On the use of log-transformation vs. nonlinear regression for analyzing biological power laws

Xiao, Xiao; White, Ethan; Hooten, Mevin B.; Durham, Susan L.

doi:10.1890/11-0538.1

Cited by 275 publications

(321 citation statements)

References 23 publications

Supporting

Mentioning

300

Contrasting

Unclassified

Order By: Relevance

“…2 had statistically significantly nonzero linear coefficient b (with P < α; here α = 0.05), and if a least-squares quadratic regression between the independent variable log(mean) and dependent variable log(variance) did not yield a statistically significant quadratic coefficient c (P > α). The use of the doubly logarithmic scale in the testing of TL and other bivariate allometric relationships (e.g., scaling of metabolic rate with body mass) has been questioned (39,(42)(43)(44) and defended (45,46).…”

Section: Methodsmentioning

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.

109

122

View full text Add to dashboard Cite

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...

show abstract

Section: Methodsmentioning

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.

109

122

View full text Add to dashboard Cite

show abstract

“…The charts showed a nonlinear mean relationship and multiplicative, heteroscedastic, lognormal error distribution for each of the independent variables ( Figure 6). Therefore, the regression models, which were tested, were fitted in log-transformed form to the logarithm of the stem biomass, as suggested by Xiao et al (2011) andSileshi (2014). Stankova et al: Aboveground dendromass estimation of juvenile Paulownia sp.…”

Section: Model Development / Razvoj Modelamentioning

confidence: 99%

Aboveground Dendromass Estimation of Juvenile Paulownia Sp.

Stankova¹,

Gyuleva²,

Dimitrov³

et al. 2017

GSFUBL

View full text Add to dashboard Cite

Species of the genus Paulownia have been introduced to Bulgaria since the beginning of the XXth century and their multipurpose uses -as ornamental trees, for wood and biomass production -have been tested ever since. We present a study, which examines the early growth of four Paulownia clones at southern locations in Bulgaria and derives biometric models for dendromass estimation of juvenile Paulownia trees. The data originated from two experimental plantations established on nursery land using one-yearold in vitro propagated plant material. Forty six, 1 to 3 year-old saplings from two clones of P. tomentosa and two P. elongata × P. fortunei hybrids were sampled. Their stem biomass was modeled as a function of the breast height tree diameter and total tree height or the stem diameter alone and a set of goodness-of-fit criteria was applied to select the most adequate among the 29 tested formulations. The regression models were fitted in log-transformed form to the logarithm of the stem biomass and MM correction factor for bias was applied to the back-transformed prediction data. Two allometric relationships were derived, which adequately assess stem dendromass of young Paulownia sp. from easily measurable tree characteristics. Both models are applicable for stem biomass estimation of juvenile Paulownia trees of diameter up to 5 cm and total height up to 3.5 m.

show abstract

“…However, the logarithm alters the data distribution, which may lead to misguided inferences from OLS [1,2]. Therefore the flexibility offered by GLS is expected to be beneficial in this case, as it allows the observed distribution to deviate from the modeled distribution.…”

Section: Effect Of Logarithmic Transformationmentioning

confidence: 99%

“…without logarithmic transformation. Whereas this prevents an analytic solution using OLS, the advantage is that the distribution of the data is left undistorted [1,2], while the implementation of both OLS and GLS is not significantly more complex. Indeed, the distribution of the right-hand side in (4) can be approximated by a Gaussian with mean µ mod = b 0n…”

Section: Nonlinear Scalingmentioning

confidence: 99%

“…However, often there is considerable uncertainty in the experimental data, including predictor variables, and in the model equations (regression model). As such, OLS regression is often unsuitable [1,2], and many scientific fields could benefit greatly from a unified regression methodology that is flexible and robust and yet is relatively simple to implement. For these reasons we have developed a new regression method, called geodesic least squares regression (GLS).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Geodesic least squares regression on information manifolds

Verdoolaege¹

2014

AIP Conference Proceedings

View full text Add to dashboard Cite

Abstract. In regression analyses for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS) is the most popular. However, concerns have been raised with respect to several assumptions underlying OLS in its application to scaling laws. We here discuss a new regression method that is robust in the presence of significant uncertainty on both the data and the regression model. The method, which we call geodesic least squares regression (GLS), is based on minimization of the Rao geodesic distance on a probabilistic manifold. We demonstrate the superiority of the method using synthetic data and we present an application to the scaling law for the power threshold for the transition to the high confinement regime in magnetic confinement fusion devices.

show abstract

On the use of log-transformation vs. nonlinear regression for analyzing biological power laws

Cited by 275 publications

References 23 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

Aboveground Dendromass Estimation of Juvenile Paulownia Sp.

Geodesic least squares regression on information manifolds

Contact Info

Product

Resources

About