Biogeographic regions are widely regarded as real entities, or at least as useful summaries of the complex patterns of spatial concordance among species. The problem is that, whereas some parts of the transition zones between regions may be strong and abrupt, other parts of the same zones may be weak or broad, so that the corresponding parts of border lines drawn on maps, although convenient, are arbitrary constructs. One approach to investigating transition zones ascribes values to the area units themselves, by quantifying the spatial turnover among species within the surrounding neighbourhoods of areas on maps. Using data for bumble bee distributions world-wide, I show that quantitative measures of neighbourhood turnover can discover many of the transition zones that are found by classification techniques when applied to the same data. But unlike classification techniques, turnover measures, particularly when used in combination, can show how a transition zone varies along its length, not only in its strength (the proportion of species contributing to the zone) but also in its breadth (the degree of spatial overlap or the degree of coincidence among species replacements across it). For bumble bees at least, these transition zones are also negatively associated with areas that have a combination of both high species richness and high species nestedness.