Estimating the mutation rate, or equivalently effective population size, is a common task in population genetics. If recombination is low or high, optimal linear estimation methods are known and well understood. For intermediate recombination rates, the calculation of optimal estimators is more challenging. As an alternative to model-based estimation, neural networks and other machine learning tools could help to develop good estimators in these involved scenarios. However, if no benchmark is available it is difficult to assess how well suited these tools are for different applications in population genetics. Here we investigate feedforward neural networks for the estimation of the mutation rate based on the site frequency spectrum and compare their performance with model-based estimators. For this we use the model-based estimators introduced by Fu, Futschik et al., and Watterson that minimize the variance or mean squared error for no and free recombination. We find that neural networks reproduce these estimators if provided with the appropriate features and training sets. Remarkably, using the model-based estimators to adjust the weights of the training data, only one hidden layer is necessary to obtain a single estimator that performs almost as well as model-based estimators for low and high recombination rates, and at the same time provides a superior estimation method for intermediate recombination rates. We apply the method to simulated data based on the human chromosome 2 recombination map, highlighting its robustness in a realistic setting where local recombination rates vary and/or are unknown.

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: When performing genome-wide association studies conventionally the additive genetic model is used to explore whether a single nucleotide polymorphism (SNP) is associated with a quantitative trait. But for variants, which do not follow an intermediate mode of inheritance (MOI), the recessive or the dominant genetic model can have more power to detect associations and furthermore the MOI is important for downstream analyses and clinical interpretation. When multiple MOIs are modelled the question arises, which describes the true underlying MOI best. RESULTS: We developed an R-package allowing for the first time to determine study specific critical values when one of the three models is more informative than the other ones for a quantitative trait locus. The package allows for user-friendly simulations to determine these critical values with predefined minor allele frequencies and study sizes. For application scenarios with extensive multiple testing we integrated an interpolation functionality to determine critical values already based on a moderate number of random draws. AVAILABILITY AND IMPLEMENTATION: The R-package pgainsim is freely available for download on Github at https://github.com/genepi-freiburg/pgainsim. 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: 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.

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/.

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.