The Study Of Eigen Model By Complex Network

We study three simple fitness landscapes of Eigen model from a new perspective about how the sequences distribute in the sequence space. They are even fitness landscapes, sharp peak landscapes and dynamic fitness landscapes. To analyze the distribution more carefully, we bring forth two tools. One tool is the variance of Hamming distance of the sequences at a given generation. It not only offers us a different avenue for accurately locating the error threshold, but also illustrates how the configuration of the distribution varies with copying fidelity q in the sequence space. The other tool is the similarity network of a certain Hamming distance d₀, by which we can get a visual and in-depth result about how the sequences distribute and know what the relationship between the sequences of the evolution is.During the research, we prove that it is logical to study evolution by bringing in similarity network. And we show the advantages of those two new tools at the same time. The results are listed as follows. In the even fitness landscapes, the outcomes of the evolution are equivalent to the random sequences distributing evenly in the sequence space. In the sharp peak landscapes: far below the threshold, the distribution is uniform in the sequence space. Near the threshold, the values of both the variance of Hamming distance var(d_ij) and the network clustering coefficient C are high, which implies that there are several local similarity optima around the center (global similarity optimum) in the similarity network of the sequences (The optimum in this paper means the optimum of similarity), that is, there are several clusters around the hub in the sequence space. Furthermore, it is...