Quasispecies distribution of Eigen model |
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Authors: | Chen Ji Li Sheng and Ma Hong-Ru |
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Institution: | Department of Physics, Shanghai Jiaotong University, Shanghai 200240, China |
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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. |
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Keywords: | Eigen model sharp peak landscapes similarity network clustering coefficient |
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