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

Power of , and in dependence of distance to selected site.

<p>Selective sweep with , , , sample size .</p>*<p>SKD-test by Schlötterer <i>et al.</i><a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003060#pcbi.1003060-Schltterer2" target="_blank">[37]</a>.</p

Test statistics and -values for the empirical data set of <i>P.falciparum</i>.

<p>Given are the theoretical -values based on the standard normal (for ) and on the product uniform (for ) distributions. Values for are given as raw data (, , ). The -value is . 5% (single star) and 1% (double star) significance are indicated. Marker positions are taken from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003060#pcbi.1003060-Nair1" target="_blank">[29]</a>. The region analyzed (about 17 kb) corresponds to about 1 cM (site under selection in bold).</p>1<p>defined in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003060#pcbi.1003060.e196" target="_blank">eq (13)</a>.</p

Traces of selection around a drug resistance locus in Plasmodium.

<p><a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003060#s2" target="_blank">Results</a> of tests (stars), (circles) and (triangles) applied to a kb region sorrounding the <i>pfmdr1</i> locus in <i>P.falciparum</i>. Shown are significant results on the 5% (open symbols) and 1% (filled symbols) levels. Positions of the examined microsatellite markers are indicated by arrows. Data from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003060#pcbi.1003060-Nair1" target="_blank">[29]</a>.</p

Mean and standard deviation of and for coalescent trees of size .

<p>Shown are the values for independent realizations. -axis: values of (black circles) and (red squares) are determined for the subtrees originating at node , . The solid gray line shows the theoretical expectation according to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003060#pcbi.1003060.e060" target="_blank">eq (3)</a>.</p

Power to detect loci under recent selection by the three tests defined in eqs (14) to (16)

<p>Parameters: level (solid) and . (dotted); selection coefficient ; time since fixation ; sample size ; mutation rate ; recombination rate . The axis shows positions to the left (negative values) and right (positive values) of the locus under selection at position . Scale is in cM x, corresponding here to kb.</p

Empirical false positive rate for varying sample size .

<p>Neutral model constant, , . Significance levels are based on theoretical formulae according to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003060#pcbi.1003060.e091" target="_blank">eqs (7)</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003060#pcbi.1003060.e096" target="_blank">(8)</a> (reference value indicated in bold).</p

Estimation of .

<p>A: estimation of by . B: estimation of by . First row: standard neutral model. Second row: Selective sweep; estimation of at distance from selected site. Third row: Selective sweep; distance from selected site. Parameters: ; (top and bottom row); (middle row); ; ; .</p

Critical values for the tests considered in eqs (14)–(16).

<p>Critical values for the tests considered in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003060#pcbi.1003060.e208" target="_blank">eqs (14)</a>–<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003060#pcbi.1003060.e210" target="_blank">(16)</a>.</p

Profile of and along a recombining chromosome.

<p>Plots in column A show the distribution of , i.e. when the tree topology is known. Plots in column B show the distribution of the estimate when the tree topology is unknown, but estimated from microsatellite polymorphism data. Each boxplot corresponds to one of marker loci located at the positions indicated on the axis. The regions spans kb in total. Symmetric step-wise mutation model with . Other parameters: , and recombination rate per <i>bp</i> (corresponding to 1 cM/Mb). First row: standard neutral model with constant . Second row: bottleneck model with severity and onset . Third row: Selective sweep at locus with which was completed time units ago. For comparison with the theoretical expectation, the leftmost boxplot in each panel shows the standard normal distribution (labeled ‘N’).</p