Comparison of analytic predictions to the pairwise distances data of Tyrannidae family with <i>M</i> = 460 species taken from the database [28] with <i>t</i> ≤ 0.8 × 10⁸Myr.

<p>The markers represent the empirical data, while the lines represent the analytic formulas with fitted parameters. (a) Pairwise distance distribution. (b) Minimal distance distribution. (c-e) <i>n</i>-minimal distance distribution. (d) Cherries distance distribution. The fit is performed for all points in the figure with <i>t</i> ≤ 0.5 to avoid clear break down of the Yule tree assumptions for larger distances (see text). The lines are based on following set of parameters: <i>λ</i>−<i>μ</i> = 8 × 10⁻⁸yr⁻¹ and <i>λσ</i> = 6.4 × 10⁻⁸yr⁻¹. For <i>μ</i> = 0, 0.2, 0.4, 0.6, 0.8 × <i>λ</i> this corresponds respectively to <i>σ</i> = 0.8, 0.64, 0.48, 0.32, 0.16.</p

Comparison of the analytic results with numerical simulations.

<p>Markers indicate numerically obtained data using the following parameters set. <i>T</i> = 1, <i>λ</i> = 6, <i>μ</i> = 0 or 3 (circles or squares) and <i>σ</i> = 1 or 0.1 (empty or filled symbols). Lines represent the analytic formulas. (a) Density of number of pairs separated by a certain time, <i>t</i>. Lines were obtained using <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0120206#pone.0120206.e015" target="_blank">Equation (14)</a>. (b) Density of number of leaves separated by a certain time, <i>t</i> with their closest leaf. Lines were obtained using <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0120206#pone.0120206.e018" target="_blank">Equation (17)</a> or <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0120206#pone.0120206.e021" target="_blank">Equation (20)</a> with <i>n</i> = 1. (c) Density of number of leaves separated by a certain time, <i>t</i> with their next-closest leaf. Lines were obtained using <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0120206#pone.0120206.e040" target="_blank">Equation (33)</a> or <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0120206#pone.0120206.e021" target="_blank">Equation (20)</a> with <i>n</i> = 2. (d) Density of number of cherries separated by a certain time, <i>t</i>. Lines were obtained using <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0120206#pone.0120206.e022" target="_blank">Equation (21)</a>.</p

An example of the rooted Yule tree of age <i>T</i>. Filled circles (1, 3, 5, 7 and 8) denote observed leaves.

<p>Empty circles (2, 4 and 6) denote survived but not observed leaves. Short horizontal lines denotes an extinction event. Long, dashed horizontal lines denote the origin of the tree, the first branching event and the time of sampling the tree, from top to bottom. After the first branching at time <i>T</i>₁ the two resulting subtrees both encompass <i>M</i>₁ = <i>M</i>₂ = 4 leaves. However, the number of observed leaves is 2 (leaves 1 and 3) for the left subtree and 3 (leaves 5, 7 and 8) for the right one. The thick green line denotes the pairwise evolutionary distance between the two observed leaves 5 and 7. The horizontal dimension is meaningless. In this example for leaf 1 the first closest observed leaf is 3, the second (as well as the third and the fourth) is 5 (or 7 or 8). The tree has two observed cherry pairs: (1, 3) and (7, 8).</p

Probability to observe a certain number of pairs separated by the time in the interval [<i>t</i>, <i>t</i>+<i>dt</i>] on a tree of age <i>T</i>, <i>N</i>¹(<i>t</i>∣<i>T</i>)<i>dt</i>.

<p>In this plot <i>T</i> = 1, <i>λ</i> = 11, <i>μ</i> = 5, <i>σ</i> = 0.01, <i>t</i> = 1.5 and <i>dt</i> = 0.00001. Circles denote the results of numerical simulation and dots were obtained using the analytic formulas <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0120206#pone.0120206.e026" target="_blank">(25)</a> for zero value and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0120206#pone.0120206.e046" target="_blank">(39)</a> for non-zero values. Note the gap between zero and non-zero probabilities due to small bin size, <i>dt</i>.</p

The correlation between the density of DNMs and various genomic variables at the 1MB scale.

<p>The correlation between the density of DNMs and various genomic variables at the 1MB scale.</p

The standardised regression coefficients from a stepwise multiple regression with forward variable selection.

<p>The standardised regression coefficients from a stepwise multiple regression with forward variable selection.</p

Gamma distributions fitted to the DNM density at the 1MB scale.

<p>In order of decreasing variance: Maroon–Wong, Blue–Francioli, Olive–Jonsson.</p

The equilibrium GC content from a simulation of sequence evolution.

<p>The equilibrium GC content from a simulation of sequence evolution is plotted against the current GC-content of the windows from which the mutation pattern was estimated. Note several of the points are coincident.</p

Testing the difference in slopes.

<p>Testing the difference in slopes.</p

The relationship between DNM density, or divergence, and GC content.

<p>The relationship was estimated from a regression of DNM density or human-chimp divergence, against GC-content and the square of the GC-content at the 1MB scale. Blue–Francioli, Light Orange–Wong, Green–Jonsson and Dark Orange–W<>W and S<>S substitutions between human and chimpanzee.</p