42 research outputs found

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

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    <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

    Relative errors of expected allele frequencies <i>q</i><sub><i>nb</i></sub> 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.

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    <p>Relative errors of expected allele frequencies <i>q</i><sub><i>nb</i></sub> 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].

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

    Values of skewness coefficient <i>γ</i>(<i>T</i><sub><i>k</i></sub>) 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.

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    <p>Values of skewness coefficient <i>γ</i>(<i>T</i><sub><i>k</i></sub>) 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].

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    <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

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

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    <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><sub><i>j</i></sub> by Gaussian, relative error with standard deviation <i>σ</i> = 10<sup>−13</sup>.</p

    The estimates of model parameters, with asymptotic confidence intervals.

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    <p>*Assuming exponential tumor growth and the estimates of K and θ, the average tumor growth rate E(λ) corresponds to a doubling time of 55 to 60 days.</p

    Probability density functions of nodal and distant metastases from the time of tumor onset, using the estimated parameters ξ = 0.01,

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    <p><b> = 8.05×10<sup>−9</sup>, </b><b> = 2.78×10<sup>−9</sup>, K = 3.80 and </b><b> = 1.15.</b></p

    Variables not directly observable for the detected tumors in the predicted lung cancer population (1988–1999).

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    <p>IQR, interquartile range; SD, standard deviation;* Here is the yearly growth rate and doubling time of primary tumor.</p

    Comparison of the model fit in the period of 1995–1999 to the data of SEER 2004–2008.

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    <p>(a) the stage distribution conditional on tumor size and (b) the tumor size distribution; (c) Comparison of the predictive model 1988–1999 and SEER 1988–1999, where the data is summarized as stage distribution conditional on tumor size.</p
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