scholarly journals The Impact of the Rate Prior on Bayesian Estimation of Divergence Times with Multiple Loci

2014 ◽  
Vol 63 (4) ◽  
pp. 555-565 ◽  
Author(s):  
Mario Dos Reis ◽  
Tianqi Zhu ◽  
Ziheng Yang
Keyword(s):  
Bayesian Estimation ◽  
Divergence Times ◽  
Multiple Loci ◽  
The Impact

scholarly journals Bayes Estimation of Species Divergence Times and Ancestral Population Sizes Using DNA Sequences From Multiple Loci

Genetics ◽  
2003 ◽  
Vol 164 (4) ◽  
pp. 1645-1656 ◽  
Author(s):  
Bruce Rannala ◽  
Ziheng Yang
Keyword(s):  
Dna Sequences ◽  
Gene Tree ◽  
Species Tree ◽  
Bayes Estimation ◽  
Ancestral Population ◽  
Divergence Times ◽  
Gene Trees ◽  
Species Divergence ◽  
Multiple Loci ◽  
Population Sizes

Abstract The effective population sizes of ancestral as well as modern species are important parameters in models of population genetics and human evolution. The commonly used method for estimating ancestral population sizes, based on counting mismatches between the species tree and the inferred gene trees, is highly biased as it ignores uncertainties in gene tree reconstruction. In this article, we develop a Bayes method for simultaneous estimation of the species divergence times and current and ancestral population sizes. The method uses DNA sequence data from multiple loci and extracts information about conflicts among gene tree topologies and coalescent times to estimate ancestral population sizes. The topology of the species tree is assumed known. A Markov chain Monte Carlo algorithm is implemented to integrate over uncertain gene trees and branch lengths (or coalescence times) at each locus as well as species divergence times. The method can handle any species tree and allows different numbers of sequences at different loci. We apply the method to published noncoding DNA sequences from the human and the great apes. There are strong correlations between posterior estimates of speciation times and ancestral population sizes. With the use of an informative prior for the human-chimpanzee divergence date, the population size of the common ancestor of the two species is estimated to be ∼20,000, with a 95% credibility interval (8000, 40,000). Our estimates, however, are affected by model assumptions as well as data quality. We suggest that reliable estimates have yet to await more data and more realistic models.

scholarly journals Using a GTR+Γ substitution model for dating sequence divergence when stationarity and time-reversibility assumptions are violated

2020 ◽  
Vol 36 (Supplement_2) ◽  
pp. i884-i894
Author(s):  
Jose Barba-Montoya ◽  
Qiqing Tao ◽  
Sudhir Kumar
Keyword(s):  
Divergence Time ◽  
Sequence Divergence ◽  
Molecular Dating ◽  
Divergence Times ◽  
Time Reversibility ◽  
Sequence Alignments ◽  
Divergence Time Estimates ◽  
Time Estimates ◽  
Substitution Process ◽  
The Impact

Abstract Motivation As the number and diversity of species and genes grow in contemporary datasets, two common assumptions made in all molecular dating methods, namely the time-reversibility and stationarity of the substitution process, become untenable. No software tools for molecular dating allow researchers to relax these two assumptions in their data analyses. Frequently the same General Time Reversible (GTR) model across lineages along with a gamma (+Γ) distributed rates across sites is used in relaxed clock analyses, which assumes time-reversibility and stationarity of the substitution process. Many reports have quantified the impact of violations of these underlying assumptions on molecular phylogeny, but none have systematically analyzed their impact on divergence time estimates. Results We quantified the bias on time estimates that resulted from using the GTR + Γ model for the analysis of computer-simulated nucleotide sequence alignments that were evolved with non-stationary (NS) and non-reversible (NR) substitution models. We tested Bayesian and RelTime approaches that do not require a molecular clock for estimating divergence times. Divergence times obtained using a GTR + Γ model differed only slightly (∼3% on average) from the expected times for NR datasets, but the difference was larger for NS datasets (∼10% on average). The use of only a few calibrations reduced these biases considerably (∼5%). Confidence and credibility intervals from GTR + Γ analysis usually contained correct times. Therefore, the bias introduced by the use of the GTR + Γ model to analyze datasets, in which the time-reversibility and stationarity assumptions are violated, is likely not large and can be reduced by applying multiple calibrations. Availability and implementation All datasets are deposited in Figshare: https://doi.org/10.6084/m9.figshare.12594638.

scholarly journals BAYESIAN ESTIMATION OF ASYMMETRIC JUMP-DIFFUSION PROCESSES

2014 ◽  
Vol 09 (03) ◽  
pp. 1450008 ◽  
Author(s):  
SAMUEL J. FRAME ◽  
CYRUS A. RAMEZANI
Keyword(s):  
Bayesian Estimation ◽  
Portfolio Choice ◽  
Stock Prices ◽  
Asset Returns ◽  
Jump Diffusion ◽  
Empirical Literature ◽  
Leverage Effect ◽  
Parameter Estimates ◽  
Price Process ◽  
The Impact

The hypothesis that asset returns are normally distributed has been widely rejected. The literature has shown that empirical asset returns are highly skewed and leptokurtic. The affine jump-diffusion (AJD) model improves upon the normal specification by adding a jump component to the price process. Two important extensions proposed by Ramezani and Zeng (1998) and Kou (2002) further improve the AJD specification by having two jump components in the price process, resulting in the asymmetric affine jump-diffusion (AAJD) specification. The AAJD specification allows the probability distribution of the returns to be asymmetrical. That is, the tails of the distribution are allowed to have different shapes and densities. The empirical literature on the "leverage effect" shows that the impact of innovations in prices on volatility is asymmetric: declines in stock prices are accompanied by larger increases in volatility than the reverse. The asymmetry in AAJD specification indirectly accounts for the leverage effect and is therefore more consistent with the empirical distributions of asset returns. As a result, the AAJD specification has been widely adopted in the portfolio choice, option pricing, and other branches of the literature. However, because of their complexity, empirical estimation of the AAJD models has received little attention to date. The primary objective of this paper is to contribute to the econometric methods for estimating the parameters of the AAJD models. Specifically, we develop a Bayesian estimation technique. We provide a comparison of the estimated parameters under the Bayesian and maximum likelihood estimation (MLE) methodologies using the S&P 500, the NASDAQ, and selected individual stocks. Focusing on the most recent spectacular market bust (2007–2009) and boom (2009–2010) periods, we examine how the parameter estimates differ under distinctly different economic conditions.

scholarly journals Testing the Impact of Calibration on Molecular Divergence Times Using a Fossil-Rich Group: The Case of Nothofagus (Fagales)

2011 ◽  
Vol 61 (2) ◽  
pp. 289-313 ◽  
Author(s):  
Hervé Sauquet ◽  
Simon Y. W. Ho ◽  
Maria A. Gandolfo ◽  
Gregory J. Jordan ◽  
Peter Wilf ◽  
...  
Keyword(s):  
Divergence Times ◽  
Molecular Divergence ◽  
The Impact

Bayesian estimation of post-Messinian divergence times in Balearic Island lizards

2008 ◽  
Vol 48 (1) ◽  
pp. 350-358 ◽  
Author(s):  
R.P. Brown ◽  
B. Terrasa ◽  
V. Pérez-Mellado ◽  
J.A. Castro ◽  
P.A. Hoskisson ◽  
...  
Keyword(s):  
Bayesian Estimation ◽  
Balearic Island ◽  
Divergence Times

scholarly journals Urbanization shapes the demographic history of a native rodent (the white-footed mouse, Peromyscus leucopus ) in New York City

2016 ◽  
Vol 12 (4) ◽  
pp. 20150983 ◽  
Author(s):  
Stephen E. Harris ◽  
Alexander T. Xue ◽  
Diego Alvarado-Serrano ◽  
Joel T. Boehm ◽  
Tyler Joseph ◽  
...  
Keyword(s):  
New York ◽  
New York City ◽  
York City ◽  
Demographic History ◽  
Peromyscus Leucopus ◽  
Genomic Diversity ◽  
Divergence Times ◽  
Nucleotide Polymorphisms ◽  
History Of ◽  
The Impact

How urbanization shapes population genomic diversity and evolution of urban wildlife is largely unexplored. We investigated the impact of urbanization on white-footed mice, Peromyscus leucopus, in the New York City (NYC) metropolitan area using coalescent-based simulations to infer demographic history from the site-frequency spectrum. We assigned individuals to evolutionary clusters and then inferred recent divergence times, population size changes and migration using genome-wide single nucleotide polymorphisms genotyped in 23 populations sampled along an urban-to-rural gradient. Both prehistoric climatic events and recent urbanization impacted these populations. Our modelling indicates that post-glacial sea-level rise led to isolation of mainland and Long Island populations. These models also indicate that several urban parks represent recently isolated P. leucopus populations, and the estimated divergence times for these populations are consistent with the history of urbanization in NYC.

scholarly journals Using a GTR+Γ substitution model for dating sequence divergence when stationarity and time-reversibility assumptions are violated

2020 ◽  
Author(s):  
Jose Barba-Montoya ◽  
Qiqing Tao ◽  
Sudhir Kumar
Keyword(s):  
Divergence Time ◽  
Sequence Divergence ◽  
Molecular Dating ◽  
Divergence Times ◽  
Time Reversibility ◽  
Sequence Alignments ◽  
Divergence Time Estimates ◽  
Time Estimates ◽  
Substitution Process ◽  
The Impact

AbstractMotivationAs the number and diversity of species and genes grow in contemporary datasets, two common assumptions made in all molecular dating methods, namely the time-reversibility and stationarity of the substitution process, become untenable. No software tools for molecular dating allow researchers to relax these two assumptions in their data analyses. Frequently the same General Time Reversible (GTR) model across lineages along with a gamma (+Γ) distributed rates across sites is used in relaxed clock analyses, which assumes time-reversibility and stationarity of the substitution process. Many reports have quantified the impact of violations of these underlying assumptions on molecular phylogeny, but none have systematically analyzed their impact on divergence time estimates.ResultsWe quantified the bias on time estimates that resulted from using the GTR+Γ model for the analysis of computer-simulated nucleotide sequence alignments that were evolved with non-stationary (NS) and non-reversible (NR) substitution models. We tested Bayesian and RelTime approaches that do not require a molecular clock for estimating divergence times. Divergence times obtained using a GTR+Γ model differed only slightly (∼3% on average) from the expected times for NR datasets, but the difference was larger for NS datasets (∼10% on average). The use of only a few calibrations reduced these biases considerably (∼5%). Confidence and credibility intervals from GTR+Γ analysis usually contained correct times. Therefore, the bias introduced by the use of the GTR+Γ model to analyze datasets, in which the time-reversibility and stationarity assumptions are violated, is likely not large and can be reduced by applying multiple calibrations.AvailabilityAll datasets are deposited in Figshare: https://doi.org/10.6084/[email protected]

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