## Measures of Diversity

### Simpson's index

Simpson's index is the first of a set of non-parametric approaches to determining sample heterogeneity. Simpson (1949) did not want to make assumptions about the distribution of the species abundance curve and so defined the following:

### Simpson's index

$$D = \displaystyle\sum\limits_{i=1}^{c} p^2_i$$ $$(1-D) = 1 - \displaystyle\sum\limits_{i=1}^{c} p^2_i$$

where D is Simpson's index of similarity and can be defined as the probability of two individuals in a random sample being in same category. Pi is the proportion of category i in the community.

Simpson's index of similarity = D ,
Range(1/categories to 1 ),
Maximum(1).
The probability that two randomly selected individuals in the community are of the same category.
Simpson's index of diversity = 1 - D ,
Range(0 to ~1),
Maximum (1 - 1/categories).
The probability that two randomly selected individuals in a community are of the different categories.
Simpson's reciprocal index = 1 / D,
Range(1 to number of categories),
Maximum(number of categories).
The number of equally common categories that will produce the observed D value. Also known as Hill's (1973) N2

Peet (1974) suggested that Simpson's index is of a type that is more sensitive to the common categories in your sample. Simpson's index values should be interperted with this in mind.

Also see:

Chapter 10 - Species Diversity Measures pages 357-360 in:

Krebs, C. J. 1989. Ecological Methodology. Harper and Row, Publishers. New York. 654 pp.
Hill, M. O. 1973. Diversity and evenness: a unifying notation and its consequences. Ecology 54:427-432.
Peet, R. K. 1974. The measurement of species diversity. Annual. Rev. Ecol. Syst. 5:285-307.
Simpson, E. H. 1949. Measurement of diversity. Nature 163:688

 Natural Resources Biometrics by David R. Larsen is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License . Author: Dr. David R. Larsen Created: March 9, 2001 Last Updated: Nov 2, 2016