The abundant centre hypothesis (ACH) assumes that population abundance, population size, density and per-capita reproductive output should peak at the centre of a species' geographic range and decline towards the periphery. Increased isolation among and decreased reproductive output within edge populations should reduce within-population genetic diversity and increase genetic differentiation among edge relative to central populations. The ACH also predicts asymmetrical gene flow, with net movement of migrants from the centre to edges. We evaluated these ecological assumptions and population-genetic predictions in the endemic flowering plant Leavenworthia stylosa. Although populations were more spatially isolated near range edges, the geographic centre was surrounded by and not coincident with areas of peak population abundance, and plant density increased towards range edges. Per-capita seed number was not associated with distance to the range centre, but seed number/m2 increased near range edges. In support of ACH predictions, allelic diversity at 12 microsatellite loci declined with distance from the range centre, and pairwise FST values were higher between edge populations than between central populations. Coalescent analyses confirmed that gene flow was most infrequent between edge populations, but there was not an asymmetric pattern of gene flow predicted by the ACH. This study shows that among-population demographic variability largely did not support the ACH, while patterns of genetic diversity, differentiation and gene flow were generally consistent with its predictions. Such mixed support has frequently been observed in tests of the ACH and raises concerns regarding the generality of this hypothesis for species range limits.