Comparison of five methods for parameter estimation under Taylor’s power law

Shi, Peijian; Ratkowsky, David A.; Wang, Ningtao; Li, Yang; Zhao, Lei; Reddy, Gadi V. P.; Li, Bai Lian

doi:10.1016/j.ecocom.2017.10.006

Cited by 17 publications

(16 citation statements)

References 41 publications

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“…Therefore, the scaling relationship of leaf weight and leaf area of bamboo plants is significantly stronger than those of the other two classes of plants based on the comparison of the coefficients of determination (i.e., R 2 ). Because the biomass (weight) is a better measurement than the area or length in describing TPL [18,23], plants with a better scaling relationship between leaf weight and leaf area will have a better TPL for describing leaf bilateral symmetry. If we could cut a leaf into different parts with equidistant intervals from the leaf base to leaf apex and measure their weights (see Figure 1), we believe that we would obtain a better goodness of fit for TPL by using the measures of leaf weight than using the measures of leaf area.…”

Section: Resultsmentioning

confidence: 99%

“…This power law has been found to be valid in many areas of study [14]. Controversy surrounding recent relevant studies is about whether the exponent β of TPL is determined by an inherent biological mechanism or is only a purely statistical feature [15][16][17][18]. Cohen and Xu demonstrated that the estimate of the exponent of TPL is proportional to the skewness of the distribution generated by random sampling in blocks [15].…”

Section: Introductionmentioning

confidence: 99%

“…Shi et al [17] used two clustering point process models to examine the effect of dispersal distance of plant seeds or rhizomes on the estimate of the exponent of TPL, and found that with increasing dispersal distance the exponent described a complex response curve. In addition, dry weights of crops at different investigation times and the development and growth rates of insects at different temperatures have also been shown to follow TPL [18]. These measures associated with TPL appear to be related to the energy distribution among different statistical units.…”

Section: Introductionmentioning

confidence: 99%

“…Then, fixing the exponent of TPL to 2.0, the estimate of the logarithm of the constant α in TPL was demonstrated to be a logarithmic function of the time interval division. These studies related to TPL have added to our understanding of the variation of a large number of ecological and non-ecological measures, for example, animal and plant population density, biomass, poikilothermic developmental rate, crime, precipitation, released energies of aftershocks, trading activity of stock, and so on [13,[18][19][20][21][22]. In our recent studies, weight is a typical representative of energy for biological measures, so the variance-mean relationship based on weight measures should reflect TPL well [23].…”

Section: Introductionmentioning

confidence: 99%

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Taylor’s Power Law for Leaf Bilateral Symmetry

Wang

Ratkowsky

Xiao

et al. 2018

Forests

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Abstract:Leaf shape and symmetry is of interest because of the importance of leaves in photosynthesis. Recently, a novel method was proposed to measure the extent of bilateral symmetry in leaves in which a leaf was divided into left and right sides by a straight line through the leaf apex and base, and a number of equidistant strips were drawn perpendicular to the straight line to generate an equivalent number of differences in area between the left and right parts. These areal differences are the basis for a measure of leaf bilateral symmetry, which was then examined to see how well it follows Taylor's power law (TPL) using three classes of plants, namely, 10 geographical populations of Parrotia subaequalis (H.T. Chang) R.M. Hao et H.T. Wei, 10 species of Bambusoideae, and 10 species of Rosaceae. The measure of bilateral symmetry followed TPL for a single species or for a class of closely related species. The estimate of the exponent of TPL for bamboo plants was significantly larger than for the dicotyledonous trees, but its goodness of fit was the best among the three classes of plants. The heterogeneity of light falling on branches and leaves due to above-ground architectural patterns is an important contributor to leaf asymmetry.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Taylor’s Power Law for Leaf Bilateral Symmetry

Wang

Ratkowsky

Xiao

et al. 2018

Forests

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“…An increasing number of investigations show that there is an interaction effect for the occurrence of aftershocks in a given area. A stress-triggering model is usually used to depict interaction between larger earthquakes in the view of physics (Harris, 1998;Stein, 1999). More and more results show that obvious increases in Coulomb stress not only promote the occurrence of upcoming middle or strong events of an earthquake sequence but also affect their spatial distribution to some degree (Robinson and Zhou, 2005).…”

Section: Introductionmentioning

confidence: 99%

Taylor's power law in the Wenchuan earthquake sequence with fluctuation scaling

Shi

et al. 2019

Nat. Hazards Earth Syst. Sci.

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Abstract. Taylor's power law (TPL) describes the scaling relationship between the temporal or spatial variance and mean of population densities by a simple power law. TPL has been widely testified across space and time in biomedical sciences, botany, ecology, economics, epidemiology, and other fields. In this paper, TPL is analytically reconfirmed by testifying the variance as a function of the mean of the released energy of earthquakes with different magnitudes on varying timescales during the Wenchuan earthquake sequence. Estimates of the exponent of TPL are approximately 2, showing that there is mutual attraction among the events in the sequence. On the other hand, the spatio-temporal distribution of the Wenchuan aftershocks tends to be nonrandom but approximately definite and deterministic, which highly indicates a stable spatio-temporally dependent energy release caused by regional stress adjustment and redistribution during the fault revolution after the mainshock. The effect of different divisions on estimation of the intercept of TPL straight line has been checked, while the exponent is kept to be 2. The result shows that the intercept acts as a logarithm function of the time division. It implies that the mean–variance relationship of the energy release from the earthquakes can be predicted, although we cannot accurately know the occurrence time and locations of imminent events.

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The effect of temperature on the developmental rates of seedling emergence and leaf-unfolding in two dwarf bamboo species

Lin

Shao

Hui

et al. 2018

Trees

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Key messageThe mean and variance of developmental rates of bamboos at different temperatures follow a power law. The rate isomorphy hypothesis, demonstrated in insects and mites, does not hold in bamboos. Abstract The developmental time of plants and poikilotherms can be significantly affected by temperature. Developmental rate (i.e. the reciprocal of developmental time) of arthropods and germination rate of some plant seeds have been demonstrated to follow a linear function with temperature. The rate isomorphy hypothesis in entomology suggests a lower developmental threshold below which development of all life stages terminates. If this hypothesis also holds for plants, the estimated lower threshold for one development stage could be used for predicting thresholds of other stages. Here, we tested this hypothesis to compare the developmental time of seedling emergence and the time from seedling emergence to the unfolding of the third leaf in two bamboo species. We used five constant thermal environments from 18.5 to 28.5 °C with an increment of 2.5 °C. Both species showed a linear relationship between temperature and developmental rate, with the mean and variance of developmental rates following a power law. Using the bootstrap percentile method, we showed that the isomorphy hypothesis does not hold for both species. The effect of temperature on the survival rate at the time of seedling emergence differed significantly between the two species.

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Comparison of five methods for parameter estimation under Taylor’s power law

Cited by 17 publications

References 41 publications

Taylor’s Power Law for Leaf Bilateral Symmetry

Taylor’s Power Law for Leaf Bilateral Symmetry

Taylor's power law in the Wenchuan earthquake sequence with fluctuation scaling

The effect of temperature on the developmental rates of seedling emergence and leaf-unfolding in two dwarf bamboo species

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