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We investigate the dependence of the site frequency spectrum (SFS) on thetopological structure of genealogical trees. We show that basic populationgenetic statistics - for instance estimators of $\theta$ or neutrality testssuch as Tajima's $D$ - can be decomposed into components of waiting timesbetween coalescent events and of tree topology. Our results clarify therelative impact of the two components on these statistics. We provide arigorous interpretation of positive or negative values of an important class ofneutrality tests in terms of the underlying tree shape. In particular, we showthat values of Tajima's $D$ and Fay and Wu's $H$ depend in a direct way on apeculiar measure of tree balance which is mostly determined by the root balanceof the tree. We present a new test for selection in the same class as Fay andWu's $H$ and discuss its interpretation and power. Finally, we determine thetrees corresponding to extreme expected values of these neutrality tests andpresent formulae for these extreme values as a function of sample size andnumber of segregating sites.

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