Taylor's power law and its decomposition in urban facilities.
Ontology highlight
ABSTRACT:
SUBMITTER: Wu L
PROVIDER: S-EPMC6458378 | biostudies-literature | 2019 Mar
REPOSITORIES: biostudies-literature
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Project description:Taylor's law (TL), a widely verified quantitative pattern in ecology and other sciences, describes the variance in a species' population density (or other nonnegative quantity) as a power-law function of the mean density (or other nonnegative quantity): Approximately, variance = a(mean)(b), a > 0. Multiple mechanisms have been proposed to explain and interpret TL. Here, we show analytically that observations randomly sampled in blocks from any skewed frequency distribution with four finite moments give rise to TL. We do not claim this is the only way TL arises. We give approximate formulae for the TL parameters and their uncertainty. In computer simulations and an empirical example using basal area densities of red oak trees from Black Rock Forest, our formulae agree with the estimates obtained by least-squares regression. Our results show that the correlated sampling variation of the mean and variance of skewed distributions is statistically sufficient to explain TL under random sampling, without the intervention of any biological or behavioral mechanisms. This finding connects TL with the underlying distribution of population density (or other nonnegative quantity) and provides a baseline against which more complex mechanisms of TL can be compared.
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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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Project description:Fluctuation scaling relationships have been observed in a wide range of processes ranging from internet router traffic to measles cases. Taylor's law is one such scaling relationship and has been widely applied in ecology to understand communities including trees, birds, human populations, and insects. We show that monthly crime reports in the UK show complex fluctuation scaling which can be approximated by Taylor's law relationships corresponding to local policing neighborhoods and larger regional and countrywide scales. Regression models applied to local scale data from Derbyshire and Nottinghamshire found that different categories of crime exhibited different scaling exponents with no significant difference between the two regions. On this scale, violence reports were close to a Poisson distribution (α = 1.057 ± 0.026) while burglary exhibited a greater exponent (α = 1.292 ± 0.029) indicative of temporal clustering. These two regions exhibited significantly different pre-exponential factors for the categories of anti-social behavior and burglary indicating that local variations in crime reports can be assessed using fluctuation scaling methods. At regional and countrywide scales, all categories exhibited scaling behavior indicative of temporal clustering evidenced by Taylor's law exponents from 1.43 ± 0.12 (Drugs) to 2.094 ± 0081 (Other Crimes). Investigating crime behavior via fluctuation scaling gives insight beyond that of raw numbers and is unique in reporting on all processes contributing to the observed variance and is either robust to or exhibits signs of many types of data manipulation.
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Project description:The macroecological pattern known as Taylor's power law (TPL) represents the pervasive tendency of the variance in population density to increase as a power function of the mean. Despite empirical illustrations in systems ranging from viruses to vertebrates, the biological significance of this relationship continues to be debated. Here we combined collection of a unique dataset involving 11 987 amphibian hosts and 332 684 trematode parasites with experimental measurements of core epidemiological outcomes to explicitly test the contributions of hypothesized biological processes in driving aggregation. After using feasible set theory to account for mechanisms acting indirectly on aggregation and statistical constraints inherent to the data, we detected strongly consistent influences of host and parasite species identity over 7 years of sampling. Incorporation of field-based measurements of host body size, its variance and spatial heterogeneity in host density accounted for host identity effects, while experimental quantification of infection competence (and especially virulence from the 20 most common host-parasite combinations) revealed the role of species-by-environment interactions. By uniting constraint-based theory, controlled experiments and community-based field surveys, we illustrate the joint influences of biological and statistical processes on parasite aggregation and emphasize their importance for understanding population regulation and ecological stability across a range of systems, both infectious and free-living.
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