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Recent studies have revealed that for the majority of species the lengthdistributions of duplicated sequences in natural DNA follow a power-law tail.We study duplication-mutation models for processes in natural DNA sequences andthe length distributions of exact matches computed from both synthetic andnatural sequences. Here we present a hierarchy of equations for various numberof exact matches for these models. The reduction of these equations to oneequation for pairs of exact repeats is found. Quantitative correspondence ofsolutions of the equation to simulations is demonstrated.

On a chain of fragmentation equations for duplication-mutation dynamics in DNA sequences