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The recent explosion of genomic data has underscored the need for interpretable and comprehensive analyses that can capture complex phylogenetic relationships within and across species. Recombination, reassortment and horizontal gene transfer constitute examples of pervasive biological phenomena that cannot be captured by tree-like representations. Starting from hundreds of genomes, we are interested in the reconstruction of potential evolutionary histories leading to the observed data. Ancestral recombination graphs represent potential histories that explicitly accommodate recombination and mutation events across orthologous genomes. However, they are computationally costly to reconstruct, usually being infeasible for more than few tens of genomes. Recently, Topological Data Analysis (TDA) methods have been proposed as robust and scalable methods that can capture the genetic scale and frequency of recombination. We build upon previous TDA developments for detecting and quantifying recombination, and present a novel framework that can be applied to hundreds of genomes and can be interpreted in terms of minimal histories of mutation and recombination events, quantifying the scales and identifying the genomic locations of recombinations. We implement this framework in a software package, called TARGet, and apply it to several examples, including small migration between different populations, human recombination, and horizontal evolution in finches inhabiting the Galapagos Islands.
Solving the recombination equation has been a long-standing challenge of emph{deterministic} population genetics. We review recent progress obtained by introducing ancestral processes, as traditionally used in the context of emph{stochastic} models o
Recently, the selection-recombination equation with a single selected site and an arbitrary number of neutral sites was solved by means of the ancestral selection-recombination graph. Here, we introduce a more accessible approach, namely the ancestra
In this article, we show how the recent statistical techniques developed in Topological Data Analysis for the Mapper algorithm can be extended and leveraged to formally define and statistically quantify the presence of topological structures coming f
Statistical analysis on object data presents many challenges. Basic summaries such as means and variances are difficult to compute. We apply ideas from topology to study object data. We present a framework for using persistence landscapes to vectoriz
Angiogenesis is the process by which blood vessels form from pre-existing vessels. It plays a key role in many biological processes, including embryonic development and wound healing, and contributes to many diseases including cancer and rheumatoid a