An official website of the United States government
Reticulations in a phylogenetic network represent processes such as gene flow, admixture, recombination and hybrid speciation. Extending definitions from the tree setting, an anomalous network is one in which some unrooted tree topology displayed in the network appears in gene trees with a lower frequency than a tree not displayed in the network. We investigate anomalous networks under the Network Multispecies Coalescent Model with possible correlated inheritance at reticulations. Focusing on subsets of 4 taxa, we describe a new algorithm to calculate quartet concordance factors on networks of any level, faster than previous algorithms because of its focus on 4 taxa. We then study topological properties required for a 4-taxon network to be anomalous, uncovering the key role of 32-cycles: cycles of 3 edges parent to a sister group of 2 taxa. Under the model of common inheritance, that is, when each gene tree coalesces within a species tree displayed in the network, we prove that 4-taxon networks are never anomalous. Under independent and various levels of correlated inheritance, we use simulations under realistic parameters to quantify the prevalence of anomalous 4-taxon networks, finding that truly anomalous networks are rare. At the same time, however, we find a significant fraction of networks close enough to the anomaly zone to appear anomalous, when considering the quartet concordance factors observed from a few hundred genes. These apparent anomalies may challenge network inference methods.
more »
« less
Identifiability of Level-1 Species Networks from Gene Tree Quartets
Abstract When hybridization or other forms of lateral gene transfer have occurred, evolutionary relationships of species are better represented by phylogenetic networks than by trees. While inference of such networks remains challenging, several recently proposed methods are based on quartet concordance factors—the probabilities that a tree relating a gene sampled from the species displays the possible 4-taxon relationships. Building on earlier results, we investigate what level-1 network features are identifiable from concordance factors under the network multispecies coalescent model. We obtain results on both topological features of the network, and numerical parameters, uncovering a number of failures of identifiability related to 3-cycles in the network. Addressing these identifiability issues is essential for designing statistically consistent inference methods.
more »
« less
- PAR ID:
- 10526649
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Bulletin of Mathematical Biology
- Volume:
- 86
- Issue:
- 9
- ISSN:
- 0092-8240
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Rapidly evolving taxa are excellent models for understanding the mechanisms that give rise to biodiversity. However, developing an accurate historical framework for comparative analysis of such lineages remains a challenge due to ubiquitous incomplete lineage sorting (ILS) and introgression. Here, we use a whole-genome alignment, multiple locus-sampling strategies, and summary-tree and single nucleotide polymorphism-based species-tree methods to infer a species tree for eastern North American Neodiprion species, a clade of pine-feeding sawflies (Order: Hymenopteran; Family: Diprionidae). We recovered a well-supported species tree that—except for three uncertain relationships—was robust to different strategies for analyzing whole-genome data. Nevertheless, underlying gene-tree discordance was high. To understand this genealogical variation, we used multiple linear regression to model site concordance factors estimated in 50-kb windows as a function of several genomic predictor variables. We found that site concordance factors tended to be higher in regions of the genome with more parsimony-informative sites, fewer singletons, less missing data, lower GC content, more genes, lower recombination rates, and lower D-statistics (less introgression). Together, these results suggest that ILS, introgression, and genotyping error all shape the genomic landscape of gene-tree discordance in Neodiprion. More generally, our findings demonstrate how combining phylogenomic analysis with knowledge of local genomic features can reveal mechanisms that produce topological heterogeneity across genomes.more » « less
-
Abstract Inferring gene regulatory networks (GRNs) from single-cell data is challenging due to heuristic limitations. Existing methods also lack estimates of uncertainty. Here we present Probabilistic Matrix Factorization for Gene Regulatory Network Inference (PMF-GRN). Using single-cell expression data, PMF-GRN infers latent factors capturing transcription factor activity and regulatory relationships. Using variational inference allows hyperparameter search for principled model selection and direct comparison to other generative models. We extensively test and benchmark our method using real single-cell datasets and synthetic data. We show that PMF-GRN infers GRNs more accurately than current state-of-the-art single-cell GRN inference methods, offering well-calibrated uncertainty estimates.more » « less
-
Inferring gene regulatory networks (GRNs) from single-cell gene expression datasets is a challenging task. Existing methods are often designed heuristically for specific datasets and lack the flexibility to incorporate additional information or compare against other algorithms. Further, current GRN inference methods do not provide uncertainty estimates with respect to the interactions that they predict, making inferred networks challenging to interpret. To overcome these challenges, we introduce Probabilistic Matrix Factorization for Gene Regulatory Network inference (PMF-GRN). PMF-GRN uses single-cell gene expression data to learn latent factors representing transcription factor activity as well as regulatory relationships between transcription factors and their target genes. This approach incorporates available experimental evidence into prior distributions over latent factors and scales well to single-cell gene expression datasets. By utilizing variational inference, we facilitate hyperparameter search for principled model selection and direct comparison to other generative models. To assess the accuracy of our method, we evaluate PMF-GRN using the model organisms Saccharomyces cerevisiae and Bacillus subtilis, benchmarking against database-derived gold standard interactions. We discover that, on average, PMF-GRN infers GRNs more accurately than current state-of-the-art single-cell GRN inference methods. Moreover, our PMF-GRN approach offers well-calibrated uncertainty estimates, as it performs gene regulatory network (GRN) inference in a probabilistic setting. These estimates are valuable for validation purposes, particularly when validated interactions are limited or a gold standard is incomplete.more » « less
-
Abstract MotivationThe abundance of gene flow in the Tree of Life challenges the notion that evolution can be represented with a fully bifurcating process which cannot capture important biological realities like hybridization, introgression, or horizontal gene transfer. Coalescent-based network methods are increasingly popular, yet not scalable for big data, because they need to perform a heuristic search in the space of networks as well as numerical optimization that can be NP-hard. Here, we introduce a novel method to reconstruct phylogenetic networks based on algebraic invariants. While there is a long tradition of using algebraic invariants in phylogenetics, our work is the first to define phylogenetic invariants on concordance factors (frequencies of four-taxon splits in the input gene trees) to identify level-1 phylogenetic networks under the multispecies coalescent model. ResultsOur novel hybrid detection methodology is optimization-free as it only requires the evaluation of polynomial equations, and as such, it bypasses the traversal of network space, yielding a computational speed at least 10 times faster than the fastest-to-date network methods. We illustrate our method’s performance on simulated and real data from the genus Canis. Availability and implementationWe present an open-source publicly available Julia package PhyloDiamond.jl available at https://github.com/solislemuslab/PhyloDiamond.jl with broad applicability within the evolutionary community.more » « less
