The biodiversity of tropical rainforest is difficult to assess. Yet, its estimation is necessary for conservation purposes, to evaluate our level of knowledge and the risks faced by the forest in relation to global change. Our contribution is to estimate the regional richness of tree species from local but widely spread inventories. We reviewed the methods available, which are nonparametric estimators based on abundance or occurrence data, log-series extrapolation and the universal species–area relationship based on maximum entropy. Appropriate methods depend on the scale considered. Harte’s self-similarity model is suitable at the regional scale, while the log-series extrapolation is not. GuyaDiv is a network of forest plots installed over the whole territory of French Guiana, where trees over 10 cm DBH are identified. We used its information (1315 species censused in 68 one-hectare plots) to estimate the exponent of the species–area relationship, assuming Arrhenius’s power law. We could then extrapolate the number of species from three local, wide inventories (over 2.5 km2). We evaluated the number of tree species around 2200 over the territory.

Over the last decade, distance-based methods have been introduced and then improved in the field of spatial economics to gauge the geographic concentration of activities. There is a growing literature on this theme including new tools, discussions on their specific properties and various applications. However, there is currently no typology of distance-based methods. This paper fills that gap. The proposed classification helps understand all the properties of distance-based methods and proves that they are variations on the same framework.

Measuring functional or phylogenetic diversity is the object of an active literature. The main issues to address are relating measures to a clear conceptual framework, allowing unavoidable estimation-bias correction and decomposing diversity along spatial scales. We provide a general mathematical framework to decompose measures of species-neutral, phylogenetic or functional diversity into $\alpha$ and $\beta$ components. We first unify the definitions of phylogenetic and functional entropy and diversity as a generalization of HCDT entropy and Hill numbers when an ultrametric tree is considered. We then derive the decomposition of diversity. We propose a bias correction of the estimates allowing meaningful computation from real, often undersampled communities. Entropy can be transformed into true diversity, that is an effective number of species or communities. Estimators of $\alpha$- and $\beta$-entropy, phylogenetic and functional entropy are provided. Proper definition and estimation of diversity is the first step towards better understanding its underlying ecological and evolutionary mechanisms.