Diversity can be decomposed into three distinct concepts, namely: variety, balance and disparity. This paper borrows from the extensive formalization and measures of diversity developed in ecology in order to evaluate the variety and balance of multiword expression annotation produced by automatic annotation systems. The measures of richness, normalized richness, and two variations of Hill's evenness are considered in this paper. We observe how these measures behave against increasingly smaller samples of gold annotations of multiword expressions and use their comportment to validate or invalidate their pertinence for multiword expressions in annotated texts. We apply the validated measures to annotations in 14 languages produced by systems during the PARSEME shared task on automatic identification of multiword expressions and on the gold versions of the corpora. We also explore the limits of such evaluation by studying the impact of lemmatization errors in the Turkish corpus used in the shared task.