### Kendal, WS (2004)

#### Taylor’s ecological power law as a consequence of scale invariant exponential dispersion models

Ecological Complexity 1(3), pp. 193-209.

**ISSN/ISBN:** Not available at this time.
**DOI:** Not available at this time.

**Abstract:** A power function relationship between the variance and the mean number of organisms per quadrat of habitat is commonly called Taylor’s power law. Taylor’s law also manifests with other seemingly disparate processes such as the transmission of infectious diseases, human sexual behavior, childhood leukemia, cancer metastases, blood flow heterogeneity, as well as with the genomic distributions of single nucleotide polymorphisms and gene structures. The theory of errors provides, through the scale invariant exponential dispersion models, a number of statistical distributions that are characterized by Taylor’s law. One of these models, the scale invariant Poisson gamma (PG) distribution, has its power function exponent constrained to range between 1 and 2, as observed with many ecological systems. The PG model can be interpreted such that each quadrat would contain a random (Poisson-distributed) number of clusters that, on average, would themselves contain gamma-distributed number of individuals presumably determined by stochastic birth, death and immigration processes. Scale invariant exponential dispersion models also serve as limiting distributions for a wide range of other general linearized models, a property which could explain the manifestation of the variance to mean power function in so many diverse and complex natural processes and simulations.

**Bibtex:**

```
@article{,
title={Taylor’s ecological power law as a consequence of scale invariant exponential dispersion models},
author={Kendal, Wayne S},
journal={Ecological Complexity},
volume={1},
number={3},
pages={193--209},
year={2004},
publisher={Elsevier}
}
```

**Reference Type:** Journal Article

**Subject Area(s):** Medical Sciences, Statistics