How numerous tree species can coexist in diverse forest communities is a key question in community ecology. Whereas neutral theory assumes that species are adapted to common field conditions and coexist by chance, niche theory predicts that species are functionally different and coexist because they are specialized for different niches. We integrated biophysical principles into a mathematical plant model to determine whether and how functional plant traits and trade-offs may cause functional divergence and niche separation of tree species. We used this model to compare the carbon budget of saplings across 13 co-occurring dry-forest tree species along gradients of light and water availability. We found that species ranged in strategy, from acquisitive species with high carbon budgets at highest resource levels to more conservative species with high tolerances for both shade and drought. The crown leaf area index and nitrogen mass per leaf area drove the functional divergence along the simulated light gradient, which was consistent with observed species distributions along light gradients in the forest. Stomatal coordination to avoid low water potentials or hydraulic failure caused functional divergence along the simulated water gradient, but was not correlated to observed species distributions along the water gradient in the forest. The trait-based biophysical model thus explains how functional traits cause functional divergence across species and whether such divergence contributes to niche separation along resource gradients.