MOTIVATION: Unique marker sequences are highly sought after in molecular diagnostics. Nevertheless, there are only few programs available to search for marker sequences, compared to the many programs for similarity search. We therefore wrote the program Fur for Finding Unique genomic Regions. RESULTS: Fur takes as input a sample of target sequences and a sample of closely related neighbors. It returns the regions present in all targets and absent from all neighbors. The recently published program genmap can also be used for this purpose and we compared it to fur. When analyzing a sample of 33 genomes representing the major phylogroups of E.coli, fur was 40 times faster than genmap but used three times more memory. On the other hand, genmap yielded three times more markers, but they were less accurate when tested in silico on a sample of 237 E.coli genomes. We also designed phylogroup-specific PCR primers based on the markers proposed by genmap and fur, and tested them by analyzing their virtual amplicons in GenBank. Finally, we used fur to design primers specific to a Lactobacillus species, and found excellent sensitivity and specificity in vitro. AVAILABILITY AND IMPLEMENTATION: Fur sources and documentation are available from https://github.com/evolbioinf/fur. The compiled software is posted as a docker container at https://hub.docker.com/r/haubold/fox. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Bioinformatics (2019) doi:http://dx.doi.org/10.1093/bioinformatics/bty922 In the originally published version of this manuscript, there was an error in the ‘Availability and implementation’ section of the Abstract. The URL for the browser tracks should be: guanine.evolbio.mpg.de/complexity This detail has been corrected only in this corrigendum to preserve the published version of record.

MOTIVATION: Tracking disease outbreaks by whole-genome sequencing leads to the collection of large samples of closely related sequences. Five years ago, we published a method to accurately compute all pairwise distances for such samples by indexing each sequence. Since indexing is slow, we now ask whether it is possible to achieve similar accuracy when indexing only a single sequence. RESULTS: We have implemented this idea in the program phylonium and show that it is as accurate as its predecessor and roughly 100 times faster when applied to all 2678 Escherichia coli genomes contained in ENSEMBL. One of the best published programs for rapidly computing pairwise distances, mash, analyzes the same dataset four times faster but, with default settings, it is less accurate than phylonium. AVAILABILITY AND IMPLEMENTATION: Phylonium runs under the UNIX command line; its C++ sources and documentation are available from github.com/evolbioinf/phylonium. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Unique sequence regions are associated with genetic function in vertebrate genomes. However, measuring uniqueness, or absence of long repeats, along a genome is conceptually and computationally difficult. Here we use a variant of the Lempel-Ziv complexity, the match complexity, Cm, and augment it by deriving its null distribution for random sequences. We then apply Cm to the human and mouse genomes to investigate the relationship between sequence complexity and function. RESULTS: We implemented Cm in the program macle and show through simulation that the newly derived null distribution of Cm is accurate. This allows us to delineate high-complexity regions in the human and mouse genomes. Using our program macle2go, we find that these regions are twofold enriched for genes. Moreover, the genes contained in these regions are more than 10-fold enriched for developmental functions. AVAILABILITY AND IMPLEMENTATION: Source code for macle and macle2go is available from www.github.com/evolbioinf/macle and www.github.com/evolbioinf/macle2go, respectively; Cm browser tracks from guanine.evolbio.mgp.de/complexity. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: In many organisms, including humans, recombination clusters within recombination hotspots. The standard method for de novo detection of recombinants at hotspots is sperm typing. This relies on allele-specific PCR at single nucleotide polymorphisms. Designing allele-specific primers by hand is time-consuming. We have therefore written a package to support hotspot detection and analysis. RESULTS: hotspot consists of four programs: asp looks up SNPs and designs allele-specific primers; aso constructs allele-specific oligos for mapping recombinants; xov implements a maximum-likelihood method for estimating the crossover rate; six, finally, simulates typing data. AVAILABILITY AND IMPLEMENTATION: hotspot is written in C. Sources are freely available under the GNU General Public License from http://github.com/evolbioinf/hotspot/ CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: A standard approach to classifying sets of genomes is to calculate their pairwise distances. This is difficult for large samples. We have therefore developed an algorithm for rapidly computing the evolutionary distances between closely related genomes. RESULTS: Our distance measure is based on ungapped local alignments that we anchor through pairs of maximal unique matches of a minimum length. These exact matches can be looked up efficiently using enhanced suffix arrays and our implementation requires approximately only 1 s and 45 MB RAM/Mbase analysed. The pairing of matches distinguishes non-homologous from homologous regions leading to accurate distance estimation. We show this by analysing simulated data and genome samples ranging from 29 Escherichia coli/Shigella genomes to 3085 genomes of Streptococcus pneumoniae. AVAILABILITY AND IMPLEMENTATION: We have implemented the computation of anchor distances in the multithreaded UNIX command-line program andi for ANchor DIstances. C sources and documentation are posted at http://github.com/evolbioinf/andi/ CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Phylogenetics and population genetics are central disciplines in evolutionary biology. Both are based on comparative data, today usually DNA sequences. These have become so plentiful that alignment-free sequence comparison is of growing importance in the race between scientists and sequencing machines. In phylogenetics, efficient distance computation is the major contribution of alignment-free methods. A distance measure should reflect the number of substitutions per site, which underlies classical alignment-based phylogeny reconstruction. Alignment-free distance measures are either based on word counts or on match lengths, and I apply examples of both approaches to simulated and real data to assess their accuracy and efficiency. While phylogeny reconstruction is based on the number of substitutions, in population genetics, the distribution of mutations along a sequence is also considered. This distribution can be explored by match lengths, thus opening the prospect of alignment-free population genomics.

MOTIVATION: Why recombination? is one of the central questions in biology. This has led to a host of methods for quantifying recombination from sequence data. These methods are usually based on aligned DNA sequences. Here, we propose an efficient alignment-free alternative. RESULTS: Our method is based on the distribution of match lengths, which we look up using enhanced suffix arrays. By eliminating the alignment step, the test becomes fast enough for application to whole bacterial genomes. Using simulations we show that our test has similar power as established tests when applied to long pairs of sequences. When applied to 58 genomes of Escherichia coli, we pick up the strongest recombination signal from a 125 kb horizontal gene transfer engineered 20 years ago. AVAILABILITY AND IMPLEMENTATION: We have implemented our method in the command-line program rush. Its C sources and documentation are available under the GNU General Public License from http://guanine.evolbio.mpg.de/rush/.

MOTIVATION: Bacterial and viral genomes are often affected by horizontal gene transfer observable as abrupt switching in local homology. In addition to the resulting mosaic genome structure, they frequently contain regions not found in close relatives, which may play a role in virulence mechanisms. Due to this connection to medical microbiology, there are numerous methods available to detect horizontal gene transfer. However, these are usually aimed at individual genes and viral genomes rather than the much larger bacterial genomes. Here, we propose an efficient alignment-free approach to describe the mosaic structure of viral and bacterial genomes, including their unique regions. RESULTS: Our method is based on the lengths of exact matches between pairs of sequences. Long matches indicate close homology, short matches more distant homology or none at all. These exact match lengths can be looked up efficiently using an enhanced suffix array. Our program implementing this approach, alfy (ALignment-Free local homologY), efficiently and accurately detects the recombination break points in simulated DNA sequences and among recombinant HIV-1 strains. We also apply alfy to Escherichia coli genomes where we detect new evidence for the hypothesis that strains pathogenic in poultry can infect humans. AVAILABILITY: alfy is written in standard C and its source code is available under the GNU General Public License from http://guanine.evolbio.mpg.de/alfy/. The software package also includes documentation and example data.

Abstract Motivation: Sequencing capacity is currently growing more rapidly than CPU speed, leading to an analysis bottleneck in many genome projects. Alignment-free sequence analysis methods tend to be more efficient than their alignment-based counterparts. They may, therefore, be important in the long run for keeping sequence analysis abreast with sequencing. Results: We derive and implement an alignment-free estimator of the number of pairwise mismatches, . Our implementation of , pim, is based on an enhanced suffix array and inherits the superior time and memory efficiency of this data structure. Simulations demonstrate that is accurate if mutations are distributed randomly along the chromosome. While real data often deviates from this ideal, remains useful for identifying regions of low genetic diversity using a sliding window approach. We demonstrate this by applying it to the complete genomes of 37 strains of Drosophila melanogaster, and to the genomes of two closely related Drosophila species, D.simulans and D.sechellia. In both cases, we detect the diversity minimum and discuss its biological implications. Availability: pim is written in standard C and its sources can be downloaded from http://guanine.evolbio.mpg.de/pim/. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics online.

MOTIVATION: Genome comparison is central to contemporary genomics and typically relies on sequence alignment. However, genome-wide alignments are difficult to compute. We have, therefore, recently developed an accurate alignment-free estimator of the number of substitutions per site based on the lengths of exact matches between pairs of sequences. The previous implementation of this measure requires n(n-1) suffix tree constructions and traversals, where n is the number of sequences analyzed. This does not scale well for large n. RESULTS: We present an algorithm to extract pairwise distances in a single traversal of a single suffix tree containing n sequences. As a result, the run time of the suffix tree construction phase of our algorithm is reduced from O(n(2)L) to O(nL), where L is the length of each sequence. We implement this algorithm in the program kr version 2 and apply it to 825 HIV genomes, 13 genomes of enterobacteria and the complete genomes of 12 Drosophila species. We show that, depending on the input dataset, the new program is at least 10 times faster than its predecessor. AVAILABILITY: Version 2 of kr can be tested via a web interface at http://guanine.evolbio.mpg.de/kr2/. It is written in standard C and its source code is available under the GNU General Public License from the same web site. CONTACT: [email protected] Supplementary informations: Supplementary data are available at Bioinformatics online.

BACKGROUND: Genome sequences vary strongly in their repetitiveness and the causes for this are still debated. Here we propose a novel measure of genome repetitiveness, the index of repetitiveness, Ir, which can be computed in time proportional to the length of the sequences analyzed. We apply it to 336 genomes from all three domains of life. RESULTS: The expected value of Ir is zero for random sequences of any G/C content and greater than zero for sequences with excess repeats. We find that the Ir of archaea is significantly smaller than that of eubacteria, which in turn is smaller than that of eukaryotes. Mouse chromosomes have a significantly higher Ir than human chromosomes and within each genome the Y chromosome is most repetitive. A sliding window analysis reveals that the human HOXA cluster and two surrounding genes are characterized by local minima in Ir. A program for calculating the Ir is freely available at http://adenine.biz.fh-weihenstephan.de/ir/. CONCLUSION: The general measure of DNA repetitiveness proposed in this paper can be efficiently computed on a genomic scale. This reveals a broad spectrum of repetitiveness among diverse genomes which agrees qualitatively with previous studies of repeat content. A sliding window analysis helps to analyze the intragenomic distribution of repeats.

BACKGROUND: Sequence comparison by alignment is a fundamental tool of molecular biology. In this paper we show how a number of sequence comparison tasks, including the detection of unique genomic regions, can be accomplished efficiently without an alignment step. Our procedure for nucleotide sequence comparison is based on shortest unique substrings. These are substrings which occur only once within the sequence or set of sequences analysed and which cannot be further reduced in length without losing the property of uniqueness. Such substrings can be detected using generalized suffix trees. RESULTS: We find that the shortest unique substrings in Caenorhabditis elegans, human and mouse are no longer than 11 bp in the autosomes of these organisms. In mouse and human these unique substrings are significantly clustered in upstream regions of known genes. Moreover, the probability of finding such short unique substrings in the genomes of human or mouse by chance is extremely small. We derive an analytical expression for the null distribution of shortest unique substrings, given the GC-content of the query sequences. Furthermore, we apply our method to rapidly detect unique genomic regions in the genome of Staphylococcus aureus strain MSSA476 compared to four other staphylococcal genomes. CONCLUSION: We combine a method to rapidly search for shortest unique substrings in DNA sequences and a derivation of their null distribution. We show that unique regions in an arbitrary sample of genomes can be efficiently detected with this method. The corresponding programs shustring (SHortest Unique subSTRING) and shulen are written in C and available at http://adenine.biz.fh-weihenstephan.de/shustring/.

Abstract Motivation: The number of Single Nucleotide Polymorphisms (SNPs) detectable in an alignment is a function of the length and the number of the aligned sequences. The latter is called sample size. However, a typical alignment, for instance obtained as a BLAST-search result of a query sequence against an EST database, does not evenly cover the query sequence. Therefore, it is usually not clear what the actual sample size is. Results: We present a method to calculate the effective sample size, called neff, for a given BLAST alignment. This method takes into account that multiple coverage contributes only logarithmically to the SNP yield of a given sequence stretch. We show that the effective sample size neff is usually much smaller than would be expected for a given amount of coverage and illustrate this with two typical examples. Availability: The algorithm is implemented in NEFF, a program written in FORTRAN90 that is accessible at http://soft.ice.mpg.de/neff. From this site also the source, except for two subroutines protected by copyright, and a LINUX compiled executable can be downloaded. Contact: [email protected] * To whom correspondence should be addressed. 2 Present address: LION Bioscience AG, Heidelberg, Germany.

Abstract Summary: LIAN is a program to test the null hypothesis of linkage equilibrium for multilocus data. LIAN incorporates both a Monte Carlo method as well as a novel algebraic method to carry out the hypothesis test. The program further returns the genetic diversity of the sample and the pairwise distances between its members. Availability: LIAN can be accessed at http://soft.ice.mpg.de/lian Contact: [email protected] To whom correspondence should be addressed.