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We can distinguish between the effects of background selection and clonal interference by using a third statistic, D3.

In the right panel, a high mutation rate increases levels of both background selection and clonal interference.

In Figure  6, values of D2and D3are shown for varying levels of background selection and clonal interference.

Using forward simulation of a Wright-Fisher process, we show that hitch-hiking of deleterious mutations with advantageous mutations can lead to overestimation of the number of adaptive substitutions, while background selection and clonal interference can distort the site frequency spectrum to obscure the signal for positive selection.

A third statistic can distinguish between the effect of background selection and clonal interference, (3) D 3 = 2 ∑ i ∈ I H i p A (i ) I H − ∑ i ∈ I M i p A (i ) I M − ∑ i ∈ I H i p S (i ) I H × ∑ i = 1 n − 1 p A (i ) ∑ i = 1 n − 1 p S (i ) + 1.

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Finally, we propose three diagnostic statistics to indicate the degree to which (a) hitch-hiking of deleterious mutations (b) background selection and (c) clonal interference affect a sample of protein-coding sequences.

In the left panel, low mutation rates generate only low levels of background selection and values of D2and D3are strongly correlated, as both are due to clonal interference.

Specifically, it is more robust against distortions of the site frequency spectrum at high frequencies caused by background selection or clonal interference.

Here, we examine the joint effects of background selection, hitch-hiking and clonal interference on the K A / K S and MK statistic.

The extent of background selection, hitch-hiking and clonal interference can be evaluated using the diagnostic statistics presented here.

In the previous section, we showed that much of the bias in the comparative estimators can be explained in terms of background selection, hitch-hiking and clonal interference.

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