【作者】 陈佳；

【导师】 李晟；

【作者基本信息】 上海交通大学 ， 理论物理， 2007， 硕士

【摘要】 本文从研究序列在序列空间如何分布这个角度出发,研究进化机制。我们引入了两个新的工具:Hamming距离的方差和相似度网络对分子进化生物学中最著名的模型——Eigen模型展开研究。分别重新研究了三个适应度景观:静止均匀适应度景观,静止单峰适应度景观和动态单峰适应度景观。我们首先利用Hamming距离的方差确定临界点的位置,并从整体上给出序列在序列空间的分布结构。然后利用在某Hamming距离d0下建立的相似度网络,具体给出序列在序列空间分布的性质;演示出不同进化情况下,序列之间的相互关系。在以上三个适应度景观的研究中,我们证明了引入相似度网络这一新工具研究进化机制是合理的,并同时也展示了两个新工具的特点。得出了以下结论:在静止均匀适应度景观中,进化产生的序列与随机序列等同,在序列空间均匀分布;静止单峰适应度景观中,远低于临界点区域,进化产生的序列在序列空间分布均匀。临界点附近区域,Hamming距离方差的平均值var(d_ij)和相似度网络的簇系数C值都较大,因此我们推测,此时进化产生的序列建立的相似度网络中,全局最优相似度点的周围应该存在着一些局部最优相似度点（在本文最优是指相似度最优）。这说明在临界点附近,序列空间中序列分布中心的周围存在着一些小集团。我们还发现,在临界点附近簇系数函数C （k）曲线服从对数正态分布（lognormal distribution）,C与d₀成线性关系。远高于临界点的区域, var(d_ij)值较小,但C值较大。因此此时进化产生的序列在序列空间的分布将会随着q趋向于1而收缩为一点。另外反铁磁状态下,得到如上类似结论。在动态单峰适应度景观中,我们得到:铁磁状态下,动态单峰更多还原

【Abstract】 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更多还原