Pokalyuk Cornelia, Pfaffelhuber Peter
Abteilung Mathematische Stochastik, Universität Freiburg, Eckerstr. 1, 79104 Freiburg, Germany.
Theor Popul Biol. 2013 Aug;87:25-33. doi: 10.1016/j.tpb.2012.09.005. Epub 2012 Oct 12.
The ancestral selection graph (ASG) was introduced by Neuhauser and Krone (1997) in order to study populations of constant size which evolve under selection. Coalescence events, which occur at rate 1 for every pair of lines, lead to joint ancestry. In addition, splitting events in the ASG at rate α, the scaled selection coefficient, produce possible ancestors, such that the real ancestor depends on the ancestral alleles. Here, we use the ASG in the case without mutation in order to study fixation of a beneficial mutant. Using our main tool, a reversibility property of the ASG, we provide a new proof of the fact that a beneficial allele fixes roughly in time (2logα)/α if α is large.
祖先选择图（ASG）由Neuhauser和Krone于1997年引入，用于研究在选择作用下大小恒定的种群。合并事件以每对谱系速率为1发生，导致共同祖先。此外，ASG中以比例选择系数α的速率发生分裂事件，产生可能的祖先，使得实际祖先取决于祖先等位基因。在此，我们在无突变的情况下使用ASG来研究有益突变体的固定。利用我们的主要工具——ASG的可逆性性质，我们为以下事实提供了一个新的证明：如果α很大，有益等位基因大致在时间(2logα)/α时固定。
