Ubiquity of synonymity: almost all large binary trees are not uniquely identified by their spectra or their immanantal polynomials

There are several common ways to encode a tree as a matrix, such as the adjacency matrix, the Laplacian matrix (that is, the infinitesimal generator of the natural random walk), and the matrix of pairwise distances between leaves. Such representations involve a specific labeling of the vertices or at least the leaves, and so it is natural to attempt to identify trees by some feature of the associated matrices that is invariant under relabeling. An obvious candidate is the spectrum of eigenvalues (or, equivalently, the characteristic polynomial). We show for any of these choices of matrix that the fraction of binary trees with a unique spectrum goes to zero as the number of leaves goes to infinity. We investigate the rate of convergence of the above fraction to zero using numerical methods. For the adjacency and Laplacian matrices, we show that that the {\em a priori} more informative immanantal polynomials have no greater power to distinguish between trees

Predicting B Cell Receptor Substitution Profiles Using Public Repertoire Data

B cells develop high affinity receptors during the course of affinity maturation, a cyclic process of mutation and selection. At the end of affinity maturation, a number of cells sharing the same ancestor (i.e. in the same "clonal family") are released from the germinal center, their amino acid frequency profile reflects the allowed and disallowed substitutions at each position. These clonal-family-specific frequency profiles, called "substitution profiles", are useful for studying the course of affinity maturation as well as for antibody engineering purposes. However, most often only a single sequence is recovered from each clonal family in a sequencing experiment, making it impossible to construct a clonal-family-specific substitution profile. Given the public release of many high-quality large B cell receptor datasets, one may ask whether it is possible to use such data in a prediction model for clonal-family-specific substitution profiles. In this paper, we present the method "Substitution Profiles Using Related Families" (SPURF), a penalized tensor regression framework that integrates information from a rich assemblage of datasets to predict the clonal-family-specific substitution profile for any single input sequence. Using this framework, we show that substitution profiles from similar clonal families can be leveraged together with simulated substitution profiles and germline gene sequence information to improve prediction. We fit this model on a large public dataset and validate the robustness of our approach on an external dataset. Furthermore, we provide a command-line tool in an open-source software package (https://github.com/krdav/SPURF) implementing these ideas and providing easy prediction using our pre-fit models.Comment: 23 page

A Bayesian phylogenetic hidden Markov model for B cell receptor sequence analysis.

The human body generates a diverse set of high affinity antibodies, the soluble form of B cell receptors (BCRs), that bind to and neutralize invading pathogens. The natural development of BCRs must be understood in order to design vaccines for highly mutable pathogens such as influenza and HIV. BCR diversity is induced by naturally occurring combinatorial "V(D)J" rearrangement, mutation, and selection processes. Most current methods for BCR sequence analysis focus on separately modeling the above processes. Statistical phylogenetic methods are often used to model the mutational dynamics of BCR sequence data, but these techniques do not consider all the complexities associated with B cell diversification such as the V(D)J rearrangement process. In particular, standard phylogenetic approaches assume the DNA bases of the progenitor (or "naive") sequence arise independently and according to the same distribution, ignoring the complexities of V(D)J rearrangement. In this paper, we introduce a novel approach to Bayesian phylogenetic inference for BCR sequences that is based on a phylogenetic hidden Markov model (phylo-HMM). This technique not only integrates a naive rearrangement model with a phylogenetic model for BCR sequence evolution but also naturally accounts for uncertainty in all unobserved variables, including the phylogenetic tree, via posterior distribution sampling

Survival analysis of DNA mutation motifs with penalized proportional hazards

Antibodies, an essential part of our immune system, develop through an intricate process to bind a wide array of pathogens. This process involves randomly mutating DNA sequences encoding these antibodies to find variants with improved binding, though mutations are not distributed uniformly across sequence sites. Immunologists observe this nonuniformity to be consistent with "mutation motifs", which are short DNA subsequences that affect how likely a given site is to experience a mutation. Quantifying the effect of motifs on mutation rates is challenging: a large number of possible motifs makes this statistical problem high dimensional, while the unobserved history of the mutation process leads to a nontrivial missing data problem. We introduce an $\ell_1$-penalized proportional hazards model to infer mutation motifs and their effects. In order to estimate model parameters, our method uses a Monte Carlo EM algorithm to marginalize over the unknown ordering of mutations. We show that our method performs better on simulated data compared to current methods and leads to more parsimonious models. The application of proportional hazards to mutation processes is, to our knowledge, novel and formalizes the current methods in a statistical framework that can be easily extended to analyze the effect of other biological features on mutation rates

Height and Body Mass on the Mating Market: Associations With Number of Sex Partners and Extra-Pair Sex Among Heterosexual Men and Women Aged 18–65

People with traits that are attractive on the mating market are better able to pursue their preferred mating strategy. Men who are relatively tall may be preferred by women because taller height is a cue to dominance, social status, access to resources, and heritable fitness, leading them to have more mating opportunities and sex partners. We examined height, education, age, ethnicity, and body mass index (BMI) as predictors of sexual history among heterosexual men and women (N = 60,058). The linear and curvilinear associations between self-reported height and sex partner number were small for men when controlling for education, BMI, and ethnicity (linear β = .05; curvilinear β = −.03). The mean and median number of sex partners for men of different heights were: very short (9.4; 5), short (11.0; 7), average (11.7; 7), tall (12.0; 7), very tall (12.1; 7), and extremely tall (12.3; 7). Men who were “overweight” reported a higher mean and median number of sex partners than men with other body masses. The results for men suggested limited variation in reported sex partner number across most of the height continuum, but that very short men report fewer partners than other men

Using genotype abundance to improve phylogenetic inference

Modern biological techniques enable very dense genetic sampling of unfolding evolutionary histories, and thus frequently sample some genotypes multiple times. This motivates strategies to incorporate genotype abundance information in phylogenetic inference. In this paper, we synthesize a stochastic process model with standard sequence-based phylogenetic optimality, and show that tree estimation is substantially improved by doing so. Our method is validated with extensive simulations and an experimental single-cell lineage tracing study of germinal center B cell receptor affinity maturation