Consider an advantageous allele that arises in a haploid population of size $N$ evolving in continuous time according to a skewed reproduction mechanism, which generates under neutrality genealogies lying in the domain of attraction of a Beta$(2-α, α)$-coalescent for $α\in (1,2)$. We prove in a setting of moderate selection that the fixation probability $π_N$ of the advantageous allele is asymptotically equal to $α^{1/(α-1)} s_N^{1/(α-1)} $ , where $s_N$ is the selection strength of the advantageous allele. Our proof uses duality with a suitable $Λ$-ancestral selection graph.
Fixation probabilities and hitting times under low levels of frequency-dependent selection
在群体遗传学中，单位区间上的扩散经常被用来模拟等位基因的频率路径。在这种情况下，我们得到近似的固定概率，预期的首中时和预期的网站下的频谱依赖于频率的选择。具体地说，我们重新推导和扩展了进化对策论的三分之一规则（Nowak et al.，2004）和随机减速的影响（Altrock和Traulsen，2009）。由于类似的效果在其他应用领域的兴趣，我们制定我们的结果一般一维扩散。
John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）；Department of Molecular and Cellular Biology, Harvard University（哈佛大学分子与细胞生物学系）；Department of Organismic and Evolutionary Biology, Harvard University（哈佛大学生物体与进化生物学系）；Department of Mathematics, Harvard University（哈佛大学数学系）
Logarithmic scaling of selective sweep curves: from tents to houses
Universität Wien, Fakultät für Mathematik（维也纳大学数学系）；Goethe-Universität Frankfurt am Main, FB 12, Institut für Mathematik（法兰克福歌德大学数学研究所）；HUN-REN Alfréd Rényi Institute of Mathematics（匈牙利科学院阿尔弗雷德·雷尼数学研究所）
