Stochastic multiplicative population growth predicts and interprets Taylor's power law of fluctuation scaling

Cohen, Joel E.; Meng, Xu; Schuster, William S. F.

doi:10.1098/rspb.2012.2955

Cited by 53 publications

(60 citation statements)

References 42 publications

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“…The higher exponent reflects greater heterogeneity from a pure random distribution. When the exponent is higher than 2, it may propose deterministic and exponential growth (Ballantyne, 2005;Cohen et al, 2013). An earlier study about individual trees also found that the scaling exponent did not fall within the proposed range (Cohen et al, 2012).…”

Section: Discussionmentioning

confidence: 99%

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Power Laws in Cone Production of Longleaf Pine across Its Native Range in the United States

Chen¹,

Guo²,

Brockway³

2017

SAR

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Longleaf pine (Pinus palustris Mill.) forests in the southeastern United States are considered endangered ecosystems, because of their dramatic decrease in area since European colonization and poor rates of recovery related to episodic natural regeneration. Sporadic seed production constrains restoration efforts and complicates sustainable management of this species. Previous studies of other tree species found invariant scaling properties in seed output. Here, using long-term monitoring data for cone production at seven sites across the native range of longleaf pine, we tested the possible presence of two types of power laws. Findings indicate that (i) the frequency distribution of cone production at seven sites, from 1958 to 2014, follows power law relationships with high level of significance; (ii) although there is no general trend in the dynamics of scaling exponents among all sites, there are dynamics of scaling exponents at each site, with sudden changes in scaling exponents generally corresponding to the years of higher or lower cone production; and (iii) Taylor"s power laws explain cone production at different locations, but the scaling exponents vary among these. Results from this computational approach provide new insight into the irregular cone production of longleaf pine at spatial and temporal scales. Integrated ecosystem monitoring will be necessary to more fully understand future changes in cone production.

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Section: Discussionmentioning

confidence: 99%

“…Taylor"s Law is one of the most widely verified empirical relationships in ecology. It was verified in hundreds of species including trees (Cohen, Xu, & Schuster, 2012;2013). For our study, Taylor"s Law can be expressed in the following way for this study:…”

Section: Methodsmentioning

confidence: 99%

Power Laws in Cone Production of Longleaf Pine across Its Native Range in the United States

Chen¹,

Guo²,

Brockway³

2017

SAR

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“…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)(22)(23), models of spatially distributed colonies (24,25), a stochastic version of logistic population dynamics (16), and the Lewontin-Cohen stochastic multiplicative population model (8). The diversity of empirical confirmations suggests that no specific biological, physical, technological, or behavioral mechanism explains all instances of TL.…”

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confidence: 99%

“…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)(3)(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).…”

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confidence: 99%

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

Cohen

Meng

2015

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

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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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“…One possible approach is a model of stochastic multiplicative population growth that has been shown to predict TL and to provide an interpretation of the parameters of TL (24). In this model, population density changes from one discrete time (e.g., day or year) to the next discrete time as a result of multiplying the earlier population density by a random positive growth factor, which is assumed to be independently and identically distributed in time.…”

Section: Discussionmentioning

confidence: 99%

Parasitism alters three power laws of scaling in a metazoan community: Taylor’s law, density-mass allometry, and variance-mass allometry

Lagrue

Poulin

Cohen

2014

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

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How do the lifestyles (free-living unparasitized, free-living parasitized, and parasitic) of animal species affect major ecological power-law relationships? We investigated this question in metazoan communities in lakes of Otago, New Zealand. In 13,752 samples comprising 1,037,058 organisms, we found that species of different lifestyles differed in taxonomic distribution and body mass and were well described by three power laws: a spatial Taylor's law (the spatial variance in population density was a power-law function of the spatial mean population density); density-mass allometry (the spatial mean population density was a power-law function of mean body mass); and variance-mass allometry (the spatial variance in population density was a power-law function of mean body mass). To our knowledge, this constitutes the first empirical confirmation of variance-mass allometry for any animal community. We found that the parameter values of all three relationships differed for species with different lifestyles in the same communities. Taylor's law and density-mass allometry accurately predicted the form and parameter values of variance-mass allometry. We conclude that species of different lifestyles in these metazoan communities obeyed the same major ecological power-law relationships but did so with parameters specific to each lifestyle, probably reflecting differences among lifestyles in population dynamics and spatial distribution.parasite | metazoan | power law | Taylor's law | allometry V ariation in population density has long been a central topic in ecology (e.g., ref. 1). Taylor's law (TL) (2, 3) is a pattern of variation that has been widely verified for population density in basic and applied ecology and for other quantities in other fields. In its ecological interpretations, TL asserts that, in multiple sets of populations, the sample variance in population density within each set is proportional to a power (usually positive) of the sample mean population density within that set. We specify TL in greater detail below.Morand and Guégan (4) showed that TL described well the variations of abundance per host in 828 populations of parasitic nematodes from 66 terrestrial mammalian species. Morand and Krasnov (5) reviewed examples of TL in parasitology and epidemiology and interpreted the exponent of the TL power law in terms of the aggregation of parasites and epidemiological dynamics. These studies used the number of individual parasites per individual host as the measure of population density. Following a suggestion of Taylor (2), these studies interpreted the exponent of the power-law relationship of variance of population density to mean of population density as an index of parasite aggregation among hosts. A purely random distribution of parasites per host leads to a Poisson distribution, which gives a TL exponent equal to 1 as the mean population density varies. A TL exponent greater than 1 reflects greater heterogeneity in numbers of individuals per host than expected from a purely random distribution. More ...

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Stochastic multiplicative population growth predicts and interprets Taylor's power law of fluctuation scaling

Cited by 53 publications

References 42 publications

Power Laws in Cone Production of Longleaf Pine across Its Native Range in the United States

Power Laws in Cone Production of Longleaf Pine across Its Native Range in the United States

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

Parasitism alters three power laws of scaling in a metazoan community: Taylor’s law, density-mass allometry, and variance-mass allometry

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