Statistical mechanics of ecological systems: Neutral theory and beyond

Azaele, Sandro; Suweis, Samir; Grilli, Jacopo; Volkov, Igor; Banavar, Jayanth R.; Maritan, Amos

doi:10.1103/revmodphys.88.035003

Cited by 148 publications

(201 citation statements)

References 194 publications

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“…This link is consistent with data from three very different empirical systems and well captured by the random-sampling model. The fact that emergent patterns can be explained by largely null models resembles again the case of biodiversity, where neutral theories ignoring species interactions and competitive exclusion appear to capture many of the emerging trends of species abundance [44,47].…”

Section: Resultsmentioning

confidence: 99%

Statistics of Shared Components in Complex Component Systems

et al. 2018

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Many complex systems are modular. Such systems can be represented as "component systems," i.e., sets of elementary components, such as LEGO bricks in LEGO sets. The bricks found in a LEGO set reflect a target architecture, which can be built following a set-specific list of instructions. In other component systems, instead, the underlying functional design and constraints are not obvious a priori, and their detection is often a challenge of both scientific and practical importance, requiring a clear understanding of component statistics. Importantly, some quantitative invariants appear to be common to many component systems, most notably a common broad distribution of component abundances, which often resembles the well-known Zipf's law. Such "laws" affect in a general and nontrivial way the component statistics, potentially hindering the identification of system-specific functional constraints or generative processes. Here, we specifically focus on the statistics of shared components, i.e., the distribution of the number of components shared by different system realizations, such as the common bricks found in different LEGO sets. To account for the effects of component heterogeneity, we consider a simple null model, which builds system realizations by random draws from a universe of possible components. Under general assumptions on abundance heterogeneity, we provide analytical estimates of component occurrence, which quantify exhaustively the statistics of shared components. Surprisingly, this simple null model can positively explain important features of empirical component-occurrence distributions obtained from large-scale data on bacterial genomes, LEGO sets, and book chapters. Specific architectural features and functional constraints can be detected from occurrence patterns as deviations from these null predictions, as we show for the illustrative case of the "core" genome in bacteria.

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Section: Resultsmentioning

confidence: 99%

Statistics of Shared Components in Complex Component Systems

et al. 2018

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“…Although we shall focus on the 2D case, it is useful to present the general calculation in D dimensions. Following [11,41,42] we write…”

Section: B Dualitymentioning

confidence: 99%

“…Although we are mainly interested in 2D, it is instructive to consider the general case in which A = L D , where L is the linear size of the sample. Following [11,42], we assume a standard scaling form for the SAD…”

Section: Power-law Scaling Relationmentioning

confidence: 99%

Stochastic Spatial Models in Ecology: A Statistical Physics Approach

et al. 2017

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Ecosystems display a complex spatial organization. Ecologists have long tried to characterize them by looking at how different measures of biodiversity change across spatial scales. Ecological neutral theory has provided simple predictions accounting for general empirical patterns in communities of competing species. However, while neutral theory in well-mixed ecosystems is mathematically well understood, spatial models still present several open problems, limiting the quantitative understanding of spatial biodiversity. In this review, we discuss the state of the art in spatial neutral theory. We emphasize the connection between spatial ecological models and the physics of non-equilibrium phase transitions and how concepts developed in statistical physics translate in population dynamics, and vice versa. We focus on non-trivial scaling laws arising at the critical dimension D = 2 of spatial neutral models, and their relevance for biological populations inhabiting two-dimensional environments. We conclude by discussing models incorporating non-neutral effects in the form of spatial and temporal disorder, and analyze how their predictions deviate from those of purely neutral theories.

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“…However, deterministic approaches neglect the effect of fluctuations, and these are now acknowledged to be both inherent and essential to the organization of communities of living systems [8]. On the one hand, the discreteness and finiteness of populations lead to demographic noise; which has been shown to be responsible of a wealth of non-trivial phenomena such as the emergence of complex statistical patterns in neutral communities [9,10], quasi-periodic oscillations in prey-predator systems [11], species formation [12], and others [13][14][15]. On the other hand, populations are strongly affected by fluctuations in external conditions [16,17], which in most of the cases are highly unpredictable.…”

Section: Introductionmentioning

confidence: 99%

Impact of environmental colored noise in single-species population dynamics

2017

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Variability on the external conditions has important consequences for the dynamics and organization of biological systems, and, in many cases, the characteristic timescale of environmental changes as well as their correlations play a fundamental role in the way living systems adapt and respond to it. A proper mathematical approach to understand population dynamic, thus, requires of approaches more refined than e.g. simple white-noise approximations. To shed further light onto this problem, in this paper we propose a unifying framework based on different analytical and numerical tools available to deal with "colored" environmental noise. In particular, we employ a "unified colored noise approximation" to map the original problem into an effective one with white noise, and then we apply a standard path integral approach to gain analytical understanding. For the sake of specificity, we present our approach using as a guideline a variation of the contact process -which can also be seen as a birth-death process of the Malthus-Verhulst class-where the propagation/birth rate varies stochastically in time. Our approach allows us to tackle in a systematic manner some of the relevant questions concerning population dynamics under environmental variability such as, for instance, determining the stationary population density, establishing the conditions under which a population may become extinct, and estimating extinction times. More in general, we put the focus on the emerging phase diagram and its possible phase transitions, underlying how these are affected by the presence of environmental noise time-correlations.

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Statistical mechanics of ecological systems: Neutral theory and beyond

Cited by 148 publications

References 194 publications

Statistics of Shared Components in Complex Component Systems

Statistics of Shared Components in Complex Component Systems

Stochastic Spatial Models in Ecology: A Statistical Physics Approach

Impact of environmental colored noise in single-species population dynamics

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