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Data · dataset · 2026

<p>Examples of -bidegreed graph families (a-f) and the size normalized sensitivity of their neutral fixation probabilities to , shown separately for each initial mutant location and evaluated at (g-j).</p>

Listed in ZivaHub and Deakin Research Online and DMU Figshare — shown once because both records carry DOI 10.1371/journal.pcbi.1014829.g003

<p>Vertices with degree <i>d</i><sub>1</sub> are represented as circles whereas vertices with degree are represented as squares.

Description

For the examples depicted, <i>d</i><sub>2</sub> is strictly greater than <i>d</i><sub>1</sub>, but it is also possible for per Definition 3.1. Let <i>n</i><sub>1</sub> denote the number of vertices with degree <i>d</i><sub>1</sub> and <i>n</i><sub>2</sub> denote the number of vertices with degree <i>d</i><sub>2</sub>, and set and .

The value is the fixation probability of a neutral mutant starting at a vertex <i>u</i> of degree , its derivative with respect to is denoted , and the sensitivity is . Panels <b>g–j</b> display the size normalized sensitivity evaluated at and . Normalizing by <i>N</i> makes the sensitivity a function of alone, since by Theorem S3 in the <a href="ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1014829#pcbi.1014829.s001" target="_blank">S1 Appendix</a> the sensitivity scales as 1/<i>N</i> at fixed .

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A graph of size <i>N</i> sitting at a plotted point therefore has sensitivity equal to the plotted value divided by <i>N</i>. <b>a,</b> a star graph, . The <i>n</i><sub>2</sub> = 1 center vertex has degree <i>d</i><sub>2</sub> = 6 while the <i>n</i><sub>1</sub> = 6 periphery vertices have degree <i>d</i><sub>1</sub> = 1 for a total of vertices. <b>b,</b> a path graph, . The intermediate vertices have degree 2 while the endpoint vertices have degree 1. <b>c,</b> a bipartite biregular graph; the vertices on the left side have degree <i>d</i><sub>2</sub> = 3 while the vertices on the right side have degree <i>d</i><sub>1</sub> = 2, for a total of <i>N</i> = 10 vertices. <b>d,</b> a fan graph .

The center vertex has degree 2<i>b</i> = 6, while each of the 2 vertices on each of the <i>b</i> = 3 blades has degree 2, for a total of <i>N</i> = 2<i>b</i> + 1 = 7 vertices. <b>e,</b> a wheel graph . The center vertex has degree <i>n</i> = 8 while the <i>n</i> vertices on the spoke ends have degree 3, for a total of <i>N</i> = <i>n</i> + 1 = 9 vertices. <b>f,</b> a book graph . Each of the <i>p</i> = 3 pages has 2 page corners with degree 2, and the 2 seam endpoints have degree <i>p</i> + 1, for a total of <i>N</i> = 2<i>p</i> + 2 = 8 vertices. <b>g,</b> A contour plot in the space, where both parameters are dimensionless.

The lines with shapes denote the values of and for the various bidegreed graphs in <b>a-f</b>. Note that the path graph has <i>n</i><sub>1</sub> = 2 and , so for . Thus as <i>N</i> increases, decreases.

The intensity of the colorbar denotes , <b>h,</b> , <b>i,</b> , and <b>j,</b> . Lighter colors indicate a larger sensitivity.</p>

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Provenance · 3 source records, 35 field assertions
SourceKeyLast seenRaw
ZivaHuboai:figshare.com:article/3403634313 d agoJSON v1
Deakin Research Onlineoai:figshare.com:article/3403634313 d agoJSON v1
DMU Figshareoai:figshare.com:article/3403634313 d agoJSON v1
FieldAssertionExtractorEvidence
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