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where ''p''<sub>0</sub> is the proportion of the sample with no individuals, ''m'' is the mean sample density, ''a'' and ''b'' are constants. Like Taylor's law this equation has been found to fit a variety of populations including ones that obey Taylor's law.
===Lloyd's index of mean crowding===
Lloyd's index of mean crowding (''IMC'') is the average number of other points contained in the sample unit that contains a randomly chosen point.<ref name=Lloyd1967>Lloyd M (1967) Mean crowding. J Anim Ecol 36: 1-30</ref>
: <math> IMC = m_i + m_i / s^2 - 1 </math>
===Patchiness regression test===
Iwao also proposed a patchiness regression to test for clumping<ref name=Iwao1968>Iwao S & Kuno E (1968) Use of the regression of mean crowding on mean density for estimating sample size and the transformation of data for the analysis of variance. Res Pop Ecology, 10, 210–214</ref><ref name=Ifoulis2006>Ifoulis AA, Savopoulou-Soultani M (2006) Developing optimum sample size and multistage sampling plans for ''Lobesia botrana'' (Lepidoptera: Tortricidae) larval infestation and injury in northern Greece. J Econ Entomol 99(5):1890–1898</ref>
Let
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''y''<sub>''i''</sub> here is Lloyd's index of mean crowding.<ref name=Lloyd1967>Lloyd M (1967) Mean crowding. J Anim Ecol 36: 1-30</ref> Perform an ordinary least squares regression of ''m''<sub>''i''</sub> against ''y''. In this regression the value of the slope is an indicator of clumping: the slope = 1 if the data is Poisson-distributed. The constant is the number of individuals that share a unit of habitat at infinitesimal density and may be < 0, 0 or > 0. These values represent regularity, randomness and aggregation of populations in spatial patterns respectively.
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