Zipf's and Taylor's laws

James, Charlotte; Azaele, Sandro; Maritan, Amos; Simini, Filippo

doi:10.1103/physreve.98.032408

Cited by 16 publications

(21 citation statements)

References 27 publications

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“…This is in agreement with previous studies [24][25][26]. It has been proved that Taylor's law can emerge in a much more general class of stochastic processes, for example when the dynamical rates of the model are affected by environmental variability [26,27]. In the case of this birth-death spatial model, the cross-over in the scaling exponent α results from the different roles of dispersal played at different spatial scales.…”

Section: A the Spatial Taylor's Lawsupporting

confidence: 91%

“…This was phenomenologically captured by assuming a scaling relationship between the variance and mean of population sizes in different areas. More generally, and recently, Taylor's law denotes any power relation between the variance and the mean of random variables in complex systems [26,27]. The law postulates a relation of the following form…”

Section: A the Spatial Taylor's Lawmentioning

confidence: 99%

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Spatial patterns emerging from a stochastic process near criticality

Peruzzo¹,

Mobilia²,

Azaele³

2019

Preprint

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There is mounting empirical evidence that many communities of living organisms display key features which closely resemble those of physical systems at criticality. We here introduce a minimal model framework for the dynamics of a community of individuals which undergoes local birth-death, immigration and local jumps on a regular lattice. We study its properties when the system is close to its critical point. Even if this model violates detailed balance, within a physically relevant regime dominated by fluctuations, it is possible to calculate analytically the probability density function of the number of individuals living in a given volume, which captures the close-to-critical behavior of the community across spatial scales. We find that the resulting distribution satisfies an equation where spatial effects are encoded in appropriate functions of space, which we calculate explicitly. The validity of the analytical formulae is confirmed by simulations in the expected regimes. We finally discuss how this model in the critical-like regime is in agreement with several biodiversity patterns observed in tropical rain forests.

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Section: A the Spatial Taylor's Lawsupporting

confidence: 91%

Section: A the Spatial Taylor's Lawmentioning

confidence: 99%

Spatial patterns emerging from a stochastic process near criticality

Peruzzo¹,

Mobilia²,

Azaele³

2019

Preprint

Self Cite

View full text Add to dashboard Cite

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“…This aggregation is phenomenologically captured by assuming a scaling relationship between the variance and mean of population sizes in different areas. More generally, and recently, Taylor's law denotes any power relation between the variance and the mean of random variables in complex systems [28,29]. The law postulates a relation of the following form:…”

Section: A the Spatial Taylor's Lawmentioning

confidence: 99%

Spatial Patterns Emerging from a Stochastic Process Near Criticality

2020

Self Cite

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There is mounting empirical evidence that many communities of living organisms display key features which closely resemble those of physical systems at criticality. We here introduce a minimal model framework for the dynamics of a community of individuals which undergoes local birth-death, immigration, and local jumps on a regular lattice. We study its properties when the system is close to its critical point. Even if this model violates detailed balance, within a physically relevant regime dominated by fluctuations, it is possible to calculate analytically the probability density function of the number of individuals living in a given volume, which captures the close-to-critical behavior of the community across spatial scales. We find that the resulting distribution satisfies an equation where spatial effects are encoded in appropriate functions of space, which we calculate explicitly. The validity of the analytical formulae is confirmed by simulations in the expected regimes. We finally discuss how this model in the critical-like regime is in agreement with several biodiversity patterns observed in tropical rain forests.

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“…dictates how the mean and the variance behave. For = 2 the pdf is the Zipf?s law that is found for many socio-ecological systems (James et al, 2018).…”

Section: Probabilistic Characterization Of Microbiome Variablesmentioning

confidence: 96%

Optimal Microbiome Networks: Macroecological Characterization and Criticality

Li¹,

Convertino²

2018

Preprint

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The human microbiome is extremely complex considering the amount of species, their interactions, and its variability over time as a function of environmental drivers. Here we untangle the complexity of the human microbiome for the Irritable Bowel Syndrome (IBS) that is the most prevalent functional gastrointestinal disorder linked to many causes. Based on a novel information theoretic network inference model (that considers conditional entropy reduction till the maximum entropy is not reduced further) we detect species interaction networks that are functionally and structurally different for healthy and unhealthy individuals. Healthy networks are characterized by a neutral symmetrical pattern of species interaction and small-world features for functional node degree and distance versus random unhealthy networks. We detect an inverse scaling relationship between species total outgoing information flow (''active flow'') and abundance. The top 10 interacting species are also the least abundant for the healthy microbiome and the most detrimental; however these species are controlled by other species (via negative feedbacks) and the microbiome is self-organized into a healthy state. On the contrary, the most abundant species for the unhealthy microbiome are the least interactive and the most detrimental. These findings support the idea about a diminishing role of network hubs and hubs should be defined considering total outgoing information flow. The healthy microbiome is characterized by high diversity growth rate, small species similarity decay over time (i.e. low species turnover), and small variability in the abundance of all species. This result challenges current views that posit an association between health states and the highest diversity in ecosystems rather than the highest biodiversity growth as in this study. In a network perspective the healthy microbiome is configured as a small-world network with a tendency toward a critical scale-free network while the unhealthy one is organized as a random network with many more interacting species. We show how the transitory microbiome at the edge of the healthy and unhealthy ones is unstable and criticality of the healthy microbiome is not at the phase transition (or second order) between order and chaos but in a meta-stable state (on the contrary of other critical systems where energy and entropy grow in the same direction and criticality is at the transition). We stress out the importance of considering interacting pairs versus single node dynamics when characterizing the microbiome nexus and of ranking these pairs in terms of their dynamics; interactions (i.e. species collective behavior) shape transition from healthy to unhealthy states. The macroecological characterization of the microbiome is useful for diagnostic purposes and disease etiognosis while species-specific analyses can detect species that are more beneficial to humans leading to personalized design of pre- and pro-biotic treatments and engineered microbiome transplants as two examples.

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Zipf's and Taylor's laws

Cited by 16 publications

References 27 publications

Spatial patterns emerging from a stochastic process near criticality

Spatial patterns emerging from a stochastic process near criticality

Spatial Patterns Emerging from a Stochastic Process Near Criticality

Optimal Microbiome Networks: Macroecological Characterization and Criticality

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