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Taylor's power law and its decomposition in urban facilities.

ABSTRACT: As one of the few generalities in ecology, Taylor's power law admits a power function relationship V = aM b between the variance V and mean number M of organisms in a quadrat. We examine the spatial distribution data of seven urban service facilities in 37 major cities in China, and find that Taylor's Law is validated among all types of facilities. Moreover, Taylor's Law is robust if we shift the observation window or vary the size of the quadrats. The exponent b increases linearly with the logarithm of the quadrat size, i.e. b(s) = b 0 + A log?(s). Furthermore, the ANOVA test indicates that b takes distinct values for different facilities in different cities. We decompose b into two different factors, a city-specific factor and a facility-specific factor (FSF). Variations in b can be explained to a large extent by the differences between cities and types of facilities. Facilities are more evenly distributed in larger and more developed cities. Competitive interchangeable facilities (e.g. pharmacy), with larger FSFs and smaller bs, are less aggregated than complementary services (e.g. restaurants).

SUBMITTER: Wu L

PROVIDER: S-EPMC6458378 | biostudies-literature | 2019 Mar

REPOSITORIES: biostudies-literature

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Taylor's power law and its decomposition in urban facilities.

Wu Liang L Gong Chi C Yan Xin X

Royal Society open science 20190313 3

As one of the few generalities in ecology, Taylor's power law admits a power function relationship V = aM b between the variance V and mean number M of organisms in a quadrat. We examine the spatial distribution data of seven urban service facilities in 37 major cities in China, and find that Taylor's Law is validated among all types of facilities. Moreover, Taylor's Law is robust if we shift the observation window or vary the size of the quadrats. T ...[more]

PMID: 31031987

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Project description:Spatial heterogeneity is a fundamental characteristic of organisms from viruses to humans. Measuring heterogeneity is challenging, especially for naked-eye invisible viruses, but of obvious importance. For example, spatial heterogeneity of virus distribution may strongly influence infection spreading and outbreaks in the case of pathogenic viruses; the spatial distribution (i.e., the inter-subject heterogeneity) of commensal viruses within/on our bodies can influence the competition, coexistence, and dispersal of viruses within or between our bodies. Taylor's power law (TPL) was first discovered in the 1960s to describe the spatial distributions of plant and/or animal populations, and since then it has been verified by numerous experimental and theoretical studies. Recently, TPL has been extended from population to community level and applied to bacterial communities. Here we report the first comprehensive testing of the TPL fitted to human virome datasets. It was found that the human virome follows the TPL as bacterial communities do. Furthermore, the TPL heterogeneity scaling parameter of human virome is virtually the same as that of the human bacterial microbiome (1.916 vs. 1.926). We postulate that the extreme closeness of human viruses and bacteria in heterogeneity scaling coefficients could be attributed to the fact that most of the viruses that were annotated in this study actually belong to bacteriophages (86% viral OTUs) that "piggyback" on their bacterial hosts, and their distributions are likely host-dependent. The scaling parameter, which measures the inter-subject heterogeneity changes, should be an innate property of human microbiomes including both bacteria and viruses. It is similar to the acceleration coefficient of the gravity (g = 9.8) as specified by Newton's law, which is invariant on the earth. Nevertheless, we caution that our postulation is contingent on an implicit assumption that the proportion of bacteriophages to total virome may not change significantly when more virus species can be identified in future.

Project description:Theoretical analysis of DNA sequencing coverage problem has been investigated with complex mathematical models such as Lander-Waterman expectation theory and Stevens' theorem for randomly covering a domain. In the field of metagenomics sequencing, several approaches have been developed to estimate the coverage of whole-genome shotgun sequencing, but surprisingly few studies addressed the coverage problem for marker-gene amplicon sequencing, for which arguably the biggest challenge is the complexity or heterogeneity of microbial communities. Overall, much of the practice still relies variously on speculation, semi-empirical and ad hoc heuristic models. Conservatively raising coverage may ensure the success of sequencing project, but often with unduly cost. In this study, we borrow the principles and approaches of optimum sampling methodology originated in applied entomology, achieved equal success in plant pathology and parasitology, and plays a critical role in the decision-making for global crop and forest protection against economic pests since 1970s when the pesticide crisis and food safety concerns forced the reduction of pesticide usages, which in turn requires reliable sampling techniques for monitoring pest populations. We realized that sequencing coverage is essentially an optimum sampling problem. Perhaps the only essential difference between sampling insects and sampling microbiome is the "instrument" used. In traditional entomology, it is usually humans that visually count the numbers of insects, occasionally aided by binocular microscope. In the metagenomics research, it is the DNA sequencers that count the number of DNA reads. Furthermore, a key theoretical foundation for sampling insect pest populations, i.e., Taylor's power law, which achieved rare status of ecological law and captures the population aggregation, has been recently extended to the community level for describing community heterogeneity and stability, namely, Taylor's power law extensions (TPLEs). This theoretical advance enabled us to develop a novel approach to assessing the quality and determining optimum reads (coverage) of amplicon sequencing operations. Specifically, two applications were developed: one is, in hindsight, to assess the quality of amplicon sequencing operation in terms of the precision and confidence levels. Another is, prior to sequencing operation, to determine the minimum sequencing efforts for a sequencing project to achieve preset precision and confidence levels.

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Taylor's power law and its decomposition in urban facilities.

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Taylor's power law and its decomposition in urban facilities.

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