CWM and Rao's quadratic diversity: a unified framework for functional ecology.

Assessing the effects of environmental constraints on community structure often relies on methods that consider changes in species functional traits in response to environmental processes. Various indices have been proposed to measure relevant aspects of community trait composition from different viewpoints and perspectives. Among these, the 'community-weighted mean trait value' (CWM) and the Rao coefficient have been widely used in ecological research for summarizing different facets of functional composition and diversity. Analyzing changes in functional diversity of bee communities along a post-fire successional gradient in southern Switzerland we show that these two measures may be used to describe two complementary aspects of community structure, such as the mean and the dispersion of functional traits within a given species assemblage. While CWM can be adequately used to summarize shifts in mean trait values within communities due to environmental selection for certain functional traits, the Rao coefficient can be effectively applied to analyze patterns of trait convergence or divergence compared to a random expectation.