Recent studies show that the distribution of many modern terrestrial species can be explained by a handful amount of large-scale dispersals and that these episodes will likely become more numerous under climatic stress. However, the underlying mechanisms governing these dispersals remain nebulous. Long-distance dispersals across marine barriers, also called sweepstakes dispersals, have always been assumed to be an unpredictable process in which taxa overcome a geographic barrier in a random manner. Yet, there are many instances of dispersals across marine barriers that appear coordinated and non-random. New paleontological findings show that during a short time period marked by extreme surface temperatures, 40 million years ago, Asian anthropoid primates and rodents crossed 500 km of Tethys Sea to reach Africa and 800 km of South Atlantic Ocean to reach South America. This proposal aims to build an empirical and theoretical basis for the origins and mechanisms of sweepstakes dispersal by resolving: how did primates and other mammals disperse across two major seaways 40 million years ago? Are there external forcing mechanisms that make sweepstakes dispersal non-random? This project proposes a combination of paleoclimatic, paleogeographic, and paleontological approaches to evaluate the mechanisms of species dispersal and diversification in deep time, applied to the early dispersal of anthropoid primates. This research will demonstrate how complex geological and climatic phenomena affect the distributions of organisms and the dynamics of invasive fauna, allowing new interpretations about the modern, past and future distribution of species; it will additionally solve one of the biggest mysteries in paleontology, as this episode ranks among the most pivotal events during all of primate evolutionary history.