Taylor's Power Law

Taylor's Power Law: Order and Pattern in Nature is a broad synthesis of this ubiquitous property of natural and man-made phenomena. This stimulating and approachable work surveys the biological and non-biological empirical data, describes the statistical uses of Taylor’s power law (TPL) and its relationship to statistical distributions, exposes the mathematical connections to other power laws, covers the competing explanatory models; and develops an argument for TPL's genesis.

Taylor’s power law relates the variability of a process or population to its average value. It was first described in relation to insect populations and then more broadly to other animal and plant populations. Subsequently it has been recognized in microbiology, genetics, economics, astronomy, physics, and computer science, and it is thought to be one of the few general laws in ecology where it is routinely used to describe the spatial and temporal distributions of populations.

Biologists who know the law as Taylor's power law and physical scientists who know it as fluctuation scaling will be interested in the bigger picture on this fascinating subject. As the relationship between variance and mean is found in so wide a range of disciplines, it seems possible it is a deep property of number, not just a phenomenon in ecology as was thought originally. Although theories abound that purport to explain or predict TPL, none is entirely satisfactory either because it fails to be very predictive, or it does not account for all the available empirical data. To uncover such a property requires a synthesis across disciplines, an acute need that is approached by this exciting work.

• Provides a single reference describing the properties, scope, and limitations of Taylor’s power law
• Reports the empirical, analytical, and theoretical work without opinion and ends with a critique of the work in order to develop a synthesis
• Collects together thoughts and suggestions of the hundreds who have written and speculated about Taylor’s power law in order to review examples (and counter-examples), as well as examine the various models developed to account for it

Biologists, ecologists, entomologists, agriculture scientists, plant pathologists, field biologists, forestry managers, fisheries managers, applied statisticians, geographers, researchers in demographics, computer scientists, applied mathematicians, physicists and other physical scientists, graduate/advanced UG students in biological sciences

1. Introduction
Part I
2. Spatial pattern
3. Measuring aggregation
4. Fitting TPL
Part II
5. Microorganisms
6. Plants
7. Nematodes and other worms
8. Insects and other arthropods
9. Other invertebrates
10. Vertebrates
11. Other biological examples
12. Nonbiological examples
13. Counter examples
Part III
14. Applications of TPL
15. Properties of TPL
16. Allometry and other power laws
17. Modeling TPL
18. Summary and synthesis
19. Epilogue