Decomposing the site frequency spectrum: the impact of tree topology on neutrality tests

We investigate the dependence of the site frequency spectrum (SFS) on the topological structure of genealogical trees. We show that basic population genetic statistics - for instance estimators of $\theta$ or neutrality tests such as Tajima's $D$ - can be decomposed into components of waiting times between coalescent events and of tree topology. Our results clarify the relative impact of the two components on these statistics. We provide a rigorous interpretation of positive or negative values of an important class of neutrality tests in terms of the underlying tree shape. In particular, we show that values of Tajima's $D$ and Fay and Wu's $H$ depend in a direct way on a peculiar measure of tree balance which is mostly determined by the root balance of the tree. We present a new test for selection in the same class as Fay and Wu's $H$ and discuss its interpretation and power. Finally, we determine the trees corresponding to extreme expected values of these neutrality tests and present formulae for these extreme values as a function of sample size and number of segregating sites.Comment: 23 pages, 8 figure

Coalescent Tree Imbalance and a Simple Test for Selective Sweeps Based on Microsatellite Variation

<div><p>Selective sweeps are at the core of adaptive evolution. We study how the shape of coalescent trees is affected by recent selective sweeps. To do so we define a coarse-grained measure of tree topology. This measure has appealing analytical properties, its distribution is derived from a uniform, and it is easy to estimate from experimental data. We show how it can be cast into a test for recent selective sweeps using microsatellite markers and present an application to an experimental data set from <i>Plasmodium falciparum</i>.</p></div

紛争主体の分裂統合 : アフリカの内戦を中心に

学位の種別: 課程博士審査委員会委員 : （主査）東京大学准教授 伊藤 伸泰, 東京外国語大学センター長/教授 武内 進一, 東京大学教授 和泉 潔, 東京大学講師 藤井 秀樹, 東京大学教授 池上 高志University of Tokyo(東京大学