mcmc.popsize: Reversible Jump MCMC to Infer Demographic History

Description

These functions implement a reversible jump MCMC framework to infer the demographic history, as well as corresponding confidence bands, from a genealogical tree. The computed demographic history is a continous and smooth function in time. mcmc.popsize runs the actual MCMC chain and outputs information about the sampling steps, extract.popsize generates from this MCMC output a table of population size in time, and plot.popsize and lines.popsize provide utility functions to plot the corresponding demographic functions.

Usage

mcmc.popsize(tree,nstep, thinning=1, burn.in=0,progress.bar=TRUE, method.prior.changepoints=c("hierarchical", "fixed.lambda"), max.nodes=30, lambda=0.5, gamma.shape=0.5, gamma.scale=2, method.prior.heights=c("skyline", "constant", "custom"), prior.height.mean, prior.height.var)
extract.popsize(mcmc.out, credible.interval=0.95, time.points=200, thinning=1, burn.in=0)
"plot"(x, show.median=TRUE, show.years=FALSE, subst.rate, present.year, ...)
"lines"(x, show.median=TRUE,show.years=FALSE, subst.rate, present.year, ...)

Arguments

tree

Either an ultrametric tree (i.e. an object of class "phylo"), or coalescent intervals (i.e. an object of class "coalescentIntervals").

nstep

Number of MCMC steps, i.e. length of the Markov chain (suggested value: 10,000-50,000).

thinning

Thinning factor (suggest value: 10-100).

burn.in

Number of steps dropped from the chain to allow for a burn-in phase (suggest value: 1000).

progress.bar

Show progress bar during the MCMC run.

method.prior.changepoints

If hierarchicalis chosen (the default) then the smoothing parameter lambda is drawn from a gamma distribution with some specified shape and scale parameters. Alternatively, for fixed.lambda the value of lambda is a given constant.

max.nodes

Upper limit for the number of internal nodes of the approximating spline (default: 30).

lambda

Smoothing parameter. For method="fixed.lambda" the specifed value of lambda determines the mean of the prior distribution for the number of internal nodes of the approximating spline for the demographic function (suggested value: 0.1-1.0).

gamma.shape

Shape parameter of the gamma function from which lambda is drawn for method="hierarchical".

gamma.scale

Scale parameter of the gamma function from which lambda is drawn for method="hierarchical".

method.prior.heights

Determines the prior for the heights of the change points. If custom is chosen then two functions describing the mean and variance of the heigths in depence of time have to be specified (via prior.height.mean and prior.height.var options). Alternatively, two built-in priors are available: constant assumes constant population size and variance determined by Felsenstein (1992), and skyline assumes a skyline plot (see Opgen-Rhein et al. 2004 for more details).

prior.height.mean

Function describing the mean of the prior distribution for the heights (only used if method.prior.heights = custom).

prior.height.var

Function describing the variance of the prior distribution for the heights (only used if method.prior.heights = custom).

mcmc.out

Output from mcmc.popsize - this is needed as input for extract.popsize.

credible.interval

Probability mass of the confidence band (default: 0.95).

time.points

Number of discrete time points in the table output by extract.popsize.

Table with population size versus time, as computed by extract.popsize.

show.median

Plot median rather than mean as point estimate for demographic function (default: TRUE).

show.years

Option that determines whether the time is plotted in units of of substitutions (default) or in years (requires specification of substution rate and year of present).

subst.rate

Substitution rate (see option show.years).

present.year

Present year (see option show.years).

...

Further arguments to be passed on to plot.

Details

Please refer to Opgen-Rhein et al. (2005) for methodological details, and the help page of skyline for information on a related approach.

References

Opgen-Rhein, R., Fahrmeir, L. and Strimmer, K. 2005. Inference of demographic history from genealogical trees using reversible jump Markov chain Monte Carlo. BMC Evolutionary Biology, 5, 6.

Examples

Run this code

# get tree
data("hivtree.newick") # example tree in NH format
tree.hiv <- read.tree(text = hivtree.newick) # load tree

# run mcmc chain
mcmc.out <- mcmc.popsize(tree.hiv, nstep=100, thinning=1, burn.in=0,progress.bar=FALSE) # toy run
#mcmc.out <- mcmc.popsize(tree.hiv, nstep=10000, thinning=5, burn.in=500) # remove comments!!

# make list of population size versus time
popsize  <- extract.popsize(mcmc.out)

# plot and compare with skyline plot
sk <- skyline(tree.hiv)
plot(sk, lwd=1, lty=3, show.years=TRUE, subst.rate=0.0023, present.year = 1997)
lines(popsize, show.years=TRUE, subst.rate=0.0023, present.year = 1997)