Abstract
Recent studies of properties of various biological networks revealed that many of them display scale-free characteristics. Since the theory of scale-free networks is applicable to evolving networks, one can hope that it provides not only a model of a biological network in its current state but also sheds some insight into the evolution of the network. In this work, we investigate the probability distributions and scaling properties underlying some models for biological networks and protein domain evolution. The analysis of evolutionary models for domain similarity networks indicates that models which include evolutionary drift are typically not scale free. Instead they adhere quite closely to the Yule distribution. This finding indicates that the direct applicability of scale-free models in understanding the evolution of biological network may not be as wide as it has been hoped for.
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