1. Positive relationships between the local abundance and the range si
ze of the species in a taxonomic assemblage are very general. 2. Expla
nations for these relationships typically focus on two mechanisms, bas
ed on differences in the niche breadths of species, or metapopulation
dynamics. Others have, however, also been suggested. 3. Here we identi
fy and clarify all the principal mechanisms proposed to explain positi
ve interspecific abundance-range size relationships. We critically ass
ess the assumptions and predictions that they make, and the evidence i
n support of them. 4. A number of predictions are common to all of the
biological (as opposed to artefactual) mechanisms, but the combinatio
n of predictions and assumptions made by each is unique, suggesting th
at, in principle, conclusive tests of all of the mechanisms are possib
le. 5. On present evidence, no single mechanism has unequivocal suppor
t. We discuss reasons why this might be the case.