After stressing the need to keep separated the concept of variability and/or inequality and dissimilarity from that of diversity, it is suggested that diversity of a system should be measured primarily by the number of different classes (K) we can define in it (richness) by classification or identification processes. An index δ, ranging between 0 and 1, that summarizes the similarity pattern within the system, can be used if necessary to transform K to a “fuzzy” diversity number, according to the idea that the higher is the similarity within the system the lower should be its diversity. Another index, ρ, is proposed to measure the “loss” of diversity due to similarity within the system, an index that fits the concept of “redundancy”. Since every diversity vector may be interpreted as a crisp symmetric similarity matrix, of which the Gini-Simpson’s index is the average dissimilarity, while the index of Shannon is the entropy of its eigenvalues, the index δ can be chosen to quantify one among the following similarities: a) the overall average similarity of the classes considering the within classes similarity equal to 1 and the between classes similarity equal to 0 (crisp similarity pattern): this is coincident with the evenness of the proportion of importance of the classes, b) the average similarity between the classes without considering evenness, or c) the combination of the two similarities (similarity between the classes and evenness). In these last two cases, the similarity between the classes is characterizing the similarity pattern of a system in a fuzzy way (fuzzy diversity). It is stressed that the diversity of vegetation systems may be of two complementary types: plant individual-based diversity and plant community-based diversity. If we assume that each plant community type corresponds to one habitat then habitat diversity (or niche width) can be calculated for each class of plant individuals according to the number of classes of plant communities in which we can find it. Habitat diversity can be used to measure the indicator value of species or other classes of plant individuals and of plant communities. In this last case, we have to consider the distribution of plant communities in classes defined by environmental factors. It is suggested that the terminology alpha, beta, gamma diversity can be useful only if used to distinguish types of diversity in vegetation systems: alpha diversity = plant individual based diversity, gamma diversity = the union of alpha diversities, beta diversity = plant community based diversity. Thanks to the availability of mathematical tools, it is concluded that rather than being worried about measuring diversity it would be more fruitful to worry about why we are willing to measure it.
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I thank P. Ganis, J. Podani, L. Orlóci, C. Ricotta and O. Wildi for having read the paper and for their comments. However, only I am responsible for possible errors. Many thanks are also addressed to the organizers of the 1st International Conference on Community Ecology (Sept 28–29, 2017, Budapest) for financial support offered to me to participate to the conference to present this paper.
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Feoli, E. Classification of plant communities and fuzzy diversity of vegetation systems. COMMUNITY ECOLOGY 19, 186–198 (2018). https://doi.org/10.1556/168.2018.19.2.11
- Fuzzy systems
- Similarity theory