Inference of demographic history from genealogical trees using reversible jump Markov chain Monte Carlo

Abstract

Background: Coalescent theory is a general framework to model genetic variation in a population. Specifically, it allows inference about population parameters from sampled DNA sequences. However, most currently employed variants of coalescent theory only consider very simple demographic scenarios of population size changes, such as exponential growth.

Results: Here we develop a coalescent approach that allows Bayesian non-parametric estimation of the demographic history using genealogies reconstructed from sampled DNA sequences. In this framework inference and model selection is done using reversible jump Markov chain Monte Carlo (MCMC). This method is computationally efficient and overcomes the limitations of related non-parametric approaches such as the skyline plot. We validate the approach using simulated data. Subsequently, we reanalyze HIV-1 sequence data from Central Africa and Hepatitis C virus (HCV) data from Egypt.

Conclusions: The new method provides a Bayesian procedure for non-parametric estimation of the demographic history. By construction it additionally provides confidence limits and may be used jointly with other MCMC-based coalescent approaches.

Figure 2

Comparison of prior and posterior demographic functions Top row: Bayesian inference using a prior demographic function with constant mean and constant variance (a 95% confidence band is indicated by showing the 2.5% and 97.5% quantiles). Bottom row: Bayesian inference using the "skyline plot" prior function.

Figure 1

Simulated data Top row: Example of a simulation with constant population size: (left) true demographic history (dashed line) and estimate obtained with the classic skyline plot; (right) point estimate obtained with rjMCMC and 95% confidence band. Bottom row: Example with exponential population growth: (left) true population growth and classic skyline plot; (right) results from rjMCMC approach.

Figure 3

HIV-1 in Central Africa Top row: a) underlying genealogy; b) classic skyline plot. Bottom row: c) population size function estimated with rjMCMC and corresponding 95% confidence band; d) comparison rjMCMC versus generalized skyline plot.

Figure 4

HCV in Egypt Top row: a) underlying reconstructed genealogy; b) classic skyline plot. Bottom row: c) population size function estimated with rjMCMC and corresponding 95% confidence band; d) comparison rjMCMC versus generalized skyline plot.