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ORIGINAL ARTICLE

A family of interaction-adjusted indices ofcommunity similarity

Thomas Sebastian Benedikt Schmidt1, João Frederico Matias Rodrigues andChristian von MeringInstitute of Molecular Life Sciences and Swiss Institute of Bioinformatics, University of Zürich, Switzerland

Interactions between taxa are essential drivers of ecological community structure and dynamics, butthey are not taken into account by traditional indices of β diversity. In this study, we propose a novelfamily of indices that quantify community similarity in the context of taxa interaction networks. Usingpublicly available datasets, we assessed the performance of two specific indices that are TaxaINteraction-Adjusted (TINA, based on taxa co-occurrence networks), and Phylogenetic INteraction-Adjusted (PINA, based on phylogenetic similarities). TINA and PINA outperformed traditional indiceswhen partitioning human-associated microbial communities according to habitat, even for extremelydownsampled datasets, and when organising ocean micro-eukaryotic plankton diversity according togeographical and physicochemical gradients. We argue that interaction-adjusted indices capturenovel aspects of diversity outside the scope of traditional approaches, highlighting the biologicalsignificance of ecological association networks in the interpretation of community similarity.The ISME Journal advance online publication, 9 December 2016; doi:10.1038/ismej.2016.139

Introduction

Understanding how patterns of diversity are estab-lished and maintained is fundamental to the ecologi-cal characterisation of living systems. FollowingWhittaker (1972, 1960), diversity is traditionallyconsidered to comprise of three components: localdiversity of individual habitats (α diversity) andbetween-site variation (β diversity) together determinethe total diversity of a given system (γ diversity).However, while referring to these definitions,researchers have studied conceptually differentphenomena under the umbrella term ‘diversity’.β diversity, in particular, has been variously reportedas species turnover or variation, further sub-defined and quantified using different mathematicalapproaches (Anderson et al., 2010; Tuomisto, 2010).Nevertheless, most authors agree that communitysimilarity, the compositional variation between sites,is an integral aspect of β diversity, and more generallyone of the most important parameters in communityecology (Vellend, 2010). To characterise the mechan-isms underlying an observed diversity structure, it isessential to quantify and appraise patterns of commu-nity similarity.

A multitude of mathematical indices of commu-nity similarity have been proposed: as of 2016, thewidely used software EstimateS (Colwell, 2013)computes 12 different indices, while the popularmicrobial ecology toolboxes mothur (Schloss et al.,2009) and phyloseq (McMurdie and Holmes, 2013)provide as many as 37 and 46 measures, respec-tively. The various available measures captureconceptually different aspects of diversity. Tradi-tional measures, such as the Jaccard (1901) or Bray–Curtis (1957) indices, focus on taxa compositionaloverlap, quantified directly from taxa count data.More recently, phylogenetically informed indiceshave become increasingly popular, which, in con-trast to census-based metrics, do not treat taxaindependently but rather quantify shared evolution-ary history between communities (Graham and Fine,2008; Swenson, 2011). Traditional and phylogeneticmetrics may provide complementary insights intothe processes driving community composition, par-ticularly since phylogenetic relatedness of taxa isconsidered a proxy for functional or ecologicalsimilarity (Webb et al., 2002).

Apart from analysing diversity patterns, anotherimportant approach to characterising ecosystemfunction focuses on studying interaction networksof ecological or functional associations between taxadirectly. Applying graph theory to food webs,mutualist or host-parasite networks and others hasrevealed an important role for interaction structurein community stability and dynamics (Polis andStrong, 1996; Proulx et al., 2005; Ings et al., 2009).This approach has been particularly fruitful in

Correspondence: TSB Schmidt or C von Mering, Institute ofMolecular Life Sciences, University of Zürich, Winterthurerstrasse190, Zürich, CH-8057, Switzerland.E-mail: [email protected] or [email protected] address: European Molecular Biology Laboratory,Meyerhofstr. 1, D-69117, Heidelberg, Germany.Received 31 March 2016; revised 16 June 2016; accepted30 August 2016

The ISME Journal (2016), 1–17© 2016 International Society for Microbial Ecology All rights reserved 1751-7362/16www.nature.com/ismej

http://dx.doi.org/10.1038/ismej.2016.139

mailto:[email protected]

mailto:[email protected]

http://www.nature.com/ismej

microbial ecology, where ‘true’ ecological interac-tions can to a certain extent be inferred fromco-occurrence networks of anonymous OperationalTaxonomic Units (OTUs; Faust and Raes, 2012;Berry and Widder, 2014). Highly informative taxaco-occurrence networks have been constructed formany ecological systems, including the human body-associated microbiota (Faust et al., 2012) or oceanplanktonic communities (Lima-Mendez et al., 2015;Sunagawa et al., 2015), as well as for global,integrated datasets across various habitats (Chaffronet al., 2010).

One main difference between such diversity-basedand network-based approaches lies in analysisscope: the latter identify drivers of communitystructure at the level of individual taxa interactions,while the former reveal compositional patterns atcommunity level. Arguably, both approaches areinformative, but they are often pursued indepen-dently: it remains challenging to interpretcommunity-level diversity changes in light of taxa-level ecological associations, and vice versa. In thisstudy, we propose to bridge this analysis gap with aset of mathematical indices that quantify communitysimilarity (or β diversity) as the average taxainteraction strength between samples. While ourmethod is applicable to many types of interactiondata, we focus on Taxa INteraction-Adjusted indices(TINA), based on taxa co-occurrence data, andPhylogenetic INteraction-Adjusted indices (PINA),based on phylogenetic similarities. In a re-analysis oftwo publicly available datasets, we show that TINAand PINA capture known diversity patterns betterthan existing indices, even for very small datasets,and that they can reveal novel and refined biologicalinterpretations.

Materials and methods

In this study, we compared a total of 11 indices ofcommunity similarity (listed in Table 1) that fallinto three categories: ‘traditional’ taxa count-basedindices, phylogenetic indices and our proposedinteraction-adjusted indices (Figure 1).

Classical and phylogenetic community similarityindicesIn his widely cited ‘comparative study of the floraldistribution of parts of the Alps and the Jura’, PaulJaccard (1901) introduced what is arguably theearliest index of β diversity. For two communites Aand B, the classical Jaccard index (JCI) is the relativetaxa overlap, that is the ratio of shared taxa amongall sampled taxa (see formula in Table 1). In thisoriginal fomulation, the JCI is incidence-based, orunweighted: it considers only the presence andabsence of taxa, but not their relative abundanceratios. Several abundance-based or weighted varia-tions of the classical Jaccard index have been

proposed (Chao et al., 2004); here, we use astraightforward weighted Jaccard (JCW) formulationthat describes community similarity as the meanfraction of individuals in shared taxa across bothfocal samples. While the JCI has proved veryversatile and is used for manifold scientific problemsbeyond biology, an ecology-specific variant thatcorrects for the characteristics of imperfect samplinghas been proposed by Chao et al (2004): Chao’sweighted Jaccard index (JCC) extrapolates the frac-tions of individuals in unseen shared taxa based onthe number of observed shared rare taxa.

One of the most widely used indices in moderncommunity ecology is arguably the Bray-Curtissimilarity (BC; Bray and Curtis, 1957), whichdescribes community overlap as the fractional mini-mum abundance of shared taxa between samples.Somewhat related to BC is the Morisita-Horn overlapindex (MH; Horn, 1966), calculated as pairwisemultiplicative taxa overlap, adjusted by a per-sample concentration index.

These classical indices and their derivations assesscommunity overlap directly from count data, treatingall observed taxa as independent (Figure 1, topbranch). Phylogenetic indices, in contrast, considerthe (phylogenetic) relationships between taxa andquantify community similarity as shared evolution-ary history (Figure 1, middle). Among these increas-ingly popular indices is UniFrac, which calculatesthe shared branch length between samples on aphylogenetic tree, either for observed taxa based onincidence (unweighted UniFrac, UFU; Lozupone andKnight, 2005), or based on taxa abundances(weighted UniFrac, UFW; Lozupone et al., 2007).

A novel family of interaction-adjusted communitysimilarity indicesConsider two communities A and B, composed of NA

and NB taxa from which a total of nA and nB

individuals have been sampled. Next, consider amatrix I that describes pairwise taxa interactions,such that Iij is the interaction between taxa i and j.Manifold types of interactions with different biolo-gical meanings, different layers of information and atdifferent levels of curation effort are suitable, such asfor example predator–prey relationships, symbiosis,parasitism, mutualism, cross-feeding, resource com-petition and so on. Here, we consider the case ofecological associations as inferred by taxa co-occurrence networks, constructed from taxa counttables by pairwise association of abundances acrosssamples (Figure 1, bottom). The scale and character-istics of such a co-occurrence interaction matrix ICwill depend on the association metric chosen; Faustand Raes (2012) have provided a comprehensivereview of different approaches to network construc-tion and interpretation. For example, a taxa abun-dance correlation network would scale from − 1(avoidance) to +1 (complete association), while otherpopular association metrics may scale differently.

Interaction-adjusted indices of community similarityTSB Schmidt and C von Mering

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Tab

le1

Ove

rview

ofdifferentindices

ofco

mmunitysimilarityusedin

this

study

Index

Abb

Form

ula

Description

Referen

ce

Jacc

ard,classica

lJCI

jA-Bj

jA,Bj

Ratio

ofsh

ared

taxa

amon

gallob

served

taxa

(relativeov

erlap)

Jaccard,19

01

Jaccard,weigh

ted

JCW

0:5ðP iA

A-BnAi

nAþP jA

A-BnBj

nBÞ

Ave

rage

frac

tion

ofindividualsin

shared

taxa

This

study

Jacc

ard,Chao

JCC

UV

UþV

�UV

Abu

ndan

ce-based

Jaccardindex

,co

rrec

tedforunseen

shared

taxa

basedon

shared

rare

taxa

Chao

etal.,20

04

Bray–

Curtis

BC

2PiA

ABminðn

Ai;nBiÞ

nAþn

BFractionof

minim

um

per-sam

ple

abundan

ceof

shared

taxa

Brayan

dCurtis,19

57

Morisita-Horn

MH

2PiA

A,BnAin

Bi

P iAAn2 Ai

n2 A

þP iABn2 Bi

n2 B

�� n

AnB

Pairw

iseov

erlapof

taxa

abundan

ces,

adjusted

byper-sam

ple

concentrationindices

Horn,19

66

UniFrac,

unweigh

ted

UFU

P iAA-BFi

P jAA,BFj

Fractionof

shared

bran

chlengthon

aphylog

enetic

tree

Loz

upon

ean

dKnight,

2005

UniFrac,

weigh

ted

UFW

1�P iA

A,BFi

nAi

nA�n

Bi

nB

� � ��

FFractionof

shared

bran

chlengthon

aphylog

enetic

tree,weigh

tedby

taxa

abundan

ces

Loz

upon

eet

al.,20

07

TIN

A,unweigh

ted

TU

P iAA

P jABC

ij

NAN

BAve

rage

pairw

isetaxa

interactionsimilarity.

This

study

TIN

A,weigh

ted

TW

P iAA

P jAB

nAi

nA

nBj

nBC

ijffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffi





ffiffiffiffiffiffiffiffiffiffiffi

P iAA

P jAA

nAin

Aj

n2 A

Cij

�� P

iAB

P jAB

nBin

Bj

n2 B

Cij

��

rAve

rage

pairw

isetaxa

interactionsimilarity,

weigh

tedby

taxa

abundan

ces

This

study

PIN

A,unweigh

ted

PU

P iAA

P jABFij

NAN

BAve

rage

taxa

phylog

enetic

similarity

This

study

PIN

A,weigh

ted

PW

P iAA

P jAB

nAi

nA

nBj

nBF

ijffiffiffiffiffiffi






ffiffiffiffiffiffiffiffiffiffiffi

P iAA

P jAA

nAin

Aj

n2 A

Fij

�� P

iAB

P jAB

nBin

Bj

n2 B

Fij

��

rAve

rage

pairw

isetaxa

phylog

enetic

similarity,

weigh

tedby

taxa

abundan

ces.

This

study

Allform

ulasan

ddescription

saregive

nas

similarities;

forordinationsan

dstatisticaltests,

correspon

dingdistancesor

dissimilaritiesareused(D

=1

−S).N

A,total

numbe

rof

taxa

insample

A;n

A

totalnumbe

rof

individualsin

sample

A;n

Ai,individualsof

taxo

niin

sample

A;Û

,estim

ator

forfraction

ofindividualsin

shared

taxa

forsample

A,a

ccordingto

form

ula

9in

Chao

etal

(200

4);φ

i,phylog

enetic

bran

chlengthof

taxo

nito

root;F

ij,phylog

enetic

associationbe

tweentaxa

ian

dj;Cij,interactionsimilaritybe

tweentaxa

ian

dj.


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Therefore, it is important to transform the interactionmatrix IC to a common scale; we do this bycorrelating taxa by their pairwise associations to allother taxa in the system (that is, row IC,i* of IC fortaxon i) and transforming this into a Pearsonsimilarity:

Cij ¼ 0:5 � ð1þ rPearsonðIC;i�; IC;j�ÞÞThus defined, a transformed co-occurrence matrix

C has several desirable properties: (i) it scales from 0(avoidance) to 0.5 (neutral association) to 1 (com-plete association); (ii) Cij corresponds to the ‘proxi-mity’ of taxa i and j on the original associationnetwork IC; (iii) the transformation generally shar-pens and smoothens network structure, amplifyingstrong associations at the expense of weaker correla-tions, but association ranks remain mostlyunchanged (see Supplementary Figure S1 in Sup-porting Information).

Given this transformed interaction matrix, wepropose to quantify the similarity between commu-nities A and B as the average interaction strengthbetween all taxa observed in A or B. We thus definean incidence-based or unweighted Taxa INteraction-Adjusted index of community similarity (unweighted

TINA, TU) as

TU ¼P

iAA

PjABCij

NANB

Likewise, an abundance-based or weighted TINAindex (TW) can be defined as weighted average taxainteraction strength, scaled by the geometric meanper-sample weighted taxa interaction strength:

TW ¼P

iAA

PjAB

nAinA

nBj

nBCijffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðP iAA

PjAA

nAinAj

n2A

CijÞðP

iAB

PjAB

nBinBj

n2BCijÞ

q

TINA values are 1 for two completely identicalcommunities, but also if all taxa in A and B areperfectly associated. If no taxa are shared, TINAvalues tend towards 0.5 if taxa interactions areneutral (neither associative nor dissociative) andtowards 0 if taxa between A and B show a strongavoidance signal. Thus, TINA resolves non-zerosimilarities even for pairs of communities that donot share any taxa (which implies zero similarityaccording to traditional, count-based indices); theo-retically, the TINA index for such disparate pairs caneven be 1 if all their taxa are perfectly associated.

Taxa CountTable

CommunitySimilarities

Analyses(e.g., ordination)

Taxa InteractionNetwork IC

InteractionSimilarities C

PhylogeneticAssociations

PINA

Phylogeny ϕ

Phylogenetic Indices

(e.g., UniFrac)Samples

Tax

a

TINA

Count-based indices

(e.g., Jaccard, Bray-Curtis, etc)

Figure 1 Overview of different approaches to quantifying community similarity. Based on a taxa-sample count table, traditional count-based indices such as Jaccard and Bray–Curtis quantify community similarity from the overlap in taxa composition (upper branch). Incontrast, phylogenetic indices such as UniFrac take into account taxa relationships, quantifying community similarity as sharedevolutionary history, based on taxa phylogeny (middle branch). Our proposed Taxa INteraction-Adjusted (TINA) and PhylogeneticINteraction-Adjusted (PINA) indices, in contrast, take into account similarities on a taxa co-occurrence network, codified in an interactionsimilarity matrix C, or in terms of cophenetic phylogenetic distances, represented in a phylogenetic association matrix F.


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TINA-like indices can be defined analogously forany kind of interaction data, given that interactionmatrices can be transformed similarly to the IC to Ctransformation described above. This is also truefor the special case of phylogenetic ‘interactions’.Consider a phylogenetic tree φ of taxa observedin a given system with a cophenetic phylogeneticsimilarity matrix Iφ, which can be interpretedas a phylogenetic association network (analogousto IC) and transformed into an association matrixF (analogous to the co-occurrence associationmatrix C). Then, we can define unweighted Phylo-genetic INteraction-Adjusted community similarity(unweighted PINA, PU) as

PU ¼P

iAA

PjAB Fij

NANB

and weighted PINA (PW) as

PW ¼P

iAA

PjAB

nAinA

nBj

nBFijffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðP iAA

PjAA

nAinAj

n2A

FijÞðP

iAB

PjAB

nBinBj

n2B

FijÞq

Human Microbiome Project data analysisTo test the performance of different communitysimilarity indices, we re-analysed two publiclyavailable datasets, provided by the Human Micro-biome Project and the TARA Oceans project,respectively. Raw 16S rRNA V35 region sequencingreads of The Human Microbiome Project (2012) weredownloaded from the NCBI Sequence Read Archive;metadata was obtained from the HMP data repository(http://hmpdacc.org). Sequences were filtered forchimeric reads using UCHIME (Edgar et al., 2011),aligned to a secondary structure-aware 16S rRNAmodel using Infernal (Nawrocki and Eddy, 2013),denoised by a global minimum read abundance at1% tolerance of 4 and clustered into OTUs at 97%average linkage sequence similarity using hpc-clust(Matias Rodrigues and von Mering, 2014), as estab-lished previously (Schmidt et al., 2014, 2015). Theresulting filtered taxa count table contained24 717 447 sequences clustered into 27 041 OTUsacross 3849 samples. A phylogenetic tree of OTUrepresentatives, selected by minimum averagewithin-OTU sequence distance, was inferred usingFastTree2 (Price et al., 2010) with default para-meters. Pairwise taxa co-occurence networks for thefull dataset and subsets were calculated using taxa-wise Bray–Curtis dissimilarity, weighted Jaccardindex, Spearman correlation and a custom R imple-mentation of SparCC (Friedman and Alm, 2012), anadapted correlation metric correcting for spuriousassociations that has been shown to approximate‘true’ ecological interactions as simulated using aGeneralized Lotka–Volterra (GLV) model (Berry andWidder, 2014).

Simulation of human microbiome samplesSimulations were conducted based on (re-sampled)real count data subsets of the HMP dataset or basedon entirely synthetic counts. GLV models wereadapted from Berry and Widder (2014), with per-sample carrying capacities set uniformly to totalsample size, initial per-sample counts set to sum to10% of sample carrying capacity, growth rates re-sampled from a uniform distribution on [0,1] unlessotherwise specified and further parameters chosentest-specifically. All simulations were repeated 20times (see online analysis code).

TARA Oceans data processing and analysisFrom the TARA Oceans eukaryotic plankton diver-sity census (De Vargas et al., 2015), we downloaded18S rRNA V9 tag data organised into an OTU-leveltaxa count table (http://doi.pangaea.de/10.1594/PANGAEA.843022) and sample metadata (http://doi.pangaea.de/10.1594/PANGAEA.843017). Data persample were pooled across filter sizes and OTUscontaining ⩽ 30 sequences as well as several orphansamples were removed (see analysis code), yielding afiltered count table of 535 903 407 sequences, 27 448OTUs and 77 samples for which a SparCC correla-tion network was computed.

Data and software availabilityAll analysis code and processed datasets are avail-able online (http://github.com/defleury/Schmidt_et_al_2016_community_similarity; http://meringlab.org/suppdata/2016-community_similarity/).

Results

TINA and PINA provide improved partitioning ofhuman body site-specific microbial communitiesFrom an ecological point of view, the human bodyappears as little more than a system of distinctmicrobial habitats (Costello et al., 2012). The HumanMicrobiome Project (HMP Consortium, 2012) hasprovided a first comprehensive census of humanbody-associated microbial communities and theirpotential functional repertoires. HMP 16S rRNA tagsequencing data are available for 18 habitats fromfive different body sites, namely oral cavity (9habitats), skin (4), female urogenital tract (3), airways(1) and gastrointestinal tract (1); see Figure 2 for a fulllist. One original goal of the HMP, similar to manyecological studies, was to establish how composi-tional similarity patterns distinguish communitiesassociated to these different habitats. In other words:are body sites distinct from each other in microbialcommunity composition, and which other factorsdrive compositional variation?

These types of questions are typically addressedby calculating pairwise community distances andthen applying multivariate statistical tests to estab-lish how much of the distance matrix structure is


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http://hmpdacc.org

http://doi.pangaea.de/10.1594/PANGAEA.843022




http://github.com/defleury/Schmidt_et_al_2016_community_similarity

http://github.com/defleury/Schmidt_et_al_2016_community_similarity

http://meringlab.org/suppdata/2016-community_similarity/

http://meringlab.org/suppdata/2016-community_similarity/

Jaccard, classicalJaccard, weighted

Jaccard, ChaoBray−Curtis

Morisita−HornUniFrac, unweighted

UniFrac, weightedTINA, unweighted

TINA, weightedPINA, unweighted

PINA, weighted

PINA, weighted

PINA, unweighted

TINA, weighted

TINA, unweighted

UniFrac, weighted

UniFrac, unweighted

Morisita-Horn

Bray-Curtis

Jaccard, Chao

Jaccard, weighted

Jaccard, classical

adonis F statistic

Oralhabitats

Skinhabitats

Urogenitalhabitats

0 0 0 2 4 86 1060 1201000 2000

AG

vs

BM

AG

vs

HP

AG

vs

PT

AG

vs

SL

AG

vs

SB

PA

G v

s S

PP

AG

vs

TH

AG

vs

TD

BM

vs

HP

BM

vs

PT

BM

vs

SL

BM

vs

SB

PB

M v

s S

PP

BM

vs

TH

BM

vs

TD

HP

vs

PT

HP

vs

SL

HP

vs

SB

PH

P v

s S

PP

HP

vs

TH

HP

vs

TD

PT

vs

SL

PT

vs

SB

PP

T v

s S

PP

PT

vs

TH

PT

vs

TD

SL

vs S

BP

SL

vs S

PP

SL

vs T

HS

L vs

TD

SB

P v

s S

PP

SB

P v

s T

HS

BP

vs

TD

SP

P v

s T

HS

BP

vs

TH

TH

vs

TD

LAF

vs

RA

FLR

C v

s R

RC

AF

vs

RC

AF

vs

AN

RC

vs

AN

VI v

s M

VV

I vs

PF

MV

vs P

F

Ora

l site

sS

kin

site

sU

roge

n.

AGBMHPPTSLSBPSPPTHTD

att. kerat. gingivabuccal mucosahard palatepalatine tonsilssalivasubgingival plaquesupraging. plaquethroattongue dorsum

LAFRAFLRCRRCAN

L antec. fossaR antec. fossaL retroaur. creaseR retroaur. creaseanterior nares

VIMVPF

vaginal introitusmid vaginaposterior fornix

0

0.00

2

0.00

4

0.00

6

0.00

8

0.01

0

0.1

0.2

0.3

0.4

R2 statistic

0

0.2

0.4

0.6

0.8 1

PINA, weighted

0 10,000 20,000 30,000

adonis F statistic Distance

All body sitesvs each other

Oral samplesvs other sites

Stool samplesvs other sites

PINA, unweighted

TINA, weighted

TINA, unweighted

UniFrac, weighted

UniFrac, unweighted

Morisita-Horn

Bray-Curtis

Jaccard, Chao

Jaccard, weighted

Jaccard, classical

0 0.5 1 0 0.5 1 0 0.5 1

intra-site distancesinter-site distances

R ~ SS / SS

F ~ SS / SS


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explained by a given model. One of the most widelyused methods is Anderson’s PERMANOVA (permu-tational analysis of variance; Anderson, 2001),implemented in the adonis function of the R packagevegan (Oksanen et al., 2015), which calculates apseudo-F statistic on group separation from the sumsof squares of inter-group distances over the sums ofsquares of intra-group distances (see Figure 2a) andthen conducts a permutational significance test.Thus, the adonis F statistic, as well as the relatedR2 statistic (the variance explained by the testedfactor) indicate an effect size of multivariate groupseparation (higher F and R2 values indicate morediscriminatory power), while a permutational Pvalue indicates significance. F and R2 statistics havepreviously been used to benchmark multivariateecological analyses, for example by Eren et al (2015).

We re-analysed the HMP data using 11 differentcommunity similarity indices (Table 1), five ofwhich are count-based (JCI, JCW, JCC, BC and MH),two phylogenetic (UFU, UFW) and four interaction-adjusted (TU, TW, PU and PW). We observed thatpartitioning of the five general body sites (oral cavity,skin, urogenital tract, airways, gut) by communitysimilarity was by far best for TINA (based on aSparCC correlation network; F = 30 455 for TW;F=16 421 for TU) and PINA (PW, 4397; PU, 6917)when compared to all other indices, with JCIproviding the weakest discrimination (F= 182). Thisimproved partitioning was due to several effects, asindicated by community distance histograms perindex (Figure 2a). First, TINA and PINA providedvery high overall resolution, distributing pairwisedissimilarities across a broader range on the interval0 (identical communities) to 1 (complete dissim-ilarity) than most count-based indices. Second, TINAand PINA assigned very low and sharply distributedintra-group dissimilarities, meaning that samplesfrom the same body sites were on average consideredvery similar to each other; in contrast, count-basedindices showed very sharp and pronounced inter-group dissimilarities, but wider distributions withingroups. Finally, intra- and inter-group dissimilaritieswere generally much clearer separated for TINA thanfor count-based indices or UniFrac.

To assess the robustness of TINA performancetowards the choice of network inference method, were-tested body site separation based on re-calculatedtaxa co-occurrences using four different approaches:(i) taxa-wise Bray–Curtis dissimilarity (TW-BC); (ii)

taxa-wise weighted Jaccard distance (TW-JCW); (iii)Spearman rank correlation of taxa across samples(TW-SP); and (iv) SparCC correlation (Friedman andAlm, 2012). We found that network inferencemethod had a strong effect on both unweighted andweighted TINA in terms of F and R2 values, but thatdiscriminative power was consistently high. SparCC-based TINA outperformed TW-SP, TW-JCW and TW-BC (in this order), and all TINA metrics outper-formed UniFrac and count-based indices (seeSupplementary Figure S2). Since by far the strongestseparation signal was observed for TINA based onSparCC, we relied on SparCC for network inferencein the subsequent tests reported below.

Combined interpretation of TINA and PINA mayprovide novel biological insightsWhile habitat partitioning was differentially pro-nounced, all indices provided significant groupseparation (P⩽ 0.001, 999 permutations). Indeed,differences in community composition betweenbody sites – which are highly distinct micro-environments – can be expected to be large, so it isnot surprising that they were picked up by allindices. We therefore conducted similar tests onmore complicated problems, such as the separationof habitats within a body site (Figure 2b) or of pairs ofsimilar habitats (Figure 2c). TINA provided by far thestrongest partitioning of oral and skin habitats,followed by PINA and JCW/JCC. For urogenital sites,in contrast, only few indices provided significantseparation at all: unweighted PINA (PU), UFU, UFWand JCI. These trends were consistent with pairwiseseparability of habitats (Figure 2c), which washighest for TINA in oral and skin, but for PU, UFUand UFW in urogenital sites.

These observations imply that diversity patterns inthese habitats are determined by different factors.TINA quantifies community similarity as an overlapin ecological associations of taxa, while PINA andUniFrac focus on shared phylogeny. Thus, it appearsthat the compositional identity of oral and skin sitesis driven by recurring cliques of associated OTUs, ascaptured by strong co-occurrence signals, whilepairwise taxa associations are less important in theurogenital tract, where communities of changingpartners are instead filtered by phylogeny, possiblyindicating a functional signal. Indeed, we detected asmall but significant phylogenetic signal for the

Figure 2 Differential partitioning of human body habitat-specific community structure. (a) Partitioning by general body sites. Left,PERMANOVA F statistics for different indices when testing community distance partitioning according to general body site, that is intooral, skin, urogenital, airways and gastrointestinal habitats. Right, histograms of community distances intra-site (orange) and inter-site(blue) for all body sites against each other, oral against other habitats and gastrointestinal against other habitats. The inset illustrates howPERMANOVA F statistics and R2 values are calculated from community distances using the adonis function of the R package vegan(Anderson, 2001; Oksanen et al., 2015). (b) Sub-partitioning of oral habitats (blue), skin habitats (yellow) and urogenital habitats (violet).(c) Pairwise separation by different indices of all pairs of oral habitats, skin habitats against each other and against airways (anterior nares)and urogenital habitats against each other, as detected by the PERMANOVA R2 value (relative variance explained by factor habitat). Notethe different colour scales, indicating overall differential partitioning power per body site.


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distribution of pooled OTU abundances acrossurogenital sites (Supplementary Figure S3; vaginalintroitus: K=0.051, P⩽0.001; mid-vagina: K=0.023,P⩽ 0.001; posterior fornix: K=0.023, P⩽ 0.001).However, body subsite was indeed not the predomi-nant determinant of per-sample community compo-sition (Supplementary Figure S4): rather, variationbetween subjects was higher than within subjects(P⩽ 0.02 for all tested metrics except, interestingly,unweighted PINA), while even this factor accountedfor a maximum of only 4% of variation (unweightedTINA). This is in line with observations in theoriginal HMP study, which moreover establishedstrong associations to other factors such as pH orBMI (HMP Consortium, 2012). Thus, a combinedinterpretation of TINA and PINA may guide biolo-gical interpretation: between-subject communitycomposition appears to be (moderately) determinedby taxa co-occurrence, whereas a weak but signifi-cant phylogenetic signal may shape differencesbetween vaginal subsites.

TINA captures habitat structure of the humanmicrobiome taxa co-occurrence networkTo illustrate how TINA captures ecological taxainteraction structure, how TINA values can beinterpreted at the level of individual sample pairsand under which conditions it provides moreintuitive results than count-based indices, weselected 16 HMP samples for which Figure 3 showsthe taxa co-occurrence network; SupplementaryFigure S5 shows the same network, coloured byOTU phylum-level taxonomy. We observed that thenetwork is structured into several habitat-specificclusters of strongly co-occurring OTUs, with slightlyless dependence on taxonomy. This is in line withthe general observation that (microbial) co-occurrence networks tend to capture ecologicalsignals, which indeed can often be much moresubtle than the present body habitat classification(Faust and Raes, 2012).

Next, we mapped three examples of sample pairsonto this network to illustrate how TINA takesinteraction structure into account to quantify diver-sity. In the first example (Figure 4a), we consider twosamples from the vaginal posterior fornix, whichwere the most similar pair according to the classicalJaccard index (lowest JCI distance). These sampleshave a high taxa overlap, while many of their non-shared taxa also share strong co-occurrence signals,so that TINA likewise assigns them a very highsimilarity. Thus, in this case, TINA and count-basedindices agree in considering both samples highlysimilar.

The second case is less trivial (Figure 4b). Here, weconsider two urogenital samples from the vaginalintroitus, which do not share any taxa at all – count-based indices assign a distance of 1, consideringthem completely dissimilar. However, the taxa foundin these samples share an attractive interaction

signal, even though some taxa form part of distinctco-occurence clusters. In this case, TINA provides amore intuitive result by ranking the similaritybetween two samples from the same habitat (vaginalintroitus) relatively high.

Finally, consider the opposite situation(Figure 4c). Here, two samples from different bodysites (skin and oral) happen to share several taxa, sothat JCI ranks them among the top 17.3% mostsimilar pairs. However, most non-shared taxa belongto distinct co-occurrence clusters, meaning that theirpairwise interactions are repulsive, such that TINAassigns a very high dissimilarity to this pair, which,again, is an arguably more realistic picture.

Interaction-adjusted indices provide strong partitioningeven for small datasetsThe HMP dataset used in this study is comparativelylarge, comprising 27 041 OTUs across 3849 samples.To test whether the observed trends were robustto dataset scope, we conducted two down-sampling experiments (Figure 5 and SupplementaryFigure S6). First, we randomly selected between 5and 50 samples per body site (25–250 samples intotal), re-calculated co-occurrence and phylogeneticinteraction strengths and assessed body site separa-tion by all 11 indices, at 10 iterations per down-sampling step (Figure 5a; see SupplementaryFigure S6A for the corresponding plot on the R2

statistic). We found that even for the smallest testeddataset, TINA and PINA indices provided muchclearer partitioning by body site, although ranks bypartitioning effect sizes varied across down-sampling iterations. Next, we randomly selected1000 samples from which we drew 1000 sequenceseach and down-sampled these to 50 sequences persample in several steps, at 10 iterations per step,recalculated co-occurrence and phylogenetic inter-actions and quantified community similarity(Figure 5b and Supplementary Figure S6B). Like-wise, we observed that TINA and PINA providedmuch better separation by body site than all otherindices, even at a drastically small size of 50sequences per sample.

TINA captures both habitat preference and taxainteraction signalsTo further investigate the behaviour of TINA indifferent scenarios, we conducted a series of simula-tions (Figure 6; raw simulation results available inSupplementary Table S1). We randomly selected 25oral and 25 gastrointestinal samples from the HMPdataset, from which we sampled 200 of the 1000most abundant OTUs. For this reduced dataset, weinferred Dirichlet multinomial mixture models usingthe software microbedmm (Holmes et al., 2012); theDMM models perfectly re-discovered the two habitatgroups. Next, we iteratively simulated count databy multinomially sampling from these models and


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re-calculated habitat separation for different commu-nity similarity indices, conducting both across-habitatcomparisons and respective within-habitat tests asnegative controls (Figure 6a). We observed that alltested indices had high discriminative power, but thatF values for TINA were up to three orders ofmagnitude larger than for count-based indices. Thisis in line with the expectation that DMM inferenceaccounts for both habitat preference and (implicitly)taxa co-abundance signals, both contributing to thetaxa co-occurrence signal underlying TINA.

Thus, to disentangle the contributions of habitatpreference and taxa interactions, we simulated count

data using GLV models with different startingconditions and parameters. In a first setup, weshuffled raw OTU abundances across samples,regardless of habitat group (oral vs gut), therebybreaking any OTU habitat preference and OTU co-abundance signals. Based on these starting condi-tions, we simulated community dynamics in aninteraction-neutral GLV model. This correspondedto a negative control setup: in the absence of anysignal of habitat preference, taxa co-abundance ortaxa interaction, none of the tested communitysimilarity indices detected any separation betweengroups (Figure 6b). Next, we tested neutral

Airways

OTU dominant body site

Gastrointestinal Skin

Oral Urogenital

Unclassified

OTU size

106 105 104 103 102 10

Figure 3 Taxa co-occurrence network for a subset of Human Microbiome Project samples. Sixteen samples from the full HMP datasetwere selected as described in the main text, comprising a total of 2671 OTUs for which all pairwise SparCC correlations ≥0.5 are shown asedges in the network. Node size indicates global OTU size, that is the total number of counts per OTU across the full HMP dataset. Nodecolour indicates OTU dominant habitat, assigned if more than 50% of all OTU abundance was in samples of the same body site.Supplementary Figure S2 shows the same network, coloured by OTU phylum-level taxonomy.


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community dynamics: we simulated data withhabitat preferences, but with neutral taxa interac-tions by shuffling OTU abundances within habitatgroups (thereby breaking co-abundance signals) as

input for an interaction-neutral GLV model. In thissetup, PERMANOVA F values for TINA wereroughly three orders of magnitude stronger than forother indices (Figure 6c), which is in line with the

SN 700024266Urogenital tract

(Vaginal introitus)110 OTUs

SN 700110806Urogenital tract

(Vaginal introitus)76 OTUs

SN 700097283Skin

(Retroaur. crease)213 OTUs

SN 700106374Oral cavity

(Palatine tonsils)389 OTUs

Case 1:

samples share taxainteractions attractive

SN 700035995Urogenital tract(Posterior fornix)

75 OTUs

SN 700096698Urogenital tract(Posterior fornix)

71 OTUs

Case 2:

samples disjointinteractions attractive

Case 3:

samples share taxainteractions repulsive

low Jaccard distancelow TINA distance

maximum Jaccard distancelow TINA distance

low Jaccard distancehigh TINA distance

0 0.5

Distance

93.7%

17.3%

1

TIN

A, w

eigh

ted

Jacc

ard,

cla

ssic

al

26.4%

98.2%

2.9%

0%

Figure 4 TINA quantifies community similarity from taxa co-occurrence. (a) For two urogenital samples that share a large taxa overlap,both traditional count-based indices (exemplified by the classical Jaccard index, JCI) and TINA assign a low-ranking community distance(as indicated in community distance histograms on the right). The middle panel shows how taxa of these samples map onto theco-occurrence network introduced in Figure 3; blue, taxa unique to sample SN700035995; green, taxa unique to sample SN700096698;blue-green, taxa shared between both samples. (b) For two urogenital samples that do not share any taxa, but whose taxa still shareattractive co-occurrence interactions, JCI assigns complete distance (JCI = 1), while TINA assigns a relatively low-ranking distance. (c) Inthe opposite case of two samples from different body sites (skin and oral), which have a significant taxa overlap, but repulsive taxainteractions, JCI assigns a low-ranking, but TINA a very high-ranking distance.


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expectation that habitat preferences alone can gen-erate strong taxa co-occurrence and avoidancesignals.

In a third GLV setup, we tested the oppositescenario: absence of habitat preferences a priori, butnon-neutral and habitat-specific taxa interactions.For this, we split the OTU set into two groups and

generated a taxa interaction matrix as follows (seeFigure 6d): within-group interactions were derivedfrom a scale-free Barabási network (Barabási andAlbert, 1999) with interaction strengths and signsrandomly assigned from a uniform distribution;between-group interactions were set to competitive,with uniform noise. Based on this interaction matrix,

Jaccard, classical

Bray-Curtis

UniFrac, unweighted

TINA, unweighted

TINA, weighted

PINA, unweighted

PINA, weighted

UniFrac, weighted

Morisita-Horn

Jaccard, weighted

Jaccard, Chao

Sequences per sample

50 100 250 500 700 900 1000

F s

tatis

tic

0

1000

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3000

4000

Samples per body site(total number of samples)

F s

tatis

tic

5(25)

0

500

1000

10(50)

20(100)

50(250)

Figure 5 TINA and PINA detect strong partitioning by body habitat even for very small datasets. Adonis F statistic for separation by bodysite according to all 11 tested indices, for datasets randomly down-sampled following two different regimes. Taxa co-occurrences andphylogenetic interactions were re-calculated for every down-sampled dataset. (a) 5, 10, 20 and 50 samples per body site were randomlyselected from the full HMP dataset, at 10 iterations per down-sampling step. (b) 1000 randomly selected samples were down-sampled to adepth of 1000 sequences per sample; this dataset was then further down-sampled to 50 sequences per sample in several steps, at 10random iterations per step. Supplementary Figure S3 shows corresponding plots on R2 values.


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initial OTU abd.interaction strength

Jaccard(classical)

Jaccard(weighted)

Bray-Curtis

Morisita-Horn

TINA(unweighted)

TINA(weighted)

TINA (w),based on IA

TINA (uw),based on IA

gut samples

oral samples

interaction matrix starting conditions simulation result

adonis F value

gut, null comparison

oral, null comparison

gut/oral separation

habitat separation

Figure 6 TINA captures both habitat preference and taxa interaction signals. (a) Separation of oral and gut samples, as simulated basedon a Dirichlet Multinomial Mixture model inferred from raw count data. An example Principal Component Analysis (PCA) of simulationresults (left) and partitioning performance for different indices when testing between-habitat and within-habitat separations (negativecontrols; right). (b–e) GLV simulations of count data. For each setup, an example interaction matrix, habitat preferences as encoded in astarting count table (oral and gut samples coloured blue and orange) and simulation outcome (as PCA ordination) are shown. The setupscorrespond to a negative control setting with no habitat preferences and neutral interactions (b), neutral community dynamics with habitatpreferences only (c), habitat-naïve conditions with non-neutral interaction structure (d) and a combination of habitat preferences andhabitat-specific interactions (e). In (d–e), light and dark red groups correspond to TINA calculated directly from the (known) interactionmatrix. Three high outlying F values were removed in (d). Raw habitat partitioning data is available in Supplementary Table S1.


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we performed GLV simulations with starting OTUcounts randomly sampled from a Poisson distribu-tion (λ=5) and invariant growth rates. From theresulting count tables, we assigned samples to mock‘habitat groups’ based on summed OTU groupabundances. We observed that partitioning powerwas very high for all tested indices, with TINAoutperforming count-based measures. Interestingly,when we computed TINA directly based on the(known) interaction matrix, it provided even higherF values than SparCC-based TINA, derived from amore indirect count-based co-occurrence signal. It isnotable that interaction structure alone, in theabsence of a priori habitat preferences, was sufficientto generate clearly discernible sample clusters in oursimulations, although there were comparativelylarge levels of noise observable in partitio-ning power.

Finally, we investigated a setup with both habitatpreferences and non-neutral interactions (Figure 6e).We assigned habitat preferences to OTUs based ontheir predominant occurrence in either oral or gutsamples and generated an interaction matrix asdescribed above with within-habitat structure. Wethen performed GLV simulations using these inter-actions and habitat-specific starting counts (assignedfrom within-group shuffling of raw OTU abun-dances). We observed that TINA had much higherpartitioning power than other indices, and that TINAbased directly on the interaction matrix outper-formed SparCC-based TINA.

Biogeographical and physicochemical gradientsstructuring oceanic micro-eukaryote planktoncommunities are best captured by TINAThe TARA Oceans project has provided a very richand multifaceted census of the world’s oceans alongseveral geographical and physicochemical gradients.We re-analysed TARA data on micro-eukaryoteplankton diversity in the sunlit ocean (De Vargaset al., 2015) to test the performance and versatility ofTINA and other indices at representing differentecological signals. The dataset contained 77 samplesfrom 43 stations along a wide geographical gradient(as shown in Figure 7a), taken at two depth levels,subsurface water (SUR) and deep chlorophyll max-imum (DCM), and with body size filters ranging from0.8 to 2000 μm. We calculated pairwise communitydistances according to JCI, JCW, JCC, BC, MH, TUand TW.

To test whether community similarity follows alatitudinal gradient, we correlated the first compo-nent of a Principal Coordinates ordination (PCoA) tolatitude, separately for the northern and southernhemispheres (Figure 7a). We observed that thedominating component of an unweighted TINA-based PCoA correlated well with latitude, both forSUR (ρSpearman = 0.75) and DCM (ρ=0.8) water layers.In contrast, an ordination based on BC (the indexused in the original study) showed much weaker

correlations for the dominating component (ρ=0.15and ρ=35, respectively). We tested for these effectsmore systematically by correlating pairwise commu-nity distances to absolute differences in latitudebetween samples (Figure 7b). While all indicesprovided positive correlations, TU and JCI showedthe strongest trend for SUR samples (ρSpearman = 0.37),while TU and TW showed the strongest signals forDCM (ρ=0.36 and ρ=0.32). Similar trends wereobserved for correlations of community distance togeographical distance (Supplementary Table S2).Thus, although JCI performed surprisingly well,TINA outperformed other indices at detecting abiogeographical signal. This can probably be ratio-nalised when considering that taxa co-occurrence isexpected to be in part determined by geography,which in turn also correlates with many otherecological parameters like water temperature, irra-diation, salinity and so on.

Finally, we tested how well pairwise communitydistances represented the factors sampling regionand depth; Figure 7c shows PCoA ordinations andPERMANOVA statistics for JCI, BC and TU. While allthree indices provided significant separation bysampling region, water layer effects were significantonly in JCI and TU, while only TU detected anyeffect of the region*depth interaction term. More-over, effect sizes as expressed in F statistics and totalvariance explained by these three factors (summedR2) were considerably higher for TU than for JCI andBC, indicating a much more pronounced partitioningaccording to these terms.

Discussion

The question of what processes are renderingcommunities similar or dissimilar to each other isfundamental to the study of diversity. Traditionally,community similarity has been quantified fromcompositional overlap, considering taxa as indepen-dent of each other and describing communitystructure based on census data. More recently,measures based on additional signals have becomeincreasingly popular, most prominently phyloge-netic indices based on shared evolutionary history.Such approaches take into account relationshipsbetween taxa, under the assumption that phyloge-netic relatedness implies ecological and functionalsimilarity. In this study, we have introduced a set ofindices that follow a different rationale: we proposeto quantify community similarity in terms of inter-actions between taxa.

There are several arguments for doing so. First,taxa interactions are a fundamental ecologicalparameter, at the heart of community ecology: theyare important drivers of community assembly,composition and dynamics. Second, it is thereforemeaningful to characterise taxa and their relation-ships based on their interactions: two taxa that arehighly similar in terms of their interactions with


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PCoA Axis 1 [60.9%] PCoA Axis 1 [15.2%]

TINA, unweighted Bray-CurtisLa

titud

e

TIN

A, w

eigh

ted

TIN

A, u

nwei

ghte

d

Jacc

ard,

Cha

oJa

ccar

d, F

ract

ions

Δlatitude (rad)

Bra

y-C

urtis

Jacc

ard,

cla

ssic

al

Axi

s 2

[19.

8%]

Axis 1 [60.9%]

F

0.608 ≤0.00130.82

5.71

1.73 0.034 0.063

0.028 0.002

R2 P

Axi

s 2

[10.

5%]

Axis 1 [15.2%]

F

0.145 ≤0.0013.02

2.01

0.50 0.024 0.94

0.024 0.09

R2 P

Axi

s 2

[8.3

%]

Axis 1 [10.8%]

Region

Depth

Region * Depth

F

0.323 ≤0.0018.98

4.22

0.98 0.035 0.441

0.038 0.004

R2 P

TINA, unweightedBray-CurtisBray-CurtisJaccard, classical

Deep Chlorophyll Maximum

SubsurfacMediterranean

Red Sea

Indian Ocean

South AtlanticPacific

Figure 7 TINA captures biogeographical and physicochemical trends in ocean planktonic community composition. (a) TARA Oceanssampling locations, coloured by assigned oceanic world region (middle). The first axes of PCoA ordinations on TINA (left) and Bray–Curtis(right) dissimilarities correlated differentially well with latitude both for subsurface (SUR, orange) and deep chlorophyll maximum (DCM,blue) samples, both for the northern and southern hemisphere. (b) Spearman correlations of six different community distances againstabsolute difference in latitude (Δlat in rad). (c) PCoA ordinations and PERMANOVA statistics on dataset partitioning by factors region,depth and the region*depth interaction term for JCI, BC and TU.


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other taxa can be considered ecologically almostequivalent, they can be assumed to fulfill similarroles in a community. Our approach captures thissignal: we argue that it is meaningful to considercommunities as similar, which contain ecologicallysimilar taxa. Third, interaction network analysishas proved to be a very powerful tool in unravellingcomplex community dynamics, but its findings areoften difficult to connect to the level of community-level diversity patterns. Our approach may help tobridge this analysis gap, by providing diversityindices that are based on networks and can beinterpreted in a network framework. For example,TINA essentially quantifies community distance asthe distance on a taxa co-occurrence network.Finally, our approach is versatile: there are manytypes of ecological interactions, at many differentlevels, and in principle, interaction-adjustedindices like TINA and PINA can be formulated forall of them.

Several previous studies have investigatedadapted versions of classical ecological diversityindices that take into account taxa dissimilarities.Most prominently, the quadratic entropy intro-duced by Rao (1982) calculates a concentrationindex, corrected for (known) dissimilaritiesbetween taxa; it is defined as the expected dissim-ilarity between randomly sampled individuals froma community and defaults to the classical Gini-Simpson index if all dissimilarities are zero. Ricottaand Marignani (2007), among others, suggesteddecompositions of Rao’s quadratic entropy into β-diversity components in the classical ecologysense, that is interpreting it as the expecteddissimilarity between individuals randomlysampled from different communities. Suchapproaches are conceptually and mathematicallydistinct from our proposed interaction-adjustedindices – the latter are formulated and interpretedas average (dis)similarities on networks, rather thanentropy decompositions. Likewise, our approachdiffers conceptually from established networkclustering methods, such as for example MarkovClustering (Enright et al., 2002), which have beensuccessfully applied to many biological problems.These exploit network structure to cluster nodes(that is, in our case, taxa) by similarity, but do notcompare pre-defined samples (that is, groups ofnodes) in terms of similarity on the network.Similarly, established metrics such as the Topolo-gical Overlap Measure (Li and Horvath, 2009) orAnet (Karpinets et al., 2012) compute node simila-rities (not sample similarities) based on relativenode positions in a network; these are analogous tothe more basic correlative transformation of theinteraction matrix IC to matrix C discussed above(Supplementary Figure S2).

In this study, we have focused on two specifictypes of interaction-adjusted indices, TINA andPINA, and benchmarked their performance in are-analysis of two large and complex datasets.

TINA by far outperformed all other indices atdiscriminating human body habitat-specific com-munities (Figure 2), even for very small datasets(Figure 5). We demonstrated how co-occurrence-based TINA captures a habitat preference signal,a taxa interaction signal and a combination ofboth in simulations (Figure 6). Moreover, TINAbest captured biogeographical trends and partition-ing by the factors ‘region’ and ‘water depth’ formicroeukaryotic plankton communities (Figure 7).These results can be interpreted in light ofhow TINA is computed. Taxa co-occurrence net-works, on which TINA is based, capture an‘integrated’ ecological association signal, in quan-tifying the observable outcome of the interplay ofdifferent levels of taxa interactions as patterns ofco-abundance and avoidance (Faust and Raes,2012). Although taxa association networks arenot equivalent to ‘true’, ecological taxa interac-tions, it has recently been shown that they mayprovide good approximations of true interactionswithin certain limits (Berry and Widder, 2014).Indeed, they can reveal network structures that arespecific to a given type of habitat (as shown forexample in Figure 3) or structured according totheir response to an ecological gradient or pertur-bance. Figure 4 illustrates anecdotally how TINAcan capture such signals to assign communitysimilarities that are more in line with ecologicalexpectations than count-based indices. The factthat TINA provides such strong separations of bodyhabitats and strong correlations with biogeographyand other factors for plankton communities meansthat these factors have a strong and specificinfluence on taxa co-occurrence; subsequent diver-sity analyses should take this into account andinterpret accordingly.

Likewise, PINA and other phylogenetic indicessuch as UniFrac are based on phylogenetic related-ness, operating under the assumption that sharedphylogeny implies not only a shared evolutionaryhistory, but similar ecological roles and functionalprofiles. However, by definition, an inference ofecological similarity from phylogeny is necessarilyindirect and imperfect, although it is arguably avalid enough assumption for many phylogeneticclades. In all relevant tests, unweighted and/orweighted PINA, based on pairwise phylogeneticsimilarities between taxa, outperformed UniFrac,based on shared phylogeny only, even for verysmall datasets. Interestingly, unweighted PINA andUniFrac were the only indices to detect partitioningby urogenital habitats (Figure 2, SupplementaryFigures S3 and S4), a task at which almost allcount-based indices, as well as TINA, failed. Asdiscussed above, this is likely due to differentialfactors and mechanisms shaping community struc-ture in urogenital habitats, compared to otherhabitats. However, the fact that we did observedifferential trends in index performance empha-sises the importance of a multifaceted approach:


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by applying count-based, phylogenetic and inter-action-adjusted indices, different aspects of com-munity similarity are quantified, which can beinterpreted in context of each other, with thepotential to reveal biological insights beyond thescope of mono-dimensional approaches.

One possible drawback of interaction-adjustedindices is that they are not context-invariant: theirvalues will always depend on analysis scope and onthe system under consideration, as they vary withvarying network structure. While count-basedindices will always assume the same similarity fortwo communities, independently of the remainingdataset, interaction-adjusted indices may changeasymptotically when more data are added, simplydue to (subtle) changes in network structure. How-ever, this behaviour can indeed also be an asset, forexample when comparing multiple datasets in ameta-study. In such a setup, ‘globally’ constructednetworks may mitigate dataset-specific noise, intro-duced for example by sampling methods or limiteddepth. Likewise, interaction-adjusted indices are notlimited to capturing static network architectures, buttheir flexibility allows to account for conditionallyvariable networks that are rewired for example overtime, gradients or in response to specific changingfactors.

In the large arsenal of measures for communitysimilarity and, more generally, β diversity, ourproposed family of interaction-adjusted indicesprovide an important, powerful and versatile alter-native. By taking taxa interactions into account, theyquantify novel aspects of ‘diversity’, at the very coreof community ecology, and may guide biologicalinterpretation of diversity patterns in novel ways.

Conflict of Interest

The authors declare no conflict of interest.

AcknowledgementsWe thank David Berry and Stefanie Widder of theUniversity of Vienna for sharing R code to conductGeneralized Lotka–Volterra modelling, and JankoTackmann, Jordi Bascompte and Bernhard Schmid ofthe University of Zurich for helpful discussionsduring the preparation of this manuscript. Thiswork was supported by an ERC starting grant (UMICIS/242870) and the Swiss National Science Foundation(31003A_160095).

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