Towards a Theory of Landscapes

Since Sewall Wright’s seminal paper [145], the notion of a fitness landscape underlying the dynamics of evolutionary adaptation optimization has proved to be one of the most powerful concepts in evolutionary theory. Implicit in this idea is a collection of genotypes arranged in an abstract metric space, with each genotype next to those other genotypes which can be reached by a single mutation, as well as a value assigned to each genotype. Such a construction is by no means restricted to biological evolution; Hamiltonians of disordered systems, such as spin glasses [14, 88], and the cost functions of combinatorial optimization problems [52] have the same mathematical structure. It has been known since Eigen’s [39] pioneering work on the molecular quasispecies that the dynamics of optimization on a landscape depends crucially on detailed structure of the landscapes itself. Extensive computer simulations, see, e.g., [2, 45, 46], have made it very clear that a complete understanding of the dynamics is impossible without a thorough investigation of the underlying landscape [40].