SummarizeMVSLOUCH: Summarize parameters estimated under a multivariate OUBM motion model

Description

Compiles a summary (appropriate moments, conditional moments, information criteria) of parameters of a multivariate OUBM model at a given time point. The user is recommended to install the suggested package PCMBaseCpp which significantly speeds up the calculations (see Details).

Usage

SummarizeMVSLOUCH(phyltree, mData, modelParams, regimes = NULL, 
regimes.times = NULL, t = c(1), dof = NULL, M.error = NULL, predictors = NULL, 
Atype = "Invertible", Syytype = "UpperTri", min_bl = 0.0003, maxiter = 50)

Value

A list for each provided time point. See the help of mvslouchModel for what the summary at each time point is.

Arguments

phyltree

The phylogeny in phylo format. The tree can be obtained from e.g. a nexus file by the read.nexus() function from the ape package. The "standard" ape node indexing is assumed: for a tree with $n$ tips, the tips should have indices 1:n and the root index n+1. The root.edge field is ignored.

mData

A matrix with the rows corresponding to the tip species while the columns correspond to the traits. The rows should be named by species
(field phyltree$tip.label), if not, then a warning is thrown and the order of the species is assumed to be the same as the order in which the species are in the phylogeny (i.e. correspond to the node indices 1:n, where $n$ is the number of tips). The columns should be named by traits, otherwise a warning is thrown and generic names are generated.

modelParams

A list of model parameters, as returned in ParamsInModel part of
mvslouchModel's output.

regimes

A vector or list of regimes. If vector then each entry corresponds to each of phyltree's branches, i.e. to each row of phyltree$edge.If list then each list entry corresponds to a tip node and is a vector for regimes on that lineage. If NULL, then a constant regime is assumed on the whole tree.

regimes.times

A list of vectors for each tree node, it starts with 0 and ends with the current time of the species. In between are the times where the regimes (niches) changed. If NULL, then each branch is considered to be constant a regime.

t

A vector of time points at which the summary is to be calculated. This allows for one to study (and plot) the (conditional) mean and covariance as functions of time. The function additionally returns the parameter summary at the tree's height.

dof

Number of unknown parameters in the model, can be extracted from the output of mvslouchModel(). If not provided all parameters are assumed unknown.

M.error

An optional measurement error covariance structure. The measurement errors between species are assumed independent. The program tries to recognize the structure of the passed matrix and accepts the following possibilities :

a single number that is a common measurement error for all tips and species,
a m element vector with each value corresponding to a variable, measurement errors are independent between variables and each species is assumed to have the same measurement errors,
a m x m ((number of variables) x (number of variables)) matrix, all species will have the same measurement error,
a list of length n (number of species), each list element is the covariance structure for the appropriate (numbering according to tree) species, either a single number (each variable has same variance), vector (of length m for each variable), or m x m matrix, the order of the list has to correspond to the order of the nodes in the phyltree object,
NULL no measurement error.

From version 2.0.0 of mvSLOUCH it is impossible to pass a single joint measurement error matrix for all the species and traits.

predictors

A vector giving the numbers of the columns from data which are to be considered predictor ones, i.e. conditioned on in the program output. If not provided then columns (kY+1):ncol(mData), i.e. the "BM" ones, are treated as predictors.

Atype

What class does the A matrix in the multivariate OUBM model belong to, possible values : "SingleValueDiagonal", "Diagonal", "UpperTri", "LowerTri", Symmetric, SymmetricPositiveDefinite,
"DecomposablePositive", "DecomposableNegative",
"DecomposableReal", "Invertible", "TwoByTwo", "Any"

Syytype

What class does the Syy matrix in the multivariate OUBM model belong to, possible values : "SingleValueDiagonal", "Diagonal", "UpperTri", "LowerTri", "Symmetric", "Any"

min_bl

Value to which PCMBase's PCMBase.Threshold.Skip.Singular should be set. It indicates that branches of length shorter than min_bl should be skipped in likelihood calculations. Short branches can result in singular covariance matrices for the transition density along a branch. The user should adjust this value if a lot of warnings are raised by PCMBase about singularities during the likelihood calculations. However, this does not concern tip branches-these cannot be skipped and hence should be long enough so that numerical issues are not raised.

maxiter

The maximum number of iterations inside the GLS estimation procedure. In the first step regime optima and B (and perhaps initial state) are estimated conditional on the other parameters and current estimate of B, then the estimate of B is update and the same phylogenetic GLS is repeated.

Author

Krzysztof Bartoszek

Details

The likelihood calculations are done by the PCMBase package. However, there is a C++ backend, PCMBaseCpp. If it is not available, then the likelihood is calculated slower using pure R. However, with the calculations in C++ up to a 100-fold increase in speed is possible (more realistically 10-20 times). The PCMBaseCpp package is available from https://github.com/venelin/PCMBaseCpp.

The setting Atype="Any" means that one assumes the matrix A is eigendecomposable. If A is defective, then the output will be erroneous.

From version 2.0.0 of mvSLOUCH the data has to be passed as a matrix. To underline this the data parameter's name has been changed to mData.

From version 2.0.0 of mvSLOUCH the parameter calcCI has been removed. The package now offers the possibility of bootstrap confidence intervals, see function parametric.bootstrap.

References

Bartoszek, K. and Pienaar, J. and Mostad. P. and Andersson, S. and Hansen, T. F. (2012) A phylogenetic comparative method for studying multivariate adaptation. Journal of Theoretical Biology 314:204-215.

Butler, M.A. and A.A. King (2004) Phylogenetic comparative analysis: a modeling approach for adaptive evolution. American Naturalist 164:683-695.

Hansen, T.F. (1997) Stabilizing selection and the comparative analysis of adaptation. Evolution 51:1341-1351.

Hansen, T.F. and Bartoszek, K. (2012) Interpreting the evolutionary regression: the interplay between observational and biological errors in phylogenetic comparative studies. Systematic Biology 61(3):413-425.

Hansen, T.F. and Pienaar, J. and Orzack, S.H. (2008) A comparative method for studying adaptation to randomly evolving environment. Evolution 62:1965-1977.

Labra, A., Pienaar, J. & Hansen, T.F. (2009) Evolution of thermophysiology in Liolaemus lizards: adaptation, phylogenetic inertia and niche tracking. The American Naturalist 174:204-220.

Pienaar et al (in prep) An overview of comparative methods for testing adaptation to external environments.

Examples

Run this code

RNGversion(min(as.character(getRversion()),"3.6.1"))
set.seed(12345, kind = "Mersenne-Twister", normal.kind = "Inversion")
### We will first simulate a small phylogenetic tree using functions from ape.
### For simulating the tree one could also use alternative functions, e.g. sim.bd.taxa 
### from the TreeSim package
phyltree<-ape::rtree(3)

## The line below is not necessary but advisable for speed
phyltree<-phyltree_paths(phyltree)

### Define a vector of regimes.
regimes<-c("small","small","large","small")

### Define SDE parameters to be able to simulate data under the mvOUBM model.
OUBMparameters<-list(vY0=matrix(1,ncol=1,nrow=1),A=matrix(0.5,ncol=1,nrow=1),
B=matrix(c(2),ncol=1,nrow=1),mPsi=cbind("small"=1,"large"=-1),
Syy=matrix(2,ncol=1,nrow=1),vX0=matrix(0,ncol=1,nrow=1),Sxx=diag(1,1,1),
Syx=matrix(0,ncol=1,nrow=1),Sxy=matrix(0,ncol=1,nrow=1))

### Now simulate the data.
OUBMdata<-simulMVSLOUCHProcPhylTree(phyltree,OUBMparameters,regimes,NULL)
OUBMdata<-OUBMdata[phyltree$tip.label,,drop=FALSE]

## Here we do not do any recovery step
OUBM.summary<-SummarizeMVSLOUCH(phyltree,OUBMdata,OUBMparameters,
regimes,t=c(1),dof=7,maxiter=2)

RNGversion(as.character(getRversion()))
if (FALSE)  ##It takes too long to run this
## now less trivial simulation setup
phyltree<-ape::rtree(5)

## The line below is not necessary but advisable for speed
phyltree<-phyltree_paths(phyltree)

### Define a vector of regimes.
regimes<-c("small","small","large","small","small","large","large","large")

### Define SDE parameters to be able to simulate data under the mvOUBM model.
OUBMparameters<-list(vY0=matrix(c(1,-1),ncol=1,nrow=2),A=rbind(c(9,0),c(0,5)),
B=matrix(c(2,-2),ncol=1,nrow=2),mPsi=cbind("small"=c(1,-1),"large"=c(-1,1)),
Syy=rbind(c(1,0.25),c(0,1)),vX0=matrix(0,1,1),Sxx=matrix(1,1,1),
Syx=matrix(0,ncol=1,nrow=2),Sxy=matrix(0,ncol=2,nrow=1))

### Now simulate the data.
OUBMdata<-simulMVSLOUCHProcPhylTree(phyltree,OUBMparameters,regimes,NULL)
OUBMdata<-OUBMdata[phyltree$tip.label,]

### Try to recover the parameters of the mvOUBM model.
OUBMestim<-mvslouchModel(phyltree,OUBMdata,2,regimes,Atype="DecomposablePositive",
Syytype="UpperTri",diagA="Positive")

### Summarize them.
OUBM.summary<-SummarizeMVSLOUCH(phyltree,OUBMdata,OUBMestim$FinalFound$ParamsInModel,
regimes,t=c(phyltree$tree_height),dof=OUBMestim$FinalFound$ParamSummary$dof,maxiter=50)

### And finally bootstrap with particular interest in the evolutionary and optimal
### regressions
OUBMbootstrap<-parametric.bootstrap(estimated.model=OUBMestim,phyltree=phyltree,
values.to.bootstrap=c("evolutionary.regression","optimal.regression"),
regimes=regimes,root.regime="small",M.error=NULL,predictors=c(3),kY=2,
numboot=5,Atype="DecomposablePositive",Syytype="UpperTri",diagA="Positive")

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