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Why does species richness vary so greatly across lineages? Traditionally, variation in species richness has been attributed to deterministic processes, although it is equally plausible that it may result from purely stochastic processes. We show that, based on the best available phylogenetic hypothesis, the pattern of cladogenesis among agamid lizards is not consistent with a random model, with some lineages having more species, and others fewer species, than expected by chance. We then use phylogenetic comparative methods to test six types of deterministic explanation for variation in species richness: body size, life history, sexual selection, ecological generalism, range size and latitude. Of eight variables we tested, only sexual size dimorphism and sexual dichromatism predicted species richness. Increases in species richness are associated with increases in sexual dichromatism but reductions in sexual …