Quantitative Comparison of Abundance Structures of Generalized Communities: From B-Cell Receptor Repertoires to Microbiomes
[['The community , i . e . the assemblage of organisms co-existing in a given space and time , is central to much of ecology [1] , and since Darwin’s “entangled bank” [2] one of the great challenges of biology is to explain the observed species diversity in communities mechanistically as a consequence of interactions and evolution .', 'Modern experimental methods of high-throughput sequencing have brought us closer to complete inventories of community diversity .', 'Moreover , these methods enable us to widen the scope of the community concept to generalized communities , that we define as assemblages of genomically diverse entities , which include , apart from communities in classical ecology , for instance B or T cell repertoires of the adaptive immune system , viral quasi-species , tumors , or human microbiomes .', 'An intuitive description of a community composition is a table with columns species and abundance , possibly ordered from most to least abundant species ( we use the term species here in a loose sense for operational taxonomic units or other genomically distinct biological entities ) .', 'A visually more accessible graphical representation of this table would be a plot that arranges the species along the horizontal axis and the abundances as vertical bars , sorted from highest to lowest bar .', 'While such a plot is expressive for a specific community , it does not lend itself to quantitative comparisons between communities .', 'To illustrate this point , consider a comparison of a community of South-American animal species with one of Sub-Saharan African animal species from regions with otherwise similar conditions .', 'The two species columns of our table would have practically no overlap so that a direct comparison of these tables or plots is not possible .', 'The same lack of overlap has to be expected for other generalized communities .', 'For instance if we compare high-throughput sequencing data of B cell receptors of two persons , it is unlikely that there are receptors on mature B cells that occur in both persons .', 'Nevertheless , it is a meaningful biological question whether the abundance structures of the two sets of B cells differ , e . g . whether the B cell repertoire is dominated by a few clones with high cell numbers , or whether it is distributed over many different clones with low cell numbers .', 'A popular method for community comparison even in the absence of species overlap is to compute for each community a diversity index [3] , i . e . a single number that characterizes one aspect of the community , for instance the species richness , the evenness of the distribution , the Shannon entropy , or one of many related measures [4] , and then to compare the values of these indices between communities .', 'The main disadvantage of this index approach is that it reduces a feature-rich abundance distribution to a single number , which may neglect important characteristics of that distribution .', 'An alternative approach that had a major influence on the development of the theoretical foundations of modern ecology is to discard the species labels of the species-abundance table , which then becomes a so-called Species Abundance Distribution ( SAD; for excellent reviews see [5] , or [6] , chapter 9 ) .', 'There are several established ways of presenting the information contained in a SAD ( see Fig 1 of [5] ) , for instance as straightforward histogram with species abundance as function of a species index , or as a binned histogram , typically with doubling bin widths with decreasing abundance .', 'Here we focus on the Rank Abundance Distribution or RAD ( Fig 1 ) as SAD representation .', 'RADs are simply vectors of species abundances sorted in decreasing order , usually visualized as two dimensional plots , possibly with one or both axes scaled logarithmically .', 'In comparison to the mentioned simple and binned histograms , RADs are more smooth due to their component sorting [7] , and they retain the full biological resolution of the sampling experiment .', 'The information content in RADs and probability distribution functions is the same , and one can be transformed into the other ( see e . g . [8 , 9] ) .', 'Obviously , RADs retain the complete shape information of species-abundance tables .', 'The abstraction of species information means that RADs enable analysis of generic abundance distribution features of generalized communities , independently of the actual species composition .', 'RADs , and more generally SADs have been a key conceptual tool in the development and benchmarking of mechanistic models of ecological communities [10–15] .', 'The mathematical functions resulting from mechanistic or statistical models , such as the log-normal distribution , were usually fitted to empirical RADs or SADs to identify the best community model .', 'This basic research has paved the way for the application of these distributions to community comparisons , for instance to the characterization of community changes with changing environmental conditions ( see e . g . [16 , 17] .', 'In these cases , the community comparison is typically a parameter comparison between fits of generic mathematical models to different RADs or SADs , or it is a purely visual comparison of these distributions [5] .', 'In real-world samples , RADs are often not adequately described by a uniform mathematical model , e . g . a single log-normal distribution [18] .', 'In macroecology , knowledge about the properties and relations between the observed animals and plants can be used to deconstruct multimodal distributions , and to fit simple models to fractions of the samples [3] .', 'This knowledge is generally not available for high-throughput sequencing data of complex generalized communities , so that RAD analyses based on simple parametric models are difficult .', 'This calls for a non-parametric approach .', 'A further problem is that in practice the number of sampled species or sequences usually differs between samples .', 'This means that RADs often have different dimensions and cannot be compared directly .', 'It is possible to test for arbitrary pairs of RADs the null hypothesis that they originate from the same distribution using the Kolmogorov-Smirnov test [3 , 19] , but this is usually not helpful for quantitative comparisons .', 'Technically , differences between a pair of RADs of different richness m , n could be also quantified by the Kolmogorov-Smirnov statistic D evaluated for the corresponding pair of cumulative distribution functions .', 'However , it is problematic to interpret D in such cases since we are forced to equate non-reporting of |m − n| ranks in the shorter RAD with zero abundance , although the non-reporting may have technical reasons , e . g . limited sequencing depth .', 'Thus , the question arises whether quantitative RAD comparisons are possible between samples of different richness .', 'We quote from the widely cited SAD review by McGill et al . [5]: “How do we compare SADs ? Nearly all comparisons of SADs along gradients , deconstructions or time trajectories to date have been purely by visual inspection ( … ) . Most particularly , these visual inspections have been performed on rank-abundance plots which , by using an x-axis that runs from 1 to S ( i . e . species richness ) , seriously confounds the effects of species richness per se with other changes in the shape of the SAD ( … ) . Changes in species richness are a legitimate factor that should be considered a change in shape of the SAD . However , changes in richness so strongly dominate in rank-abundance plots that no other changes are easily considered . Is there any other change in the shape of an SAD after controlling for the fact that productivity affects richness ? We cannot say at the present time ( … ) More rigorous multivariate methods are needed . ”', 'Here , we introduce MaxRank normalization of RADs , a new method that enables quantitative comparison of RADs , including their shapes .', 'The approach is non-parametric and allows for the direct quantitative comparison of complex RADs without deconstruction and model fitting .', 'An essential component of the method is the re-sampling of RADs up to a given richness .', 'Consequently , the resulting normalized RADs ( NRADs ) are largely agnostic about the true richness of the original sample .', 'The fact MaxRank normalization uses re-sampling may lead to conflation with rarefaction and rarefying ( on the distinction between the terms see [20] ) , two other techniques that also use re-sampling .', 'Rarefaction [21] is typically used to estimate and compare richness between samples , i . e . exactly the quantity that is not of interest in MaxRank normalization .', 'Rarefying ( e . g . [22] ) is applied to normalize OTU counts between samples .', 'However , it is precisely the purpose of RADs and MaxRank normalization to abandon OTUs , and thus to make quantitative comparisons of abundance structures of different communities possible , irrespective of OTUs .', 'We show here that results from the quantitative comparison of normalized RADs reflect biological differences between samples .', 'To emphasize the versatility of the method , we have chosen a diverse set of high-throughput sequencing data representing different types of generalized communities , namely , human B cell receptor repertoires , and various human and environmental microbiomes .', 'As one example of generalized communities we use human B cell receptor ( BCR ) repertoires .', 'The diversity of BCRs in an individual is crucial for the recognition of antigens and the adaptive immune response [23] .', 'Here we focus on the so-called heavy part of the receptor encoded by combinations of gene segments of the Ig heavy chain ( IGHV ) locus ( Fig 2A; [24] ) , and especially on the diversity of the “variable” VH segments in that part ( Fig 2B ) .', 'Based on sequence homology , the VH segments are grouped into seven families ( VH1—VH7 ) , with members of a family having more than 80% sequence homology [25] .', 'The sizes of the families vary from 1 ( VH6 family ) to 18–21 ( VH3 family ) .', 'The primary repertoire of rearranged IGHV genes among naïve , antigen-inexperienced B cells ( Fig 2C ) typically encompasses all available VH segments , although abundances can vary considerably between VH gene segments .', 'Exposure to antigens leads to a selective adaptation of the BCR repertoire that results in individual-specific sets of memory B cells ( Fig 2D ) .', 'In the course of this complex maturation process , the usage of VH segments in BCR rearrangement repertoires may change .', 'On top of this layer of complexity , several classes of BCRs with different biological functions , such as IgG or IgM , are generated by class switching .', 'Depending on the chronological order of these different processes , and on the individual immune histories , we can expect more similar or more divergent IGHV gene diversity between receptor classes and individuals in memory B cells .', 'We study this question with RADs computed from High-Throughput Sequencing ( HTSeq ) data .', 'HTSeq technology is also transforming the study of microbial communities , because it allows us for the first time to see these complex assemblages in their full diversity [26 , 27] .', 'For instance , we now start to see the diverse composition of human gut microbiomes , and we begin to understand the links between the human microbiome , health and disease [28] .', 'However , the deluge of data makes us also aware of the need for new ways to analyze and model such complex systems , e . g . with methods developed in ecology [29] , such as RADs .', 'We have selected three HTSeq data sets to demonstrate the potential and limitations of RADs for the analysis and the modeling of microbiomes: the considerable effect of antibiotics on gut microbiomes [30] , a large collection of gut microbiomes from countries where different life styles prevail [31] , and a diverse set of human and environmental microbiomes [32] .', 'In these examples , we use RADs as an analytic tool to generate easily interpretable results , and as a basis for quantitative models .'], ['In the work presented here we used high-throughput sequencing ( HTSeq ) amplicon data from four different sources to compute and analyze NRADs , as described in the following .', 'For each dataset we followed the flowchart in Fig 3 .', 'The last box of the flowchart Fig 3 indicates that sets of RADs normalized to a common R can be analyzed in numerous ways .', 'In this article we used methods from three branches of data analysis: ordination , clustering , and classification .', 'Since many ordination and clustering methods require a distance between the studied objects , we first describe how we computed distances between pairs of NRADs , and then the actual analysis methods .'], ['With their highly diverse repertoire of antigen-binding receptors , human memory B cells are an example of what we have earlier termed generalized community .', 'This diversity is achieved by a process that is only partly understood and currently subject of intense research [43 , 44]: it starts with the genetic recombination of triplets of specific VH , DH , and JH gene segments from genetic pools of these segments , followed by various mutation and selection steps , and eventually leads to distinct classes and sub-classes of memory B cells .', 'We assume as a working hypothesis that all memory B cells underwent the same diversity generating process .', 'If this is true , we should see a very similar VH gene rearrangement pattern ( Fig 2 ) in all sub-classes of memory B cells , leading to the same normalized RADs ( NRADs ) of memory B cells in all sub-classes .', 'To test this hypothesis , we used HTSeq data of the immunoglobulin heavy-chain variable ( IGHV ) regions of four large memory B cell sub-classes , IgG+ , IgG+CD27+ , I g M o n l y + C D 27 + , IgM+IgD+CD27+ , from two donors .', 'The IGHV regions derive from the genomic pool of 38–46 VH segments ( Fig 2A ) and have been modified by mutation and selection steps .', 'If we interpret the original set of VH segments as the “species” to be ranked according to their abundances , we should under our working hypothesis see the same NRADs in all memory B cell sub-classes .', 'To exclude distortions of abundances due to primer bias , we collapsed abundances of VH segments from the measured read numbers to the numbers of distinct VH sequence variants .', 'Thus , in this case an abundance is the number of distinct sequences that originate from the same VH segment , and that have been diversified by somatic mutations and clonal expansions .', 'Fig 4 summarizes the results .', 'The non-normalized RADs ( top left of Fig 4 ) have similar , boomerang-like shapes , although direct comparisons is difficult since differences in abundance span more than one order of magnitude , and maximum ranks differ between 35 and 40 .', 'For direct comparison we therefore normalized the RADs to a MaxRank R = 35 ( top right of Fig 4 ) .', 'The resulting NRADs have overall very similar shapes , lending support to our working hypothesis of a common generation and selection process .', 'However , there are notable features that differentiate between groups of NRADs .', 'For instance at rank 1 the most diverse IGHV regions in IgM receptors of donor 1 ( green curves in Fig 4 ) are more abundant than all other rank 1 abundances .', 'Conversely , for donor 2 the most diverse IGHV regions in IgM ( blue curves ) are the least abundant of all rank 1 abundances .', 'Towards higher ranks , IgM abundances of both donors ( blue and green ) are more similar to each other .', 'IgG receptors ( red and orange ) have more similar abundance structures throughout all ranks , and have stronger right tails than IgM receptors , indicating a more even VH segment diversity in IgG than IgM receptors .', 'The differences between the NRAD curves are subtle , but they emerge clearly when we quantitatively analyze NRAD distances ( Eq 2 ) .', 'In the hierarchical clustering tree of the distances ( Fig 4 ) we see three main clusters of NRADs , a big cluster of IgG+ and IgG+CD27+ NRADs on the right of the tree in red and orange , and two clusters of IgM related NRADs .', 'These three clusters appear robustly , no matter whether the average linkage or the complete linkage criterion is used for clustering .', 'As expected for replicates , ( A , B ) and ( C , D ) of the same sub-class coming from the same donor yield NRADs that are most similar and thus fall into the same lowest-level clusters .', 'Beyond this , memory B cell sub-classes have remarkably different cluster structures .', 'The big IgG+/IgG+CD27+ cluster ( red and orange ) of eight NRADs has a substructure of an IgG+ cluster and a separate IgG+CD27+ cluster , i . e . here the memory B cell sub-class has a stronger impact on the NRAD than inter-donor differences .', 'This is different for the I g M o n l y + C D 27 + and IgM+IgD+CD27+ clusters .', 'There , each of the two donors forms a cluster of its own that combines both I g M o n l y + C D 27 + and IgM+IgD+CD27+ NRADs , i . e . in these two IgM sub-classes , inter-personal differences in VH diversity patterns are stronger than differences between sub-classes .', 'Our working hypothesis was that we have basically a single , diversity generating process for all memory B cell sub-classes , leading to the same NRADs for VH gene rearrangement pattern in all sub-classes .', 'Overall , our results are consistent with this big picture since all NRADs are variants of the same boomerang shaped template .', 'However , the quantitative analysis of NRAD distances picked up differences that require refinements of this model .', 'This is not surprising since some of the steps that potentially affect VH rearrangement diversity , for instance class switching , cannot apply equally to all memory B cell sub-classes .', 'What is surprising are the specific differences in VH rearrangement diversity between IgM and IgG sub-classes , e . g . the structure of the IgG cluster discussed above suggests that there could be significantly different selection pressures towards the final memory B cells in the two sub-classes IgG+ ( i . e . IgG+CD27− ) and IgG+CD27+ .', 'Recently , we have used the same HTSeq data for a detailed sequence-based analysis of the clonal composition and genealogy of memory B cells [33] .', 'Although our current NRAD-based analysis disregards much of the information used in [33] , results are consistent: First , the VH gene rearrangement composition is mostly very similar across the studied sub-classes of memory B cells , in agreement with a shared generation process [45] .', 'Second , IgM+IgD+CD27+ and I g M o n l y + C D 27 + show almost the same VH gene rearrangement diversity , likely due to their clonal relatedness as described in [33] .', 'Third , there are significant and consistent differences between IgG+CD27+ and IgG+CD27− with respect to mutation load in both donors , also in agreement with [46] or [47] .', 'To conclude this section , we return to the conspicuous boomerang shape that is the template common to all B cell receptor RADs and NRADs ( Fig 4 ) .', 'When testing for similarity to standard model distributions in ecology , we found that the broken stick distribution [13] is a good description for the NRADs of sub-class IgG+CD27+ ( Fig 5 ) .', 'If included in the hierarchical clustering , the broken stick NRAD appears among the branches of the IgG+CD27+ sub-tree ( inset of Fig 5 ) .', 'However , even for the other sub-classes , we cannot reject the broken stick distribution ( p-values from Kolmogorov-Smirnov tests between 1 . 0 and 0 . 87 with a median of 0 . 99 ) , though they deviate more than IgG+CD27+ .', 'Note that the normalized broken stick distribution in Fig 5 has no free parameters and therefore has not been fitted .', 'Several mechanisms in community ecology and elsewhere lead to broken stick RADs [13 , 48–50] .', 'A simple explanation for the observed RADs of VH segment usage could be the following .', 'Assume a fixed number n V H of VH segments in the genome , and a fixed total number Nt of all BCR sequence variants ( i . e . summed over all VH segments ) .', 'The biological purpose of fixing Nt could be to provide a sufficient number of BCR variants to cover the typical antigen diversity .', 'These two assumptions fix the average number N t / n V H of sequence variants per VH segment .', 'If this is all we know , the Maximum Entropy principle states that the geometric distribution is the most parsimonious explanation fulfilling these requirements [51] .', 'The geometric distribution is the discrete equivalent of the continuous exponential distribution , which generates the broken stick RAD [48] .', 'Thus , our argument posits a random process that produces numbers of sequence variants per VH segment with a geometric distribution .', 'In fact , sequence counts of most RADs are compatible with geometric distributions according to Kolmogorov-Smirnov tests at significance level 0 . 05 ( exception: sample D of IgM+IgD+CD27+ with p = 0 . 04 ) .', 'Given that there is good agreement between the RADs of the BCR sub-classes ( Fig 4 ) , and also good agreement in the usage of individual VH segments between human donors [33] , our argument suggests the following two testable hypotheses .', 'First , the random mechanism leading to the broken stick RAD could be encoded in the human genome and conserved among individuals with intact immune systems .', 'Second , since our argument is generic , we should see the broken stick RAD also in other species with similar BCR rearrangement mechanisms .', 'Dethlefsen et al . [30] reported the effects of a short course of Ciprofloxacin ( Cp ) treatment on the gut microbiomes of three healthy human individuals .', 'When comparing gut microbiomes prior to treatment and during treatment , they found markedly perturbed taxonomic composition , richness , diversity , and evenness .', 'These perturbations varied between individuals .', 'After treatment , the community compositions recovered within four weeks to states close to pre-treatment , though with some species lost .', 'We tested whether the dynamics of perturbation and recovery is reflected by changes of NRADs .', 'The NRADs fall into two clusters , one well-defined “off-Cp” cluster of NRADs before and after treatment ( blue and green in Fig 6 ) , and one wider “on-Cp” cluster during treatment ( red in Fig 6 ) .', 'All on-CP NRADs have heavier heads and less weight in the tails , consistent with the decreased gut microbiome diversity under treatment discovered by [30] .', 'After normalization , we could compute distances between all pairs of NRADs and apply multidimensional scaling ( MDS ) to the distance matrix .', 'The MDS plot Fig 6B captures the abundance dynamics from the well-defined off-Cp cluster on the right to the wider on-Cp cluster on the left and back again to the off-Cp cluster on the right .', 'We usually find in MDS analyses a strong correlation of the first coordinate with Shannon entropy .', 'Hence , the dynamics in the MDS plot Fig 6B from right ( pre-Cp ) to left ( Cp ) to right ( post-Cp ) corresponds to a succession of high-low-high entropy .', 'This can also be seen directly from the NRADs: the off-Cp NRADs have a relatively heavy tail and weak head , i . e . a more even distribution with higher entropy , corresponding to a more diverse gut microbiome .', 'Conversely , the on-Cp NRADs have a more heavy head and weaker tail , i . e . a less even distribution with lower entropy , corresponding to a less diverse gut microbiome , partly decimated by the effect of the antibiotic .', 'Dethlefsen et al . [30] remarked that after treatment several taxa failed to recover , while the participants in the study had normal intestinal function , and they argued that the eliminated taxa after treatment may have been replaced by other taxa with similar functions .', 'The fact that pre- and post-Cp NRAD ensembles have the same shapes and form a single compact off-Cp cluster ( Fig 6 ) supports this assessment .', 'It is instructive to compare our analysis based on the abundance structure with an OTU composition analysis as in Fig 6 of Ref [30] .', 'The OTU based PCA in Ref [30] has a cluster structure that is influenced by both the individual microbiome donor and by the treatment state .', 'The conflation of both influences makes the result of the PCA richer but also more difficult to interpret: If we consider individual microbiome compositions , all three individuals have different microbiome dynamics under treatment .', 'Conversely , the NRAD based analysis is blind to individual differences in microbiome composition .', 'This blindness to composition means on the other hand to focus on the abundance structure , which makes the result in our Fig 6 more easy to interpret: In terms of the abundance structure , all three individuals behave in the same way , clearly showing a generic effect of the antibiotic treatment .', 'Yatsunenko et al . [31] found in 528 gut microbiomes from Malawi , United States and Venezuela , that ( 1 ) species richness of gut microbiomes increased with age from birth to about the third year , and then was much less variable , and ( 2 ) taxonomic composition of adult gut microbiomes from the Unites States differed strongly from those of Malawi and Venezuela , while the latter two showed less pronounced differences .', 'In our analysis we do neither use richness ( we normalize to a common richness ) , nor taxonomic labels , but we use solely the abundance vectors ( Eq 1 ) as quantitative descriptors of NRAD shapes .', 'Nevertheless , we will in the following show results consistent with key results from [31] with NRADs .', 'Additionally , we will present a novel NRAD-based quantitative model for the development of gut microbiome entropy as function of age .', 'Prior to normalization , the richness of the samples covered three orders of magnitude , from 4105 to 296214 different ranks .', 'All 528 RADs were normalized to the same MaxRank of R = 4105 to make RAD shapes and quantities computed thereof comparable .', 'Analyses with NRADs are complementary to taxonomy-based analyses: NRADs are blind to taxonomy , which is both a limitation and an advantage .', 'It is a limitation because community biology is a function of taxonomic composition .', 'It is an advantage because it enables quantitative comparison between taxonomically different generalized communities and thus discovery of generic community biology that is independent of actual taxonomic composition .', 'A dataset where these aspects can be explored is the GlobalPattern dataset of Caporaso et al . [32] with 26 samples from human microbiomes , various environments , and mock communities .', 'We transformed OTU tables to RADs and normalized them to MaxRank R = 2067 , the minimum richness in the set , and we computed a distance matrix of all pairs of NRADs .', 'Hierarchical clustering of the distance matrix ( dendrogram in Fig 10A ) led to close clustering of some samples that also form taxonomic clusters [32] , namely the creek samples and a lake sample , the mock communities , or the human tongue and most feces communities .', 'The NRADs in these clusters have low distances and thus are similar ( e . g . Fig 10B ) .', 'Other relationships are more unexpected .', 'The taxonomy-based analysis by [32] clusters tongue and palm microbiomes together and clearly separates human microbiomes from environmental samples .', 'Conversely , NRADs of microbiomes of human palms do cluster closer with environmental samples than with microbiomes of tongues or feces .', 'For instance , the NRAD palm1 does not cluster with the microbiome tongue1 of the same individual , but most closely with the sediment samples .', 'NRADs of both palm1 and sediment2 have a lower abundance of rank 1 than tongue1 but more heavy tails ( Fig 10C ) , were palm1 and sediment2 fit almost perfectly .', 'Reasons for this unexpected clustering are not known .', 'It could be that microbiomes in tongue and feces are more strictly controlled by the host body and the microbiome itself , while microbiomes on palms are more exposed to the environment .', 'In the GlobalPatterns dataset , entropies HR range from 2 . 67 ( tongue2 ) to 6 . 58 ( soil2 ) with a median of 4 . 10 and a standard deviation of 1 . 06 , and one may be tempted to explain the observed clustering by different entropies .', 'However , such a simple approach is not successful here .', 'For instance , the three NRADs in Fig 10D have almost the same entropies ( H R c r e e k 3 = 3 . 98 , H R m o c k 2 = 3 . 95 , H R t o n g u e 1 = 3 . 91 ) , but have completely different shapes , and are members of different clusters .', 'In general , the rich information content of an NRAD cannot be reduced to a single scalar quantity .', 'In the introduction we have mentioned that a theoretical possibility to quantitatively compare pairs of RADs of different richness ( a strength of MaxRank normalization ) is the use of the Kolmogorov-Smirnov statistic D , without RAD normalization .', 'This corresponds to using the Chebyshev distance between the corresponding two cumulative distribution functions with different support .', 'Although it is obvious that this approach treats the tail regions in a problematic way , it is unclear whether this problem is of practical relevance .', 'To test this , we treated D as a distance and reran the hierarchical clustering with this distance .', 'In fact , this D-based tree recovers some of the features of Fig 10A , but in general shows less biologically meaningful clusters ( S1 Fig ) .', 'We conclude that a D-based analysis is in practice no alternative to MaxRank normalization .', 'As mentioned in the introduction , one commonly used procedure for quantitative RAD comparisons is a parametric approach .', 'Typically , a standard distribution such as the log-normal is fitted to a set of RADs and the comparison is then reduced to a comparison of the fitted parameters .', 'We have tested the viability of this approach by fitting to the RADs of all GlobalPatterns samples five standard distributions , broken stick as null model , preemption , log-normal , Zipf , and Mandelbrot [41] .', 'For most samples , with the exception of some soil and sediment samples , we found clear qualitative deviations from all five fitted distributions ( S2 Fig ) , or , in other words , only few fitted distributions reflected the actual RAD shapes .', 'This means that this parametric approach is in general not an option for quantitative analysis of HTSeq data .', 'In contrast , with our non-parametric approach we can quantitatively compare all information-rich NRADs in a consistent and detailed way .', 'The key feature of MaxRank normalization is that it enables quantitative RAD comparisons by mapping RADs with diverse richness values to NRADs of a common richness R . It is clear that the lower R , the less information can be carried by NRADs .', 'This could make analyses based on NRADs sensitive to R . To test this , we have tested how the choice of R affects NRAD based classification , NRAD distances , and NRAD entropies , as used in the previous sections .', 'First , we address the question whether NRAD based classification is sensitive to R using the classification of gut microbiomes described earlier .', 'We use the same random forest classification and threefold cross validation as before to classify NRADs of gut microbiomes of individuals older than 3 years into MV ( Malawi/Venezuela ) or US ( United States ) .', 'The results for R = 4105 , 1000 , and 250 are summarized in Table', '2 . The table shows a weak reduction in accuracy and κ statistic with decreasing R and increasing errors , both explainable by a loss of information stored in the NRADs with lower R . However , the reduction of R from 4105 to 1000 affects the accuracy of the classifier barely , and even the classifier computed from NRADs with R = 250 has still a good accuracy .', 'The weak dependency is consistent with the importance plot ( Fig 7B ) where the regions of high importance cover two extended rank intervals that can be mapped down to NRADs with R = 250 or lower , though with some losses .', 'Secondly , we test the effect of R reduction on NRAD distances for the GlobalPatterns data set .', 'Fig 11A demonstrates that NRAD distances ( Eq 2 ) are well-conserved even if R is an order of magnitude lower than the richness of the original RADs .', 'Approximately halving R from 
['Introduction', 'Materials and Methods', 'Results', 'Discussion']
['The 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 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 generalized communities .']
['Living things are parts of complex communities , similar to humans living in cities .', 'A quantitative way of describing such communities is to measure the abundance of each species in the community so that a sorted list of abundance numbers is produced , a so-called Rank Abundance Distribution ( RAD ) .', 'With recent breakthroughs in genome analysis this approach can also be applied to very complex communities , such as the community of the myriads of microbes in a human gut ( gut microbiome ) , or the diverse set of human immune cells .', 'One problem with this approach is that it is not trivial to quantitatively compare RADs for different communities , especially if they are highly complex .', 'We show that it is possible to computationally “normalize” RADs so that they can be quantitatively compared across many different communities .', 'In this way , this normalization enables insight into structures and dynamics of arbitrary communities .', 'We demonstrate this with applications to human immune cells , gut microbiomes under antibiotic treatment or under different nutritional regimes , and environmental microbiomes .']
['blood cells', 'taxonomy', 'medicine and health sciences', 'ecology and environmental sciences', 'immune cells', 'microbiome', 'immunology', 'microbiology', 'data management', 'b cell receptors', 'memory b cells', 'thermodynamics', 'microbial genomics', 'ecological metrics', 'immune system proteins', 'computer and information sciences', 'white blood cells', 'entropy', 'animal cells', 'proteins', 'medical microbiology', 'microbial taxonomy', 'species diversity', 'physics', 'community ecology', 'antibody-producing cells', 'biochemistry', 'signal transduction', 'cell biology', 'b cells', 'ecology', 'genetics', 'biology and life sciences', 'cellular types', 'physical sciences', 'genomics', 'immune receptors']