The cost of sequencing the genome is dropping at a much faster rate compared to assembling and finishing the genome. The use of lightly sampled genomes (genome-skims) could be transformative for genomic ecology, and results using k-mers have shown the advantage of this approach in identification and phylogenetic placement of eukaryotic species. Here, we revisit the basic question of estimating genomic parameters such as genome length, coverage, and repeat structure, focusing specifically on estimating the k-mer repeat spectrum. We show using a mix of theoretical and empirical analysis that there are fundamental limitations to estimating the k-mer spectra due to ill-conditioned systems, and that has implications for other genomic parameters. We get around this problem using a novel constrained optimization approach (Spline Linear Programming), where the constraints are learned empirically. On reads simulated at 1X coverage from 66 genomes, our method, REPeat SPECTra Estimation (RESPECT), had 2.2% error in length estimation compared to 27% error previously achieved. In shotgun sequenced read samples with contaminants, RESPECT length estimates had median error 4%, in contrast to other methods that had median error 80%. Together, the results suggest that low-pass genomic sequencing can yield reliable estimates of the length and repeat content of the genome. The RESPECT software will be publicly available at https://urldefense.proofpoint.com/v2/url?u=https-3A__github.com_shahab-2Dsarmashghi_RESPECT.git&d=DwIGAw&c=-35OiAkTchMrZOngvJPOeA&r=ZozViWvD1E8PorCkfwYKYQMVKFoEcqLFm4Tg49XnPcA&m=f-xS8GMHKckknkc7Xpp8FJYw_ltUwz5frOw1a5pJ81EpdTOK8xhbYmrN4ZxniM96&s=717o8hLR1JmHFpRPSWG6xdUQTikyUjicjkipjFsKG4w&e=.

MOTIVATION: Consider a simple computational problem. The inputs are (i) the set of mixed reads generated from a sample that combines two organisms and (ii) separate sets of reads for several reference genomes of known origins. The goal is to find the two organisms that constitute the mixed sample. When constituents are absent from the reference set, we seek to phylogenetically position them with respect to the underlying tree of the reference species. This simple yet fundamental problem (which we call phylogenetic double-placement) has enjoyed surprisingly little attention in the literature. As genome skimming (low-pass sequencing of genomes at low coverage, precluding assembly) becomes more prevalent, this problem finds wide-ranging applications in areas as varied as biodiversity research, food production and provenance, and evolutionary reconstruction. RESULTS: We introduce a model that relates distances between a mixed sample and reference species to the distances between constituents and reference species. Our model is based on Jaccard indices computed between each sample represented as k-mer sets. The model, built on several assumptions and approximations, allows us to formalize the phylogenetic double-placement problem as a non-convex optimization problem that decomposes mixture distances and performs phylogenetic placement simultaneously. Using a variety of techniques, we are able to solve this optimization problem numerically. We test the resulting method, called MIxed Sample Analysis tool (MISA), on a varied set of simulated and biological datasets. Despite all the assumptions used, the method performs remarkably well in practice. AVAILABILITY AND IMPLEMENTATION: The software and data are available at https://github.com/balabanmetin/misa and https://github.com/balabanmetin/misa-data. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

The gene family-free framework for comparative genomics aims at providing methods for gene order analysis that do not require prior gene family assignment, but work directly on a sequence similarity graph. We study two problems related to the breakpoint median of three genomes, which asks for the construction of a fourth genome that minimizes the sum of breakpoint distances to the input genomes. We present a model for constructing a median of three genomes in this family-free setting, based on maximizing an objective function that generalizes the classical breakpoint distance by integrating sequence similarity in the score of a gene adjacency. We study its computational complexity and we describe an integer linear program (ILP) for its exact solution. We further discuss a related problem called family-free adjacencies for k genomes for the special case of $$k \le 3$$ and present an ILP for its solution. However, for this problem, the computation of exact solutions remains intractable for sufficiently large instances. We then proceed to describe a heuristic method, FFAdj-AM, which performs well in practice. The developed methods compute accurate positional orthologs for genomes comparable in size of bacterial genomes on simulated data and genomic data acquired from the OMA orthology database. In particular, FFAdj-AM performs equally or better when compared to the well-established gene family prediction tool MultiMSOAR. We study the computational complexity of a new family-free model and present algorithms for its solution. With FFAdj-AM, we propose an appealing alternative to established tools for identifying higher confidence positional orthologs.