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High-dimensional mixed-effects models are an increasingly important form of regression in which the number of covariates rivals or exceeds the number of samples, which are collected in groups or clusters. The penalized likelihood approach to fitting these models relies on a coordinate descent algorithm that lacks guarantees of convergence to a global optimum. Here, we empirically study the behavior of this algorithm on simulated and real examples of three types of data that are common in modern biology: transcriptome, genome-wide association, and microbiome data. Our simulations provide new insights into the algorithm’s behavior in these settings, and, comparing the performance of two popular penalties, we demonstrate that the smoothly clipped absolute deviation (SCAD) penalty consistently outperforms the least absolute shrinkage and selection operator (LASSO) penalty in terms of both variable selection and estimation accuracy across omics data. To empower researchers in biology and other fields to fit models with the SCAD penalty, we implement the algorithm in a Julia package,HighDimMixedModels.jl. 

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. 

Abstract Scientists world-wide are putting together massive efforts to understand how the biodiversity that we see on Earth evolved from single-cell organisms at the origin of life and this diversification process is represented through the Tree of Life. Low sampling rates and high heterogeneity in the rate of evolution across sites and lineages produce a phenomenon denoted “long branch attraction” (LBA) in which long non-sister lineages are estimated to be sisters regardless of their true evolutionary relationship. LBA has been a pervasive problem in phylogenetic inference affecting different types of methodologies from distance-based to likelihood-based. Here, we present a novel neural network model that outperforms standard phylogenetic methods and other neural network implementations under LBA settings. Furthermore, unlike existing neural network models in phylogenetics, our model naturally accounts for the tree isomorphisms via permutation invariant functions which ultimately result in lower memory and allows the seamless extension to larger trees. 

Abstract Phylogenetic regression is a type of generalised least squares (GLS) method that incorporates a modelled covariance matrix based on the evolutionary relationships between species (i.e. phylogenetic relationships). While this method has found widespread use in hypothesis testing via phylogenetic comparative methods, such as phylogenetic ANOVA, its ability to account for non‐linear relationships has received little attention.To address this, here we implement a phylogenetic Kernel Ridge Regression (phyloKRR) method that utilises GLS in a high‐dimensional feature space, employing linear combinations of phylogenetically weighted data to account for non‐linearity. We analysed two biological datasets using the Radial Basis Function and linear kernel function. The first dataset contained morphometric data, while the second dataset comprised discrete trait data and diversification rates as response variable. Hyperparameter tuning of the model was achieved through cross‐validation rounds in the training set.In the tested biological datasets, phyloKRR reduced the error rate (as measured by RMSE) by around 20% compared to linear‐based regression when data did not exhibit linear relationships. In simulated datasets, the error rate decreased almost exponentially with the level of non‐linearity.These results show that introducing kernels into phylogenetic regression analysis presents a novel and promising tool for complementing phylogenetic comparative methods. We have integrated this method into Python package named phyloKRR, which is freely available at:https://github.com/ulises‐rosas/phylokrr.