Abstract: Motivation: Directed evolution, in addition to its principal application of obtaining novel biomolecules, offers significant potential as a vehicle for obtaining useful information about the topologies of biomolecular fitness landscapes. In this article, we make use of a special type of model of fitness landscapes—based on finite state machines—which can be inferred from directed evolution experiments. Importantly, the model is constructed only from the fitness data and phylogeny, not sequence or structural information, which is often absent. The model, called a landscape state machine (LSM), has already been used successfully in the evolutionary computation literature to model the landscapes of artificial optimization problems. Here, we use the method for the first time to simulate a biological fitness landscape based on experimental evaluation. Results: We demonstrate in this study that LSMs are capable not only of representing the structure of model fitness landscapes such as NK-landscapes, but also the fitness landscape of real DNA oligomers binding to a protein (allophycocyanin), data we derived from experimental evaluations on microarrays. The LSMs prove adept at modelling the progress of evolution as a function of various controlling parameters, as validated by evaluations on the real landscapes. Specifically, the ability of the model to ‘predict’ optimal mutation rates and other parameters of the evolution is demonstrated. A modification to the standard LSM also proves accurate at predicting the effects of recombination on the evolution.