Aim To analyse how the patterns of species richness for the whole family Phyllostomidae determine the structure of diversity fields (sets of species-richness values) within the ranges of individual bat species. Location The range of the family Phyllostomidae in North and South America. Methods We generated a database of the occurrence of 143 phyllostomid bat species in 6794 quadrats, analysing the species-richness frequency distribution for all sites, and for subsets of sites defined by the geographic ranges of species. Range-diversity plots, depicting simultaneously the size and the mean species richness of ranges, were built to explore the patterns of co-occurrence in widespread and restricted species. We compared the empirical patterns against two null models: (1) with scattered (non-cohesive) ranges, and (2) with cohesive ranges modelled with the spreading-dye algorithm. Diversity fields were analysed with richness maps for individual species and with comparisons of species-richness frequency distributions. Results Overall richness frequency distribution showed a multimodal pattern, whereas simulated distributions showed lower values of variance, and were unimodal (for model 1) and bimodal (for model 2). Range-diversity plots for the empirical data and for the cohesive-ranges simulation showed a strong tendency of species to co-occur in high-diversity sites. The scattered-ranges simulation showed no such tendency. Diversity fields varied according to idiosyncratic features of species generating particular geographic patterns and richness frequency distributions. Main conclusions Phyllostomid bats show a higher level of co-occurrence than expected from null models. That tendency in turn implies a higher variance in species richness among sites, generating a wider species-richness frequency distribution. The diversity field of individual species results from the size, shape and location of ranges, but also depends on the general pattern of richness for the whole family.