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A simple agent‐based model is presented that produces results matching the experimental data found by Lenski's group for ≤50,000 generations of Escherichia coli bacteria under continuous selective pressure. Although various mathematical models have been devised previously to model the Lenski data, the present model has advantages in terms of overall simplicity and conceptual accessibility. The model also clearly illustrates a number of features of the evolutionary process that are otherwise not obvious, such as the roles of epistasis and historical contingency in adaptation and why evolution is time irreversible ('Dollo's law'). The reason for this irreversibility is that genomes become increasingly integrated or organized, and this organization becomes a novel selective factor itself, against which future generations must compete. Selection for integrated or synergistic networks, systems or sets of mutations or traits, not for individual mutations, confers the main adaptive advantage. The result is a punctuated form of evolution that follows a logarithmic occurrence probability, in which evolution proceeds very quickly when interactomes begin to form but which slows as interactomes become more robust and the difficulty of integrating new mutations increases. Sufficient parameters exist in the game to suggest not only how equilibrium or stasis is reached but also the conditions in which it will be punctuated, the factors governing the rate at which genomic organization occurs and novel traits appear, and how population size, genome size and gene variability affect these. [ABSTRACT FROM AUTHOR]