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Despite the importance of this protein property, there has been limited investigation of the impact of the stability of the influenza virus hemagglutinin protein\u2014the primary antibody target of the immune system\u2014on its evolution. Using a combination of computational estimates of stability and experiments, our analysis found that viruses with more-stable hemagglutinin proteins were associated with long-term persistence in the population. There are two potential reasons for the observed persistence. One is that more-stable proteins tolerate destabilizing mutations that less-stable proteins could not, thus increasing opportunities for immune escape. The second is that greater stability increases the fitness of the virus through increased production of infectious particles. 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