Comment on "Evidence for Positive Epistasis in HIV-1"
Kai Wang,
John E. Mittler and
Ram Samudrala*
Department of Microbiology, University of Washington, Seattle, WA 98195, USA.
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Fig. 1. Mean and standard error (circles and bars) of log10 fitness values versus the number of mutations (Hamming distance) for a simulated data set in which there is no epistasis. The smooth lines here and in Fig. 2 are cubic-spline fits to the data. (A) Plot using all 10,000 samples in our simulated data set. (B) Plot with the 5% lowest fitness values removed from the data set. (C) Plot with the 25% lowest fitness values removed. The decelerating trend in the smooth curve in (B) and (C) [similar to figure 1B in (1)] indicates that selection against viruses with low fitness can result in misleading evidence for positive epistasis.
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Fig. 2. Evaluation of the phenomenon shown in Fig. 1 for the original Bonhoeffer et al. clinical data set. (A) Distribution of log10 fitness values of 9466 sequences in the data set, similar to their figure 1A. (B) Mean log10 fitness values are plotted against the number of mutations (Hamming distance), similar to their figure 1B. The error bars, which are numerically identical to those in Bonhoeffer et al., are the standard deviation divided by number of observations (SD/n) [mistakenly referred to as the "standard error" ( ) in Bonhoeffer et al.] (C and D) The log10 fitness values versus Hamming distance after removing samples with the lowest 5% or 25% fitness values, respectively. Compared with (B), we observe a more severe change of slope (or even a reversal of slope) in the tail of the smooth curves in both plots. (E and F) The log10 fitness values versus Hamming distance after removing samples with the highest 5% or 25% fitness values, respectively. The heads of the smooth curves (corresponding to samples with less than 20 mutations) are approximately linear curves. The approximate slopes for (E) (0.0085) and (F) (0.0088) at the head of the curves are both less steep than that for (B) (0.013). These results indicate that evidence for epistasis from their data set could in fact be affected by data biases.
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