each case, the dynamics of global features of the model are investigated. Compared to the well-known Lotka–Volterra type model, the model proposed in this paper exhibits much richer and more complex dynamic behaviors, such as the Allee effect, the sensitivity to the initial conditions caused by the strong Allee effect, the oscillatory behavior and the Hopf and heteroclinic bifurcations. Furthermore, the stability and Hopf bifurcation of the model with the density dependent feedback time delay in prey are investigated. By the normal form method and center manifold theory, the explicit formulas are presented to determine the direction of Hopf bifurcation and the stability and period of Hopf-bifurcating periodic solutions. Theoretical analysis and numerical simulation indicate that the delay may destabilize the model, and cause the Hopf bifurcation not only at the interior equilibrium but also at a boundary equilibrium.

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“…That is why it is importaint to understand population dynamics in a complex or fragmented habitat and there is indeed a large number empirical and theoretical studies addressing this issue [7][8][9][10][11][12][13][14][15][16]. The most widely used models of population dynamics in a fragmented habitat are metapopulation models [4,[17][18][19][20][21][22]. In this framework, a fragmented habitat is viewed as a collection of separate sites, with subpopulations of a species residing in these sites.…”

Section: Introductionmentioning

confidence: 99%

Extinctions in a Metapopulation with Nonlinear Dispersal Coupling

Korotkov,

Petrovskii

2023

Mathematics

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Major threats to biodiversity are climate change, habitat fragmentation (in particular, habitat loss), pollution, invasive species, over-exploitation, and epidemics. Over the last decades habitat fragmentation has been given special attention. Many factors are causing biological systems to extinct; therefore, many issues remain poorly understood. In particular, we would like to know more about the effect of the strength of inter-site coupling (e.g., it can represent the speed with which species migrate) on species extinction or persistence in a fragmented habitat consisting of sites with randomly varying properties. To address this problem we use theoretical methods from mathematical analysis, functional analysis, and numerical methods to study a conceptual single-species spatially-discrete system. We state some simple necessary conditions for persistence, prove that this dynamical system is monotone and we prove convergence to a steady-state. For a multi-patch system, we show that the increase of inter-site coupling leads to the formation of clusters—groups of populations whose sizes tend to align as coupling increases. We also introduce a simple one-parameter sufficient condition for a metapopulation to persist.

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Population dispersal and Allee effect

Cited by 12 publications

References 33 publications

Multiple Attractors and Long Transients in Spatially Structured Populations with an Allee Effect

Multiple Attractors and Long Transients in Spatially Structured Populations with an Allee Effect

Dynamics of a Predator–Prey Model with the Additive Predation in Prey

Extinctions in a Metapopulation with Nonlinear Dispersal Coupling

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