Unravelling why species richness shows such dramatic spatial variation is an ongoing challenge. Common to many theories is that increasing species richness (e.g. with latitude) requires a compensatory trade-off on an axis of species' ecology. Spatial variation in species richness may also affect genetic diversity if large numbers of coexisting, related species result in smaller population sizes.Here, we test whether increasing species richness results in differential occupation of morphospace by the constituent species, or decreases species' genetic diversity. We test for two potential mechanisms of morphological accommodation: denser packing in ecomorphological space, and expansion of the space. We then test whether species differ in their nucleotide diversity depending on allopatry or sympatry with relatives, indicative of potential genetic consequences of coexistence that would reduce genetic diversity in sympatry. We ask these questions in a spatially explicit framework, using a global database of avian functional trait measurements in combination with >120,000 sequences downloaded from GenBank.We find that higher species richness within families is not systematically correlated with either packing in morphological space or overdispersion but, at the Class level, we find a general positive relationship between packing and species richness, but that points sampled in the tropics have comparatively greater packing than temperate ones relative to their species richness. We find limited evidence that geographical co-occurrence with closely related species or tropical distributions decreases nucleotide diversity of nuclear genes; however, this requires further analysis.Our results suggest that avian families can accumulate species regionally with minimal tradeoffs or cost, implying that external biotic factors do not limit species richness. Read the free Plain Language Summary for this article on the Journal blog.