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bioRxiv · 10.1101/042044

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

Alice Ledda·Guillaume Achaz·Thomas Wiehe·Luca Ferretti
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Abstract

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 Tajimas 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 Tajimas D and Fay and Wus 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 Wus 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.

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Alice Ledda, Guillaume Achaz, Thomas Wiehe, Luca Ferretti. 2016-03-01. Decomposing the site frequency spectrum: the impact of tree topology on neutrality tests. https://doi.org/10.1101/042044

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