Abstract. – I consider a class of fitness landscapes, in which the fitness is a function of a finite number of phenotypic “traits”, which are themselves linear functions of the genotype. I show that the stationary trait distribution in such a landscape can be explicitly evaluated in a suitably defined “thermodynamic limit”, which is a combination of infinite-genome and strong selection limits. These considerations can be applied in particular to identify relevant features of the evolution of promoter binding sites, in spite of the shortness of the corresponding sequences. The quasispecies (QS) model [1,2] is extremely useful to investigate the behavior of populations evolving in a given fitness landscape , although it is based on a rather unrealistic infinite-population approximation. It leads to the QS equation, which is a deterministic evolution equation for the fraction of individuals in the population carrying a given genotype. The dimensionality of the QS equation is in principle equal to the number of possible genotypes— an enormously large number even for the smallest organism. Most analytical treatments of the QS equation have therefore focused on situations where this number could be reduced by lumping together genotypes in a small number of classes. In some “master-sequence
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