Quantitative Comparison of Abundance Structures of Generalized Communities: From B-Cell Receptor Repertoires to Microbiomes

The \emph{community}, the assemblage of organisms co-existing in a given space and time, has the potential to become one of the unifying concepts of biology, especially with the advent of high-throughput sequencing experiments that reveal genetic diversity exhaustively. In this spirit we show that a tool from community ecology, the Rank Abundance Distribution (RAD), can be turned by the new MaxRank normalization method into a generic, expressive descriptor for quantitative comparison of communities in many areas of biology. To illustrate the versatility of the method, we analyze RADs from various \emph{generalized communities}, i.e.\ assemblages of genetically diverse cells or organisms, including human B cells, gut microbiomes under antibiotic treatment and of different ages and countries of origin, and other human and environmental microbial communities. We show that normalized RADs enable novel quantitative approaches that help to understand structures and dynamics of complex generalize communities

The effect of temporal pattern of injury on disability in learning networks

How networks endure damage is a central issue in neural network research. This includes temporal as well as spatial pattern of damage. Here, based on some very simple models we study the difference between a slow-growing and acute damage and the relation between the size and rate of injury. Our result shows that in both a three-layer and a homeostasis model a slow-growing damage has a decreasing effect on network disability as compared with a fast growing one. This finding is in accord with clinical reports where the state of patients before and after the operation for slow-growing injuries is much better that those patients with acute injuries.Comment: Latex, 17 pages, 7 figures, 2 table

GlobalPatterns dataset.

<p>(A) Hierarchical clustering dendrogram based on distances between NRADs. (B) NRADs of three samples of similar origin that form a cluster. (C) Microbiome of human palm of human individual 1 clusters closely with sediments 2 and 3, but is more distant to tongue microbiome of individual 1. (D) Three differently shaped NRADs with same entropy.</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

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

Country of origin and age as determinants of gut microbiomes NRADs.

<p>(A) MDS-ordination of NRADs of those 489 gut microbiomes from Malawi/Venezuela (MV) and United States (US) with age information. Small symbols represent individual NRADs, large symbols are averages. Error bars are 90% confidence intervals of the averages. The two coordinates of the MDS plot explain 83% of the NRAD distances. (B) Importance of each of the 4105 NRAD ranks for the random forest classification according to country of origin (MV vs. US). The two peaks around ranks 20 and 200 are the NRAD regions that carry most information about the country of origin.</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

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

Robustness of NRADs against varying sampling depth.

<p>(A) original RAD of first sample of [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005362#pcbi.1005362.ref031" target="_blank">31</a>] (black) and down-sampled RAD (red). (B) the two NRADs obtained by MaxRank normalization to <i>R</i> = 1000 of the RADs in panel A are almost indistinguishable. (C) comparison of NRAD distances of the first 50 samples of the data set of [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005362#pcbi.1005362.ref031" target="_blank">31</a>]. Left violin plot: density of distances between NRADs computed by MaxRank normalization to <i>R</i> = 1000 of the original RADs; middle violin plot: same for down-sampled RADs; right violin plot: distances between corresponding original and down-sampled NRADs. The biologically meaningful NRAD distance distributions are robust against differences in sample size (left and middle violin). In comparison, the distances related to differences in sample size are negligible (right violin).</p