Comparison of measures of crowding, group size, and diversity

In ecology, diversity is often measured as the mean rarity of species in a community. In behavioral sciences and parasitology, mean crowding is the size of the group to which a typical individual belongs. In this paper, focusing mostly on the mathematical aspect, we demonstrate that diversity and crowding are closely related notions. We show that mean crowding can be transformed into diversity and vice versa. Based on this general equivalence rule, notions, relationships, and methods developed in one field can be adapted to the other one. In relation to crowding, we introduce the notion "effective number of groups" that corresponds to the "effective number of species" used in diversity studies. We define new aggregation indices that mirror evenness indices known from diversity theory. We also construct aggregation profiles and orderings of populations based on aggregation indices. By uniting the mathematical interpretation of the ecological notion of diversity and the ethological notion of typical group size (or crowding, in parasitology), our insight opens a new avenue of both theoretical and methodological research. This is exemplified here using real-life abundance data of avian parasites.