statistical approaches for dna barcoding

162 SYSTEMATIC BIOLOGY VOL. 55

ACKNOWLEDGMENTS

I thank Phil Cantino, Mike Lee, Jason Anderson, and Kurt Pickett forcomments on an earlier version of this paper and Bob O'Hara (ca. 1994)for increasing my own awareness of the distinction between taxonomyand nomenclature.

REFERENCES

Cantino, P. D., and K. de Queiroz. 2004. PhyloCode: A phy-logenetic code of biological nomenclature. [http://www.ohiou.edu/phylocode/]

de Queiroz, K. 1992. Phylogenetic definitions and taxonomic philoso-phy. Biol. Philos. 7:295-313.

de Queiroz, K. 1997. The Linnaean hierarchy and the evolutionizationof taxonomy, with emphasis on the problem of nomenclature. Aliso15:125-144.

de Queiroz, K. 2005. Linnaean, rank-based, and phylogenetic nomen-clature: Restoring primacy to the link between names and taxa. Symb.Bot. Ups. 33(3):127-140.

de Queiroz, K., and P. D. Cantino. 2001. Phylogenetic nomenclatureand the PhyloCode. Bull. Zool. Nomencl. 58:254-271.

de Queiroz, K., and J. Gauthier. 1990. Phylogeny as a central principlein taxonomy: Phylogenetic definitions of taxon names. Syst. Zool.39:307-322.

de Queiroz, K., and J. Gauthier. 1992. Phylogenetic taxonomy. Annu.Rev. Ecol. Syst. 23:449-480.

de Queiroz, K., and J. Gauthier. 1994. Toward a phylogenetic system ofbiological nomenclature. Trends Ecol. Evol. 9:27-31.

International Botanical Congress. 2000. International Code of Botan-ical Nomenclature. Edition adopted by the Sixteenth InternationalBotanical Congress, St. Louis, Missouri, July-August 1999. KoeltzScientific Books, Konigstein.

International Commission on Zoological Nomenclature. 1999. Interna-tional Code of Zoological Nomenclature, 4th edition. InternationalTrust for Zoological Nomenclature, London.

International Union of Microbiological Societies. 1992. InternationalCode of Nomenclature of Bacteria and Statutes of the InternationalCommittee on Systematic Bacteriology and Statutes of the Bacteriol-ogy and Applied Microbiology Section of The International Unionof Microbiological Societies. American Society for Microbiology,Washington.

Laurin, M., K. de Queiroz, P. Cantino, N. Cellinese, and R. Olmstead.2005. The PhyloCode, types, ranks, and monophyly: A response toPickett. Cladistics 21:605-607.

Pickett, K. M. 2005. The new and improved PhyloCode, now with types,ranks, and even polyphyly: A conference report from the First In-ternational Phylogenetic Nomenclature Meeting. Cladistics 21:79-82.

First submitted 15 April 2005; reviews returned 8 August 2005;final acceptance 24 August 2005

Associate Editor: Rod Page

Sysl. Biol. 55(1):162-169, 2006Copyright © Society of Systematic BiologistsISSN: 1063-5157 print / 1076-836X onlineDOI: 10.1080/10635150500431239

Statistical Approaches for DNA Barcoding

RASMUS NIELSEN1 AND MIKHAIL MATZ2

7 Department of Biological Statistics and Computational Biology, Center for Bioinformatics, University of Copenhagen Universitetsparken 15,2100 Copenhagen, Denmark; E-mail: [email protected]

2 Whitney Laboratory and Department of Molecular Genetics and Microbiology, University of Florida, 9505 Ocean Shore Blvd, Saint Augustine,FL 32080, USA

The use of DNA as a tool for species identification hasbecome known as "DNA barcoding" (Floyd et al., 2002;Hebert et al., 2003; Remigio and Hebert, 2003). The basicidea is straightforward: a small amount of DNA is ex-tracted from the specimen, amplified and sequenced. Thegene region sequenced is chosen so that it is nearly iden-tical among individuals of the same species, but differentbetween species, and therefore its sequence, can serve asan identification tag for the species ("DNA barcode").By matching the sequence obtained from an unidenti-fied specimen ("query" sequence) to the database of se-quences from known species, one can thus determinethe species affiliation of the specimen. Importantly, thespecimen may represent any developmental stage or bejust a small fragment of the whole organism, displayingno morphological traits required for standard identifi-cation. Although this technique will by no means elim-inate the need for the traditional descriptive taxonomy(Dunn, 2003; Lipscomb et al, 2003; Seberg et al., 2003),it is nevertheless envisioned as a key element of futuretaxonomy research (Stoeckle, 2003; Tautz et al., 2003). The

idea of DNA barcoding, although perhaps not surpris-ingly being a matter of heated debate among dedicatedtaxonomists (see Trends in Ecology and Evolution, volume18, no. 2, 2003; Will and Rubinoff, 2004), gained rapidacceptance among biologists from other fields. Accord-ing to the news report in the April 2004 issue of Nature,the Barcode of Life Initiative—an international consor-tium of museums with the secretariat at the NationalMuseum of Natural History in Washington DC—is be-ing established with the goal of creating a database ofDNA barcodes from known animal species based on mi-tochondrial gene cytochrome c oxidase subunit I. TheDNA barcoding protocol has been already adopted bythe Census of Marine Life, a growing global network ofresearchers in more than 50 countries engaged in a 10-year initiative to assess and explain the diversity, distri-bution, and abundance of life in the ocean (O'Dor, 2004).

The weakest spot of DNA barcoding is the obviousfact that no gene can serve as an ideal barcode, i.e.,be always invariant within species but different amongspecies. It has been pointed out by several authors that

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2006 POINTS OF VIEW 163

DNA-based identification, if it is to become a rigorousanalysis, should be concerned about distinguishing in-traspecific from interspecific variation rather than sim-ply recording perfect and imperfect sequence matches(Dunn, 2003; Lipscomb et al, 2003; Stoeckle, 2003). Toget around this problem, at present it is assumed that theinterspecific sequence variation should exceed a certainthreshold, say, 2% or 3% dissimilarity, set on the basis ofempirical observations of sequence differences amongcongeneric species (Hebert et al., 2003a, 2003b). Such anapproach seems to be too simplistic to avoid inconclusiveor erroneous results. Clearly, there is a need for statisti-cal methods for assessing if a sampled query sequence issufficiently similar to a particular data base sequence tojustify a species assignment of the query.

There are several possible statistical approaches to thisproblem. In the classical hypothesis-based (frequentist)approach, the null hypothesis could be that the querysequence is a member of a particular species. Such a testwould control the rate at which the query is assignedto the true species, i.e., it controls the rate of false nega-tives. In the Bayesian approach the posterior probabilityof a species assignment is calculated by assuming a priordistribution of species assignments. We will discuss theproblems and merits of these approaches and providesome guidelines towards the use of statistics in DNAbarcoding experiments.

WHEN SIMILARITY IS MISLEADING

The most obvious source of error is that the databasesequence most similar to the query may not be from thespecies to which the query belongs (the true species).Beside human error (incorrect identification of the spec-imen used to derive the database sequence), there are atleast three reasons why this may happen. First, the truespecies may not be represented in the database. Second,because of lineage sorting, the random coalescences oflineages in a common ancestral species, the query maynot be genetically most closely related to the databasesequence from the true species. Third, even if the truespecies sequence and the query sequence share a mostrecent common ancestor before either of them share anancestor with any sequences from other species, the ran-dom process at which mutations arise on lineages maycause the sequence representing another species to bemost similar to the query. The probabilities that the lat-ter two events occur can be assessed using populationgenetic theory. For simplicity, we will assume that thereare two possible database species, a 'true' and a 'wrong'species. Assuming that both species are panmictic andof constant size, the probability that the query sequencedoes not share a most recent common ancestor with thetrue species, before either of them share a common ances-tor with the wrong species, is simply (2/3)e~T/W, where Tis the divergence time between the two species in num-ber of generations and N is the effective chromosomalpopulation size of the true species (see, e.g., Hudson,1990). When taking into account the mutational process,and assuming an infinite sites model (e.g., Watterson,

cqd

d

FIGURE 1. The probability that the number of nucleotide differ-ences between the query sequence and another sequence from the samespecies is smaller than the number of nucleotide differences betweenthe query sequence and a sequence from a different species, as a func-tion of the (scaled) divergence time (T) between the two species for9 = 1.0 (solid) and 6 = 5.0 (dotted line). The probability has been calcu-lated conditional on at least one nucleotide difference between the twodatabase sequences.

1975), calculations can be done numerically, or by simu-lation to determine assignment probabilities. For exam-ple, we might be interested in evaluating the probabilitythat the number of nucleotide differences between thequery sequence and the true species sequence is smallerthan the number of nucleotide differences between thequery sequence and the wrong species sequence [Pr(XtrUe< Kfaise)]- This probability is shown in Figure 1 assum-ing that the population size did not change after thespeciation of the two species. The probability is calcu-lated for two different values of 0( = 2N/x, where \i is themutation rate for the entire sequence per generation). Tohave more than a 95% chance of assigning the sequenceto the correct species, the divergence time (scaled by thepopulation size) must be larger than 2.7 when 9 = 5.0 and4.6 when 0 = 1.0.

The corresponding probability that the number of nu-cleotide differences is smallest between the query se-quence and the false sequence, Pr(Ktrue > Kfaise)/ is shownin Figure 2. Notice that for relatively small mutationrates (9 = 1), the probability of assigning the sequenceto the wrong species is larger than 5% until T/N is largerthan 3. These results demonstrates that it is not possi-ble to avoid the problem of within species variability bychoosing genes that show very little variability withinspecies, since such genes will tend to provide the low-est discriminatory power. For a given divergence time,it is always better to have as high as possible a muta-tion rate in the genetic region under investigation. How-ever, for any particular species there may of course begenes that for random reasons are more diagnostic thanothers.

In the literature, is has been suggested to use a fixedcut-off in terms of pairwise difference for the purposeof species assignment (Hebert et al., 2003a, 2003b). How





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1

01

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FIGURE 2. The probability that the number of nucleotide differ-ences between the query sequence and another sequence from thesame species is larger than the number of nucleotide differences be-tween the query sequence and a sequence from a different species, asa function of the (scaled) divergence time (T) between the two speciesfor 6 = 1.0 (solid) and 9 =5.0 (dashed line). The probability has beencalculated conditional on at least one nucleotide difference betweenthe two database sequences.

well such a strategy performs depends on the value of 9.Figure 3 shows the probability of observing more than 3,6, and 9 nucleotide differences between two sequencesof the same species as a function of 9, calculated us-ing standard methods from coalescence theory. Clearly,the appropriate cut-off depends strongly on the effectivepopulation size of the species, indicating that the choicesregarding species assignment must take effective popu-lation sizes of the relevant species into account.

ber of mutational events between the query sequenceand the database sequence from the focal species, as atest statistic. Other test statistics could be defined, forexample, likelihood ratio tests. However, it should benoted that such tests would have to make more assump-tions than the current tests. Also, we will assume aninfinite sites model of mutation (Watterson, 1975), al-though the results easily could be generalized to othermodels.

First, consider the unrealistic case where 9 is knownwith absolute certainty. Then the probability of observingK nucleotide differences between two sequences of thesame species is geometrically distributed with parameter1/(1 + 0), (see, e.g., Hudson, 1990), so

Pr(X < k I 0) = 1 -+ 1

k+l

(1)

9 can never be known exactly, so we must represent ourknowledge regarding 9 in a form of a distribution ratherthan a single value. This distribution should have a fairlyflexible functional form and sample space on (0, 00). Wewill use the gamma distribution, which meets these cri-teria (although other distributions, such as a truncatednormal distribution, could also be considered). Underthe assumption of a gamma distribution

Pr(X r<k) =

Jo

Pr(X < k I 9)f{9)d9, (2)

where

DNA BARCODING USING HYPOTHESIS TESTING

The simplest frequentist approach to consider wouldbe where the null hypothesis is defined as membershipin a predefined species. The test procedure should thencontrol the proportion of time the true null hypothe-sis of species membership is falsely rejected. Here wewill explore the properties of such a test using the num-

f(0) = r-ie-t (3)

o o

FIGURE 3. The probability of observing more than 3 (solid), 6(dashed), and 9 (dotted) nucleotide differences between two sequencesof the same species as a function of 6.

and the parameters a and f$ must be positive. Although,Equation 2 does not have an analytical solution, it canbe evaluated very fast numerically. The cut-off shouldthen be chosen as the minimum value of k for whichPr(X < k) > 1 - a, where a is the chosen significancelevel. The power of this test for a = 0.05 to reject a falsenull hypothesis is shown in Figure 4, as a function of thedivergence time.

This test provides a more rigorous way of determin-ing cut-offs for hypotheses regarding species member-ships based on pairwise differences. However, we notethat there are many problems associated with this ap-proach, including the fact it does not come with a suitablemethod for correcting for multiple testing when appliedto database searches and that it is based on restrictiveassumptions regarding the underlying population ge-netics. In particular, it relies on assumptions regarding9, and its distribution. If only a single sequence is avail-able from each species, information regarding 9 is notavailable. Also, focusing on pairwise differences in thepresence of multiple sequences clearly leads to a loss ofinformation.





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1

5

i

10E(T/N)

i

15

i

20

FIGURE 4. The power to reject the membership in the wrong speciesfor different values 9 and different values of the divergence time T/Nwhen a species is only represented by a single sequence, for 6 = 1,(dotted line) and 6 = 3 (solid line). It is assumed that the variance in 6equals 0.256* .

The previous discussion illustrates that it is not possi-ble to make DNA barcoding inferences without assump-tions about 9. But what happens if we try to use as littleprior information regarding 9 as possible in DNA bar-coding inferences? Mathematically this corresponds toassuming that 9 is uniformly distributed between 0 andm, and then considering the limit of m ->• oo. In that casePr(K < k) -> 0 for any fixed value of k, suggesting thatwe should always accept the species assignment. Indeed,any pairwise divergence, however large, may be dueto within-species variation caused by a correspondinglylarge value of 9. In other words, DNA barcoding basedon single sequences is impossible without implicit or ex-plicit assumptions regarding 9. In particular, very largevalues of 9 must be excluded a priori.

In practical applications, there are several populationgenetic tools that can be used to estimate 9 (Nielsenand Wakeley, 2001; Rannala and Yang, 2003; Wilson andBalding, 1998). For a situation in which only a singlesequence has been obtained to represent a species inthe database, the easiest solution would be to assumethat its 9 is the same as 9 in the related species of sim-ilar ecology. More sophisticated methods for such aninterpolation may be envisioned, which would allowthe population size to vary according to some stochas-tic process along the lineage of a phylogeny. Althoughsuch procedures would obviously be of great value forDNA barcoding, they are not the topic of this paperand will not be discussed further. Also, in the casewhere multiple sequences are known from each species,the problem regarding the true value of 9 is reducedbecause the sequences themselves contain informationabout 9.

BAYESIAN APPROACH

In some cases a frequentist framework may not be themost suitable for assignment of individuals to species. Inparticular, when multiple hypotheses are considered at

the same time (i.e., potential membership in many possi-ble candidate species), generating a need for procedurescorrecting for multiple testing, frequentist proceduresbased on hypothesis testing may have little power. Ifwe are willing to make assumptions regarding the evo-lutionary relationships among species, a more naturalframework may in some cases be to calculate the poste-rior probability that the query sequence belongs to anyparticular database species. Such a Bayesian procedurewill be outlined here.

Let D = {Di, D2,..., Dk} be the set of database DNAsequences and let Xbe the query sequence. We considerDj to represent a larger collection of sequences all be-longing to the same species, i.e., D; e S,, where S, is theset of mostly unobserved sequences belonging to speciesi. We are then interested in assessing the probability ofX e S; given the model of evolution and all the databasesequences. Using Bayes' formula and assuming that Xcould belong to any species with equal probability a pri-ori, we have

Pr(X e Si | D, X) =Pr(X,D| XeS,)Pr(X€S,)

E - = 1 P r ( X , D | X e S / ) P r ( X e S / )

Pr(X, D | X e S,)

£*=1Pr(X,D|XeS;)(4)

In this notation, the presence of nuisance parame-ters, such as effective population sizes and diver-gence times has been suppressed. It is important tonote that Pr(X, D | X e S,-) is not in general propor-tional toPr(X, D,! | X € Si)—in other words, probabili-ties of query assignments to different species are notindependent—because of evolutionary correlations dueto the shared phylogeny. Methods based on approximat-ing Pr(X, D | X e S,)byPr(X, Df | X e S,) will,therefore,not perform well (results not shown). Establishing a validBayesian assignment method for DNA barcoding is,therefore, more difficult than in other apparently similarcases, such as paternity assignment based on unrelatedindividuals.

Equation 4 can be evaluated using Markov chainMonte Carlo (MCMC) procedures. Importantly for DNAbarcoding, established MCMC methods allow explicit in-tegration over the set of nuisance parameters and incor-poration of information from multiple sequences fromeach species. Here, we will modify the procedure ofNielsen and Wakeley (2001) for the purpose of speciesassignment. In brief, for two species (or populations)this method establishes a Markov chain with state-spacegiven by the set of all possible gene trees, effectivepopulation sizes, divergence times, and migration ratesbetween the two species, and stationary distribution pro-portional to the joint posterior of these parameters. In-ferences are then done by simulating this chain andsampling parameter values from the chain at stationar-ity (when it has reached equilibrium). The distributionof these parameter values then provides an estimate ofthe posterior density (for further details see Nielsen and





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Wakeley, 2001). This procedure can be modified to eval-uate Equation (4) by allowing the population identity ofan individual to be a random variable, with prior prob-ability of belonging to each species (population) of 50%.To model species divergence, we will assume that the mi-gration rate between the two populations is zero. Uncer-tainty regarding the population-affiliation of a particularsequence (the query sequence) can then be accommo-dated by incorporating updates of the affiliation of thesequence into the MCMC scheme. Without migration,such updates will only be accepted when the most recentcoalescent between the query sequence and any otherlineage in the genealogy occur before the two popula-tions diverge. The update implemented here then simplyconsists of switching the affiliation of a species withoutchanging the coalescence times or any other aspect of thegene tree. The acceptance probability of such an updateis then min {1, p(G' | 0 ) /p (G | 0 )} , where G' is the newproposed gene tree and 0 is a vector of population levelparameters. At stationarity, the expected proportion oftime in the chain the query sequence belongs to speciesi is given by Equation 5. Similar schemes could also beused to develop barcoding-aimed procedures on the ba-sis of other methods (Rannala and Yang, 2003; Wilsonand Balding, 1998).

The method is currently implemented for the HKYmodel of DNA sequence evolution and the infinite sitesmodel. At the taxonomic level where barcoding is am-

TRIGO N = 51

B

biguous, the exact model of substitution probably makeslittle difference.

DATA ANALYSIS EXAMPLES

We examined two real data sets that may present aproblem for DNA barcoding, representing two marginalcases of extremely low and extremely high sequencevariability, both at the intra- and interspecific levels.The first data set contains sequences from the skipperbutterfly Astraptes fulgerator, which recently has beenproposed to be a complex of perhaps as many as 12 sep-arate species (Hebert et a l , 2004). Genetic differentia-tion between these species was originally identified bythe phylogeny of cytochrome c oxidase subunit I (COI)sequences, and was corroborated by the presence of amorphological difference in caterpillars and the speciesof plants preferred by them as food. Still, both the de-gree of divergence within and between these species isvery small (Fig. 5A). In sharp contrast to the butterflies,our second example—four species of the Australian rain-forest frogs of the genus Litoria—displayed intraspecificCOI sequence often exceeding 10% pairwise difference(Fig. 5B) (Schneider et al., 1998). High levels of COI vari-ability appear to be common in amphibians (Vences et al.,2005).

To evaluate the power and accuracy of the hypothesis-based test (K-test) in application to these two cases,

L. rheocolaN = 30

I L. nannotisI N = 33

L fallaxA/= 83

FIGURE 5. Consensus maximum parsimony trees for COI sequences from the two models analyzed here. (A) Skipper butterfly Astraptesfulgerator species complex. (B) Four species of the tree frogs of the genus Litoria. Scale bars: 10 nucleotide changes. The number of individualsequences per species is indicates near species names.





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we performed simulations where in each replicate,"database" sequences (one per species) and one "query"sequence were randomly drawn from the available COIdata. These simulated data sets were analyzed using thevalues of 6 and their variances estimated from the com-plete collection of sequences for each species. For eachspecies, we performed 100 replicates. When the querysequence matched the database with a P-value exceed-ing 0.05 for one and only one species, the identificationwas designated "correct" if the query sequence was in-deed derived from that species, and would be "wrong" ifnot. If the test sequence matched more than one databasespecies, it was considered a "tie." Occasionally, the querysequence did not match any of the database species withsufficient P-value, which was designated "no ID." Wealso performed the same analysis using identical valuesof the mean and variance of 6 for all species, which wereequal to their averages over all the analyzed species. Thisanalysis was intended to approximate a situation whereno population genetic data are available for one or morespecies in the database, and their values of 9 are interpo-lated using data from related species of similar ecology.

The results of the iC-test simulations are summarizedin Table 1. Notably, we never encountered a case of wrongidentification. Using the experimental values of 6, of thenine tested groups within the Astraptes fulgerator com-plex, four could be identified with very high power (0.99-1) at the 0.05 significance level, while another three wereidentifiable with the power 0.83-0.91. The power forthe two remaining groups—INGCUP and HIHAMP—was 0.33 and 0.25, respectively, due to frequent ties be-tween themselves and also with the third very closelyrelated FABOV group (Fig. 5). LOHAMP or LONCHOqueries, although matching the database sequence oftheir own groups with high P-value, in about 10 per-cent of cases matched the YESENN database sequencewith P-value slightly exceeding 0.05 due to higher ge-netic diversity within YESENN, thereby generating ties.The great number of ties observed for Litoria species was

due to a similar situation: in the majority of cases thequery matched the species with highest estimate of 6 (L.fallax and/or L. serrata) with P-value that exceeded 0.05slightly, in addition to providing a good match to thecorrect species. No "no ID" cases were observed duringLitoria simulations. Interestingly, the use of the average 6and variance for all competing species resulted in 100%correct identification in Litoria and not much change ofpower for Astraptes fulgerator, except for FABOV group(Table 1), suggesting that in these cases, interpolation of6 from related species may be a reasonable option.

We then investigated whether a Bayesian methodcould help in resolving the ties such as the ones suggestedby the K -test. Because the current version of the methodis able to discriminate between only two species, we fo-cused on the two pairs from our examples that were rep-resented by more than 20 sequences each and producedmost ties: INGCUP and FABOV groups of the butter-flies and L. fallax and L. serrata species of the frogs. Wegenerated 100 datasets that each included one, three, orfive randomly chosen database sequences from the twocompeting species plus one test sequence from FABOVor L. serrata. This data was then analyzed assuming atruncated uniform prior for 6 (U[0, 10]) and the scaleddivergence time t.

The accuracy of the Bayesian sorting at the 0.95 con-fidence level exceeded 0.9 both for butterflies and frogswhen three or five database sequences were used, beingconsiderably less for one database sequence (Fig. 6).

We also studied the behavior of the Bayesian sortingwhen the query sequence was not derived from one ofthe two database species (L. fallax and L. nannotis), butfrom the third one (L serrata). In these simulations (100replicates), the database for each of the two species in-cluded one or three sequences. These experiments mimicthe case when the query comes from an "unrecorded"species. In such a situation the X-test would tend to as-sign the query to the species with the highest value of6—L. fallax. In contrast, in Bayesian sorting the posterior

TABLE 1. Results of the K-test simulations.

9" SD

Skipper butterfly Astraptes fulgerator complex:CELTTRIGOSENNOVINGCUPFABOVHIHAMPLOHAMPLONCHOYESENNAverage

Tree frogs Litoria:I. fallaxL serrataL nannotisL rheocolaAverage

0.910.311.450.150.70.130.360.271.590.65

3831251126

0.730.360.990.240.610.230.390.331.060.55

1916126

13

Correct

100100993391258389

100

81058

Experimental0/SDTie

000

657

758

110

191009592

No ID

001220900

0000

Correct

97100921

221

9910099

100100100100

Average0/SDTie

300

997699101

0000

No ID

008020000

0000

"6 was estimated as nucleotide diversity per locus.





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0.3

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0.6 0.7 0.8 0.9posterior probability

r-, I loneWM three

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0.2 0.3 0.4 0.5 0.6 0.7 0.8posterior probability

FIGURE 6. Histograms of posterior probabilities obtained inBayesian assignment simulations, for different number of sequencesper species in the database. (A) A. fulgerator, FABOV versus INGCUP;the query sequence comes from FABOV. (B) Litoriafallax versus Litoriaserrata, the query sequence comes from L. serrata. (C) Litoriafallax versusLitoria nannotis, the query sequence comes from L. serrata ("unrecordedspecies"). X-axis: posterior probabilities (bins of 0.05); Y-axis: fractionof replicates (out of 100).

probabilities were grouped around 0.50 and were neverless than 0.25 or more than 0.70, rightfully suggestingthat the query sequence does not belong to any of thedatabase species (Fig. 6). The probabilities were more

tightly grouped around 0.5 when one database sequencewas used, reflecting the tendency seen on Figure 6A andB: the method is reluctant to assign a query to any specieswhen the database is small.

DISCUSSION

Once the unrealistic assumption of perfect sequenceidentity within species is abandoned, it becomes clearthat DNA barcoding cannot be performed without mak-ing population genetic assumptions. Establishing mea-sures of statistical uncertainty in DNA barcoding hasto rely on strong assumptions regarding the popula-tion genetics of the analyzed species. Still, the inferenceprocedures based on the number of pairwise sequencedifferences should often be relatively robust to the pop-ulation genetic assumptions. Most violations of assump-tions regarding demography will simply change the(coalescence) effective population size, and only have aminor effect on the distribution of the test statistic. How-ever, it is important to note that there can be cases, partic-ularly cases with strong population subdivision withinspecies, where species assignment may fail because theunderlying demographics have not been modeled ade-quately. An extreme case is a sequence sampled from asub-population that has no ongoing gene-flow with anyof the populations from which the database sequenceshave sampled. The statistical method discussed here willthen be likely not to categorize the query sequence as amember of the focal species, even if taxonomists wouldrecognize it as belonging to it. In this case DNA barcod-ing may fail because the recognized taxonomic units donot correspond to populations that are reproductivelyisolated.

Here we have primarily focused on the number ofnucleotide changes (K) as a statistic in the hypothesis-based (frequentist) approach. Our results suggest thata procedure that examines the number of nucleotidechanges only between a query sequence and its bestmatch in the database is not optimal. More accuratemethods can be established by simultaneously consid-ering the number of changes between other divergentspecies in the database and the query sequence. Ul-timately, DNA barcoding methods should simultane-ously consider the phylogenetic information from allthe (relevant) species in the database (be based on thespecies tree), and the population genetic informationavailable from multiple sequences (incorporate informa-tion regarding the coalescent process within species). TheBayesian method presented here is a first step in thisdirection. Still, it is highly desirable to modify it to ac-count for possible unsampled species, to deal with anarbitrary number of species and to deal with uncertaintyregarding 6 for species represented by none, or very few,sequences.

The K-test and Bayesian assignment method pre-sented here are the first methods developed thus far toapproach DNA barcoding from a perspective of statis-tical population genetics. Overall, the performance of





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the K-test was good for the case of Astraptes fulgeratorcomplex, but less so for the Litoria species, where thehigh values of 0 in L.fallax and L. serrata produced many"ties." Given a complete database of barcodes, this couldbe viewed as a conservative behavior, because the test isreluctant to assign a query to one particular species inthe view of the great intraspecific variation observed inthe Litoria genus. However, if some species were miss-ing from the database, such a behavior could result inincorrect assignment of queries derived from these "un-recorded" species.

The Bayesian approach described here has obviousadvantages over the K-test in terms of accuracy andability to deal adequately with more than one sequenceper species in the database. Furthermore, this methoddirectly integrates over possible values of 6 alleviatingthe need to provide estimates of 9 for each species. Asmentioned above, we believe that a generalized ver-sion of this approach would be the method of choicefor DNA barcoding in the future. However, we alsonote that this method is not without problems, partic-ularly in making phylogenetic assumptions, and specieslevel assumptions that may not always be correct. Fur-thermore, the availability of a full Bayesian approachmay not eliminate the need for inference procedureswith controlled frequentist properties. The computa-tional machinery used in devising the Bayesian approachcould also be used in the development of frequentist ap-proaches. Such methods may be used to devise betterstatistics incorporating more of the information in thedata, while appropriately taking uncertainty in the nui-sance parameters, such as species divergence times, intoaccount.

The interrelationship between classical taxonomy andDNA barcoding has been a matter of extensive debates.In our view, the situation is quite simple. DNA bar-coding can undoubtedly be a useful tool to assign un-known specimens to predefined groups (i.e., species asdefined by a classical taxonomy), but never a methodfor identifying these groups in the first place. The factthat it is possible to assign a sequence from a specimento a predefined group does not mean that the group it-self deserves taxonomic recognition. For example, forAstraptes fulgerator, one may define the whole collectionof sequences as one group, or separate it into a dozensmaller phylogenetic clades and define these units asspecies within a species complex. In both cases, statis-tical approaches, such as the ones described here, couldbe successfully used to assign query sequences to taxo-nomic units. When encountering a query that cannot beassigned to any of the groups recorded in the database,one should not automatically infer that this query repre-sents a new species, because the possibility will alwaysremain that one or more of the database species wereundersampled. A taxonomic decision concerning such aquery should be made on the basis of independent linesof evidence.

ACKNO WLEDG EMENTS

Funding for this project was provided by grants from NIH(GM066243) and US Department of Defense (SERDP program) toMVM, and HFSP grant RGY0055/2001-M, NSF grant DEB-0089487,and NSF/NIH grant DMS/NIGMS-0201037 to RN.

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First submitted 17 January 2005; reviews returned 3 May 2005;

final acceptance 30 August 2005

Associate Editor: Paul Lewis





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