The Modern Evolutionary Synthesis formalizes the role of variation, heredity, differential reproduction and mutation in population genetics. Here we explore a mathematical structure, based on the asymptotic limit theorems of information theory, that instantiates the punctuated dynamic relations of organisms and their embedding environments. The mathematical overhead is considerable, and we conclude that the model must itself be extended even further to allow the possibility of the transfer of heritage information between different classes of organisms. In essence, we provide something of a formal roadmap for the modernization of the Modern Synthesis
