Lam Si Tung Ho

A Linear-Time Algorithm for Gaussian and Non-Gaussian Trait Evolution Models

We developed a linear-time algorithm applicable to a large class of trait evolution models, for efficient likelihood calculations and parameter inference on very large trees. Our algorithm solves the traditional computational burden associated with two key terms, namely the determinant of the phylogenetic covariance matrix V and quadratic products involving the inverse of V. Applications include Gaussian models such as Brownian motion-derived models like Pagels lambda, kappa, delta, and the early-burst model; Ornstein-Uhlenbeck models to account for natural selection with possibly varying selection parameters along the tree; as well as non-Gaussian models such as phylogenetic logistic regression, phylogenetic Poisson regression, and phylogenetic generalized linear mixed models. Outside of phylogenetic regression, our algorithm also applies to phylogenetic principal component analysis, phylogenetic discriminant analysis or phylogenetic prediction. The computational gain opens up new avenues for complex models or extensive resampling procedures on very large trees. We identify the class of models that our algorithm can handle as all models whose covariance matrix has a 3-point structure. We further show that this structure uniquely identifies a rooted tree whose branch lengths parametrize the trait covariance matrix, which acts as a similarity matrix. The new algorithm is implemented in the R package phylolm, including functions for phylogenetic linear regression and phylogenetic logistic regression.

Intrinsic inference difficulties for trait evolution with Ornstein‐Uhlenbeck models

Summary For the study of macroevolution, phenotypic data are analysed across species on a dated phylogeny using phylogenetic comparative methods. In this context, the Ornstein-Uhlenbeck (OU) process is now being used extensively to model selectively driven trait evolution, whereby a trait is attracted to a selection optimum μ. We report here theoretical properties of the maximum-likelihood (ML) estimators for these parameters, including their non-uniqueness and inaccuracy, and show that theoretical expectations indeed apply to real trees. We provide necessary conditions for ML estimators to be well defined and practical implications for model parametrization. We then show how these limitations carry over to difficulties in detecting shifts in selection regimes along a phylogeny. When the phylogenetic placement of these shifts is unknown, we identify a ‘large p - small n’ problem where traditional model selection criteria fail and favour overly complex scenarios. Instead, we propose a modified criterion that is better adapted to change-point models. The challenges we identify here are inherent to trait evolution models on phylogenetic trees when observations are limited to present-day taxa, and require the addition of fossil taxa to be alleviated. We conclude with recommendations for empiricists.

Asymptotic theory with hierarchical autocorrelation: Ornstein–Uhlenbeck tree models

Hierarchical autocorrelation in the error term of linear models arises when sampling units are related to each other according to a tree. The residual covariance is parametrized using the tree-distance between sampling units. When observations are modeled using an Ornstein–Uhlenbeck (OU) process along the tree, the autocorrelation between two tips decreases exponentially with their tree distance. These models are most often applied in evolutionary biology, when tips represent biological species and the OU process parameters represent the strength and direction of natural selection. For these models, we show that the mean is not microergodic: no estimator can ever be consistent for this parameter and provide a lower bound for the variance of its MLE. For covariance parameters, we give a general sufficient condition ensuring microergodicity. This condition suggests that some parameters may not be estimated at the same rate as others. We show that, indeed, maximum likelihood estimators of the autocorrelation parameter converge at a slower rate than that of generally microergodic parameters. We showed this theoretically in a symmetric tree asymptotic framework and through simulations on a large real tree comprising 4507 mammal species.

Mel-frequency Cepstral Coefficients for Eye Movement Identification

Human identification is an important task for various activities in society. In this paper, we consider the problem of human identification using eye movement information. This problem, which is usually called the eye movement identification problem, can be solved by training a multiclass classification model to predict a persons identity from his or her eye movements. In this work, we propose using Mel-frequency cepstral coefficients (MFCCs) to encode various features for the classification model. Our experiments show that using MFCCs to represent useful features such as eye position, eye difference, and eye velocity would result in a much better accuracy than using Fourier transform, cepstrum, or raw representations. We also compare various classification models for the task. From our experiments, linear-kernel SVMs achieve the best accuracy with 93.56% and 91.08% accuracy on the small and large datasets respectively. Besides, we conduct experiments to study how the movements of each eye contribute to the final classification accuracy.

Phase transition on the convergence rate of parameter estimation under an Ornstein–Uhlenbeck diffusion on a tree

Diffusion processes on trees are commonly used in evolutionary biology to model the joint distribution of continuous traits, such as body mass, across species. Estimating the parameters of such processes from tip values presents challenges because of the intrinsic correlation between the observations produced by the shared evolutionary history, thus violating the standard independence assumption of large-sample theory. For instance (Ho and Ané, Ann Stat 41:957–981, 2013) recently proved that the mean (also known in this context as selection optimum) of an Ornstein–Uhlenbeck process on a tree cannot be estimated consistently from an increasing number of tip observations if the tree height is bounded. Here, using a fruitful connection to the so-called reconstruction problem in probability theory, we study the convergence rate of parameter estimation in the unbounded height case. For the mean of the process, we provide a necessary and sufficient condition for the consistency of the maximum likelihood estimator (MLE) and establish a phase transition on its convergence rate in terms of the growth of the tree. In particular we show that a loss of

Statistical evidence for common ancestry: Application to primates

\sqrt{n}

Consistency and convergence rate of phylogenetic inference via regularization

n-consistency (i.e., the variance of the MLE becomes