View source for Alignment-free sequence analysis

{{Short description|Methods in computational biology}}
In [[bioinformatics]], '''alignment-free sequence analysis''' approaches to molecular sequence and structure data provide alternatives over alignment-based approaches.<ref name="Vinga"/>

The emergence and need for the analysis of different types of data generated through biological research has given rise to the field of [[bioinformatics]].<ref>{{cite journal | vauthors = Rothberg J, Merriman B, Higgs G | title = Bioinformatics. Introduction | journal = The Yale Journal of Biology and Medicine | volume = 85 | issue = 3 | pages = 305–308 | date = September 2012 | pmid = 23189382 | pmc = 3447194 }}</ref> Molecular sequence and structure data of [[DNA]], [[RNA]], and [[proteins]], [[gene expression]] profiles or [[microarray]] data, [[metabolic pathway]] data are some of the major types of data being analysed in bioinformatics. Among them sequence data is increasing at the exponential rate due to advent of next-generation sequencing technologies. Since the origin of bioinformatics, [[sequence analysis]] has remained the major area of research with wide range of applications in database searching, [[genome annotation]], [[comparative genomics]], [[molecular phylogeny]] and [[gene prediction]]. The pioneering approaches for sequence analysis were based on [[sequence alignment]] either global or local, pairwise or [[multiple sequence alignment]].<ref>{{cite journal | vauthors = Batzoglou S | title = The many faces of sequence alignment | journal = Briefings in Bioinformatics | volume = 6 | issue = 1 | pages = 6–22 | date = March 2005 | pmid = 15826353 | doi = 10.1093/bib/6.1.6 | doi-access = free }}</ref><ref>{{cite journal | vauthors = Mullan L | title = Pairwise sequence alignment--it's all about us! | journal = Briefings in Bioinformatics | volume = 7 | issue = 1 | pages = 113–115 | date = March 2006 | pmid = 16761368 | doi = 10.1093/bib/bbk008 | doi-access =  }}</ref> Alignment-based approaches generally give excellent results when the sequences under study are closely related and can be reliably aligned, but when the sequences are divergent, a reliable alignment cannot be obtained and hence the applications of sequence alignment are limited. Another limitation of alignment-based approaches is their computational complexity and are time-consuming and thus, are limited when dealing with large-scale sequence data.<ref>{{cite journal | vauthors = Kemena C, Notredame C | title = Upcoming challenges for multiple sequence alignment methods in the high-throughput era | journal = Bioinformatics | volume = 25 | issue = 19 | pages = 2455–2465 | date = October 2009 | pmid = 19648142 | pmc = 2752613 | doi = 10.1093/bioinformatics/btp452 }}</ref> The advent of [[next-generation sequencing]] technologies has resulted in generation of voluminous sequencing data. The size of this sequence data poses challenges on alignment-based algorithms in their assembly, annotation and comparative studies.

== Alignment-free methods ==
Alignment-free methods can broadly be classified into five categories: a) methods based on ''k''-mer/word frequency, b) methods based on the length of common substrings, c) methods based on the number of (spaced) word matches, d) methods based on ''micro-alignments'', e) methods based on information theory and f) methods based on graphical representation. Alignment-free approaches have been used in sequence similarity searches,<ref name=Hide>{{cite journal | vauthors = Hide W, Burke J, Davison DB | title = Biological evaluation of d2, an algorithm for high-performance sequence comparison | journal = Journal of Computational Biology | volume = 1 | issue = 3 | pages = 199–215 | date = 1994 | pmid = 8790465 | doi = 10.1089/cmb.1994.1.199 }}</ref> clustering and classification of sequences,<ref name=Miller>{{cite journal | vauthors = Miller RT, Christoffels AG, Gopalakrishnan C, Burke J, Ptitsyn AA, Broveak TR, Hide WA | title = A comprehensive approach to clustering of expressed human gene sequence: the sequence tag alignment and consensus knowledge base | journal = Genome Research | volume = 9 | issue = 11 | pages = 1143–1155 | date = November 1999 | pmid = 10568754 | pmc = 310831 | doi = 10.1101/gr.9.11.1143 }}</ref> and more recently in phylogenetics<ref name="Domazet-Lošo 1466–72"/><ref name=Ragan>{{cite journal | vauthors = Chan CX, Ragan MA | title = Next-generation phylogenomics | journal = Biology Direct | volume = 8 | pages = 3 | date = January 2013 | pmid = 23339707 | pmc = 3564786 | doi = 10.1186/1745-6150-8-3 | doi-access = free }}</ref> ('''Figure 1''').

Such molecular phylogeny analyses employing alignment-free approaches are said to be part of ''next-generation phylogenomics''.<ref name="Ragan"/> A number of review articles provide in-depth review of alignment-free methods in sequence analysis.<ref name=Vinga>{{cite journal | vauthors = Vinga S, Almeida J | title = Alignment-free sequence comparison-a review | journal = Bioinformatics | volume = 19 | issue = 4 | pages = 513–523 | date = March 2003 | pmid = 12611807 | doi = 10.1093/bioinformatics/btg005 | doi-access = free }}</ref><ref name=Song>{{cite journal | vauthors = Song K, Ren J, Reinert G, Deng M, Waterman MS, Sun F | title = New developments of alignment-free sequence comparison: measures, statistics and next-generation sequencing | journal = Briefings in Bioinformatics | volume = 15 | issue = 3 | pages = 343–353 | date = May 2014 | pmid = 24064230 | pmc = 4017329 | doi = 10.1093/bib/bbt067 | author3-link = Gesine Reinert }}</ref><ref name=Haubold>{{cite journal | vauthors = Haubold B | title = Alignment-free phylogenetics and population genetics | journal = Briefings in Bioinformatics | volume = 15 | issue = 3 | pages = 407–418 | date = May 2014 | pmid = 24291823 | doi = 10.1093/bib/bbt083 | doi-access = free }}</ref><ref name=BonhamCarter>{{cite journal | vauthors = Bonham-Carter O, Steele J, Bastola D | title = Alignment-free genetic sequence comparisons: a review of recent approaches by word analysis | journal = Briefings in Bioinformatics | volume = 15 | issue = 6 | pages = 890–905 | date = November 2014 | pmid = 23904502 | pmc = 4296134 | doi = 10.1093/bib/bbt052 }}</ref><ref name=Zielezinski>{{cite journal | vauthors = Zielezinski A, Vinga S, Almeida J, Karlowski WM | title = Alignment-free sequence comparison: benefits, applications, and tools | journal = Genome Biology | volume = 18 | issue = 1 | pages = 186 | date = October 2017 | pmid = 28974235 | pmc = 5627421 | doi = 10.1186/s13059-017-1319-7 | doi-access = free }}</ref><ref name=Bernard>{{cite journal | vauthors = Bernard G, Chan CX, Chan YB, Chua XY, Cong Y, Hogan JM, Maetschke SR, Ragan MA | display-authors = 6 | title = Alignment-free inference of hierarchical and reticulate phylogenomic relationships | journal = Briefings in Bioinformatics | volume = 20 | issue = 2 | pages = 426–435 | date = March 2019 | pmid = 28673025 | pmc = 6433738 | doi = 10.1093/bib/bbx067 }}</ref><ref name=Ren>{{cite journal | vauthors = Ren J, Bai X, Lu YY, Tang K, Wang Y, Reinert G, Sun F | title = Alignment-Free Sequence Analysis and Applications | journal = Annual Review of Biomedical Data Science | volume = 1 | pages = 93–114 | date = July 2018 | pmid = 31828235 | pmc = 6905628 | doi = 10.1146/annurev-biodatasci-080917-013431 | arxiv = 1803.09727 | bibcode = 2018arXiv180309727R }}</ref>

The ''AFproject'' is an international collaboration to benchmark and compare software tools for alignment-free sequence comparison.<ref name="ZielezinskiGirgis2019">{{cite journal | vauthors = Zielezinski A, Girgis HZ, Bernard G, Leimeister CA, Tang K, Dencker T, Lau AK, Röhling S, Choi JJ, Waterman MS, Comin M, Kim SH, Vinga S, Almeida JS, Chan CX, James BT, Sun F, Morgenstern B, Karlowski WM | display-authors = 6 | title = Benchmarking of alignment-free sequence comparison methods | journal = Genome Biology | volume = 20 | issue = 1 | pages = 144 | date = July 2019 | pmid = 31345254 | pmc = 6659240 | doi = 10.1186/s13059-019-1755-7 | doi-access = free }}</ref>

=== Methods based on ''k''-mer/word frequency ===
The popular methods based on ''k''-mer/word frequencies include feature frequency profile (FFP),<ref name="FFP">{{cite journal | vauthors = Sims GE, Jun SR, Wu GA, Kim SH | title = Whole-genome phylogeny of mammals: evolutionary information in genic and nongenic regions | journal = Proceedings of the National Academy of Sciences of the United States of America | volume = 106 | issue = 40 | pages = 17077–17082 | date = October 2009 | pmid = 19805074 | pmc = 2761373 | doi = 10.1073/pnas.0909377106 | doi-access = free | bibcode = 2009PNAS..10617077S }}</ref><ref>{{cite journal | vauthors = Sims GE, Kim SH | title = Whole-genome phylogeny of Escherichia coli/Shigella group by feature frequency profiles (FFPs) | journal = Proceedings of the National Academy of Sciences of the United States of America | volume = 108 | issue = 20 | pages = 8329–8334 | date = May 2011 | pmid = 21536867 | pmc = 3100984 | doi = 10.1073/pnas.1105168108 | doi-access = free | bibcode = 2011PNAS..108.8329S }}</ref> Composition vector (CV),<ref>{{cite journal | vauthors = Gao L, Qi J | title = Whole genome molecular phylogeny of large dsDNA viruses using composition vector method | journal = BMC Evolutionary Biology | volume = 7 | issue = 1 | pages = 41 | date = March 2007 | pmid = 17359548 | pmc = 1839080 | doi = 10.1186/1471-2148-7-41 | doi-access = free | bibcode = 2007BMCEE...7...41G }}</ref><ref>{{cite journal | vauthors = Wang H, Xu Z, Gao L, Hao B | title = A fungal phylogeny based on 82 complete genomes using the composition vector method | journal = BMC Evolutionary Biology | volume = 9 | issue = 1 | pages = 195 | date = August 2009 | pmid = 19664262 | pmc = 3087519 | doi = 10.1186/1471-2148-9-195 | doi-access = free | bibcode = 2009BMCEE...9..195W }}</ref> Return time distribution (RTD),<ref name="RTD1">{{cite journal | vauthors = Kolekar P, Kale M, Kulkarni-Kale U | title = Alignment-free distance measure based on return time distribution for sequence analysis: applications to clustering, molecular phylogeny and subtyping | journal = Molecular Phylogenetics and Evolution | volume = 65 | issue = 2 | pages = 510–522 | date = November 2012 | pmid = 22820020 | doi = 10.1016/j.ympev.2012.07.003 }}</ref> frequency chaos game representation (FCGR).<ref>{{cite journal | vauthors = Hatje K, Kollmar M | title = A phylogenetic analysis of the brassicales clade based on an alignment-free sequence comparison method | journal = Frontiers in Plant Science | volume = 3 | pages = 192 | year = 2012 | pmid = 22952468 | pmc = 3429886 | doi = 10.3389/fpls.2012.00192 | doi-access = free }}</ref> and Spaced Words.<ref name=spaced />

==== Feature frequency profile (FFP) ====
The methodology involved in FFP based method starts by calculating the count of each possible ''k''-mer (possible number of ''k''-mers for nucleotide sequence: 4<sup>k</sup>, while that for protein sequence: 20<sup>k</sup>) in sequences. Each ''k''-mer count in each sequence is then normalized by dividing it by total of all ''k''-mers' count in that sequence. This leads to conversion of each sequence into its feature frequency profile. The pair wise distance between two sequences is then calculated [[Jensen–Shannon divergence|Jensen–Shannon (JS) divergence]] between their respective FFPs. The [[distance matrix]] thus obtained can be used to construct [[phylogenetic tree]] using clustering algorithms like [[neighbor-joining]], [[UPGMA]] etc.

==== Composition vector (CV) ====
In this method frequency of appearance of each possible ''k''-mer in a given sequence is calculated. The next characteristic step of this method is the subtraction of random background of these frequencies using [[Markov model]] to reduce the influence of random neutral [[mutations]] to highlight the role of selective evolution. The normalized frequencies are put a fixed order to form the composition vector (CV) of a given sequence. [[Cosine distance]] function is then used to compute pairwise distance between CVs of sequences. The distance matrix thus obtained can be used to construct phylogenetic tree using clustering algorithms like [[neighbor-joining]], [[UPGMA]] etc. This method can be extended through resort to efficient pattern matching algorithms to include in the computation of the composition vectors: (i) all ''k''-mers for any value of ''k'', (ii) all substrings of any length up to an arbitrarily set maximum ''k'' value, (iii) all maximal substrings, where a substring is maximal if extending it by any character would cause a decrease in its occurrence count.<ref>{{cite journal | vauthors = Apostolico A, Denas O | title = Fast algorithms for computing sequence distances by exhaustive substring composition | journal = Algorithms for Molecular Biology | volume = 3 | pages = 13 | date = October 2008 | pmid = 18957094 | pmc = 2615014 | doi = 10.1186/1748-7188-3-13 | doi-access = free }}</ref><ref>{{cite journal | vauthors = Apostolico A, Denas O, Dress A | title = Efficient tools for comparative substring analysis | journal = Journal of Biotechnology | volume = 149 | issue = 3 | pages = 120–126 | date = September 2010 | pmid = 20682467 | doi = 10.1016/j.jbiotec.2010.05.006 }}</ref>

==== Return time distribution (RTD) ====
The RTD based method does not calculate the count of ''k''-mers in sequences, instead it computes the time required for the reappearance of 
''k''-mers. The time refers to the number of residues in successive appearance of particular ''k''-mer. Thus the occurrence of each ''k''-mer in a sequence is calculated in the form of RTD, which is then summarised using two statistical parameters [[mean]] (μ) and [[standard deviation]] (σ). Thus each sequence is represented in the form of numeric vector of size 2&sdot;4<sup>''k''</sup> containing ''μ'' and ''σ'' of 4<sup>''k''</sup> RTDs. The pair wise distance between sequences is calculated using [[Euclidean distance]] measure. The distance matrix thus obtained can be used to construct phylogenetic tree using clustering algorithms like [[neighbor-joining]], [[UPGMA]] etc. A recent approach Pattern Extraction through Entropy Retrieval (PEER) provides direct detection of the k-mer length and summarised the occurrence interval using entropy.

==== Frequency chaos game representation (FCGR) ====
The FCGR methods have evolved from chaos game representation (CGR) technique, which provides scale independent representation for genomic sequences.<ref name="Jeffrey 2163–70">{{cite journal | vauthors = Jeffrey HJ | title = Chaos game representation of gene structure | journal = Nucleic Acids Research | volume = 18 | issue = 8 | pages = 2163–2170 | date = April 1990 | pmid = 2336393 | pmc = 330698 | doi = 10.1093/nar/18.8.2163 }}</ref> The CGRs can be divided by grid lines where each grid square denotes the occurrence of oligonucleotides of a specific length in the sequence. Such representation of CGRs is termed as Frequency Chaos Game Representation (FCGR). This leads to representation of each sequence into FCGR. The pair wise distance between FCGRs of sequences can be calculated using the Pearson distance, the Hamming distance or the Euclidean distance.<ref>{{cite journal | vauthors = Wang Y, Hill K, Singh S, Kari L | title = The spectrum of genomic signatures: from dinucleotides to chaos game representation | journal = Gene | volume = 346 | pages = 173–185 | date = February 2005 | pmid = 15716010 | doi = 10.1016/j.gene.2004.10.021 }}</ref>

==== Spaced-word frequencies====
While most alignment-free algorithms compare the word-composition of sequences, Spaced Words uses a pattern of care and don't care positions. The occurrence of a spaced word in a sequence is then defined by the characters at the match positions only, while the characters at the don't care positions are ignored.  Instead of comparing the frequencies of contiguous words in the input sequences, this approach compares the frequencies of the spaced words according to the pre-defined pattern.<ref name=spaced/> Note that the pre-defined pattern can be selected by analysis of the [[Variance]] of the number of matches,<ref name=rasbhari>{{cite journal | vauthors = Hahn L, Leimeister CA, Ounit R, Lonardi S, Morgenstern B | title = rasbhari: Optimizing Spaced Seeds for Database Searching, Read Mapping and Alignment-Free Sequence Comparison | journal = PLOS Computational Biology | volume = 12 | issue = 10 | pages = e1005107 | date = October 2016 | pmid = 27760124 | pmc = 5070788 | doi = 10.1371/journal.pcbi.1005107 | arxiv = 1511.04001 | doi-access = free | bibcode = 2016PLSCB..12E5107H }}</ref> the probability of the first occurrence on several models,<ref name=bhit>{{cite journal | vauthors = Noé L | title = Best hits of 11110110111: model-free selection and parameter-free sensitivity calculation of spaced seeds | journal = Algorithms for Molecular Biology | volume = 12 | issue = 1 | pages = 1 | date = Feb 14, 2017 | pmid = 28289437 | pmc = 5310094 | doi = 10.1186/s13015-017-0092-1 | doi-access = free }}</ref> or the [[Pearson correlation coefficient]] between the expected word frequency and the true alignment distance.<ref name=Cov/>

=== Methods based on length of common substrings ===

The methods in this category employ the [[Semantic similarity|similarity]] and differences of substrings in a pair of sequences. These algorithms
were mostly used for string processing in [[computer science]].<ref>{{cite book | vauthors = Gusfield D |title=Algorithms on strings, trees, and sequences: computer science and computational biology |year=1997 |publisher=Cambridge Univ. Press|location=Cambridge [u.a.]|isbn=9780521585194|edition=Reprinted (with corr.)}}</ref>

==== Average common substring (ACS) ====

In this approach, for a chosen pair of sequences (A and B of lengths ''n'' and ''m'' respectively), [[Longest common substring problem|longest substring]] starting at some position is identified in one sequence (A) which exactly matches in the other sequence (B) at any position. In this way, lengths of longest substrings starting at different positions in sequence A and having exact matches at some positions in sequence B are calculated. All these lengths are averaged to derive a measure <math>L(A, B)</math>. Intuitively, larger the <math>L(A, B)</math>, the more similar the two sequences are. To account for the differences in the length of sequences, <math>L(A, B)</math> is normalized [i.e. <math>L(A, B)/\log(m)</math>]. This gives the similarity measure between the sequences.

In order to derive a distance measure, the inverse of [[similarity measure]] is taken and a [[correction term]] is subtracted from it to assure that <math>d(A, A)</math> will be zero. Thus

: <math>d(A, B) = \left [ \frac{\log m}{L(A, B)} \right] - \left[\frac{\log n}{L(A, A)} \right]. </math>

This measure <math>d(A, B)</math> is not symmetric, so one has to compute <math>d_s(A, B) = d_s(B, A) = (d(A, B) + d(B, A))/2</math>, which gives final ACS measure between the two strings (A and B).<ref>{{cite journal | vauthors = Ulitsky I, Burstein D, Tuller T, Chor B | title = The average common substring approach to phylogenomic reconstruction | journal = Journal of Computational Biology | volume = 13 | issue = 2 | pages = 336–350 | date = March 2006 | pmid = 16597244 | doi = 10.1089/cmb.2006.13.336 | citeseerx = 10.1.1.106.5122 }}</ref> The subsequence/substring search can be efficiently performed by
using [[suffix tree]]s.<ref>{{cite book| vauthors = Weiner P |doi=10.1109/SWAT.1973.13|title=14th Annual Symposium on Switching and Automata Theory (swat 1973)|pages=1–11|year=1973|chapter=Linear pattern matching algorithms|citeseerx=10.1.1.474.9582}}</ref><ref>{{cite book| vauthors = He D |title=2006 International Conference of the IEEE Engineering in Medicine and Biology Society |chapter=Using suffix tree to discover complex repetitive patterns in DNA sequences |year=2006|volume=1|pages=3474–7|pmid=17945779|doi=10.1109/IEMBS.2006.260445|isbn=978-1-4244-0032-4|s2cid=5953866}}</ref><ref>{{cite journal | vauthors = Välimäki N, Gerlach W, Dixit K, Mäkinen V | title = Compressed suffix tree--a basis for genome-scale sequence analysis | journal = Bioinformatics | volume = 23 | issue = 5 | pages = 629–630 | date = March 2007 | pmid = 17237063 | doi = 10.1093/bioinformatics/btl681 | doi-access = free }}</ref>

==== ''k''-mismatch average common substring approach (kmacs) ====
This approach is a generalization of the ACS approach. To define the distance between two DNA or protein sequences, kmacs estimates for each position ''i'' of the first sequence the longest substring starting at ''i'' and matching a substring of the second sequence with up to ''k'' mismatches. It defines the average of these values as a measure of similarity between the sequences and turns this into a symmetric distance measure. Kmacs does not compute exact ''k''-mismatch substrings, since this would be computational too costly, but approximates such substrings.<ref name=kmacs/>

==== Mutation distances (Kr) ====

This approach is closely related to the ACS, which calculates the number of substitutions per site between two DNA sequences using the shortest 
absent substring (termed as {{Not a typo|shustring}}).<ref>{{cite journal | vauthors = Haubold B, Pfaffelhuber P, Domazet-Loso M, Wiehe T | title = Estimating mutation distances from unaligned genomes | journal = Journal of Computational Biology | volume = 16 | issue = 10 | pages = 1487–1500 | date = October 2009 | pmid = 19803738 | doi = 10.1089/cmb.2009.0106 | hdl-access = free | hdl = 11858/00-001M-0000-000F-D624-D }}</ref>

==== Length distribution of k-mismatch common substrings ====

This approach uses the program kmacs<ref name=kmacs/> to calculate [[longest common substring]]s with up to ''k'' mismatches for a pair of DNA sequences. The phylogenetic distance between the sequences can then be estimated from a local maximum in the length distribution of the k-mismatch common substrings.<ref>{{cite journal | vauthors = Morgenstern B, Schöbel S, Leimeister CA | title = Phylogeny reconstruction based on the length distribution of ''k''-mismatch common substrings | journal = Algorithms for Molecular Biology | volume = 12 | pages = 27 | date = 2017 | pmid = 29238399 | pmc = 5724348 | doi = 10.1186/s13015-017-0118-8 | doi-access = free }}</ref>

=== Methods based on the number of (spaced) word matches ===

==== <math>D_2^S</math> and <math>D_2^*</math> ====
These approachese are variants of the <math>D_2</math> statistics that counts the number of <math>k</math>-mer matches between two sequences. They improve the simple <math>D_2</math> statistics by taking the background distribution of the compared sequences into account.<ref>{{cite journal | vauthors = Reinert G, Chew D, Sun F, Waterman MS | title = Alignment-free sequence comparison (I): statistics and power | journal = Journal of Computational Biology | volume = 16 | issue = 12 | pages = 1615–1634 | date = December 2009 | pmid = 20001252 | pmc = 2818754 | doi = 10.1089/cmb.2009.0198 }}</ref>

====  MASH ====
This is an extremely fast method that uses the MinHash bottom sketch strategy for estimating the [[Jaccard index]] of the multi-sets of <math>k</math>-mers of two input sequences. That is, it estimates the ratio of  <math>k</math>-mer matches to the total number of  <math>k</math>-mers of the sequences. This can be used, in turn, to estimate the evolutionary distances between the compared sequences, measured as the number of substitutions per sequence position since the sequences evolved from their last common ancestor.<ref>{{cite journal | vauthors = Ondov BD, Treangen TJ, Melsted P, Mallonee AB, Bergman NH, Koren S, Phillippy AM | title = Mash: fast genome and metagenome distance estimation using MinHash | journal = Genome Biology | volume = 17 | issue = 1 | pages = 132 | date = June 2016 | pmid = 27323842 | pmc = 4915045 | doi = 10.1186/s13059-016-0997-x | doi-access = free }}</ref>

==== Slope-Tree ====
This approach calculates a distance value between two protein sequences based on the decay of the number of  <math>k</math>-mer matches if <math>k</math> increases.<ref>{{cite journal | vauthors = Bromberg R, Grishin NV, Otwinowski Z | title = Phylogeny Reconstruction with Alignment-Free Method That Corrects for Horizontal Gene Transfer | journal = PLOS Computational Biology | volume = 12 | issue = 6 | pages = e1004985 | date = June 2016 | pmid = 27336403 | pmc = 4918981 | doi = 10.1371/journal.pcbi.1004985 | doi-access = free | bibcode = 2016PLSCB..12E4985B }}</ref>

==== Slope-SpaM ====
This method calculates the number <math>N_k</math> of <math>k</math>-mer or spaced-word matches 
(''SpaM'') for different values for the word length or number of match positions <math>k</math> in the underlying pattern, respectively. The slope of an affine-linear function  <math>F</math> that depends on <math>N_k</math> is calculated to estimate the Jukes-Cantor distance between the input sequences .<ref>{{cite journal | vauthors = Röhling S, Linne A, Schellhorn J, Hosseini M, Dencker T, Morgenstern B | title = The number of k-mer matches between two DNA sequences as a function of k and applications to estimate phylogenetic distances | journal = PLOS ONE | volume = 15 | issue = 2 | pages = e0228070 | date = 2020 | pmid = 32040534 | pmc = 7010260 | doi = 10.1371/journal.pone.0228070 | doi-access = free | bibcode = 2020PLoSO..1528070R }}</ref>

==== Skmer ====
''Skmer'' calculates distances between species from unassembled sequencing reads. Similar to ''MASH'', it uses the [[Jaccard index]] on the sets of <math>k</math>-mers from the input sequences. In contrast to ''MASH'', the program is still accurate for low sequencing coverage, so it can be used for [[genome skimming]].<ref>{{cite journal | vauthors = Sarmashghi S, Bohmann K, P Gilbert MT, Bafna V, Mirarab S | title = Skmer: assembly-free and alignment-free sample identification using genome skims | journal = Genome Biology | volume = 20 | issue = 1 | pages = 34 | date = February 2019 | pmid = 30760303 | pmc = 6374904 | doi = 10.1186/s13059-019-1632-4 | doi-access = free }}</ref>

=== Methods based on micro-alignments ===

Strictly spoken, these methods are not ''alignment-free''. They are using simple gap-free ''micro-alignments'' where sequences are required to match at certain pre-defined positions. The positions aligned at the remaining positions of the ''micro-alignments'' where mismatches are allowed, are then used for phylogeny inference.

==== Co-phylog ====

This method searches for so-called ''structures'' that are defined as pairs of ''k''-mer matches between two DNA sequences that are one position apart in both sequences. The two ''k''-mer matches are called the ''context'', the position between them is called the ''object''. Co-phylog then defines the distance between two sequences the fraction of such ''structures'' for which the two nucleotides in the ''object'' are different. The approach can be applied to unassembled sequencing reads.<ref name="Co-phylog: an assembly-free phyloge">{{cite journal | vauthors = Yi H, Jin L | title = Co-phylog: an assembly-free phylogenomic approach for closely related organisms | journal = Nucleic Acids Research | volume = 41 | issue = 7 | pages = e75 | date = April 2013 | pmid = 23335788 | pmc = 3627563 | doi = 10.1093/nar/gkt003 }}</ref>

==== andi ====

andi estimates phylogenetic distances between genomic sequences based on ungapped local alignments that are flanked by maximal exact word matches. Such word matches can be efficiently found using suffix arrays. The gapfree alignments between the exact word matches are then used to estimate phylogenetic distances between genome sequences. The resulting distance estimates are accurate for up to around 0.6  substitutions per position.<ref>{{cite journal | vauthors = Haubold B, Klötzl F, Pfaffelhuber P | title = andi: fast and accurate estimation of evolutionary distances between closely related genomes | journal = Bioinformatics | volume = 31 | issue = 8 | pages = 1169–1175 | date = April 2015 | pmid = 25504847 | doi = 10.1093/bioinformatics/btu815 | doi-access = free }}</ref>

==== Filtered Spaced-Word Matches (FSWM) ====

FSWM uses a pre-defined binary pattern ''P'' representing so-called ''match positions'' and ''don't-care positions''. For a pair of input DNA sequences, it then searches for ''spaced-word matches'' w.r.t. ''P'', i.e. for local gap-free alignments with matching nucleotides at the ''match positions'' of ''P'' and possible mismatches at the ''don't-care positions''. Spurious low-scoring spaced-word matches are discarded, evolutionary distances between the input sequences are estimated based on the nucleotides aligned to each other at the ''don't-care positions'' of the remaining, homologous spaced-word matches.<ref name="Leimeister 2017 971–979">{{cite journal | vauthors = Leimeister CA, Sohrabi-Jahromi S, Morgenstern B | title = Fast and accurate phylogeny reconstruction using filtered spaced-word matches | journal = Bioinformatics | volume = 33 | issue = 7 | pages = 971–979 | date = April 2017 | pmid = 28073754 | pmc = 5409309 | doi = 10.1093/bioinformatics/btw776 }}</ref> FSWM has been adapted to estimate distances based on unassembled NGS reads, this version of the program is called ''Read-SpaM''.<ref>{{cite journal | vauthors = Lau AK, Dörrer S, Leimeister CA, Bleidorn C, Morgenstern B | title = Read-SpaM: assembly-free and alignment-free comparison of bacterial genomes with low sequencing coverage | journal = BMC Bioinformatics | volume = 20 | issue = Suppl 20 | pages = 638 | date = December 2019 | pmid = 31842735 | pmc = 6916211 | doi = 10.1186/s12859-019-3205-7 | doi-access = free }}</ref>

==== Prot-SpaM ====

Prot-SpaM (<u>Prot</u>eome-based <u>Spa</u>ced-word <u>M</u>atches) is an implementation of the FSWM algorithm for partial or whole proteome sequences.<ref name="Leimeister 2018 giy148">{{cite journal | vauthors = Leimeister CA, Schellhorn J, Dörrer S, Gerth M, Bleidorn C, Morgenstern B | title = Prot-SpaM: fast alignment-free phylogeny reconstruction based on whole-proteome sequences | journal = GigaScience | volume = 8 | issue = 3 | pages = giy148 | date = March 2019 | pmid = 30535314 | pmc = 6436989 | doi = 10.1093/gigascience/giy148 }}</ref>

==== Multi-SpaM ====

Multi-SpaM (<u>Multi</u>ple<u>Spa</u>ced-word <u>M</u>atches) is an approach to genome-based phylogeny reconstruction that extends the FSWM idea to multiple sequence comparison.<ref>{{cite journal | vauthors = Dencker T, Leimeister CA, Gerth M, Bleidorn C, Snir S, Morgenstern B | title = 'Multi-SpaM': a maximum-likelihood approach to phylogeny reconstruction using multiple spaced-word matches and quartet trees | journal = NAR Genomics and Bioinformatics | volume = 2 | issue = 1 | pages = lqz013 | date = March 2020 | pmid = 33575565 | pmc = 7671388 | doi = 10.1093/nargab/lqz013 | doi-access = free }}</ref> Given a binary pattern ''P'' of ''match positions'' and ''don't-care positions'', the program searches for ''P''-blocks, i.e. local gap-free four-way alignments with matching nucleotides at the ''match positions'' of ''P'' and possible mismatches at the ''don't-care positions''.  Such four-way alignments are randomly sampled from a set of input genome sequences. For each  ''P''-block, an unrooted tree topology is calculated using ''RAxML''.<ref>{{cite journal | vauthors = Stamatakis A | title = RAxML-VI-HPC: maximum likelihood-based phylogenetic analyses with thousands of taxa and mixed models | journal = Bioinformatics | volume = 22 | issue = 21 | pages = 2688–2690 | date = November 2006 | pmid = 16928733 | doi = 10.1093/bioinformatics/btl446 | doi-access = free }}</ref> The program ''Quartet MaxCut'' is then used to calculate a supertree from these trees.

=== Methods based on information theory ===

[[Information Theory]] has provided successful methods for alignment-free sequence analysis and comparison. The existing applications of information theory include global and local characterization of DNA, RNA and proteins, estimating genome entropy to motif and region classification. It also holds promise in [[gene mapping]], [[next-generation sequencing]] analysis and [[metagenomics]].<ref>{{cite journal | vauthors = Vinga S | title = Information theory applications for biological sequence analysis | journal = Briefings in Bioinformatics | volume = 15 | issue = 3 | pages = 376–389 | date = May 2014 | pmid = 24058049 | pmc = 7109941 | doi = 10.1093/bib/bbt068 | doi-access = free }}</ref>

==== Base–base correlation (BBC) ====

Base–base correlation (BBC) converts the genome sequence into a unique 16-dimensional numeric vector using the following equation,

: <math>T_{ij}(K) = \sum_{\ell=1}^K P_{ij}(\ell) \cdot \log_2 \left ( \frac{P_{ij}(\ell)}{P_i P_j} \right)</math>

The <math>P_i</math> and <math>P_j</math> denotes the probabilities of bases ''i'' and ''j'' in the genome. The <math>P_{ij}(\ell)</math> indicates the probability of bases ''i'' and ''j'' at distance ''ℓ'' in the genome. The parameter ''K'' indicates the maximum distance between the bases ''i'' and ''j''. The variation in the values of 16 parameters reflect variation in the genome content and length.<ref>{{cite journal | vauthors = Liu Z, Meng J, Sun X | title = A novel feature-based method for whole genome phylogenetic analysis without alignment: application to HEV genotyping and subtyping | journal = Biochemical and Biophysical Research Communications | volume = 368 | issue = 2 | pages = 223–230 | date = April 2008 | pmid = 18230342 | doi = 10.1016/j.bbrc.2008.01.070 }}</ref><ref>{{cite journal | vauthors = Liu ZH, Sun X | title = Coronavirus phylogeny based on base-base correlation | journal = International Journal of Bioinformatics Research and Applications | volume = 4 | issue = 2 | pages = 211–220 | year = 2008 | pmid = 18490264 | doi = 10.1504/ijbra.2008.018347 }}</ref><ref>{{cite journal | vauthors = Cheng J, Zeng X, Ren G, Liu Z | title = CGAP: a new comprehensive platform for the comparative analysis of chloroplast genomes | journal = BMC Bioinformatics | volume = 14 | pages = 95 | date = March 2013 | pmid = 23496817 | pmc = 3636126 | doi = 10.1186/1471-2105-14-95 | doi-access = free }}</ref>

==== Information correlation and partial information correlation (IC-PIC) ====
IC-PIC ([[information correlation]] and partial information correlation) based method employs the base correlation property of DNA sequence. IC and PIC were calculated using following formulas,

: <math> IC_\ell = -2 \sum_i P_i \log_2 P_i + \sum_{ij} P_{ij} (\ell) \log_2 P_{ij} (\ell)</math>

: <math> PIC_{ij} (\ell) = (P_{ij} (\ell) - P_i P_j (\ell))^2</math>

The final vector is obtained as follows:

: <math>V = {IC_\ell \over PIC_{ij} (\ell)} \text{ where } \ell \isin \left \{ \ell_0, \ell_0 + 1, \ldots, \ell_0 + n \right \}, </math>

which defines the range of distance between bases.<ref>{{cite journal | vauthors = Gao Y, Luo L | title = Genome-based phylogeny of dsDNA viruses by a novel alignment-free method | journal = Gene | volume = 492 | issue = 1 | pages = 309–314 | date = January 2012 | pmid = 22100880 | doi = 10.1016/j.gene.2011.11.004 }}</ref>

The pairwise distance between sequences is calculated using [[Euclidean distance]] measure. The distance matrix thus obtained can be used to construct phylogenetic tree using clustering algorithms like [[neighbor-joining]], [[UPGMA]], etc..

==== Compression ====
Examples are effective approximations to [[Kolmogorov complexity]], for example [[Lempel-Ziv complexity]]. In general compression-based methods use the [[mutual information]] between the sequences. This is expressed in conditional [[Kolmogorov complexity]], that is, the length of the shortest self-delimiting program required to generate a string given the prior knowledge of the other string. This measure has a relation to measuring ''k''-words in a sequence, as they can be easily used to generate the sequence. It is sometimes a computationally intensive method. The theoretic basis for the [[Kolmogorov complexity]] approach was 
laid by Bennett, Gacs, Li, Vitanyi, and Zurek (1998) by proposing the  [[information distance]].<ref>Bennett, C.H., Gacs, P., Li, M., Vitanyi, P. and Zurek, W., Information distance, IEEE Trans. Inform. Theory, 44, 1407--1423</ref> The [[Kolmogorov complexity]] being incomputable it was approximated by compression algorithms. The better they compress the better they are. Li, Badger, Chen, Kwong,, Kearney, and Zhang (2001) used a non-optimal but normalized form of this approach,<ref>Li, M., Badger, J.H., Chen, X., Kwong, S., Kearney, P. and
Zhang, H., (2001) An information-based sequence distance and
its application to whole mitochondrial genome phylogeny.
Bioinformatics, 17:(2001), 149--154</ref> and the optimal normalized form by Li, Chen, Li, Ma, and Vitanyi (2003) appeared in <ref>M. Li, X. Chen, X. Li, B. Ma, P.M.B. Vitanyi.
The similarity metric, IEEE Trans. Inform. Th., 50:12(2004),
3250--3264</ref> and more extensively and proven by Cilibrasi and Vitanyi (2005) in.<ref>R.L. Cilibrasi and P.M.B. Vitanyi, Clustering by compression,
IEEE Trans. Informat. Th., 51:4(2005), 1523--1545</ref>
Otu and Sayood (2003) used the [[Lempel-Ziv complexity]] method to construct five different distance measures for [[phylogenetic tree]] construction.<ref>{{cite journal | vauthors = Otu HH, Sayood K | title = A new sequence distance measure for phylogenetic tree construction | journal = Bioinformatics | volume = 19 | issue = 16 | pages = 2122–2130 | date = November 2003 | pmid = 14594718 | doi = 10.1093/bioinformatics/btg295 | doi-access = free }}</ref>

==== Context modeling compression ====

In the context modeling complexity the next-symbol predictions, of one or more statistical models, are combined or competing to yield a prediction that is based on events recorded in the past. The algorithmic information content derived from each symbol prediction can be used to compute algorithmic information profiles with a time proportional to the length of the sequence. The process has been applied to DNA sequence analysis.<ref>{{cite journal | vauthors = Pinho AJ, Garcia SP, Pratas D, Ferreira PJ | title = DNA sequences at a glance | journal = PLOS ONE | volume = 8 | issue = 11 | pages = e79922 | date = Nov 21, 2013 | pmid = 24278218 | pmc = 3836782 | doi = 10.1371/journal.pone.0079922 | doi-access = free | bibcode = 2013PLoSO...879922P }}</ref>

=== Methods based on graphical representation ===

==== Iterated maps ====
The use of iterated maps for sequence analysis was first introduced by HJ Jefferey in 1990<ref name="Jeffrey 2163–70"/> when he proposed to apply the [[Chaos game|Chaos Game]] to map genomic sequences into a unit square. That report coined the procedure as Chaos Game Representation (CGR). However, only 3 years later this approach was first dismissed as a projection of a Markov transition table by N Goldman.<ref>{{cite journal | vauthors = Goldman N | title = Nucleotide, dinucleotide and trinucleotide frequencies explain patterns observed in chaos game representations of DNA sequences | journal = Nucleic Acids Research | volume = 21 | issue = 10 | pages = 2487–2491 | date = May 1993 | pmid = 8506142 | pmc = 309551 | doi = 10.1093/nar/21.10.2487 }}</ref> This objection was overruled by the end of that decade when the opposite was found to be the case – that CGR bijectively maps Markov transition is into a fractal, order-free (degree-free) representation.<ref>{{cite journal | vauthors = Almeida JS, Carriço JA, Maretzek A, Noble PA, Fletcher M | title = Analysis of genomic sequences by Chaos Game Representation | journal = Bioinformatics | volume = 17 | issue = 5 | pages = 429–437 | date = May 2001 | pmid = 11331237 | doi = 10.1093/bioinformatics/17.5.429 | doi-access = free }}</ref> The realization that iterated maps provide a bijective map between the symbolic space and numeric space led to the identification of a variety of alignment-free approaches to sequence comparison and characterization. These developments were reviewed in late 2013 by JS Almeida in.<ref>{{cite journal | vauthors = Almeida JS | title = Sequence analysis by iterated maps, a review | journal = Briefings in Bioinformatics | volume = 15 | issue = 3 | pages = 369–375 | date = May 2014 | pmid = 24162172 | pmc = 4017330 | doi = 10.1093/bib/bbt072 }}</ref> A number of web apps such as https://github.com/usm/usm.github.com/wiki,<ref name="Almeida 12">{{cite journal | vauthors = Almeida JS, Grüneberg A, Maass W, Vinga S | title = Fractal MapReduce decomposition of sequence alignment | journal = Algorithms for Molecular Biology | volume = 7 | issue = 1 | pages = 12 | date = May 2012 | pmid = 22551205 | pmc = 3394223 | doi = 10.1186/1748-7188-7-12 | doi-access = free }}</ref> are available to demonstrate how to encode and compare arbitrary symbolic sequences in a manner that takes full advantage of modern [[MapReduce]] distribution developed for cloud computing.

== Comparison of alignment based and alignment-free methods ==
{| class="wikitable"
|-
! Alignment-based methods !! Alignment-free methods
|-
| These methods assume that homologous regions are contiguous (with gaps) || Does not assume such contiguity of homologous regions
|-
| Computes all possible pairwise comparisons of sequences; hence computationally expensive || Based on occurrences of sub-sequences; composition; computationally inexpensive, can be memory-intensive
|-
| Well-established approach in phylogenomics || Relatively recent and application in phylogenomics is limited; needs further testing for robustness and scalability
|-
| Requires substitution/evolutionary models || Less dependent on substitution/evolutionary models
|-
| Sensitive to stochastic sequence variation, recombination, horizontal (or lateral) genetic transfer, rate heterogeneity and sequences of varied lengths, especially when similarity lies in the "twilight zone" || Less sensitive to stochastic sequence variation, recombination, horizontal (or lateral) genetic transfer, rate heterogeneity and sequences of varied lengths
|-
| Best practice uses inference algorithms with complexity at least O(n<sup>2</sup>); less time-efficient || Inference algorithms typically O(n<sup>2</sup>) or less; more time-efficient
|-
| Heuristic in nature; statistical significance of how alignment scores relate to homology is difficult to assess || Exact solutions; statistical significance of the sequence distances (and degree of similarity) can be readily assessed
|-
|Relies on dynamic programming (computationally expensive) to find alignment that has optimal score.
|side-steps computational expensive dynamic programming by indexing word counts or positions in fractal space.<ref>{{cite journal | vauthors = Vinga S, Carvalho AM, Francisco AP, Russo LM, Almeida JS | title = Pattern matching through Chaos Game Representation: bridging numerical and discrete data structures for biological sequence analysis | journal = Algorithms for Molecular Biology | volume = 7 | issue = 1 | pages = 10 | date = May 2012 | pmid = 22551152 | pmc = 3402988 | doi = 10.1186/1748-7188-7-10 | doi-access = free }}</ref>
|}

== Applications of alignment-free methods ==
* Genomic rearrangements<ref name="rearrang">{{cite journal | vauthors = Pratas D, Silva RM, Pinho AJ, Ferreira PJ | title = An alignment-free method to find and visualise rearrangements between pairs of DNA sequences | journal = Scientific Reports | volume = 5 | pages = 10203 | date = May 2015 | pmid = 25984837 | pmc = 4434998 | doi = 10.1038/srep10203 | number = 10203 | bibcode = 2015NatSR...510203P }}</ref><ref name="smashpp">{{cite journal | vauthors = Hosseini M, Pratas D, Morgenstern B, Pinho AJ | title = Smash++: an alignment-free and memory-efficient tool to find genomic rearrangements | journal = GigaScience | volume = 9 | issue = 5 | pages = giaa048 | date = May 2020 | pmid = 32432328 | pmc = 7238676 | doi = 10.1093/gigascience/giaa048 | doi-access = free }}</ref>
* Molecular phylogenetics<ref name=Ragan /><ref name=Bernard /><ref>{{cite journal | vauthors = Bernard G, Greenfield P, Ragan MA, Chan CX | title = ''k''-mer Similarity, Networks of Microbial Genomes, and Taxonomic Rank | journal = mSystems | volume = 3 | issue = 6 | pages = e00257–18 | date = Nov 20, 2018 | pmid = 30505941 | pmc = 6247013 | doi = 10.1128/mSystems.00257-18 | ref = Bernard2 }}</ref>
* Metagenomics<ref name="NGS">{{cite journal | vauthors = Song K, Ren J, Reinert G, Deng M, Waterman MS, Sun F | title = New developments of alignment-free sequence comparison: measures, statistics and next-generation sequencing | journal = Briefings in Bioinformatics | volume = 15 | issue = 3 | pages = 343–353 | date = May 2014 | pmid = 24064230 | pmc = 4017329 | doi = 10.1093/bib/bbt067 }}</ref><ref name="Metagenomics2">{{cite journal | vauthors = Břinda K, Sykulski M, Kucherov G | title = Spaced seeds improve k-mer-based metagenomic classification | journal = Bioinformatics | volume = 31 | issue = 22 | pages = 3584–3592 | date = November 2015 | pmid = 26209798 | doi = 10.1093/bioinformatics/btv419 | arxiv = 1502.06256 | s2cid = 8626694 | bibcode = 2015Bioin..31.3584B }}</ref><ref name="CLARK-S">{{cite journal | vauthors = Ounit R, Lonardi S | title = Higher classification sensitivity of short metagenomic reads with CLARK-S | journal = Bioinformatics | volume = 32 | issue = 24 | pages = 3823–3825 | date = December 2016 | pmid = 27540266 | doi = 10.1093/bioinformatics/btw542 | doi-access = free }}</ref><ref name="falcon">{{cite bioRxiv | vauthors = Pratas D, Pinho AJ, Silva RM, Rodrigues JM, Hosseini M, Caetano T, Ferreira PJ |title=FALCON: a method to infer metagenomic composition of ancient DNA |date=February 2018 |biorxiv= 10.1101/267179 }}</ref><ref name="kraken">{{cite journal | vauthors = Wood DE, Salzberg SL | title = Kraken: ultrafast metagenomic sequence classification using exact alignments | journal = Genome Biology | volume = 15 | issue = 3 | pages = R46 | date = March 2014 | pmid = 24580807 | pmc = 4053813 | doi = 10.1186/gb-2014-15-3-r46 | doi-access = free }}</ref>
* Next generation sequence data analysis<ref name=NGS /><ref name=Cov>{{cite journal | vauthors = Noé L, Martin DE | title = A coverage criterion for spaced seeds and its applications to support vector machine string kernels and k-mer distances | journal = Journal of Computational Biology | volume = 21 | issue = 12 | pages = 947–963 | date = December 2014 | pmid = 25393923 | pmc = 4253314 | doi = 10.1089/cmb.2014.0173 | arxiv = 1412.2587 | bibcode = 2014arXiv1412.2587N }}</ref>
* Epigenomics<ref>{{cite journal | vauthors = Pinello L, Lo Bosco G, Yuan GC | title = Applications of alignment-free methods in epigenomics | journal = Briefings in Bioinformatics | volume = 15 | issue = 3 | pages = 419–430 | date = May 2014 | pmid = 24197932 | pmc = 4017331 | doi = 10.1093/bib/bbt078 }}</ref> 
* Barcoding of species<ref>{{cite journal | vauthors = La Rosa M, Fiannaca A, Rizzo R, Urso A | title = Alignment-free analysis of barcode sequences by means of compression-based methods | journal = BMC Bioinformatics | volume = 14 | issue = Suppl 7 | pages = S4 | year = 2013 | pmid = 23815444 | pmc = 3633054 | doi = 10.1186/1471-2105-14-S7-S4 | doi-access = free }}</ref> 
* Population genetics<ref name="Haubold"/> 
* Horizontal gene transfer<ref name="Domazet-Lošo 1466–72">{{cite journal | vauthors = Domazet-Lošo M, Haubold B | title = Alignment-free detection of local similarity among viral and bacterial genomes | journal = Bioinformatics | volume = 27 | issue = 11 | pages = 1466–1472 | date = June 2011 | pmid = 21471011 | doi = 10.1093/bioinformatics/btr176 | doi-access = free }}</ref> 
* Sero/genotyping of viruses<ref name=RTD1 /><ref name="RTD3">{{cite journal | vauthors = Kolekar P, Hake N, Kale M, Kulkarni-Kale U | title = WNV Typer: a server for genotyping of West Nile viruses using an alignment-free method based on a return time distribution | journal = Journal of Virological Methods | volume = 198 | pages = 41–55 | date = March 2014 | pmid = 24388930 | doi = 10.1016/j.jviromet.2013.12.012 | doi-access = free }}</ref><ref name="COMET">{{cite journal | vauthors = Struck D, Lawyer G, Ternes AM, Schmit JC, Bercoff DP | title = COMET: adaptive context-based modeling for ultrafast HIV-1 subtype identification | journal = Nucleic Acids Research | volume = 42 | issue = 18 | pages = e144 | date = October 2014 | pmid = 25120265 | pmc = 4191385 | doi = 10.1093/nar/gku739 }}</ref>
* Allergenicity prediction<ref name="AllergenFP">{{cite journal | vauthors = Dimitrov I, Naneva L, Doytchinova I, Bangov I | title = AllergenFP: allergenicity prediction by descriptor fingerprints | journal = Bioinformatics | volume = 30 | issue = 6 | pages = 846–851 | date = March 2014 | pmid = 24167156 | doi = 10.1093/bioinformatics/btt619 | doi-access = free }}</ref>
* SNP discovery<ref name="SNP">{{cite journal | vauthors = Gardner SN, Hall BG | title = When whole-genome alignments just won't work: kSNP v2 software for alignment-free SNP discovery and phylogenetics of hundreds of microbial genomes | journal = PLOS ONE | volume = 8 | issue = 12 | pages = e81760 | date = Dec 9, 2013 | pmid = 24349125 | pmc = 3857212 | doi = 10.1371/journal.pone.0081760 | doi-access = free | bibcode = 2013PLoSO...881760G }}</ref>
* Recombination detection<ref name="rush">{{cite journal | vauthors = Haubold B, Krause L, Horn T, Pfaffelhuber P | title = An alignment-free test for recombination | journal = Bioinformatics | volume = 29 | issue = 24 | pages = 3121–3127 | date = December 2013 | pmid = 24064419 | pmc = 5994939 | doi = 10.1093/bioinformatics/btt550 }}</ref>
* Viral Classification <ref name=landscape>{{cite journal | vauthors = Silva JM, Pratas D, Caetano T, Matos S | title = The complexity landscape of viral genomes | journal = GigaScience | volume = 11 | pages = 1–16 | date = August 2022 | pmid = 35950839 | pmc = 9366995 | doi = 10.1093/gigascience/giac079 }}</ref>
* Archaea Taxonomic Identification<ref>{{Citation | vauthors = Silva JM, Pratas D, Caetano T, Matos S |title=Feature-Based Classification of Archaeal Sequences Using Compression-Based Methods |date=2022 |url=https://link.springer.com/10.1007/978-3-031-04881-4_25 |work=Pattern Recognition and Image Analysis |volume=13256 |pages=309–320 | veditors = Pinho AJ, Georgieva P, Teixeira LF, Sánchez JA |place=Cham |publisher=Springer International Publishing |language=en |doi=10.1007/978-3-031-04881-4_25 |isbn=978-3-031-04880-7 |access-date=2022-08-31 |series=Lecture Notes in Computer Science }}</ref>
* Taxonomic Classification<ref name=":1">{{Cite journal |last1=Silva |first1=Jorge Miguel |last2=Almeida |first2=João Rafael |date=2024-10-01 |title=Enhancing metagenomic classification with compression-based features |url=https://linkinghub.elsevier.com/retrieve/pii/S0933365724001908 |journal=Artificial Intelligence in Medicine |volume=156 |pages=102948 |doi=10.1016/j.artmed.2024.102948 |pmid=39173422 |issn=0933-3657|doi-access=free }}</ref>
* Temporal Analysis<ref name=":2">{{Cite journal |last1=Silva |first1=Jorge M |last2=Pinho |first2=Armando J |last3=Pratas |first3=Diogo |date=2024 |title=AltaiR: a C toolkit for alignment-free and temporal analysis of multi-FASTA data |journal=GigaScience |volume=13 |doi=10.1093/gigascience/giae086 |issn=2047-217X |pmc=11590114 |pmid=39589438}}</ref>
* Low-complexity Regions Identification<ref name=":0">{{cite journal | vauthors = Silva JM, Qi W, Pinho AJ, Pratas D | title = AlcoR: alignment-free simulation, mapping, and visualization of low-complexity regions in biological data | journal = GigaScience | volume = 12 | date = December 2022 | pmid = 38091509 | pmc = 10716826 | doi = 10.1093/gigascience/giad101 }}</ref>

== List of web servers/software for alignment-free methods ==
{| class="wikitable"
|-
! Name !! Description !! Availability !! Reference
|-
| Protcomp || Most Expressed Features scoring approach || [https://yadamp.unisa.it/PROTCOMP PROTCOMP] || <ref name=protcomp>{{cite conference | vauthors = Di Biasi L, Piotto S | title = ARISE: Artificial Intelligence Semantic Search Engine | conference = WIVACE2021 }}</ref>  
|-
| kmacs || ''k''-mismatch average common substring approach || [http://kmacs.gobics.de/ kmacs] || <ref name=kmacs>{{cite journal | vauthors = Leimeister CA, Morgenstern B | title = Kmacs: the k-mismatch average common substring approach to alignment-free sequence comparison | journal = Bioinformatics | volume = 30 | issue = 14 | pages = 2000–2008 | date = July 2014 | pmid = 24828656 | pmc = 4080746 | doi = 10.1093/bioinformatics/btu331 }}</ref>  
|-
| Spaced words || Spaced-word frequencies || [http://spaced.gobics.de/ spaced-words] || <ref name=spaced>{{cite journal | vauthors = Leimeister CA, Boden M, Horwege S, Lindner S, Morgenstern B | title = Fast alignment-free sequence comparison using spaced-word frequencies | journal = Bioinformatics | volume = 30 | issue = 14 | pages = 1991–1999 | date = July 2014 | pmid = 24700317 | pmc = 4080745 | doi = 10.1093/bioinformatics/btu177 }}</ref> 
|-
| Co-phylog || assembly-free micro-alignment approach || [https://github.com/yhg926/co-phylog Co-phylog] || <ref name="Co-phylog: an assembly-free phyloge"/>
|-
|Prot-SpaM || Proteome-based spaced-word matches || [https://github.com/jschellh/ProtSpaM Prot-SpaM] ||   <ref name="Leimeister 2018 giy148"/> 
|-
|FSWM || Filtered Spaced-Word Matches || [http://fswm.gobics.de/ FSWM] || <ref name="Leimeister 2017 971–979"/> 
|-
| FFP || Feature frequency profile based phylogeny || [http://sourceforge.net/projects/ffp-phylogeny/ FFP] || <ref name=FFP /> 
|-
| CVTree || Composition vector based server for phylogeny|| [http://tlife.fudan.edu.cn/cvtree/ CVTree] || <ref>{{cite journal | vauthors = Xu Z, Hao B | title = CVTree update: a newly designed phylogenetic study platform using composition vectors and whole genomes | journal = Nucleic Acids Research | volume = 37 | issue = Web Server issue | pages = W174–W178 | date = July 2009 | pmid = 19398429 | pmc = 2703908 | doi = 10.1093/nar/gkp278 }}</ref> 
|-
| RTD Phylogeny || Return time distribution based server for phylogeny|| [http://bioinfo.net.in/RTD/home.html RTD Phylogeny] || <ref name=RTD1 /> 
|-
| AGP || A multimethods web server for alignment-free genome phylogeny || [https://web.archive.org/web/20140109135217/http://www.herbbol.org:8000/agp AGP] || <ref>{{cite journal | vauthors = Cheng J, Cao F, Liu Z | title = AGP: a multimethods web server for alignment-free genome phylogeny | journal = Molecular Biology and Evolution | volume = 30 | issue = 5 | pages = 1032–1037 | date = May 2013 | pmid = 23389766 | pmc = 7574599 | doi = 10.1093/molbev/mst021 | doi-access = free }}</ref> 
|-
| Alfy || Alignment-free detection of local similarity among viral and bacterial genomes || [http://guanine.evolbio.mpg.de/alfy/ Alfy] || <ref name="Domazet-Lošo 1466–72"/> 
|-
| decaf+py || DistancE Calculation using Alignment-Free methods in PYthon || [http://acb.qfab.org/acb/decaf+py/ decaf+py] || <ref>{{cite journal | vauthors = Höhl M, Rigoutsos I, Ragan MA | title = Pattern-based phylogenetic distance estimation and tree reconstruction | journal = Evolutionary Bioinformatics Online | volume = 2 | pages = 359–375 | date = February 2007 | pmid = 19455227 | pmc = 2674673 | bibcode = 2006q.bio.....5002H | arxiv = q-bio/0605002 }}</ref>  
|-
| Dengue Subtyper || Genotyping of Dengue viruses based on RTD || Dengue Subtyper ||  <ref name=RTD1 /> 
|-
| WNV Typer || Genotyping of West nile viruses based on RTD || WNV Typer ||  <ref name=RTD3 /> 
|-
| AllergenFP || Allergenicity prediction by descriptor fingerprints || [http://ddg-pharmfac.net/AllergenFP/ AllergenFP] || <ref name=AllergenFP />  
|-
| kSNP v2 || Alignment-Free SNP Discovery || [http://sourceforge.net/projects/ksnp/ kSNP v2] || <ref name=SNP />  
|-
| d2Tools || Comparison of Metatranscriptomic Samples Based on ''k''-Tuple Frequencies || [https://code.google.com/p/d2-tools/ d2Tools] || <ref>{{cite journal | vauthors = Wang Y, Liu L, Chen L, Chen T, Sun F | title = Comparison of metatranscriptomic samples based on k-tuple frequencies | journal = PLOS ONE | volume = 9 | issue = 1 | pages = e84348 | date = Jan 2, 2014 | pmid = 24392128 | pmc = 3879298 | doi = 10.1371/journal.pone.0084348 | doi-access = free | bibcode = 2014PLoSO...984348W }}</ref> 
|-
| rush || Recombination detection Using SHustrings || [http://guanine.evolbio.mpg.de/rush/ rush] || <ref name=rush /> 
|-
| smash || Genomic rearrangements detection and visualisation || [http://bioinformatics.ua.pt/software/smash/ smash] || <ref name=rearrang /> 
|-
| Smash++ || Finding and visualizing genomic rearrangements || [https://github.com/smortezah/smashpp Smash++] || <ref name=smashpp />
|-
| GScompare|| Oligonucleotide-based fast clustering of bacterial genomes  || [http://gscompare.ehu.eus/ GScompare] || – 
|-
| COMET || Alignment-free subtyping of HIV-1, HIV-2 and HCV viral sequences || [http://comet.lih.lu/ COMET] || <ref name="COMET"/> 
|-
|USM
|Fractal MapReduce decomposition of sequence alignment
|[https://usm.github.io usm.github.io]
|<ref name="Almeida 12"/>
|-
| FALCON || Alignment-free method to infer metagenomic composition of ancient DNA || [http://github.com/pratas/falcon FALCON] || <ref name="falcon"/> 
|-
| Kraken || Taxonomic classification using exact k-mer matches || [http://github.com/DerrickWood/kraken2 Kraken 2] || <ref name="kraken"/> 
|-
| EAGLE || An ultra-fast tool to find relative absent words in genomic data || [https://github.com/cobilab/eagle EAGLE2] || <ref name="Pratas2020">{{cite journal | vauthors = Pratas D, Silva JM | title = Persistent minimal sequences of SARS-CoV-2 | journal = Bioinformatics | volume = 36 | issue = 21 | pages = 5129–5132 | date = January 2021 | pmid = 32730589 | pmc = 7559010 | doi = 10.1093/bioinformatics/btaa686 | doi-access = free }}</ref>
|-
| CLC|| Phylogenetic trees using reference-free k-mer based matching|| [https://www.qiagenbioinformatics.com/products/clc-microbial-genomics-module/ CLC Microbial Genome Module] || <ref>{{cite web |url=https://www.qiagenbioinformatics.com/products/clc-microbial-genomics-module/ |title= CLC Microbial Genomics Module |date=2019 |website=QIAGEN Bioinformatics}}</ref>
|-
|xgTaxonomy
|A tool for metagenomic classification that uses data compression algorithms to classify genomic sequences.
|[https://github.com/ieeta-pt/xgTaxonomy xgTaxonomy]
|<ref name=":1" />
|-
|AlcoR
|An extremely efficient method for identifying and visualizing low-complexity regions in genomic and proteomic sequences.
|[https://cobilab.github.io/alcor/ AlcoR]
|<ref name=":0" />
|-
|AltaiR
|A C toolkit for alignment-free and temporal analysis of multi-FASTA data.
|[https://github.com/cobilab/altair AltaiR]
|<ref name=":2" />
|}

== See also ==
*[[Sequence analysis]]
*[[Multiple sequence alignment]]
*[[Phylogenomics]]
*[[Bioinformatics]]
*[[Metagenomics]]
*[[Next-generation sequencing]]
*[[Population genetics]]
*[[SNPs]]
*[[Recombination detection program]]
*[[Genome skimming]]

== References ==

{{Reflist}}

[[Category:Bioinformatics]]
[[Category:Computational biology]]