Influence of round-off errors on accuracy of computation of expected allele frequencies by using expressions Eqs (22)–(25).

<p>The plot shows upper bounds of maximum relative error for the scenario of exponential growth of population with different values of product parameter <i>ρ</i>, obtained by corrupting values of expected times <i>e</i>_<i>j</i> by Gaussian, relative error with standard deviation <i>σ</i> = 10⁻¹³.</p

Relative errors of approximations for <i>ETMRCA</i> (upper plot) and <i>ETBLT</i> (lower plot) proposed by Chen and Chen (2013) [16].

<p>Relative errors of approximations for <i>ETMRCA</i> (upper plot) and <i>ETBLT</i> (lower plot) proposed by Chen and Chen (2013) [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0170701#pone.0170701.ref016" target="_blank">16</a>].</p

Values of skewness coefficient <i>γ</i>(<i>T</i>_<i>k</i>) of probability distributions of times in the coalescence tree computed for different genealogy sizes, <i>n</i> = 100 (upper plot) and <i>n</i> = 1000 (lower plot) and for different scenarios of population size change constant (<i>ρ</i> = 0) and exponentially growing with <i>ρ</i> = 1, <i>ρ</i> = 10 and <i>ρ</i> = 100.

<p>Values of skewness coefficient <i>γ</i>(<i>T</i>_<i>k</i>) of probability distributions of times in the coalescence tree computed for different genealogy sizes, <i>n</i> = 100 (upper plot) and <i>n</i> = 1000 (lower plot) and for different scenarios of population size change constant (<i>ρ</i> = 0) and exponentially growing with <i>ρ</i> = 1, <i>ρ</i> = 10 and <i>ρ</i> = 100.</p

Log-likelihood curves for the exponential model of population growth for data on segregating sites from the mtDB database [25].

<p>Each segregating site from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0170701#pone.0170701.t002" target="_blank">Table 2</a> was treated as a separate SNP. The curve marked with asterisks shows the exact log likelihood function and the one marked with open circles is the approximate log likelihood function. The maximum of the exact log likelihood function is attained at and the maximum of the approximate log likelihood function is attained at .</p

Relative errors of expected allele frequencies <i>q</i>_<i>nb</i> versus allele type <i>b</i> for two values of genealogy size <i>n</i> = 1000 (upper plot) and <i>n</i> = 10000 (lower plot) for different values of the product parameter of the population growth <i>ρ</i> = 1, <i>ρ</i> = 10, <i>ρ</i> = 100 and <i>ρ</i> = 1000.

<p>Relative errors of expected allele frequencies <i>q</i>_<i>nb</i> versus allele type <i>b</i> for two values of genealogy size <i>n</i> = 1000 (upper plot) and <i>n</i> = 10000 (lower plot) for different values of the product parameter of the population growth <i>ρ</i> = 1, <i>ρ</i> = 10, <i>ρ</i> = 100 and <i>ρ</i> = 1000.</p

Statistics of segregating sites in mtDNA data from Human mtDNA database [22].

<p>Elements in <i>b</i> are possible numbers of copies of the rare allele, and elements in <i>c</i>_<i>k</i> are numbers of segregating sites in the sample that have the number of copies of the rare allele equal <i>b</i>.</p