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Evenness is generally regarded as the constituent of species diversity which is independent of species richness. The group of most popular evenness indices has recently changed, following the influential work of Smith and Wilson (1996). My first point is to argue that this work failed to define coherently what evenness should be and thus advocated the use of indices of different nature. Instead, I propose to use the Lorenz partial order to choose indices that have a behaviour compatible with it. I then suggest a list of such evenness indices and build four series of . new. evenness indices. Finally, I discuss the interest of the Lorenz partial order and of the various evenness indices that are compatible with it

Lorenz partial order: the best known logical framework to define evenness indices