mvSLOUCH-package: Multivariate Ornstein-Uhlenbeck type stochastic differential...
In mvSLOUCH: Multivariate Stochastic Linear Ornstein-Uhlenbeck Models for Phylogenetic Comparative Hypotheses
mvSLOUCH-package R Documentation
Multivariate Ornstein-Uhlenbeck type stochastic differential equation models
for phylogenetic comparative data.
Description
The package allows for maximum likelihood estimation, simulation and study of properties
of multivariate Brownian motion
\begin{array}{rcl}dX(t) & = & \Sigma dB(t),\end{array}
OU
\begin{array}{rcl}dY(t) & = & -A(Y(t)-\Psi(t))dt + \Sigma dB(t)\end{array}
and OUBM
\begin{array}{rcl}
dY(t) & = & -A(Y(t)-(\Psi(t)- A^{-1}BX(t)))dt + \Sigma_{yy} dB(t) \\ dX(t) & = & \Sigma_{xx} dB(t)
\end{array}
models that evolve on a phylogenetic tree.
This software comes AS IS in the hope that it will be useful WITHOUT ANY WARRANTY,
NOT even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
Please understand that there may still be bugs and errors. Use it at your own risk.
We take no responsibility for any errors or omissions in this package or for any misfortune
that may befall you or others as a result of its use. Please send comments and report
bugs to Krzysztof Bartoszek at krzbar@protonmail.ch .
Details
Package: mvSLOUCH
Type: Package
Version: 2.7.6
Date: 2023-11-19
License: GPL (>= 2)
LazyLoad: yes
The package allows for maximum likelihood estimation, simulation and study of properties
of multivariate Brownian motion
\begin{array}{rcl}dX(t) & = & \Sigma dB(t),\end{array}
OU
\begin{array}{rcl}dY(t) & = & -A(Y(t)-\Psi(t))dt + \Sigma dB(t)\end{array}
and OUBM
\begin{array}{rcl}
dY(t) & = & -A(Y(t)-\Psi(t)- A^{-1}BX(t))dt + \Sigma_{yy} dB(t) \\ dX(t) & = & \Sigma_{xx} dB(t)
\end{array}
models that evolve on a phylogenetic tree.
The estimation functions are BrownianMotionModel, ouchModel (OUOU) and
mvslouchModel (mvOUBM). They rely on a combination of least squares and numerical
optimization techniques. A wrapper function for all of them is estimate.evolutionary.model,
it tries all three models with different matrix parameter classes and then returns the best model
based on the AICc.
The simulation functions are simulBMProcPhylTree, simulOUCHProcPhylTree,
simulMVSLOUCHProcPhylTree.
The phylogeny provided to them should be of the phylo (package ape) format.
The package uses the functions .sym.par() and .sym.unpar() from the
ouch package to parametrize symmetric matrices.
In the case the mvOUBM model with a single response trait the package slouch is a
recommended alternative.
The package uses PCMBase's PCMLik() function as the engine to do calculate
the likelihood and phylogenetic least squares. If the PCMBaseCpp package is
installed mvSLOUCH can take advantage of it to significantly decrease
the running time. The PCMBaseCpp package is available from
https://github.com/venelin/PCMBaseCpp.
Author(s)
Krzysztof Bartoszek
Maintainer: <krzbar@protonmail.ch>
References
Bartoszek, K. and Fuentes-Gonzalez, J. and Mitov, V. and Pienaar, J. and Piwczynski, M.
and Puchalka, R. and Spalik, K. and Voje, K. L. (2023)
Model Selection Performance in Phylogenetic Comparative Methods Under Multivariate
Ornstein-Uhlenbeck Models of Trait Evolution, Systematic Biology 72(2):275-293.
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.
Felsenstein, J. (1985)
Phylogenies and the comparative method.
American Naturalist 125:1-15.
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.
Mitov, V. and Bartoszek, K. and Asimomitis, G. and Stadler, T. (2020)
Fast likelihood calculation for multivariate Gaussian phylogenetic models with shifts
Theoretical Population Biology 131:66-78.
Pienaar et al (in prep) An overview of comparative methods for
testing adaptation to external environments.
Examples
## Set the version of the random number generator
## so that the results are always reproducible
RNGversion(min(as.character(getRversion()),"3.6.1"))
## Set the random seed, and random number generator
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(5)
## The line below is not necessary but advisable for speed.
## It enhances the phylo object with multiple additional fields, e.g.,
## the lineage for each tip, that are used by subsequent mvSLOUCH functions.
phyltree<-phyltree_paths(phyltree)
## Define a vector of regimes. There are two of them: small and large;
## their layout is random.
regimes<-c("small","small","large","small","small","large","large","large")
### Define SDE parameters to be able to simulate data under the different models.
### There is no particular meaning attached to these parameters.
### BM parameters
BMparameters<-list(vX0=matrix(0,nrow=3,ncol=1),
Sxx=rbind(c(1,0,0),c(0.2,1,0),c(0.3,0.25,1)))
### OUOU parameters
OUOUparameters<-list(vY0=matrix(c(1,-1,0.5),nrow=3,ncol=1),
A=rbind(c(9,0,0),c(0,5,0),c(0,0,1)),mPsi=cbind("small"=c(1,-1,0.5),
"large"=c(-1,1,0.5)),Syy=rbind(c(1,0.25,0.3),c(0,1,0.2),c(0,0,1)))
### OUBM parameters
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 under 3D BM, OUOU and OUBM (the third variable is the
### BM one) models of evolution.
BMdata<-simulBMProcPhylTree(phyltree,X0=BMparameters$vX0,Sigma=BMparameters$Sxx)
### extract just the values at the tips of the phylogeny
BMdata<-BMdata[phyltree$tip.label,,drop=FALSE]
OUOUdata<-simulOUCHProcPhylTree(phyltree,OUOUparameters,regimes,NULL)
### extract just the values at the tips of the phylogeny
OUOUdata<-OUOUdata[phyltree$tip.label,,drop=FALSE]
OUBMdata<-simulMVSLOUCHProcPhylTree(phyltree,OUBMparameters,regimes,NULL)
### extract just the values at the tips of the phylogeny
OUBMdata<-OUBMdata[phyltree$tip.label,,drop=FALSE]
### Recover the parameters of the SDEs.
### Recover under the BM model.
BMestim<-BrownianMotionModel(phyltree,BMdata)
### reset to the original version of the random number generator.
RNGversion(as.character(getRversion()))
## Not run:
### It takes too long to run this from this point.
### We do not reduce the number of iterations of the optimier
### (as we did in other manual page examples, so the running
### times will be as with default settings.
### Recover under the OUOU model.
OUOUestim<-ouchModel(phyltree,OUOUdata,regimes,Atype="DecomposablePositive",
Syytype="UpperTri",diagA="Positive")
### Recover under the OUBM model.
OUBMestim<-mvslouchModel(phyltree,OUBMdata,2,regimes,Atype="DecomposablePositive",
Syytype="UpperTri",diagA="Positive")
### Usage of the wrapper function that allows for estimation under multiple
### models in one call, here we use the default collection of models offered
### by mvSLOUCH. This includes BM, a number of OUOU and OUBM models.
### For data simulated under BM.
estimResultsBM<-estimate.evolutionary.model(phyltree,BMdata,regimes=NULL,
root.regime=NULL,M.error=NULL,repeats=3,model.setups=NULL,predictors=c(3),
kY=2,doPrint=TRUE)
### For data simulated under OUOU.
estimResultsOUOU<-estimate.evolutionary.model(phyltree,OUOUdata,regimes=regimes,
root.regime="small",M.error=NULL,repeats=3,model.setups=NULL,predictors=c(3),
kY=2,doPrint=TRUE)
### For data simulated under OUBM.
estimResultsOUBM<-estimate.evolutionary.model(phyltree,OUBMdata,regimes=regimes,
root.regime="small",M.error=NULL,repeats=3,model.setups=NULL,predictors=c(3),
kY=2,doPrint=TRUE)
## In the wrapper function the resulting best found model parameters are in
## estimResultsBM$BestModel$ParamsInModel
## estimResultsOUOU$BestModel$ParamsInModel
## estimResultsOUBM$BestModel$ParamsInModel
### Summarize the best found models.
### Under the BM model for BM data. One needs to check whether the
### model in BMestim$ParamsInModel corresponds to a BM model (here it does).
BM.summary<-SummarizeBM(phyltree,BMdata,BMestim$ParamsInModel,t=c(1),
dof=BMestim$ParamSummary$dof)
### Under the OUOU model for OUOU data. One needs to check whether the
### model in OUOUestim$ParamsInModel corresponds to an OUOU model (here it does).
OUOU.summary<-SummarizeOUCH(phyltree,OUOUdata,OUOUestim$FinalFound$ParamsInModel,
regimes,t=c(1),dof=OUOUestim$FinalFound$ParamSummary$dof)
### Under the OUBM model for OUBM data. One needs to check whether the
### model in OUBMestim$ParamsInModel corresponds to a OUBM model (here it does).
OUBM.summary<-SummarizeMVSLOUCH(phyltree,OUBMdata,OUBMestim$FinalFound$ParamsInModel,
regimes,t=c(1),dof=OUBMestim$FinalFound$ParamSummary$dof)
### Now run the parametric bootstrap to obtain confidence intervals for some parameters.
### For the BM model, we want CIs for the ancestral state, and the "sqaure" of the
### diffusion (evolutionary rate) matrix. The number of bootstrap replicates
### is very small, 5 (to reduce running times). In reality it should be much more, e.g.,
### 100 or more if the computational budget allows.
BMbootstrap<-parametric.bootstrap(estimated.model=BMestim,phyltree=phyltree,
values.to.bootstrap=c("vX0","StS"),M.error=NULL,numboot=5)
### For the OUOU model, we want a CI for the evolutionary regression coefficient vector.
### The number of bootstrap replicates is very small, 5 (to reduce running times).
### In reality it should be much more, e.g., 100 or more if the
### computational budget allows.
OUOUbootstrap<-parametric.bootstrap(estimated.model=estimResultsOUOU,phyltree=phyltree,
values.to.bootstrap=c("evolutionary.regression"),regimes=regimes,root.regime="small",
M.error=NULL,predictors=c(3),kY=NULL,numboot=5,Atype=NULL,Syytype=NULL,diagA=NULL)
### For the OUBM model, we want CIs for the evolutionary and optimal regression
### coefficient vectors. The number of bootstrap replicates is very small,
### 5 (to reduce running times). In reality it should be much more, e.g.,
### 100 or more if the computational budget allows.
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")
## End(Not run)
mvSLOUCH documentation built on Nov. 21, 2023, 1:08 a.m.
R Package Documentation
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| mvSLOUCH-package | R Documentation |
Multivariate Ornstein-Uhlenbeck type stochastic differential equation models for phylogenetic comparative data.
Description
The package allows for maximum likelihood estimation, simulation and study of properties of multivariate Brownian motion
\begin{array}{rcl}dX(t) & = & \Sigma dB(t),\end{array}
OU
\begin{array}{rcl}dY(t) & = & -A(Y(t)-\Psi(t))dt + \Sigma dB(t)\end{array}
and OUBM
\begin{array}{rcl}
dY(t) & = & -A(Y(t)-(\Psi(t)- A^{-1}BX(t)))dt + \Sigma_{yy} dB(t) \\ dX(t) & = & \Sigma_{xx} dB(t)
\end{array}
models that evolve on a phylogenetic tree.
This software comes AS IS in the hope that it will be useful WITHOUT ANY WARRANTY, NOT even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. Please understand that there may still be bugs and errors. Use it at your own risk. We take no responsibility for any errors or omissions in this package or for any misfortune that may befall you or others as a result of its use. Please send comments and report bugs to Krzysztof Bartoszek at krzbar@protonmail.ch .
Details
| Package: | mvSLOUCH |
| Type: | Package |
| Version: | 2.7.6 |
| Date: | 2023-11-19 |
| License: | GPL (>= 2) |
| LazyLoad: | yes |
The package allows for maximum likelihood estimation, simulation and study of properties of multivariate Brownian motion
\begin{array}{rcl}dX(t) & = & \Sigma dB(t),\end{array}
OU
\begin{array}{rcl}dY(t) & = & -A(Y(t)-\Psi(t))dt + \Sigma dB(t)\end{array}
and OUBM
\begin{array}{rcl}
dY(t) & = & -A(Y(t)-\Psi(t)- A^{-1}BX(t))dt + \Sigma_{yy} dB(t) \\ dX(t) & = & \Sigma_{xx} dB(t)
\end{array}
models that evolve on a phylogenetic tree.
The estimation functions are BrownianMotionModel, ouchModel (OUOU) and
mvslouchModel (mvOUBM). They rely on a combination of least squares and numerical
optimization techniques. A wrapper function for all of them is estimate.evolutionary.model,
it tries all three models with different matrix parameter classes and then returns the best model
based on the AICc.
The simulation functions are simulBMProcPhylTree, simulOUCHProcPhylTree, simulMVSLOUCHProcPhylTree.
The phylogeny provided to them should be of the phylo (package ape) format.
The package uses the functions .sym.par() and .sym.unpar() from the
ouch package to parametrize symmetric matrices.
In the case the mvOUBM model with a single response trait the package slouch is a recommended alternative.
The package uses PCMBase's PCMLik() function as the engine to do calculate
the likelihood and phylogenetic least squares. If the PCMBaseCpp package is
installed mvSLOUCH can take advantage of it to significantly decrease
the running time. The PCMBaseCpp package is available from
https://github.com/venelin/PCMBaseCpp.
Author(s)
Krzysztof Bartoszek Maintainer: <krzbar@protonmail.ch>
References
Bartoszek, K. and Fuentes-Gonzalez, J. and Mitov, V. and Pienaar, J. and Piwczynski, M. and Puchalka, R. and Spalik, K. and Voje, K. L. (2023) Model Selection Performance in Phylogenetic Comparative Methods Under Multivariate Ornstein-Uhlenbeck Models of Trait Evolution, Systematic Biology 72(2):275-293.
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.
Felsenstein, J. (1985) Phylogenies and the comparative method. American Naturalist 125:1-15.
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.
Mitov, V. and Bartoszek, K. and Asimomitis, G. and Stadler, T. (2020) Fast likelihood calculation for multivariate Gaussian phylogenetic models with shifts Theoretical Population Biology 131:66-78.
Pienaar et al (in prep) An overview of comparative methods for testing adaptation to external environments.
Examples
## Set the version of the random number generator
## so that the results are always reproducible
RNGversion(min(as.character(getRversion()),"3.6.1"))
## Set the random seed, and random number generator
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(5)
## The line below is not necessary but advisable for speed.
## It enhances the phylo object with multiple additional fields, e.g.,
## the lineage for each tip, that are used by subsequent mvSLOUCH functions.
phyltree<-phyltree_paths(phyltree)
## Define a vector of regimes. There are two of them: small and large;
## their layout is random.
regimes<-c("small","small","large","small","small","large","large","large")
### Define SDE parameters to be able to simulate data under the different models.
### There is no particular meaning attached to these parameters.
### BM parameters
BMparameters<-list(vX0=matrix(0,nrow=3,ncol=1),
Sxx=rbind(c(1,0,0),c(0.2,1,0),c(0.3,0.25,1)))
### OUOU parameters
OUOUparameters<-list(vY0=matrix(c(1,-1,0.5),nrow=3,ncol=1),
A=rbind(c(9,0,0),c(0,5,0),c(0,0,1)),mPsi=cbind("small"=c(1,-1,0.5),
"large"=c(-1,1,0.5)),Syy=rbind(c(1,0.25,0.3),c(0,1,0.2),c(0,0,1)))
### OUBM parameters
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 under 3D BM, OUOU and OUBM (the third variable is the
### BM one) models of evolution.
BMdata<-simulBMProcPhylTree(phyltree,X0=BMparameters$vX0,Sigma=BMparameters$Sxx)
### extract just the values at the tips of the phylogeny
BMdata<-BMdata[phyltree$tip.label,,drop=FALSE]
OUOUdata<-simulOUCHProcPhylTree(phyltree,OUOUparameters,regimes,NULL)
### extract just the values at the tips of the phylogeny
OUOUdata<-OUOUdata[phyltree$tip.label,,drop=FALSE]
OUBMdata<-simulMVSLOUCHProcPhylTree(phyltree,OUBMparameters,regimes,NULL)
### extract just the values at the tips of the phylogeny
OUBMdata<-OUBMdata[phyltree$tip.label,,drop=FALSE]
### Recover the parameters of the SDEs.
### Recover under the BM model.
BMestim<-BrownianMotionModel(phyltree,BMdata)
### reset to the original version of the random number generator.
RNGversion(as.character(getRversion()))
## Not run:
### It takes too long to run this from this point.
### We do not reduce the number of iterations of the optimier
### (as we did in other manual page examples, so the running
### times will be as with default settings.
### Recover under the OUOU model.
OUOUestim<-ouchModel(phyltree,OUOUdata,regimes,Atype="DecomposablePositive",
Syytype="UpperTri",diagA="Positive")
### Recover under the OUBM model.
OUBMestim<-mvslouchModel(phyltree,OUBMdata,2,regimes,Atype="DecomposablePositive",
Syytype="UpperTri",diagA="Positive")
### Usage of the wrapper function that allows for estimation under multiple
### models in one call, here we use the default collection of models offered
### by mvSLOUCH. This includes BM, a number of OUOU and OUBM models.
### For data simulated under BM.
estimResultsBM<-estimate.evolutionary.model(phyltree,BMdata,regimes=NULL,
root.regime=NULL,M.error=NULL,repeats=3,model.setups=NULL,predictors=c(3),
kY=2,doPrint=TRUE)
### For data simulated under OUOU.
estimResultsOUOU<-estimate.evolutionary.model(phyltree,OUOUdata,regimes=regimes,
root.regime="small",M.error=NULL,repeats=3,model.setups=NULL,predictors=c(3),
kY=2,doPrint=TRUE)
### For data simulated under OUBM.
estimResultsOUBM<-estimate.evolutionary.model(phyltree,OUBMdata,regimes=regimes,
root.regime="small",M.error=NULL,repeats=3,model.setups=NULL,predictors=c(3),
kY=2,doPrint=TRUE)
## In the wrapper function the resulting best found model parameters are in
## estimResultsBM$BestModel$ParamsInModel
## estimResultsOUOU$BestModel$ParamsInModel
## estimResultsOUBM$BestModel$ParamsInModel
### Summarize the best found models.
### Under the BM model for BM data. One needs to check whether the
### model in BMestim$ParamsInModel corresponds to a BM model (here it does).
BM.summary<-SummarizeBM(phyltree,BMdata,BMestim$ParamsInModel,t=c(1),
dof=BMestim$ParamSummary$dof)
### Under the OUOU model for OUOU data. One needs to check whether the
### model in OUOUestim$ParamsInModel corresponds to an OUOU model (here it does).
OUOU.summary<-SummarizeOUCH(phyltree,OUOUdata,OUOUestim$FinalFound$ParamsInModel,
regimes,t=c(1),dof=OUOUestim$FinalFound$ParamSummary$dof)
### Under the OUBM model for OUBM data. One needs to check whether the
### model in OUBMestim$ParamsInModel corresponds to a OUBM model (here it does).
OUBM.summary<-SummarizeMVSLOUCH(phyltree,OUBMdata,OUBMestim$FinalFound$ParamsInModel,
regimes,t=c(1),dof=OUBMestim$FinalFound$ParamSummary$dof)
### Now run the parametric bootstrap to obtain confidence intervals for some parameters.
### For the BM model, we want CIs for the ancestral state, and the "sqaure" of the
### diffusion (evolutionary rate) matrix. The number of bootstrap replicates
### is very small, 5 (to reduce running times). In reality it should be much more, e.g.,
### 100 or more if the computational budget allows.
BMbootstrap<-parametric.bootstrap(estimated.model=BMestim,phyltree=phyltree,
values.to.bootstrap=c("vX0","StS"),M.error=NULL,numboot=5)
### For the OUOU model, we want a CI for the evolutionary regression coefficient vector.
### The number of bootstrap replicates is very small, 5 (to reduce running times).
### In reality it should be much more, e.g., 100 or more if the
### computational budget allows.
OUOUbootstrap<-parametric.bootstrap(estimated.model=estimResultsOUOU,phyltree=phyltree,
values.to.bootstrap=c("evolutionary.regression"),regimes=regimes,root.regime="small",
M.error=NULL,predictors=c(3),kY=NULL,numboot=5,Atype=NULL,Syytype=NULL,diagA=NULL)
### For the OUBM model, we want CIs for the evolutionary and optimal regression
### coefficient vectors. The number of bootstrap replicates is very small,
### 5 (to reduce running times). In reality it should be much more, e.g.,
### 100 or more if the computational budget allows.
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")
## End(Not run)
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