The history of biodiversity is characterized by a continual replacement of branches in the tree of life. The rise and demise of these branches (clades) are ultimately determined by changes in speciation and extinction rates, often interpreted as a response to varying abiotic and biotic factors. However, understanding the relative importance of these factors remains a major challenge in evolutionary biology. Here we analyze the rich North American fossil record of the dog family Canidae and of other carnivores to tease apart the roles of competition, body size evolution, and climate change on the sequential replacement of three canid subfamilies (two of which have gone extinct). We develop a novel Bayesian analytic framework to show that competition from multiple carnivore clades successively drove the demise and replacement of the two extinct canid subfamilies by increasing their extinction rates and suppressing their speciation. Competitive effects have likely come from ecologically similar species from both canid and felid clades. These results imply that competition among entire clades, generally considered a rare process, can play a more substantial role than climate change and body size evolution in determining the sequential rise and decline of clades.