Stochastic multiplicative population growth predicts and interprets taylor's power law of fluctuation scaling

Proceedings of the Royal Society B: Biological Sciences

Volumn 280, Issue 1757, 2013, Pages

  Cohen, Joel E ^a   Xu, Meng ^a   Schuster, William S F ^b  

^a The Rockefeller University and Columbia University ^*  (United States)

^b Black Rock Forest Consortium   (United States)

Author keywords

Fluctuation scaling; Forestry; Geometric random walk; Lewontin cohen model; Power law; Taylor's law

Indexed keywords

EMPIRICAL ANALYSIS; FORESTRY MODELING; GEOMETRY; LONG-TERM CHANGE; POPULATION GROWTH; POWER LAW; PREDICTION; SPATIAL VARIATION; STOCHASTICITY;

BADEN-WURTTEMBERG; BLACK FOREST; GERMANY;

EID: 84874275201     PISSN: 09628452     EISSN: 14712954     Source Type: Journal    
DOI: 10.1098/rspb.2012.2955     Document Type: Article

References (49)

1. Eisler Z, Bartos I, Kertész J. 2008 Fluctuation scaling in complex systems: Taylor's law and beyond. Adv. Phys. 57, 89-142. (doi:10.1080/00018730801893043)
2. Azevedo RBR, Leroi AM. 2001 A power law for cells. Proc. Natl Acad. Sci. USA 98, 5699-5704. (doi:10. 1073/pnas.091485998)
3. Taylor LR. 1961 Aggregation, variance and the mean. Nature 189, 732-735. (doi:10.1038/189732a0)
4. Taylor LR, Woiwod IP. 1980 Temporal stability as a density-dependent species characteristic. J. Anim. Ecol. 49, 209-224. (doi:10.2307/4285)
5. Taylor LR, Woiwod IP. 1982 Comparative synoptic dynamics. I. Relationships between inter- and intraspecific spatial and temporal variance/mean population parameters. J. Anim. Ecol. 51, 879-906. (doi:10.2307/4012)
6. Klein AM, Simons BD. 2011 Universal patterns of stem cell fate in cycling adult tissues. Development 138, 3103-3111. (doi:10.1242/dev.060103)
7. Ramsayer J, Fellous S, Cohen JE, Hochberg ME. 2011 Taylor's law holds in experimental bacterial populations but competition does not influence the slope. Biol. Lett. 8, 316-319. (doi:10.1098/rsbl.2011.0895)
8. Kaltz O, Escobar-Paramo P, Hochberg M, Cohen JE. 2012 Bacterial microcosms obey Taylor's law: effects of abiotic and biotic stress and genetics on mean and variance of population density. Ecol. Process. 1, 5. (doi:10.1186/2192-1709-1-5)
9. Hekstra DR, Leibler S. 2012 Contingency and statistical laws in replicate microbial closed ecosystems. Cell 149, 1164-1173. (doi:10.1016/j.cell.2012.03.040)
10. Kilpatrick AM, Ives AR. 2003 Species interactions can explain Taylor's power law for ecological time series. Nature 422, 65-68. (doi:10.1038/nature01471)
11. Anderson RM, Gordon DM, Crawley MJ, Hassell MP. 1982 Variability in the abundance of animal and plant species. Nature 296, 245-248. (doi:10.1038/296245a0)
12. Ballantyne IV F, Kerkhoff AJ. 2007 The observed range for temporal mean-variance scaling exponents can be explained by reproductive correlation. Oikos 116, 174-180. (doi:10.1111/j. 2006.0030-1299.15383.x)
13. Engen S, Lande R, Saether B-E. 2008 A general model for analyzing Taylor's spatial scaling laws. Ecology 89, 2612-2622. (doi:10.1890/07-1529.1)
14. Gillis DM, Kramer DL, Bell G. 1986 Taylor's power law as a consequence of Fretwell's ideal free distribution. J. Theor. Biol. 123, 281-287. (doi:10. 1016/S0022-5193(86)80243-0)
15. Keeling MJ. 2000 Simple stochastic models and their power-law type behavior. Theor. Popul. Biol. 58, 21-31. (doi:10.1006tpbi.2000.1475)
16. Perry JN. 1988 Some models for spatial variability of animal species. Oikos 51, 124-130. (doi:10.2307/ 3565634)
17. Kemp AW. 1987 Families of discrete distributions satisfying Taylor's power law. Biometrics 43, 693-699. (doi:10.2307/2532005)
18. Kendal WS. 2004 Taylor's ecological power law as a consequence of scale invariant exponential dispersion models. Ecol. Complex. 1, 193-209. (doi:10.1016/j.ecocom.2004.05.001)
19. Jørgensen B. 1987 Exponential dispersion models. J. Royal Stat. Soc. B 49, 127-162. See http://www. jstor.org/stable/2345415.
20. Tweedie MCK. 1946 The regression of the sample variance on the sample mean. J. Lond. Math. Soc. 21, 22-28. (doi:10.1112/jlms/s1-21.1.22)
21. Tweedie MCK. 1947 Functions of a statistical variate with given means, with special reference to Laplacian distributions. Proc. Cambridge Philos. Soc. 43, 41-49. (doi:10.1017/S0305004100023185)
22. Tweedie MCK. 1984 An index which distinguishes between some important exponential families. In Statistics: applications and new directions (eds JK Ghosh, J Roy), pp. 579-604. Calcutta, India: Indian Statistical Institute.
23. Perry JN, Taylor LR. 1985 Ades: new ecological families of species-specific frequency distributions that describe repeated spatial samples with an intrinsic power-law variance-mean property. J. Anim. Ecol. 54, 931-953. (doi:10.2307/4388)
24. Taylor LR, Woiwod IP, Perry JN. 1978 The densitydependence of spatial behavior and the rarity of randomness. J. Anim. Ecol. 47, 383-406. See http://www.jstor.org/stable/3790.
25. Schuster WSF, Griffin KL, Roth H, Turnbull MH, Whitehead D, Tissue DT. 2008 Changes in composition, structure and aboveground biomass over seventy-six years (1930-2006) in the Black Rock Forest, Hudson Highlands, southeastern New York State. Tree Physiol. 28, 537-549. (doi:10. 1093/treephys/28.4.537)
26. Goodman LA. 1960 On the exact variance of products. J. Am. Stat. Assoc. 55, 708-713. (doi:10. 1080/01621459.1960.10483369)
27. Shellard GD. 1952 Estimating the product of several random variables. J. Am. Stat. Assoc. 47, 216-221. (doi:10.1080/01621459.1952.10501165)
28. Goodman LA. 1962 The variance of the product of K random variables. J. Am. Stat. Assoc. 57, 54-60. (doi:10.1080/01621459.1962.10482151)
29. Cohen JE, Xu M, Schuster WSF. 2012 Allometric scaling of population variance with mean body size is predicted from Taylor's law and density-mass allometry. Proc. Natl Acad. Sci. USA 109, 15829-15834. (doi:10.1073/pnas.1212883109)
30. Snedecor GW, Cochran WG. 1980 Statistical methods, 7th edn. Ames, IA: Iowa State University Press.
31. Cohen JE, Carpenter SR. 2005 Species' average body mass and numerical abundance in a community food web: statistical questions in estimating the relationship. In Dynamic food webs: multispecies assemblages, ecosystem development and environmental change (eds PC de Ruiter, V Wolters, JC Moore), pp. 137-156. Amsterdam, The Netherlands: Elsevier.
32. MathWorks Inc. 2011 MATLAB R2011b. Natick, MA: MathWorks Inc.
33. SAS Institute Inc. 2010 JMP 9.0.2. Cary, NC: SAS Institute Inc.
34. Lewontin RC, Cohen D. 1969 On population growth in a randomly varying environment. Proc. Natl Acad. Sci. USA 62, 1056-1060. (doi:10.1073/pnas. 62.4.1056)
35. Smith RH, Mead R. 1975 A note on population growth in a variable environment. Oecologia 20, 333-337. (doi:10.1007/BF00345523)
36. Williams BK, Nichols JD, Conroy MJ. 2002 Analysis and management of animal populations: modeling, estimation, and decision making. San Diego, CA: Academic Press.
37. Drake JM. 2005 Population effects of increased climate variation. Proc. R. Soc. B 272, 1823-1827. (doi:10.1098/rspb.2005.3148)
38. Aitchison J, Brown JAC. 1957 The lognormal distribution with special reference to its uses in economics. Cambridge, UK: Cambridge University Press.
39. Johnson NL, Kotz S. 1970 Continuous univariate distributions 1, 2nd edn. New York, NY: Wiley- Interscience.
40. Niwa H-S. 2007 Random-walk dynamics of exploited fish populations. ICES J. Mar. Sci. 64, 496-502. (doi:10. 1093/icesjms/fsm004)
41. Ballantyne F. 2005 The upper limit for the exponent of Taylor's power law is a consequence of deterministic population growth. Evol. Ecol. Res. 7, 1213-1220.
42. Jørgensen B. 1997 The theory of dispersion models. London, UK: Chapman & Hall.
43. Taylor LR, Taylor RAJ. 1977 Aggregation, migration and population mechanics. Nature 265, 415-421. (doi:10.1038/265415a0)
44. Taylor LR, Woiwod IP, Perry JN. 1980 Variance and the large scale spatial stability of aphids, moths and birds. J. Anim. Ecol. 49, 831-854. (doi:10.2307/ 4230)
45. Taylor LR, Taylor RAJ, Woiwod IP, Perry JN. 1980 Behavioural dynamics. Nature 303, 801-804. (doi:10.1038/303801a0)
46. Taylor LR. 1984 Assessing and interpreting the spatial distributions of insect populations. Annu. Rev. Entomol. 29, 321-357. (doi:10.1146/annurev. en.29.010184.001541)
47. Hanski I. 1980 Spatial patterns and movements in coprophagous beetles. Oikos 34, 293-310. (doi:10. 2307/3544289)
48. Hanski I. 1987 Cross-correlation in population dynamics and the slope of spatial variance: mean regressions. Oikos 50, 148-151. (doi:10.2307/ 3565413)
49. Hanski I. 1982 On patterns of temporal and spatial variation in animal populations. Ann. Zool. Fennici 19, 21-37.