The uneven distribution of biodiversity on Earth is one of the most general and puzzling patterns in ecology. Many hypotheses have been proposed to explain it, based on evolutionary processes or on constraints related to geography and energy. However, previous studies investigating these hypotheses have been largely descriptive due to the logistical difficulties of conducting controlled experiments on such large geographical scales. Here, we use bird migration-the seasonal redistribution of approximately 15% of bird species across the world-as a natural experiment for testing the species-energy relationship, the hypothesis that animal diversity is driven by energetic constraints. We develop a mechanistic model of bird distributions across the world, and across seasons, based on simple ecological and energetic principles. Using this model, we show that bird species distributions optimize the balance between energy acquisition and energy expenditure while taking into account competition with other species. These findings support, and provide a mechanistic explanation for, the species-energy relationship. The findings also provide a general explanation of migration as a mechanism that allows birds to optimize their energy budget in the face of seasonality and competition. Finally, our mechanistic model provides a tool for predicting how ecosystems will respond to global anthropogenic change.