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Baumgartner MT, Peláez Zapata OE. Taylor's power law for freshwater fishes: Functional traits beyond statistical inevitability. J Anim Ecol 2024. [PMID: 38953244 DOI: 10.1111/1365-2656.14135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2023] [Accepted: 05/07/2024] [Indexed: 07/03/2024]
Abstract
Taylor's power law (TPL) describes the expected range of parameters of the mean-variance scaling relationship and has been extensively used in studies examining temporal variations in abundance. Few studies though have focused on biological and ecological covariates of TPL, while its statistical inherences have been extensively debated. In the present study, we focused on species-specific features (i.e. functional traits) that could be influential to temporal TPL. We combined field surveys of 180 fish species from 972 sites varying from small streams to large rivers with data on 31 ecological traits describing species-specific characteristics related to three main niche dimensions (trophic ecology, life history, and habitat use). For each species, the parameters of temporal TPL (intercept and slope) were estimated from the log-log mean-variance relationships while controlling for spatial dependencies and biological covariates (species richness and evenness). Then, we investigated whether functional traits explained variations in TPL parameters. Differences in TPL parameters among species were explained mostly by life history and environmental determinants, especially TPL slope. Life history was the main determinant of differences in TPL parameters and thereby aggregation patterns, with traits related to body size being the most influential, thus showing a high contrast between small-sized species with short lifespans and large-bodied migratory fishes, even after controlling for phylogenetic resemblances. We found that life history traits, especially those related to body size, mostly affect TPL and, as such, can be determinants of temporal variability of fish populations. We also found that statistical effects and phylogenetic resemblances are embedded in mean-variance relationships for fish, and that environmental drivers can interact with ecological characteristics of species in determining temporal fluctuations in abundance.
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Affiliation(s)
- Matheus T Baumgartner
- Graduate Program in Ecology of Freshwater Environments (PEA), Department of Biology (DBI), Center for Biological Sciences (CCB), State University of Maringá (UEM), Paraná, Brazil
- Department of Statistics (DES), Center for Exact Sciences (CCE), State University of Maringá (UEM), Paraná, Brazil
| | - Oscar Eduardo Peláez Zapata
- Graduate Program in Ecology of Freshwater Environments (PEA), Department of Biology (DBI), Center for Biological Sciences (CCB), State University of Maringá (UEM), Paraná, Brazil
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Carpenter S, Callens S, Brown C, Cohen JE, Webb BZ. Taylor's law for exponentially growing local populations linked by migration. Theor Popul Biol 2023; 154:118-125. [PMID: 37949177 DOI: 10.1016/j.tpb.2023.10.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2022] [Revised: 10/23/2023] [Accepted: 10/28/2023] [Indexed: 11/12/2023]
Abstract
We consider the dynamics of a collection of n>1 populations in which each population has its own rate of growth or decay, fixed in continuous time, and migrants may flow from one population to another over a fixed network, at a rate, fixed over time, times the size of the sending population. This model is represented by an ordinary linear differential equation of dimension n with constant coefficients arrayed in an essentially nonnegative matrix. This paper identifies conditions on the parameters of the model (specifically, conditions on the eigenvalues and eigenvectors) under which the variance of the n population sizes at a given time is asymptotically (as time increases) proportional to a power of the mean of the population sizes at that given time. A power-law variance function is known in ecology as Taylor's Law and in physics as fluctuation scaling. Among other results, we show that Taylor's Law holds asymptotically, with variance asymptotically proportional to the mean squared, on an open dense subset of the class of models considered here.
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Affiliation(s)
- Samuel Carpenter
- Department of Mathematics, Brigham Young University, Provo, UT 84602, USA.
| | - Scout Callens
- Department of Mathematics, Brigham Young University, Provo, UT 84602, USA.
| | - Clark Brown
- Department of Mathematics, Brigham Young University, Provo, UT 84602, USA.
| | - Joel E Cohen
- Laboratory of Populations, Rockefeller University, 1230 York Avenue, Box 20, New York, NY 10065, USA; Earth Institute & Department of Statistics, Columbia University, New York, NY 10027, USA; Department of Statistics, University of Chicago, Chicago, IL 60637, USA.
| | - Benjamin Z Webb
- Department of Mathematics, Brigham Young University, Provo, UT 84602, USA.
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Sassi AS, Garcia-Alcala M, Aldana M, Tu Y. Protein concentration fluctuations in the high expression regime: Taylor's law and its mechanistic origin. PHYSICAL REVIEW. X 2022; 12:011051. [PMID: 35756903 PMCID: PMC9233241 DOI: 10.1103/physrevx.12.011051] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Protein concentration in a living cell fluctuates over time due to noise in growth and division processes. In the high expression regime, variance of the protein concentration in a cell was found to scale with the square of the mean, which belongs to a general phenomenon called Taylor's law (TL). To understand the origin for these fluctuations, we measured protein concentration dynamics in single E. coli cells from a set of strains with a variable expression of fluorescent proteins. The protein expression is controlled by a set of constitutive promoters with different strength, which allows to change the expression level over 2 orders of magnitude without introducing noise from fluctuations in transcription regulators. Our data confirms the square TL, but the prefactor A has a cell-to-cell variation independent of the promoter strength. Distributions of the normalized protein concentration for different promoters are found to collapse onto the same curve. To explain these observations, we used a minimal mechanistic model to describe the stochastic growth and division processes in a single cell with a feedback mechanism for regulating cell division. In the high expression regime where extrinsic noise dominates, the model reproduces our experimental results quantitatively. By using a mean-field approximation in the minimal model, we showed that the stochastic dynamics of protein concentration is described by a Langevin equation with multiplicative noise. The Langevin equation has a scale invariance which is responsible for the square TL. By solving the Langevin equation, we obtained an analytical solution for the protein concentration distribution function that agrees with experiments. The solution shows explicitly how the prefactor A depends on strength of different noise sources, which explains its cell-to-cell variability. By using this approach to analyze our single-cell data, we found that the noise in production rate dominates the noise from cell division. The deviation from the square TL in the low expression regime can also be captured in our model by including intrinsic noise in the production rate.
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Affiliation(s)
| | - Mayra Garcia-Alcala
- Department of Molecular and Cellular Biology, John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
- Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Cuernavaca, Morelos 62210, México
| | - Maximino Aldana
- Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Cuernavaca, Morelos 62210, México
- Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, Ciudad de México 04510, México
| | - Yuhai Tu
- IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, U.S.A
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Kojima H, Mitsui Y, Ikegami T. Spatial and temporal Taylor's law in 1D chaotic maps. CHAOS (WOODBURY, N.Y.) 2021; 31:033111. [PMID: 33810725 DOI: 10.1063/5.0036892] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2020] [Accepted: 02/09/2021] [Indexed: 06/12/2023]
Abstract
By using low-dimensional chaotic maps, the power-law relationship established between the sample mean and variance called Taylor's Law (TL) is studied. In particular, we aim to clarify the relationship between TL from the spatial ensemble (STL) and the temporal ensemble (TTL). Since the spatial ensemble corresponds to independent sampling from a stationary distribution, we confirm that STL is explained by the skewness of the distribution. The difference between TTL and STL is shown to be originated in the temporal correlation of a dynamics. In case of logistic and tent maps, the quadratic relationship in the sample mean and variance, called Bartlett's law, is found analytically. On the other hand, TTL in the Hassell model can be well explained by the chunk structure of the trajectory, whereas the TTL of the Ricker model has a different mechanism originated from the specific form of the map.
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Affiliation(s)
- Hiroki Kojima
- The Graduate School of Arts and Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
| | - Yuzuru Mitsui
- The Graduate School of Arts and Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
| | - Takashi Ikegami
- The Graduate School of Arts and Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
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Gompertz, Makeham, and Siler models explain Taylor's law in human mortality data. DEMOGRAPHIC RESEARCH 2018. [DOI: 10.4054/demres.2018.38.29] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022] Open
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Kohyama TS, Kohyama TI, Sheil D. Definition and estimation of vital rates from repeated censuses: Choices, comparisons and bias corrections focusing on trees. Methods Ecol Evol 2017. [DOI: 10.1111/2041-210x.12929] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
| | - Tetsuo I. Kohyama
- Faculty of Environmental Earth ScienceHokkaido University Sapporo Japan
| | - Douglas Sheil
- Faculty of Environmental Sciences and Natural Resource ManagementNorwegian University of Life Sciences Ås Norway
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Cohen JE, Rodríguez-Planes LI, Gaspe MS, Cecere MC, Cardinal MV, Gürtler RE. Chagas disease vector control and Taylor's law. PLoS Negl Trop Dis 2017; 11:e0006092. [PMID: 29190728 PMCID: PMC5734788 DOI: 10.1371/journal.pntd.0006092] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2017] [Revised: 12/18/2017] [Accepted: 11/01/2017] [Indexed: 11/18/2022] Open
Abstract
BACKGROUND Large spatial and temporal fluctuations in the population density of living organisms have profound consequences for biodiversity conservation, food production, pest control and disease control, especially vector-borne disease control. Chagas disease vector control based on insecticide spraying could benefit from improved concepts and methods to deal with spatial variations in vector population density. METHODOLOGY/PRINCIPAL FINDINGS We show that Taylor's law (TL) of fluctuation scaling describes accurately the mean and variance over space of relative abundance, by habitat, of four insect vectors of Chagas disease (Triatoma infestans, Triatoma guasayana, Triatoma garciabesi and Triatoma sordida) in 33,908 searches of people's dwellings and associated habitats in 79 field surveys in four districts in the Argentine Chaco region, before and after insecticide spraying. As TL predicts, the logarithm of the sample variance of bug relative abundance closely approximates a linear function of the logarithm of the sample mean of abundance in different habitats. Slopes of TL indicate spatial aggregation or variation in habitat suitability. Predictions of new mathematical models of the effect of vector control measures on TL agree overall with field data before and after community-wide spraying of insecticide. CONCLUSIONS/SIGNIFICANCE A spatial Taylor's law identifies key habitats with high average infestation and spatially highly variable infestation, providing a new instrument for the control and elimination of the vectors of a major human disease.
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Affiliation(s)
- Joel E. Cohen
- Laboratory of Populations, Rockefeller University, New York, NY, United States of America
- Earth Institute and Department of Statistics, Columbia University, New York, NY, United States of America
- Department of Statistics, University of Chicago, Chicago, IL, United States of America
| | - Lucía I. Rodríguez-Planes
- Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales, Laboratory of Eco-Epidemiology, Ciudad Universitaria, Buenos Aires, Argentina
- Consejo Nacional de Investigaciones Científicas y Técnicas-Universidad de Buenos Aires. Instituto de Ecología, Genética y Evolución de Buenos Aires (IEGEBA), Ciudad Universitaria, Buenos Aires, Argentina
| | - María S. Gaspe
- Consejo Nacional de Investigaciones Científicas y Técnicas-Universidad de Buenos Aires. Instituto de Ecología, Genética y Evolución de Buenos Aires (IEGEBA), Ciudad Universitaria, Buenos Aires, Argentina
| | - María C. Cecere
- Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales, Laboratory of Eco-Epidemiology, Ciudad Universitaria, Buenos Aires, Argentina
- Consejo Nacional de Investigaciones Científicas y Técnicas-Universidad de Buenos Aires. Instituto de Ecología, Genética y Evolución de Buenos Aires (IEGEBA), Ciudad Universitaria, Buenos Aires, Argentina
| | - Marta V. Cardinal
- Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales, Laboratory of Eco-Epidemiology, Ciudad Universitaria, Buenos Aires, Argentina
- Consejo Nacional de Investigaciones Científicas y Técnicas-Universidad de Buenos Aires. Instituto de Ecología, Genética y Evolución de Buenos Aires (IEGEBA), Ciudad Universitaria, Buenos Aires, Argentina
| | - Ricardo E. Gürtler
- Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales, Laboratory of Eco-Epidemiology, Ciudad Universitaria, Buenos Aires, Argentina
- Consejo Nacional de Investigaciones Científicas y Técnicas-Universidad de Buenos Aires. Instituto de Ecología, Genética y Evolución de Buenos Aires (IEGEBA), Ciudad Universitaria, Buenos Aires, Argentina
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Watanabe H, Sano Y, Takayasu H, Takayasu M. Statistical properties of fluctuations of time series representing appearances of words in nationwide blog data and their applications: An example of modeling fluctuation scalings of nonstationary time series. Phys Rev E 2016; 94:052317. [PMID: 27967017 DOI: 10.1103/physreve.94.052317] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2016] [Indexed: 11/07/2022]
Abstract
To elucidate the nontrivial empirical statistical properties of fluctuations of a typical nonsteady time series representing the appearance of words in blogs, we investigated approximately 3×10^{9} Japanese blog articles over a period of six years and analyze some corresponding mathematical models. First, we introduce a solvable nonsteady extension of the random diffusion model, which can be deduced by modeling the behavior of heterogeneous random bloggers. Next, we deduce theoretical expressions for both the temporal and ensemble fluctuation scalings of this model, and demonstrate that these expressions can reproduce all empirical scalings over eight orders of magnitude. Furthermore, we show that the model can reproduce other statistical properties of time series representing the appearance of words in blogs, such as functional forms of the probability density and correlations in the total number of blogs. As an application, we quantify the abnormality of special nationwide events by measuring the fluctuation scalings of 1771 basic adjectives.
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Affiliation(s)
- Hayafumi Watanabe
- Hottolink,Inc., 6 Yonbancho Chiyoda-ku, Tokyo 102-0081, Japan.,Risk Analysis Research Center, The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan
| | - Yukie Sano
- Faculty of Engineering, Information and Systems, University of Tsukuba, Tennodai, Tsukuba, Ibaraki 305-8573, Japan
| | - Hideki Takayasu
- Sony Computer Science Laboratories, 3-14-13 Higashi-Gotanda, Shinagawa-ku, Tokyo 141-0022, Japan
| | - Misako Takayasu
- Institute of Innovative Research, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8502, Japan
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Ma ZS. Power law analysis of the human microbiome. Mol Ecol 2015; 24:5428-45. [DOI: 10.1111/mec.13394] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2014] [Revised: 08/10/2015] [Accepted: 09/21/2015] [Indexed: 01/14/2023]
Affiliation(s)
- Zhanshan Sam Ma
- Computational Biology and Medical Ecology Lab; State Key Laboratory of Genetic Resources and Evolution; Kunming Institute of Zoology; The Chinese Academy of Sciences; Kunming 650223 China
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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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Random sampling of skewed distributions implies Taylor's power law of fluctuation scaling. Proc Natl Acad Sci U S A 2015; 112:7749-54. [PMID: 25852144 DOI: 10.1073/pnas.1503824112] [Citation(s) in RCA: 60] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
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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Gürtler RE, Cohen JE. Invasive axis deer and wild boar in a protected area in Argentina, controlled hunting, and Taylor. WILDLIFE RESEARCH 2015. [DOI: 10.1071/wr20119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Mean and variance of population density and temporal Taylor’s law in stochastic stage-structured density-dependent models of exploited fish populations. THEOR ECOL-NETH 2014. [DOI: 10.1007/s12080-014-0242-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Population age and initial density in a patchy environment affect the occurrence of abrupt transitions in a birth-and-death model of Taylor's law. Ecol Modell 2014. [DOI: 10.1016/j.ecolmodel.2014.06.022] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Cohen JE. Stochastic population dynamics in a Markovian environment implies Taylor’s power law of fluctuation scaling. Theor Popul Biol 2014; 93:30-7. [DOI: 10.1016/j.tpb.2014.01.001] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2013] [Revised: 01/02/2014] [Accepted: 01/10/2014] [Indexed: 01/20/2023]
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