A Process-Independent Explanation for the General Form of Taylor’s Law

Xiao, Xiao; Locey, Kenneth J; White, Ethan

doi:10.1086/682050

Cited by 51 publications

(71 citation statements)

References 38 publications

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“…Such empirical ubiquity suggests that TL could be another of the so-called universal laws (26) like the laws of large numbers (27) and the central limit theorem (28). For example, independently of the present study, Xiao et al (29) showed numerically (not analytically) that random partitions and compositions of integers led to TL with slopes often between 1 and 2, as commonly observed in empirical examples of TL.…”

supporting

confidence: 74%

Random sampling of skewed distributions implies Taylor’s power law of fluctuation scaling

Cohen

Meng

2015

Proc. Natl. Acad. Sci. U.S.A.

109

122

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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. or equivalently as a linear function when mean and variance are logarithmically transformed:Eqs. 1 and 2 may be exact if the mean and variance are population moments calculated from certain parametric families of probability distributions (e.g., a = 1 and b = 1 for a Poisson distribution). Eqs. 1 and 2 may be approximate if the mean and variance are sample moments based on finite random samples of observations. Most empirical tests of TL have not specified the random error associated with Eqs. 1 or 2. TL has been verified for hundreds of biological species and nonbiological quantities in more than a thousand papers in ecology, epidemiology, biomedical sciences, and other fields (2-4). Recently, examples of TL were found in bacterial microcosms (5, 6), forest trees (7, 8), human populations (9), coral reef fish populations (10), and barnacles (11,12). TL has been used practically in the design of sampling plans for the control of insect pests of soybeans (13,14) and cotton (15).Scientific studies of TL largely focus on the power-law exponent b (or slope b in the linear form), which Taylor believed to contain information about how populations of a species aggregate in space (1). Empirically, b often lies between 1 and 2 (16). Ballantyne and Kerkhoff (17) suggested that individuals' reproductive correlation determines the size of b. Ballantyne (18) proposed that b = 2 is a consequence of deterministic population growth. Cohen (19) showed that b = 2 arose from exponentially growing, noninteracting clones. Kilpatrick and Ives (20) proposed that interspecific competition could reduce the value of b. Other models that implied TL were the exponential dispersion model (21-23), models of spatially distributed colonies (24, 25), a stochastic version of logistic population dyn...

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supporting

confidence: 74%

Random sampling of skewed distributions implies Taylor’s power law of fluctuation scaling

Cohen

Meng

2015

Proc. Natl. Acad. Sci. U.S.A.

109

122

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“…Importantly, this relationship applies to samples from different systems and does not pertain to cumulative patterns (e.g., collector's curves), which are based on resampling (20)(21)(22). Recent studies have also shown that N constrains universal patterns of commonness and rarity by imposing a numerical constraint on how abundance varies among species, across space, and through time (23,24). Most notably, greater N leads to increasingly uneven distributions and greater rarity.…”

mentioning

confidence: 99%

Scaling laws predict global microbial diversity

Locey

Lennon

2016

Proc. Natl. Acad. Sci. U.S.A.

Self Cite

870

380

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Scaling laws underpin unifying theories of biodiversity and are among the most predictively powerful relationships in biology. However, scaling laws developed for plants and animals often go untested or fail to hold for microorganisms. As a result, it is unclear whether scaling laws of biodiversity will span evolutionarily distant domains of life that encompass all modes of metabolism and scales of abundance. Using a global-scale compilation of ∼35,000 sites and ∼5.6·10 6 species, including the largest ever inventory of high-throughput molecular data and one of the largest compilations of plant and animal community data, we show similar rates of scaling in commonness and rarity across microorganisms and macroscopic plants and animals. We document a universal dominance scaling law that holds across 30 orders of magnitude, an unprecedented expanse that predicts the abundance of dominant ocean bacteria. In combining this scaling law with the lognormal model of biodiversity, we predict that Earth is home to upward of 1 trillion (10 12 ) microbial species. Microbial biodiversity seems greater than ever anticipated yet predictable from the smallest to the largest microbiome.biodiversity | microbiology | macroecology | microbiome | rare biosphere T he understanding of microbial biodiversity has rapidly transformed over the past decade. High-throughput sequencing and bioinformatics have expanded the catalog of microbial taxa by orders of magnitude, whereas the unearthing of new phyla is reshaping the tree of life (1-3). At the same time, discoveries of novel forms of metabolism have provided insight into how microbes persist in virtually all aquatic, terrestrial, engineered, and host-associated ecosystems (4, 5). However, this period of discovery has uncovered few, if any, general rules for predicting microbial biodiversity at scales of abundance that characterize, for example, the ∼10 14 cells of bacteria that inhabit a single human or the ∼10 30 cells of bacteria and archaea estimated to inhabit Earth (6, 7). Such findings would aid the estimation of global species richness and reveal whether theories of biodiversity hold across all scales of abundance and whether socalled law-like patterns of biodiversity span the tree of life.A primary goal of ecology and biodiversity theory is to predict diversity, commonness, and rarity across evolutionarily distant taxa and scales of space, time, and abundance (8-10). This goal can hardly be achieved without accounting for the most abundant, widespread, and metabolically, taxonomically, and functionally diverse organisms on Earth (i.e., microorganisms). However, tests of biodiversity theory rarely include both microbial and macrobial datasets. At the same time, the study of microbial ecology has yet to uncover quantitative relationships that predict diversity, commonness, and rarity at the scale of host microbiomes and beyond. These unexplored opportunities leave the understanding of biodiversity limited to the most conspicuous species of plants and animals. This lack of synthesi...

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“…Another opportunity is to study 'within species over samples' characteristics. We point to the abundance-occupancy relation [33], to Taylor's law (fluctuation scaling [34] [35]) and to sampling theory [36]. Hopefully, all patterns can be integrated and applied for analysis with resampling statistics [37] (see also Wikipedia headwords 'Nonparametric statistics' and 'Resampling (statistics)') to obtain robust results, especially on the SAD.…”

Section: And Discussionmentioning

confidence: 99%

The stretched exponential as one of the alternatives for the power law to fit ranked species abundance data

Straatsma

Egli

2017

Matters

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A central object in community ecology is species abundance distribution. We are interested in the power law and its allies for ranked species abundance data. We collected 12 large data sets consisting of many samples. The preliminary fitting result makes a robust impression (12 systems at three scales of integration) that the stretched exponential is an interesting alternative for the power law. For further work, advanced statistics are required. Not only 'our' data but, quite often, other data as well consist of sample×species cross-tables. With cross-tables, also 'within species over samples' characteristics can be studied. An integrated view on data patterns in multi-sample sets may help to identify generative processes for and the formulation of a relatively simple model for species abundance data.

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A Process-Independent Explanation for the General Form of Taylor’s Law

Cited by 51 publications

References 38 publications

Random sampling of skewed distributions implies Taylor’s power law of fluctuation scaling

Random sampling of skewed distributions implies Taylor’s power law of fluctuation scaling

Scaling laws predict global microbial diversity

The stretched exponential as one of the alternatives for the power law to fit ranked species abundance data

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