Repeated emergence of SARS-CoV-2 variants with increased fitness necessitates rapid detection and characterization of new lineages. To address this need, we developed PyR₀, a hierarchical Bayesian multinomial logistic regression model that infers relative prevalence of all viral lineages across geographic regions, detects lineages increasing in prevalence, and identifies mutations relevant to fitness. Applying PyR₀ to all publicly available SARS-CoV-2 genomes, we identify numerous substitutions that increase fitness, including previously identified spike mutations and many non-spike mutations within the nucleocapsid and nonstructural proteins. PyR₀ forecasts growth of new lineages from their mutational profile, identifies viral lineages of concern as they emerge, and prioritizes mutations of biological and public health concern for functional characterization.