Phylodynamic techniques combine epidemiological and genetic information to analyze the evolutionary and spatiotemporal dynamics of rapidly evolving pathogens, such as influenza A or human immunodeficiency viruses. We introduce 'allele dynamics plots' (AD plots) as a method for visualizing the evolutionary dynamics of a gene in a population. Using AD plots, we propose how to identify the alleles that are likely to be subject to directional selection. We analyze the method's merits with a detailed study of the evolutionary dynamics of seasonal influenza A viruses. AD plots for the major surface protein of seasonal influenza A (H3N2) and the 2009 swine-origin influenza A (H1N1) viruses show the succession of substitutions that became fixed in the evolution of the two viral populations. They also allow the early identification of those viral strains that later rise to predominance, which is important for the problem of vaccine strain selection. In summary, we describe a technique that reveals the evolutionary dynamics of a rapidly evolving population and allows us to identify alleles and associated genetic changes that might be under directional selection. The method can be applied for the study of influenza A viruses and other rapidly evolving species or viruses.