A De Novo Robust Clustering Approach for Amplicon-Based Sequence Data

Introduction

Studying the structure of the communities in an ecosystem is central in environmental microbiology [ 8, 14 ]. The biosphere's diversity can be determined by amplifying and sequencing speci c phylogenetic markers (e.g. 16S rRNA). From there, these amplicons need to be clusterized in "species" named Operational Taxonomic Units (OTUs) [ 4, 9, 11, 15 ]. As the volume of sequences has drastically increased in recent times, new clustering tools have emerged to treat the data in reasonable time. The currently used algorithms are, from the point of view of algorithmic complexity, the fastest available that do not produce random results. However, due to their simplicity, the reliability of the results are often discussed. These tools being essentially black boxes, their sensitivity to the sequence order, clustering threshold and structure of the data makes it that the users have no way of knowing whether better Operational Taxonomic Units (OTUs) could have been obtained with di erent parameters or even whether they correctly represent the data. In these circumstances, there is no choice but to blindly trust them.

Distance-based greedy clustering algorithms such as the ones implemented in OTUclust [ 1 ], VSEARCH [ 13 ], CD-HIT [ 10 ] or USEARCH [ 5 ] all share the same base naive algorithm. While more sophisticated algorithms [ 3, 6, 12, 7, 2 ] could produce better results quality-wise, their runtime would render them unusable on millions of sequences. As the quality of the OTUs is important, we have to nd a way to improve it without increasing the runtime. The di erent available implementations use a variety of heuristics to counterbalance the simplicity of the algorithm but, to the best of our knowledge, no approach has tried to add a measure of uncertainty to the process. This is why, in order to help increase the quality and trustworthiness of the clustering, we propose to add uncertainty to this simple algorithm through the use of fuzzy clustering.

uncertainty to clus2

Adding tering

Distance-based greedy clustering algorithms, such as the one in VSEARCH, produce a number of OTUs and assign each sequence to one of them. The OTU to which a sequence is said to belong to is usually the rst one to be encountered that is su ciently close, i.e. within the speci ed threshold. This makes a sequence belong only to a single OTU and OTUs either completely include or exclude a sequence. While these would not be problems were the clustering optimal, the need for fast algorithms gives rise to results that are not always trustworthy. The OTUs being presented as absolute, the end user has no choice, should consider them correct and cannot know whether the algorithm has encountered ambiguity. We believe that being less strict in the way the OTUs partition sequences would help produce better results from the end user's point of view. To help increase the quality of the clustering and maximize the information that can be gathered from the data, we propose to add uncertainty to the clustering by means of fuzzy sets.

Using fuzzy OTUs allows us to discern the di erence between sequences close to the OTU and sequences extremely far. Using the parameters t1 and t2, we can tune the \detection radius" around OTUs to gather information that would normally be discarded by the clustering algorithm.

Evaluating fuzzy OTUs

An ideal OTU would contain only sequences with a membership value of 1, meaning a group of sequences has been perfectly regrouped with a good threshold and no sequence lies ambiguously on the border. More realistically, a good OTU would contain many sequences with high membership values and little sequences with low values. A bad OTU with the majority of its sequences having low membership values could mean that the algorithm has chosen as a center a sequence on the border of a group or, even worse, between two distinct groups.

We can quickly evaluate the quality of an OTU with this repartition. If we suppose that each sequence lowers the quality of the OTU depending on its membership value, we can use the following formula : Quality(OT U ) = 1

Pi9=1 !i # sequences with membership value i 0:1 # sequences in the OTU with !i being the \cost" of having a sequence with membership value i 0:1.

A problem arises with singletons that always have perfect quality but these can safely be treated separately. A sequence can belong to multiple OTUs due to fuzzy membership. However, in the end, we want each sequence to be assigned to a single OTU. Hence, we have to choose one of the possible OTUs. We have two types of values left from the clustering process : membership and quality. The rst one is based on the distance between the OTU and the sequence and the second one is used to recognize bad OTUs. Choosing the OTU with the best membership value is akin to running VSEARCH. Choosing the OTU with the best quality tends to create bigger OTUs that absorb distant sequences. To better compromise, we can use a linear combination of both values : quality + membership Increasing the importance of the quality reduces the number of OTUs containing sequences. When is low, the \best" OTUs quality-wise absorb very close sequences that would have been attributed to other OTUs. When gets too high, the best OTUs start absorbing all the sequences around them, e ectively acting like an increase of the distance threshold. 4 4.1

Experimental Results

Data

We used our algorithm on a dataset containing 5977 sequences of length between 900 and 3081 for an average of 1442 and taxonomies extracted from the SILVA database. We used a threshold of 0.97 (97% similarity) for determining new OTUs and a threshold of 0.95 for fuzzy membership. For the choice of the OTU for each sequence, we present the results of three strategies : best quality ( = 1 and = 0), compromise ( = 0:5 and = 0:5) and distance ( = 0 and = 1). The comparison with VSEARCH is done using identical parameters when applicable.

The program, dataset and corresponding taxonomy are available on http://projets.isima.fr/sclust/ Expe.html. 4.2 To measure the e ects of introducing uncertainty to the clustering, we consider the computation time, memory usage, number of OTUs, singletons and pairs and average distance in the taxonomy tree between sequences in the same cluster. 4.3

Analysis

Results show that the choice strategy a ects every metric relevant to the quality of the clustering : number of OTUs, singletons and pairs, average misclassi cation. The fuzzy approach uses slightly more memory than VSEARCH but all choice strategies are similar on this metric. When using the default {maxaccepts and {maxrejects values, computation time is lower for VSEARCH. However, when using higher values for these parameters { and thus more precise clustering the computation time is the same for both approaches. We observe that increasing the importance of the quality in the OTU choice strategy lowers the nal number of OTUs. This is due to the fact that some OTUs are initially created centered on isolated sequences near good OTUs. That isolation lowers their quality and the good OTUs absorb their sequences.

Using the quality also lowers the number of singletons and increases the number of pairs. This most likely means that singletons were created close to either good clusters or one another. The fuzzy approach allows the algorithm to merge those sequences that were slightly too far from the center with their corresponding OTU. The increase in the number of pairs appears to be due to the merging of singletons lying too close to one another. The average taxonomy distance in OTUs is shown to vary wildly. Using only the quality to choose OTUs increases this number as the \best" OTUs attract all the sequences in their fuzzy surroundings. This causes some sequences belonging to di erent species to be classi ed together. However, using a compromise between quality and distance lowers this metric as the best clusters only absorb sequences that are su ciently close to them and should probably be together while rejecting the sequences that are too di erent. acknowledgements This work was supported by the European Union's \Fonds Europeen de Developpement Regional (FEDER)" program and the Auvergne-Rhone-Alpes region.

Method Fuzzy (best quality) Fuzzy (compromise)

Fuzzy (distance)

VSEARCH

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