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Taylor's power law

The distribution of organisms is such that the variance is generally not independent of the mean. If the mean and variance of a series of samples are plotted, they tend to increase together.

Taylor's power law states that that the variance to mean relationship conforms to a power law, namely:

Algebraically speaking -

σ2    =    a μb
where
  • σ2 is the population variance and μ is the population mean;
  • a and b are constants.

This can be tested on field data by plotting log s2 against log:
log s2    =    log a + blog
where

  • s2 is the sample variance and is the sample mean;
  • a is a sampling parameter and b can be used as an index of aggregation.