PARENT SESSION
Contributed Oral Session 6: Biodiversity: Management, Theory, and Techniques
Monday, August 8, 8:00 AM - 11:30 AM, Meeting Room 516 D, Level 5, Palais des congrès de Montréal
When and why Rao's quadratic entropy may be a good biodiversity measure?
Pavoine, Sandrine*,1, Ollier, Sébastien1, 1 University Claude Bernard Lyon 1, Villeurbanne, France
ABSTRACT- Biodiversity is the multiplicity of life on all the scales between the community and the individual. When the reference entity is the species, several criteria are possible in order to describe each species: for example, its taxonomic or phylogenic groups, its phenotype and its nucleotide pattern. Among all indices of biodiversity measures, Rao's quadratic entropy makes it possible to take into account these criteria. It allows us to measure diversity using the frequencies of the species and choosing a suitable measurement of the differences between species. In spite of several attempts, this index is not very used. Why? From an ecological standpoint, this index may have relevant or unacceptable behaviors. For example, the variance and Simpson's index, which are two particular cases of the quadratic entropy, have two radically opposite behaviors when they reach their maximal value. Indeed it is widely accepted in ecology that Simpson's index is maximum when all the possible species are present in equal proportions. However the variance is maximum when only the two most different species are present, which drastically reduces the species richness. Thus the quadratic entropy presents these two extreme behaviors as well as all the intermediate behaviors. We suggest that the three following rules must be verified by an index H to be considered as a measure of diversity. First H should be maximum when each species has a frequency which reflects its originality, therefore no species should have a null frequency. Next given S a set of species and j another species, then the maximal value of H measured on S should be lower than the maximal value of H applied to the union of S and j. Then H should be concave, i.e. decomposable, for example in order to study the spatial changes of biodiversity. The presentation will show that these three properties are verified when the quadratic entropy is applied to phylogenetic dissimilarities among species.
Key words: biodiversity, feature richness, measurement, phylogenetics