make.bm: Brownian Motion and Related Models of Character Evolution

In diversitree: Comparative 'Phylogenetic' Analyses of Diversification

Brownian Motion and Related Models of Character Evolution

Description

Create a likelihood function for models of simple Brownian Motion (BM), Ornstein-Uhlenbeck (OU), or Early Burst (EB) character evolution, or BM on a “lambda” rescaled tree. This function creates a likelihood function that can be used in maximum likelihood or Bayesian inference.

Usage

make.bm(tree, states, states.sd=0, control=list())
make.ou(tree, states, states.sd=0, with.optimum=FALSE, control=list())
make.eb(tree, states, states.sd=0, control=list())
make.lambda(tree, states, states.sd=0, control=list())

Arguments

tree	A bifurcating phylogenetic tree, in ape “phylo” format.
states	A vector of continuous valued character states. This vector must be named with the tip labels of tree.
states.sd	An optional vector of measurement errors, as standard deviation around the mean. If a single value is given it is used for all tips, otherwise the vector must be named as for states.
with.optimum	Should the optimum (often "theta") be considered a free parameter? The default, FALSE, makes this behave like geiger's fitContinuous. Setting TRUE leaves the optimim to be a free parameter to be estimated. This setting can (currently) only be set to TRUE with method="pruning".
control	A list of control parameters. See details below.

Details

The control argument is a named list of options.

The main option is method. Specifying control=list(method="vcv") uses a variance-covariance matrix based approach to compute the likelihood. This is similar to the approach used by geiger, and is the default.

Two alternative approaches are available. control=list(method="pruning") uses the transition density function for brownian motion along each branch, similar to how most methods in diversitree are computed. This second approach is much faster for very large trees. control=list(method="contrasts") uses Freckleton (2012)'s contrasts based approach, which is also much faster on large trees.

When method="pruning" is specified, backend="R" or backend="C" may also be provided, which switch between a slow (and stable) R calculator and a fast (but less extensively tested) C calculator. backend="R" is currently the default.

The VCV-based functions are heavily based on fitContinuous in the geiger package.

For non-ultrametric trees with OU models, computed likelihoods may differ because of the different root treatments. This is particularly the case for models where the optimum is estimated.

For the EB model, the parameter intepretation follows geiger; the 'a' parameter is equivalent to -log(g) in Bloomberg et al. 2003; when negative it indicates a decelerating rate of trait evolution over time. When zero, it reduces to Brownian motion.

Author(s)

Richard G. FitzJohn

See Also

See https://www.zoology.ubc.ca/prog/diversitree/examples/ou-nonultrametric/ for a discussion about calculations on non-ultrametric trees.

Examples

## Random data (following APE)
data(bird.orders)
set.seed(1)
x <- structure(rnorm(length(bird.orders$tip.label)),
               names=bird.orders$tip.label)

## Not run: 
## With the VCV approach
fit1 <- find.mle(make.bm(bird.orders, x), .1)

## With the pruning calculations
lik.pruning <- make.bm(bird.orders, x, control=list(method="pruning"))
fit2 <- find.mle(lik.pruning, .1)

## All the same (need to drop the function from this though)
all.equal(fit1[-7], fit2[-7])

## If this is the same as the estimates from Geiger, to within the
## tolerances expected for the calculation and optimisation:
fit3 <- fitContinuous(bird.orders, x)
all.equal(fit3$Trait1$lnl, fit1$lnLik)
all.equal(fit3$Trait1$beta, fit1$par, check.attributes=FALSE)

## End(Not run)

diversitree documentation built on Oct. 2, 2024, 9:13 a.m.