What causes species richness to vary among different groups of organisms? Two hypotheses are that large geographical ranges and fast life history either reduce extinction rates or raise speciation rates, elevating a clade's rate of diversification. Here we present a comparative analysis of these hypotheses using data on the phylogenetic relationships, geographical ranges and life history of the terrestrial mammal fauna of Australia. By comparing species richness patterns to null models, we show that species are distributed nonrandomly among genera. Using sister-clade comparisons to control for clade age, we then find that faster diversification is significantly associated with larger geographical ranges and larger litters, but there is no evidence for an effect of body size or age at first breeding on diversification rates. We believe the most likely explanation for these patterns is that larger litters and geographical ranges increase diversification rates because they buffer species from extinction. We also discuss the possibility that positive effects of litter size and range size on diversification rates result from elevated speciation rates.