Estimating Mutation Parameters, Population History and Genealogy Simultaneously From Temporally Spaced Sequence Data

Abstract

Molecular sequences obtained at different sampling times from populations of rapidly evolving pathogens and from ancient subfossil and fossil sources are increasingly available with modern sequencing technology. Here, we present a Bayesian statistical inference approach to the joint estimation of mutation rate and population size that incorporates the uncertainty in the genealogy of such temporally spaced sequences by using Markov chain Monte Carlo (MCMC) integration. The Kingman coalescent model is used to describe the time structure of the ancestral tree. We recover information about the unknown true ancestral coalescent tree, population size, and the overall mutation rate from temporally spaced data, that is, from nucleotide sequences gathered at different times, from different individuals, in an evolving haploid population. We briefly discuss the methodological implications and show what can be inferred, in various practically relevant states of prior knowledge. We develop extensions for exponentially growing population size and joint estimation of substitution model parameters. We illustrate some of the important features of this approach on a genealogy of HIV-1 envelope (env) partial sequences.

Predator-Prey Dynamics of Intra-Host Simian Immunodeficiency Virus Evolution Within the Untreated Host

“…Although often 2-3 distinct lineages were observed for each macaque phylogeny, dating back as early as the pretransmission interval (46) (Figures 1 and S1), each of these lineages appeared to be temporally structured, giving rise to multiple population turnover events in the estimated within-host viral effective population size (N e ) (Figures 2A and S2) and a periodicity demonstrated by auto-correlation (Figure S3). Peak N e values ranged from the previously observed estimate in the blood [10 3 (7,8,(13)(14)(15)49)] to as high as 10 7 ; however, collective N e values were consistently about one order of magnitude greater than that of plasma and/or PBMCs, supporting the hypothesis that a more representative sampling of the population was required to increase estimates of within-host N e .…”

“…Genetic diversity provided from the sequence data and inferred coalescent tree can be used to estimate N e at intervals along the time-scaled phylogeny, including periods during which sampling is unattainable, by assuming that the estimated time to a coalescent event within the tree for two sequences is proportional to the population size. This approach has produced conflicting results regarding both N e estimates and thus the impact of selection on the population (7,(12)(13)(14)(15). However, the seemingly paradoxical heavy influence of selection on a small population has been reconciled by da Silva (16) using a model of known HIV-specific parameters that affect population size (e.g., mutation rate, generation time), but also immune selection pressure targeting a large number of HIV epitopes (5) simultaneously.…”

Are Skyline Plot-Based Demographic Estimates Overly Dependent on Smoothing Prior Assumptions?

“…In some instances, only sampled sequence data, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\boldsymbol{D}$\end{document} , are available and a distribution over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\mathcal{T}$\end{document} must be reconstructed from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\boldsymbol{D}$\end{document} under a model of molecular evolution with parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\boldsymbol{\theta}$\end{document} . Equation 2 becomes embedded in the more complex expression \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\text{P}{\left( {\mathcal{T}, \boldsymbol{\theta}, \boldsymbol{N} \, | \, \boldsymbol{D}} \right)} \propto\text{P}{\left( {\boldsymbol{D} \, | \, \mathcal{T}, \boldsymbol{\theta}} \right)} \text{P}{\left( {\mathcal{T} \, | \, \boldsymbol{N} } \right)} \text{P}{\left( {\boldsymbol{N} } \right)} \text{P}{\left( {\boldsymbol{\theta}} \right)}$\end{document} , which then involves inferring both the tree and population size ( Drummond et al 2002 ).…”

Spatially Enriched Paralog Rearrangements Argue Functionally Diverse Ribosomes Arise during Cold Acclimation in Arabidopsis

“…The alignment was analyzed using a lognormal relaxed clock [155], a GTR + i model (as determined by the corrected AIC criteria in jModelTest 2.1.10 [156,157]-see Table S7), and a uniformly distributed Yule process speciation tree [158]. Markov chain Monte Carlo (MCMC) was set to 10,000,000 generations [159]; sampling was performed every 1000 generations and the burn-in set to 10%. The MCMC trace files generated were visualized in Tracer v1.7.1 [160], which presented statistical ESS summaries over 300 (Table S7).…”