Abstract We have studied sharp peak landscapes of the Eigen model from a new perspective about how the quasispecies are distributed in the sequence space. To analyse the distribution more carefully, we bring in 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 and illustrates how the configuration of the distribution varies with copying fidelity $q$ in the sequence space, but also divides the copying fidelity into three distinct regimes. The other tool is the similarity network of a certain Hamming distance $d_{0}$, by which we can gain a visual and in-depth result about how the sequences are distributed. We find that there are several local similarity optima around the centre (global similarity optimum) in the distribution of the sequences reproduced near the threshold. Furthermore, it is interesting that the distribution of clustering coefficient $C(k)$ follows lognormal distribution and the curve of clustering coefficient $C$ of the network versus $d_{0}$ appears to be linear near the threshold.
Received: 11 December 2006
Revised: 24 January 2007
Accepted manuscript online:
PACS:
87.10.-e
(General theory and mathematical aspects)
Fund: Project supported by the National Natural
Science Foundation of China (Grant Nos~10105007 and 10334020).
Cite this article:
Chen Jia(陈佳), Li Sheng(李晟), and Ma Hong-Ru(马红孺) Quasispecies distribution of Eigen model 2007 Chinese Physics 16 2600
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