Some mathematical remarks on forest biodiversity

Biological diversity, currently and briefly denoted as biodiversity, probably is one of the key features of living world, as it has been wonderfully emphasised by Mayr (Mayr 1982). It is one of the field where a true biological quest, i.e. for the understanding of diversity, meets sophisticated mathematical tools, with a great biological relevance. Diversity studies may be summed up as the research of regular time and space pattern in allocation of individuals between species. The obvious way to study it, and the oldest one from an historical point of view, is just counting the number of different species at given location during a given time period. More sophisticated tools appeared after the Second World War, with the construction of indices which aim at comparing two samples on species diversity and evenness (see Margurran 1988, for a review). After the renewal of theoretical ecology in the early fifties, a great deal of effort was devoted to the understanding of diversity and evenness as a consequence of current ecological processes. In this article, we briefly sketch out some of the keystone ideas, with our own personal bias, which have contributed to the development of this field. Our presentation is divided into two parts: the first one dedicated to the quest for indices, and the second to the quest for understanding.