Convex hulls, habitat filtering, and functional diversity: mathematical elegance versus ecological interpretability

There is a recent proposal to apply convex hulls to the measurement of habitat filtering, trophic diversity and functional richness. Although this approach has successful applications, some conceptual difficulties with the interpretation of results should not be overlooked. The basic assumption that trait convergence and the associated deflation of the convex hull is a result of environmental (habitat) filtering does not always hold, because 1) some traits may converge as a result of competition as well, and 2) environmental factors, such as disturbance, may lead to divergence, rather than convergence for certain characters. There is neither evidence nor theoretical proof that increasing correlations between traits and reduction in trait combinations are always caused by habitat filtering, especially when individual trait ranges are unchanged. Diversity measurements in terms of convex hull volumes may be misleading because zero or near zero values may result no matter how wide the individual trait ranges are. For these reasons, applications of convex hulls cannot be viewed uncritically, and considerable care must be taken even if the method is used in combination with other techniques.