Genetic variants drive the evolution of traits and diseases. We previously modeled these variants as small displacements in fitness landscapes and estimated their functional impact by differentiating the evolutionary relationship between genotype and phenotype. Conversely, here we integrate these derivatives to identify genes steering specific traits. Over cancer cohorts, integration identified 460 likely tumor-driving genes. Many have literature and experimental support but had eluded prior genomic searches for positive selection in tumors. Beyond providing cancer insights, these results introduce a general calculus of evolution to quantify the genotype-phenotype relationship and discover genes associated with complex traits and diseases.