Taylor's law
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. It is named after the ecologist who first proposed it in 1961, Lionel Roy Taylor (1924–2007). Taylor's original name for this relationship was the law of the mean.
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’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:
The first use of a double log-log plot was by Reynolds in 1879 on thermal aerodynamics.Pareto used a similar plot to study the proportion of a population and their income.
The term variance was coined by Fisher in 1918.
Fisher in 1921 proposed the equation
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