Time scales and species coexistence in chaotic flows

Galla, Tobias; Pérez‐Muñuzuri, V.

doi:10.1209/0295-5075/117/68001

Cited by 5 publications

(7 citation statements)

References 44 publications

(92 reference statements)

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“…In-line with the literature we will describe this by the so-called Damköhler number, Da (see e.g. 30 – 33 ); in the context of our model, the Damköhler number characterises the ratio of the time scales of the flow and the evolutionary process. In our simulations, one evolutionary event occurs every 1/( NDa ) time units.…”

Section: Results and Methodsmentioning

confidence: 79%

Stirring does not make populations well mixed

Herrerías-Azcué

Pérez‐Muñuzuri

Galla

2018

Sci Rep

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In evolutionary dynamics, the notion of a ‘well-mixed’ population is usually associated with all-to-all interactions at all times. This assumption simplifies the mathematics of evolutionary processes, and makes analytical solutions possible. At the same time the term ‘well-mixed’ suggests that this situation can be achieved by physically stirring the population. Using simulations of populations in chaotic flows, we show that in most cases this is not true: conventional well-mixed theories do not predict fixation probabilities correctly, regardless of how fast or thorough the stirring is. We propose a new analytical description in the fast-flow limit. This approach is valid for processes with global and local selection, and accurately predicts the suppression of selection as competition becomes more local. It provides a modelling tool for biological or social systems with individuals in motion.

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Section: Results and Methodsmentioning

confidence: 79%

Stirring does not make populations well mixed

Herrerías-Azcué

Pérez‐Muñuzuri

Galla

2018

Sci Rep

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“…We also anticipate that the results of this letter may inspire interesting investigations beyond the realms of political campaigning, for example to biological competition [33]. Indeed, there are clear parallels between this work and that of [7], who demonstrated that faster diffusing individuals dominate in spatial models of biological competition, and [34] who examine the evolutionary dynamics of mobile agents in chaotic flows. The underlying competition dynamics and mechanisms of establishing dominance are, however, entirely different.…”

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confidence: 66%

Noise-driven bias in the non-local voter model

Minors

Rogers

Yates³

2018

EPL

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Is it more effective to have a strong influence over a small domain, or a weaker influence over a larger one? Here, we introduce and analyse an off-lattice generalisation of the voter model, in which the range and strength of agents' influence are control parameters. We consider both low and high density regimes and, using distinct mathematical approaches, derive analytical predictions for the evolution of agent densities. We find that, even when the agents are equally persuasive on average, those whose influence is wider but weaker have an overall noise-driven advantage allowing them to reliably dominate the entire population. We discuss the implications of our results and the potential of our model (or adaptations thereof) to improve the understanding of political campaign strategies and the evolution of disease. p-1

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“…In-line with the literature we will characterise this by the so-called Damköhler number, Da (see e.g. [27][28][29][30] ). In our simulations, one evolutionary event occurs every 1/(N Da) time units.…”

Section: Models Of Stirred Populationsmentioning

confidence: 86%

Fast flowing populations are not well mixed

Herrerías-Azcué,

Pérez-Muñuzuri,

Galla

2017

Preprint

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In evolutionary dynamics, well-mixed populations are almost always associated with all-to-all interactions; mathematical models are based on complete graphs. In most cases, these models do not predict fixation probabilities in groups of individuals mixed by flows. We propose an analytical description in the fast-flow limit. This approach is valid for processes with global and local selection, and accurately predicts the suppression of selection as competition becomes more local. It provides a modelling tool for biological or social systems with individuals in motion.

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Time scales and species coexistence in chaotic flows

Cited by 5 publications

References 44 publications

Stirring does not make populations well mixed

Stirring does not make populations well mixed

Noise-driven bias in the non-local voter model

Fast flowing populations are not well mixed

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