The Genom of Homo sapiens.pdf

250 CHIAROMONTE ET AL.can use this formula to calculate the expected fraction ofwindows in C that are under selection as1___Σ Pr(w selected|S(w)) (6)N wεCIf, for example, we apply Equation 6 with C defined as allW = 50-bp WA-windows (alignment threshold T = 40),we recover the mixture coefficient p 1 = 0.192 discussedabove, because p 1 is the fraction of these WA-windowsthat are estimated by the mixture decomposition to be underselection, and this must be the same as the expectedfraction of windows under selection. Here Equation 6merely provides another way of calculating the samenumber, and hence a nice test for our software. However,if we apply Equation 6 with C defined as W = 50-bpWAC-windows, then we can calculate something moreinteresting; namely, the expected fraction of well-alignedcoding windows that are under selection. We performedthis calculation for various window sizes.For 200-bp windows we obtained 86%, for 100-bpwindows 78%, for 50-bp windows 65%, but for 30-bpwindows, we obtained only 48%. This further indicateshow our mixture decomposition method produces a veryconservative lower bound for the share under selectionwhen applied to the normalized percent identity distributionof small windows.A Tighter Lower Bound: SplittingWell-aligned WindowsOur computational strategy requires enough separationbetween the neutral and selected distribution of normalizedpercent identity for the mixture to reliably detect thedifference. In fact, the definition of well-aligned windows(T = 25 for W = 30 bp, T = 40 for W = 50 bp, T = 80for W = 100 bp, T = 160 for W = 200 bp) and choice ofwindow size for the main analysis (W = 50 bp) stemmedfrom separation considerations; see also the Discussionsection below. However, if ancestral transposon relics area good neutral model, our figure of 5.2% may still representa fairly conservative lower bound for the share underselection. As a means to tighten this lower bound, we canfurther isolate extremely well-aligned genome-wide andneutral windows, splitting WA-windows into a high anda low alignment range. We tried, respectively, 20–24 and25–30 aligned bases for W = 30, 40–44 and 45–50 forW = 50, 80–94, and 95–100 for W = 100, and 160–194and 195–200 for W = 200.We repeated our calculations (estimating smooth densitiesfor neutral and genome-wide scores, decomposingthe genome-wide score distribution into a neutral and aselected component, computing a share under selectionbased on the mixture weight estimate and coverage) separatelyfor high- and low-range WA-windows, and addedthe results. As shown in Table 2, this consistently producesslightly higher share figures.The reason for the tighter lower bound is that neutraland genome-wide normalized percent identity distributionsare more dissimilar within each of the two groupsthan they are for WA-windows as a whole; that is, the splitincreases separation between neutral and selected behavior.From a purely theoretical point of view, splitting couldeither increase or decrease separation (this represents aninteresting area for further theoretical study), but if it increasesseparation, then still finer partitions of WA-windowsmay lead to even higher share estimates. However,finer partitions lead to the compounding of errors in thecalculations performed for each group, and this limits theirutility. We address the issue of statistical error next.Control ExperimentsAs a control for the error associated with our Gaussiansmoothing and mixture decomposition, using 50-bp windowswith a threshold of 40 aligned bases, we divided theWA-windows in ancestral repeats into two sets, A and B,at random. Set A was used to estimate the neutral scoredistribution. Set B was used to estimate a genome-widedistribution under a “null” scenario of no selection. Sinceboth data sets contain neutral windows, one expects anear 0 estimate for the fraction under selection: Iff neutral (S) = f genome (S) exactly for all scores S, we wouldhave p o = min S [f genome (S)/f neutral (S)] = 1, and hence 1 – p o= 0. However, random differences between f neutral (S) andf genome (S) do occur, especially for extreme values of Swhere very few observations are available and thus bothdensities are very close to 0. These differences betweensmall density values can generate fairly wide fluctuationsin the ratio, resulting in a minimum sizably smaller than1 (on some control experiments the minimum was