Evolutionary theory has long proposed a connection between trait evolution and diversification rates. In this work, we used phylogenetic methods to evaluate the relationship of lineage-specific speciation rates and the mode of evolution of body size and tooth morphology in the Neogene and Quaternary radiation of horses (7 living and 131 extinct species). We show that diversification pulses are a recurrent feature of equid evolution but that these pulses are not correlated with rapid bursts in phenotypic evolution. Instead, rapid cladogenesis seems repeatedly associated with extrinsic factors that relaxed diversity bounds, such as increasing productivity and geographic dispersals into the Old World. This evidence suggests that diversity dynamics in Equinae were controlled mainly by ecological limits under diversity dependence rather than rapid ecomorphological differentiation.
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