The perfect mixing paradox and the logistic equation: Verhulst vs. Lotka: Comment

Ramos‐Jiliberto, Rodrigo; Espanés, Pablo Moisset de

doi:10.1002/ecs2.1895

Cited by 7 publications

(7 citation statements)

References 19 publications

(66 reference statements)

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“…Equality (

K_{normalT} = K_{1} + K_{2}

) occurs in two special cases only. Ramos‐Jiliberto and Moisset de Espanés ()'s model corresponds to the full black point, showing that this model is not a representative of the general case (values used in this figure for illustrative purpose:

r_{1} = 2, r_{2} = 1, K_{1} = 3, K_{2} = 1

).…”

Section: A General Model With Asymmetrical Migrationmentioning

confidence: 99%

“…This phenomenon was demonstrated in a simple model that assumed identical dispersal rates in each patch. In an article published in the present issue of Ecosphere , Ramos‐Jiliberto and Moisset de Espanés () (RJME) show that this paradox does not occur when assuming balanced dispersal. In our present Reply, we will study a more general dispersal model that encompasses both our original model and RJME's new model.…”

mentioning

confidence: 97%

“…Ramos‐Jiliberto and Moisset de Espanés () propose the following alternative model:

\begin{matrix} \frac{d N_{1}}{d t} = r_{1} N_{1} (1 - \frac{N_{1}}{K_{1}}) + β (\frac{N_{2}}{K_{2}} - \frac{N_{1}}{K_{1}}), \\ \frac{d N_{2}}{d t} = r_{2} N_{2} (1 - \frac{N_{2}}{K_{2}}) + β (\frac{N_{1}}{K_{1}} - \frac{N_{2}}{K_{2}}) . \end{matrix}

…”

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confidence: 99%

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The perfect mixing paradox and the logistic equation: Verhulst vs. Lotka: Reply

2017

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“…Equality (

K_{normalT} = K_{1} + K_{2}

r_{1} = 2, r_{2} = 1, K_{1} = 3, K_{2} = 1

).…”

Section: A General Model With Asymmetrical Migrationmentioning

confidence: 99%

mentioning

confidence: 97%

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The perfect mixing paradox and the logistic equation: Verhulst vs. Lotka: Reply

2017

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“…which is known as the balanced dispersal (see [22,26]) or the evolutionarily stable strategy (see [3,8]), and gives ideal free distribution. Therefore, the balanced dispersal with given dispersal rates c ij is not distinguishable from symmetric dispersal in a homogeneous environment.…”

Section: Contentsmentioning

confidence: 99%

“…This two-patch system serves as a basic model and provides key insights on population dynamics and dispersal (see [2,9,10,15]). In spite of the simplicity of the model system, there are still unresolved aspects (see [1,26]). We first consider the two-patch system with a starvation-dependent dispersal,…”

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confidence: 99%

Asymmetric dispersal and evolutional selection in two-patch system

Kim¹,

Seo²,

Yoon³

2020

Discrete &Amp; Continuous Dynamical Systems - A

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Biological organisms leave their habitat when the environment becomes harsh. The essence of a biological dispersal is not in the rate, but in the capability to adjust to the environmental changes. In nature, conditional asymmetric dispersal strategies appear due to the spatial and temporal heterogeneity in the environment. Authors show that such a dispersal strategy is evolutionary selected in the context two-patch problem of Lotka-Volterra competition model. They conclude that, if a conditional asymmetric dispersal strategy is taken, the dispersal is not necessarily disadvantageous even for the case that there is no temporal fluctuation of environment at all.

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Pollinator declines and the stability of plant–pollinator networks

2020

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Population declines of pollinators constitute a major concern for the fate of biodiversity and associated ecosystem services in a context of global change. Massive declines of pollinator populations driven by habitat loss, pollution, and climate change have been reported, whose consequences at community and ecosystem levels remain elusive. We conducted a mathematical modeling and computer simulation study to assess the dynamic consequences of pollinator declines for the biodiversity of plants and pollinators. Specifically, we evaluated the effects of increased mortality and decreased carrying capacity of specialist vs. generalist and effective vs. ineffective pollinators visiting specialist vs. generalist plants on long‐term community biomass and species persistence. Our results reveal that increased larval mortality and increased competition for space among larvae had the greatest impacts on the decline of pollinator diversity. In contrast, the largest sustained decreases in pollinator biomass were driven by increased adult mortality in spite of a small increase in pollinator species persistence. Decreased pollinator diversity led in turn to decreased plant diversity. Attacking pollinators with high degree and connected mostly to low‐degree plants produced the greatest losses of plant diversity. Pollinator effectiveness had no noticeable effect on persistence. Our results illuminate our understanding of the consequences of pollinator declines for the maintenance of biodiversity.

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The perfect mixing paradox and the logistic equation: Verhulst vs. Lotka: Comment

Cited by 7 publications

References 19 publications

The perfect mixing paradox and the logistic equation: Verhulst vs. Lotka: Reply

The perfect mixing paradox and the logistic equation: Verhulst vs. Lotka: Reply

Asymmetric dispersal and evolutional selection in two-patch system

Pollinator declines and the stability of plant–pollinator networks

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