Table 5. Summary of distinct diversity indices, as used in ecology.

pi = ni / N: relative abundance of a species

N = number of individuals ni = number of individuals of species i

S= total number of species




Species number (richness“)

[e.g.. Whittaker 1960, 1977]

S = number of species

The number of species in a given habitat, biotope, community or assemblage.


also “Shannon-Index“ or Shannon-Weaver-Index“

[Shannon & Weaver 1949]

Measures insecurity of predicting to which species an individual within a sample belongs. Mostly calculated with natural logarithms.


[Pielou 1966]



Relation between observed diversity to maximal possible diversity [Hmax : equal distribution of individuals among all species within sample]


[Simpson 1949]

1 - D = Simpson‘s diversity index

1/D = Simpson‘s reciprocal index

D measures the probability of two randomly selected individuals belonging to the same species. The frequently used reciprocal index calculates the number of species with the same number of individuals, necessary to give the same diversity index.

Alpha-Index ( Fisher’s alpha)

[Fisher et al. 1943]

S = α ln (1 + N / α)

Results in a straight line within a log-normal display of a species-individual curve


Fisher, R.A., Corbet, A.S. & Williams, C.B. (1943): The relation between the number of species and the number of individuals in a random sample of an animal population.  J. Anim. Ecol. 12: 42-58.

Magurran, A.E. (1988): Ecological diversity and its measurement.  Princeton University Press: Princeton, NJ: X + 179S.

Pielou, E.C. (1966): Species-Diversity and Pattern-Diversity in the Study of Ecological Succession.  J. Theoret. Biol. 10: 370-383.

Shannon, C.E. & Weaver, W. (1949): The Mathematical Theory of Communication. - Univ. of Illinois Press: Urbana.

Simpson, E.H. (1949): Measurement of diversity.  Nature 163: 688.

Sörensen, T. (1948). A method of establishing groups of equal amplitude in plant sociology based on similarity of species content. - Kong. Danske Vidensk. Selsk. Biol. Skr. 5 (4): 1-34.

Whittaker, R.H. (1960): Vegetation of the Siskiyou Mountains, Oregon and California.  Ecol. Monogr. 26: 1-80.

Whittaker, R.H. (1977): Evolution of Species Diversity in Land Communities. - Evolutionary Biology 10: 1-67.