Back to Search
Start Over
Sample and population exponents of generalized Taylor’s law
- Source :
- Proceedings of the National Academy of Sciences. 112:7755-7760
- Publication Year :
- 2015
- Publisher :
- Proceedings of the National Academy of Sciences, 2015.
-
Abstract
- Taylor's law (TL) states that the variance $V$ of a non-negative random variable is a power function of its mean $M$, i.e. $V=a M^b$. The ubiquitous empirical verification of TL, typically displaying sample exponents $b \simeq 2$, suggests a context-independent mechanism. However, theoretical studies of population dynamics predict a broad range of values of $b$. Here, we explain this apparent contradiction by using large deviations theory to derive a generalized TL in terms of sample and populations exponents $b_{jk}$ for the scaling of the $k$-th vs the $j$-th cumulant (conventional TL is recovered for $b=b_{12}$), with the sample exponent found to depend predictably on the number of observed samples. Thus, for finite numbers of observations one observes sample exponents $b_{jk}\simeq k/j$ (thus $b\simeq2$) independently of population exponents. Empirical analyses on two datasets support our theoretical results.<br />Comment: 41 pages, 10 figures, 6 tables
- Subjects :
- 0106 biological sciences
Population Dynamics
Population
Sample (statistics)
Multiplicative growth
Empirical Research
Fluctuation scaling
010603 evolutionary biology
01 natural sciences
Power law
Theoretical
Models
0103 physical sciences
Statistics
Range (statistics)
Statistical physics
Quantitative Biology - Populations and Evolution
010306 general physics
education
Scaling
Mathematics
education.field_of_study
Environmental stochasticity
Markovian environment
Models, Theoretical
Multidisciplinary
Taylor's law
Populations and Evolution (q-bio.PE)
Biological Sciences
FOS: Biological sciences
Exponent
Large deviations theory
Subjects
Details
- ISSN :
- 10916490 and 00278424
- Volume :
- 112
- Database :
- OpenAIRE
- Journal :
- Proceedings of the National Academy of Sciences
- Accession number :
- edsair.doi.dedup.....8c128fd811730d094e9f3287f1876521