A probabilistic cellular automata model for the dynamics of a population driven by logistic growth and weak Allee effect

Mendonça, J. Ricardo G.

doi:10.1088/1751-8121/aab165

Cited by 3 publications

(2 citation statements)

References 55 publications

(80 reference statements)

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“…When long‐range dispersal is considered, a discontinuous shift is still found. Departures from the mean field predictions are known to occur when the role played by space becomes explicit (see for example, Bascompte and Solé ; Mendonça ). However, in this case the difference goes far beyond a displacement of the parameters associated with the transitions: the nature of the transition itself is changed and no catstrophic shift is observed separating the survival from the extinction phases.…”

Section: Discussionmentioning

confidence: 99%

Habitat loss‐induced tipping points in metapopulations with facilitation

2019

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Habitat loss is known to pervade extinction thresholds in metapopulations. Such thresholds result from a loss of stability that can eventually lead to collapse. Several models have been developed to understand the nature of these transitions and how they are affected by the locality of interactions, fluctuations or external drivers. Most models consider the impact of grazing or aridity as a control parameter that can trigger sudden shifts, once critical values are reached. Others explore instead the role played by habitat loss and fragmentation. Here we consider a minimal model incorporating facilitation between the individuals of the same species along with habitat destruction, with the aim of understanding how local cooperation and habitat loss interact with each other. A mathematical model incorporating facilitation and habitat destruction is derived, along with a spatially explicit simulation model. It is found that a catastrophic shift is expected for increasing levels of habitat loss, but the bifurcation becomes continuous when dispersal is local. Under these conditions, spatial patchiness is found and the qualitative change from discontinuous to continuous results are in agreement with previous studies on ecological systems. Our results suggest that species exhibiting facilitation and displaying short‐range dispersal will be markedly more capable of avoiding catastrophic tipping points.

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Section: Discussionmentioning

confidence: 99%

Habitat loss‐induced tipping points in metapopulations with facilitation

2019

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“…Like functional response of predators, positive interaction such as the Allee effect, introduced by the renowned ecologist Allee, plays a vital role in ecological communities [1,5,7,28]. The concept of fitness is the central topic to the study of Allee effect.…”

Section: Introductionmentioning

confidence: 99%

Crucial impact of component Allee effect in predator-prey system

Sahoo,

Sahoo

2024

J. Phys. A: Math. Theor.

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Allee effect in models in interacting species of predator prey system has great significance in ecological context. Allee effect plays crucial role in population dynamics in ecology, where it is the challenging fact that per capita population growth rate is positively dependent on the population density of a species. In this paper, we inspect the famous Hastings and Powell (HP) model incorporating component Allee effect on top predator's reproduction. We analyse the updated model with the help of both analytical and numerical phenomena. Considering cost of Allee effect, half-saturation constant of prey as the key parameters, the Hopf bifurcations are also analysed. The directions of Hopf bifurcations at the critical values of Allee parameter and half-saturation constant of prey are studied theoretically by using normal form theory introduced by Hassard et al. The formulated model indicates that the system demonstrates chaotic, periodic and stable dynamics in the variation of key parameters. The chaos can be controlled for proper application of the large values of parameter used as the cost of Allee effect and also for small values of the parameter used as the half saturation constant of prey population. The results of this study are applicable in the field of wild ecosystem dynamics.

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A statistical approach to the identification of diploid cellular automata based on incomplete observations

Bołt

Wolnik

et al. 2019

Biosystems

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A probabilistic cellular automata model for the dynamics of a population driven by logistic growth and weak Allee effect

Cited by 3 publications

References 55 publications

Habitat loss‐induced tipping points in metapopulations with facilitation

Habitat loss‐induced tipping points in metapopulations with facilitation

Crucial impact of component Allee effect in predator-prey system

A statistical approach to the identification of diploid cellular automata based on incomplete observations

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