make.mkn {diversitree}R Documentation

Mk2 and Mk-n Models of character evolution

Description

Prepare to run a Mk2/Mk-n model on a phylogenetic tree and binary/discrete trait data. This fits the Pagel 1994 model, duplicating the ace function in ape. Differences with that function include (1) alternative root treatments are possible, (2) easier to tweak parameter combinations through constrain, and (3) run both MCMC and MLE fits to parameters. Rather than exponentiate the Q matrix, this implementation solves the ODEs that this matrix defines. This may or may not be robust on trees leading to low probabilities.

Usage

make.mk2(tree, states, strict=TRUE, control=list())
make.mkn(tree, states, k, strict=TRUE, control=list())
make.mkn.meristic(tree, states, k, control=list())

Arguments

tree

An ultrametric bifurcating phylogenetic tree, in ape “phylo” format.

states

A vector of character states, each of which must be 0 or 1 for make.mk2 or 1 to k for make.mkn.

k

Number of states to model.

strict

The states vector is always checked to make sure that the values are integers on 0:1 (mk2) or 1:k (mkn). If strict is TRUE (the default), then the additional check is made that every state is present. The likelihood models tend to be poorly behaved where states are missing, but there are cases (missing intermediate states for meristic characters) where allowing such models may be useful.

control

List of control parameters for the ODE solver. See Details below.

Details

make.mk2 and make.mkn return functions of class mkn. These functions have argument list (and default values)

    f(pars, pars, prior=NULL, root=ROOT.OBS, root.p=NULL, fail.value=NULL)
  

The arguments are interpreted as

With more than 9 states, qij can be ambiguous (e.g. is q113 1->13 or 11->3?). To avoid this, the numbers are zero padded (so that the above would be q0113 or q1103 for 1->13 and 11->3 respectively). It might be easier to rename the arguments in practice though.

The control argument controls how the calculations will be carried out. It is a list, which may contain elements in make.bisse. In addition, the list element method may be present, which selects between three different ways of computing the likelihood:

Author(s)

Richard G. FitzJohn

See Also

constrain for making submodels, find.mle for ML parameter estimation, mcmc for MCMC integration, and make.bisse for state-dependent birth-death models.

Examples

## Simulate a tree and character distribution.  This is on a birth-death
## tree, with high rates of character evolution and an asymmetry in the
## character transition rates.
pars <- c(.1, .1, .03, .03, .1, .2)
set.seed(3)
phy <- trees(pars, "bisse", max.taxa=25, max.t=Inf, x0=0)[[1]]

## Here is the 25 species tree with the true character history coded.
## Red is state '1', which has twice the character transition rate of
## black (state '0').
h <- history.from.sim.discrete(phy, 0:1)
plot(h, phy)

## Maximum likelihood parameter estimation:
p <- c(.1, .1) # initial parameter guess

## Not run: 
lik <- make.mk2(phy, phy$tip.state)
fit.mk2 <- find.mle(lik, p)
coef(fit.mk2)   # q10 >> q01
logLik(fit.mk2) # -10.9057

## This can also be done using the more general Mk-n.
## This uses an approximation for the likelihood calculations.  make.mkn
## assumes that states are numbered 1, 2, ..., k, so 1 needs to be added
## to the states returned by trees.
lik.mkn <- make.mkn(phy, phy$tip.state + 1, 2)
fit.mkn <- find.mle(lik.mkn, p)
fit.mkn[1:2]

## These are the same (except for the naming of arguments)
all.equal(fit.mkn[-7], fit.mk2[-7], check.attr=FALSE, tolerance=1e-7)

## Equivalence to ape's \link{ace} function:
model <- matrix(c(0, 2, 1, 0), 2)
fit.ape <- ace(phy$tip.state, phy, "discrete", model=model, ip=p)

## To do the comparison, we need to rerun the diversitree version with
## the same root conditions as ape.
fit.mk2 <- find.mle(lik, p, root=ROOT.GIVEN, root.p=c(1,1))

## These are the same to a reasonable degree of accuracy, too (the
## matrix exponentiation is slightly less accurate than the ODE
## solving approach.  The make.mk2 version is exact)
all.equal(fit.ape[c("rates", "loglik")], fit.mk2[1:2],
          check.attributes=FALSE, tolerance=1e-4)

## The ODE calculation method may be useful when there are a large
## number of possible states (say, over 20).
lik.ode <- make.mkn(phy, phy$tip.state + 1, 2,
                    control=list(method="ode"))
fit.ode <- find.mle(lik.ode, p)
fit.ode[1:2]

all.equal(fit.ode[-7], fit.mkn[-7], tolerance=1e-7)

## End(Not run)

[Package diversitree version 0.9-16 Index]