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Sustained forests; sustained profits
evolving since March 30, 1999
of an Alternative Wildlife Resource Management
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Similarity may be part of discussions of diversity but it is a separate topic. It has played a major role in discussions and work on associations. It is a word behind which are hidden many assumptions and statistical issues that are rarely resolved (See Green, Statistics for Ecologists, p. 130-131)
For the resource manager who has a plant or animal community that is "good" , satisfactory, a standard, or meets a set of objectives, similarity may become an objective. The manager wants the new community to be similar to the standard.
The scientist may simply inquire into how similar are two entities such as foraging behavior, plants present, or animals present.
The restoration expert may wish that some observation a restored area may become more and more similar to that in an adjacent or "undisturbed" area.
Theorists may define a niche and then seek the overlap in niche-space between species, a re-definition of the quest: "how similar are the niches?"
The simplest way to express association is to say: species a occurred in x percent of the collections that contained species b.
When comparing an item within two communities, the values may be
The index should have intuitive appeal, the higher values having greater similarity. The index should be zero when species never occur in both samples, a and b.
The Jaccard index (herein) is:
S1 = c/ (a + b + c)
Example 1:
a = 6
b = 8
c = 5 and thus S1 = 0.26
Example 2:
a = 6
b = 8
c = 1 (obviously not very similar, having only one species in common) and thus S1 = 0.07
Example 3:
a = 6
b = 8
c = 6 and thus S1 =0.30
Note that c cannot be greater that the smallest value of a or b. Only when a = b = c does the index become maximum at 0.50.
Sorensen used 2c / (a + b) making the final results move toward an a maximum index value of 1.0. Dice used 2c / (2c + a + b) for a harmonic mean.
The Mountford index, herein is S2, is:
S2 = 2c / 2 ab - (a + b) c
Example 1:
a = 6
b = 8
c = 5 and thus S2 = 0.38
Example 2:
a = 6
b = 8
c = 1 and thus S2 = 0.02
Example 3:
a = 6
b = 8
c = 6 and thus S2 =0.50
The Orloci or Ochiai index, herein S3, the geometric mean is:
S3 = c / ((c + b) (c + a))0.5
Example 1:
a = 6
b = 8
c = 5 and thus S3 = 0.42
Example 2:
a = 6
b = 8
c = 1 and thus S3 = 0.13
Example 3:
a = 6
b = 8
c = 6 and thus S3 = 0.46
Note also that great difference in a and b, without consideration of the species held in common (B), can cause major shifts in the indices.
The greater the difference between a and b, the smaller will be the similarity index.
Regression may allow analyses of species presence as a function of the presence of another species or species group (multi-independent variables).
These indices do not have included within them measures of variance related to sample size. Rank correlation (number in each species) may be a useful expression. A 2x2 Chi-square test has been used by Cole (Ecology 1949:414). Steinhorst said that the only solution to many scalar and analytical problems in the past use of similarity indices is "to assess the overlap of niches and the similarity of communities in multivariate terms."
One good way to comprehend these indices, test them, and to understand their performance is to make entries in the following Visualbasic program to see the results that are likely from field data. Enter representative data but then make entries of extreme but realistic data, for example, a = 20, b = 20, and c = 20. Mentally determine the expected values (in this case identical similarity!) and then make the entries to test whether the indices perform as expected. Compare, for example, a = 100, b = 3, c = 2. Could c = 22? (Ans: c in this case could only have a value of 3 since there are only 3 species in the samples from b.
Programming in progress
References
Orloci, L. 1966. Geometric models in ecology. I. The theory and application of some ordination methods. J. Ecol. 54:193-215.
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Last revision July 10, 2001.