Odds-ratio plot and Tartan plot for visualization of statistical associations.

<p><b>A</b> Odds-ratio plot, based on an alignment of region of HIV-1 gp120 around the V3 loop (C296-C331). Here, the feature is the predicted co-receptor tropism of HIV-1 [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146409#pone.0146409.ref017" target="_blank">17</a>] (R5 vs. X4 tropic). Bar heights and colors indicate logarithms of odds ratios and negative logarithms of <i>p</i> values, respectively. A reference sequence and sequence positions can be added in the top and bottom rows for orientation. <b>B</b> Tartan plot for the synopsis of two alignment pair association measures, here: −log <i>p</i> from association test between alignment position pairs (upper right triangle) vs. Direct Information between these pairs (lower left triangle). Association strengths are color coded (color legend on the right). For orientation, axes can be annotated and sequence substructures can be indicated by lines.</p

Comparison of statistical indicators of association.

<p>200 random contingency tables with total count <i>N</i> = 100, a typical order of magnitude for analyses of sequence-feature association in practice, are analyzed by Fisher’s exact test, yielding <i>p</i> values for the rejection of independence (horizontal axis, not corrected for multiple testing), and by four different BF models, namely <i>K</i> = 1, <i>K</i> = 100, <i>K</i>_<i>D</i>, and uniform model, with corresponding BFs on vertical axis. Solid horizontal black line at <i>BF</i> = 1 and dashed vertical line at <i>p</i> = 0.05 for orientation.</p

Comparison of frequentist approach and Bayes factors (BF).

<p>Discovery of association of alignment positions of HBV core proteins with patient HLA types, here: A*01 (top row) and B*44 (bottom row). Sequence numbers in panel titles are feature-carrying fractions of the total of 148 sequences included in the alignment. Association of sequences with feature HLA were analyzed by Fisher’s exact test (panels A, D), BF with <i>K</i> = 1 (panels B, E), and BF with <i>K</i>_<i>D</i> (panels C, F). Alignment positions with association above certain thresholds (horizontal dashed lines) are marked by red stars and vertical dashed lines, namely <i>p</i> < 0.01 (A, D), or <i>BF</i> > 10 (B, C, E, F). The <i>p</i> values and BFs shown are the best for each alignment position (lowest <i>p</i> values, highest <i>BF</i>s).</p

Phylogenetic distribution of feature-carrying sequences and phylogenetic bias indicator <i>B</i>.

<p>The distance-based phylogenetic tree in all six panels was computed for the same set of 788 East Asian HIV-1 gag protein sequences obtained from the HIV sequence database at <a href="http://www.hiv.lanl.gov" target="_blank">http://www.hiv.lanl.gov</a>. In each panel, those branches are colored red that correspond to sequences that carry an amino acid substitution apparently associated with a certain HLA type. The numbers to the upper right of each tree are the corresponding values of the bias indicator <i>B</i>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146409#pone.0146409.e005" target="_blank">Eq (4)</a>.</p

Broken stick distribution (solid line) and NRADs of <i>IgG</i>⁺<i>CD</i>27⁺ fractions (points).

<p>Inset: section of hierarchical clustering dendrogram where broken stick distribution appears. This plot adopts the usual presentation of the broken stick distribution in the literature with linear horizontal axis and logarithmic vertical axis. Therefore the boomerang shapes of the log-log <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005362#pcbi.1005362.g004" target="_blank">Fig 4</a> appear horizontally stretched.</p

General process employed in this work.

<p>Flowchart of procedure from original species/abundances or sequence/reads data (top box) to original RADs, then to NRADs, and analyses based on NRADs.</p

Rank abundance distributions of memory B cell receptors.

<p>Four different B cell receptor sub-classes from donors 1 (replicate samples A, B) and 2 (replicates C, D) are compared. Top left panel: Log-log plot of RADs prior to normalization. Top right: Log-log plot of corresponding NRADs. Legend for RADs and NRADs is given in bottom right panel. Bottom left: Hierarchical clustering tree based on all pairwise distances between the 16 NRADs.</p

Averaged NRADs of gut microbiome data in six age groups.

<p>The number of NRADs per group from youngest to oldest were 9, 18, 55, 64, 34, and 309, respectively. Solid lines are mean NRADs, shaded areas are 90% confidence intervals for the means.</p

A typical Rank Abundance Distribution (RAD).

<p>A RAD with species abundances plotted in decreasing order from the most abundant (rank 10⁰ = 1) on the left to the least abundant species sampled from the community on the right. Both axes are scaled logarithmically to reveal the global structure of the RAD. Quantities such as the number of sampled individuals or the richness of the sample can be easily retrieved from the RAD.</p

Development of gut microbiome entropy <i>H</i>_<i>R</i> with age <i>t</i>.

<p>(A) Entropies (with <i>R</i> = 4105) in nats for 181 samples from Malawi and Venezuela (MV, blue dots), and 308 samples from the United States (US, orange dots). Log-scaled horizontal axis is age in years. Superimposed are models for (blue line) and (orange line) according to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005362#pcbi.1005362.e023" target="_blank">Eq (6)</a>. Areas around the model lines shaded in blue and orange are the corresponding 90% confidence intervals of the respective models. (B) and (C) Comparison of mean entropies of measured data (red points) and their corresponding 90% confidence intervals (error bars), with the model (solid gray lines) and its 90% confidence interval (shaded areas), for MV (panel B) and US (panel C). Model lines and shaded areas are the same as in panel A.</p