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Taylor's law (also known as ''Taylor’s power law'') is an empirical law in ecology that relates the variance of the number of individuals of a species per unit area of habitat to the corresponding mean by a power law relationship.〔Taylor LR (1961) Aggregation, variance and the mean. ''Nature'' 189, 732–735〕 ==Definition== This law was originally defined for ecological systems, specifically to assess the spatial clustering of organisms. For a population count ''Y'' with mean ''µ'' and variance var(''Y''), Taylor’s law is written, : , where ''a'' and ''b'' are both positive constants. Taylor proposed this relationship in 1961, suggesting that the exponent ''b'' be considered a species specific index of aggregation.〔 This power law has subsequently been confirmed for many hundreds of species.〔Taylor LR & Woiwod, IP (1980) Temporal Stability as a Density-Dependent Species Characteristic. ''J Animal Ecol'' 49, 209–224〕〔Taylor LR & Woiwod (1982) Comparative Synoptic Dynamics. I. Relationships Between Inter- and Intra-Specific Spatial and Temporal Variance/Mean Population Parameters. ''J Animal Ecol'' 51, 879–906〕 Taylor’s law has also been applied to assess the time dependent changes of population distributions.〔 Related variance to mean power laws have also been demonstrated in several non-ecological systems: *cancer metastasis〔Kendal WS & Frost P (1987) Experimental metastasis: a novel application of the variance-to-mean power function. ''J Natl Cancer Inst'' 79, 1113-1115〕 *the numbers of houses built over the Tonami plain in Japan.〔Kendal WS (1995) A probabilistic model for the variance to mean power law in ecology. Ecological Modelling 80, 293-297〕 *measles epidemiology〔Keeling M & Grenfell B (1999) Stochastic dynamics and a power law for measles variability. ''Phil Trans R Soc Lond B Biol Sci'' 354, 769-776〕 *HIV epidemiology,〔Anderson RM & May RM (1989) Epidemiological parameters of HIV transmission. ''Nature'' 333, 514–519〕 *the geographic clustering of childhood leukemia〔Philippe P (1999) The scale-invariant spatial clustering of leukemia in San Francisco. ''J Theor Biol'' 199, 371-381〕 *blood flow heterogeneity〔Bassingthwaighte JB (1989) Fractal nature of regional myocardial blood flow heterogeneity. ''Circ Res'' 65, 578-590〕〔Kendal WS (2001) A stochastic model for the self-similar heterogeneity of regional organ blood flow. ''Proc Natl Acad Sci U S A'' 98, 837-841〕 *the genomic distributions of single- nucleotide polymorphisms (SNPs)〔Kendal WS (2003) An exponential dispersion model for the distribution of human single nucleotide polymorphisms. Mol Biol Evol 20 579-590〕 *gene structures〔Kendal WS (2004) A scale invariant clustering of genes on human chromosome 7. ''BMC Evol Biol'' 4(1), 3〕 *in number theory with sequential values of the Mertens function〔Kendal WS & Jørgensen B (2011) Taylor's power law and fluctuation scaling explained by a central-limit-like convergence. ''Phys. Rev. E'' 83,066115〕 and also with the distribution of prime numbers *from the eigenvalue deviations of Gaussian orthogonal and unitary ensembles of random matrix theory〔Kendal WS & Jørgensen BR (2011) Tweedie convergence: a mathematical basis for Taylor's power law, ''1/f'' noise and multifractality. ''Phys. Rev E'' 84, 066120〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Taylor's law」の詳細全文を読む スポンサード リンク
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