ArticleProceedings of the National Academy of Sciences of the United States of America2015
Sample and population exponents of generalized Taylor's law.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 18 papers.
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18 citing papers in PubMed, 84 citations in OpenAlex.
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- Fine scale prediction of ecological community composition using a two-step sequential Machine Learning ensemble.PLoS computational biology · 2021Article
- Taylor's law of fluctuation scaling for semivariances and higher moments of heavy-tailed data.Proceedings of the National Academy of Sciences of the United States of America · 2021Article
- Direct Scaling of Measure on Vortex Shedding through a Flapping Flag Device in the Open Channel around a Cylinder atSensors (Basel, Switzerland) · 2021Article
- Joint assessment of density correlations and fluctuations for analysing spatial tree patterns.Royal Society open science · 2021Article
- Macroecological laws describe variation and diversity in microbial communities.Nature communications · 2020Article
- Taylor's Law in Innovation Processes.Entropy (Basel, Switzerland) · 2020Article
- Macroecological dynamics of gut microbiota.Nature microbiology · 2020Article
- Yeast facilitates the multiplication of Drosophila bacterial symbionts but has no effect on the form or parameters of Taylor's law.PloS one · 2020Article
- Estimating the Optimum Coverage and Quality of Amplicon Sequencing With Taylor's Power Law Extensions.Frontiers in bioengineering and biotechnology · 2020Article
- Internode morphometrics and allometry of Tonkin CaneEcology and evolution · 2017Article
- Covariations in ecological scaling laws fostered by community dynamics.Proceedings of the National Academy of Sciences of the United States of America · 2017Article
- Biological and statistical processes jointly drive population aggregation: using host-parasite interactions to understand Taylor's power law.Proceedings. Biological sciences · 2017Article
- Synchrony affects Taylor's law in theory and data.Proceedings of the National Academy of Sciences of the United States of America · 2017Article
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5 authors at 4 institutions in 4 countries.
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No grant is acknowledged in the PubMed record.
Abstract
Taylor's law (TL) states that the variance V of a nonnegative random variable is a power function of its mean M; i.e., V = aM(b). TL has been verified extensively in ecology, where it applies to population abundance, physics, and other natural sciences. Its ubiquitous empirical verification suggests a context-independent mechanism. Sample exponents b measured empirically via the scaling of sample mean and variance typically cluster around the value b = 2. Some theoretical models of population growth, however, predict a broad range of values for the population exponent b pertaining to the mean and variance of population density, depending on details of the growth process. Is the widely reported sample exponent b ≃ 2 the result of ecological processes or could it be a statistical artifact? Here, we apply large deviations theory and finite-sample arguments to show exactly that in a broad class of growth models the sample exponent is b ≃ 2 regardless of the underlying population exponent. We derive a generalized TL in terms of sample and population exponents b(jk) for the scaling of the kth vs. the jth cumulants. The sample exponent b(jk) depends predictably on the number of samples and for finite samples we obtain b(jk) ≃ k = j asymptotically in time, a prediction that we verify in two empirical examples. Thus, the sample exponent b ≃ 2 may indeed be a statistical artifact and not dependent on population dynamics under conditions that we specify exactly. Given the broad class of models investigated, our results apply to many fields where TL is used although inadequately understood.
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