Description Usage Arguments Details Value Note Author(s) References Examples
fitting macroevolutionary models to phylogenetic trees
1 2 3 4 
phy 
a phylogenetic tree of class phylo 
dat 
data vector for a single trait, with names matching tips in 
SE 
a single value or named vector of standard errors associated with values in 
model 
model to fit to comparative data (see Details) 
bounds 
range to constrain parameter estimates (see Details) 
control 
settings used for optimization of the model likelihood 
ncores 
Number of cores. If 
... 
additional arguments to be passed to the internal likelihood function 
This function fits various likelihood models for continuous character evolution. The function returns parameter estimates and the likelihood for univariate datasets.
The model likelihood is maximized using methods available in optim
as well as subplex
.
Optimization methods to be used within optim
can be specified through the control
object (i.e., control$method
).
A number of random starting points are used in optimization and are given through the niter
element within the control
object
(e.g., control$niter
). The FAIL
value within the control
object should be a large value
that will be considerably far from lnL of the maximum model likelihood. In most cases, the default setting
for control$FAIL
will be appropriate. The Hessian may be used to compute confidence intervals
(CI
) for the parameter estimates if the hessian
element in control
is TRUE.
Beware: difficulty in finding the optimal solution is determined by an interaction between the nature and complexity of the
likelihood space (which is data and modeldependent) and the numerical optimizer used to explore the space. There is never a
guarantee that the optimal solution is found, but using many random starting points (control$niter
) and many optimization methods
(control$method
) will increase these odds.
Bounds for the relevant parameters of the fitted model may be given through the bounds
argument. Bounds
may be necessary (particularly under the OU
model) if the likelihood surface is characterized by a long,
flat ridge which can be exceedingly difficult for optimization methods. Several bounds can be given at a time
(e.g., bounds=list(SE=c(0,0.1),alpha=c(0,1))
would constrain measurement error as well as the 'constraint'
parameter of the OrnsteinUhlenbeck model). Default bounds under the different models are given below.
Possible models are as follows:
BM is the Brownian motion model (Felsenstein 1973), which assumes the correlation structure among trait values is proportional to the extent of shared ancestry
for pairs of species. Default bounds on the rate parameter are sigsq=c(min=exp(500),max=exp(100))
. The same bounds are applied to all other
models, which also estimate sigsq
OU is the OrnsteinUhlenbeck model (Butler and King 2004), which fits a random walk with a central tendency with an attraction strength proportional to the parameter alpha
.
The OU
model is called the hansen
model in ouch, although the way the parameters are fit is slightly different here. Default
bounds are alpha = c(min = exp(500), max = exp(1))
EB is the Earlyburst model (Harmon et al. 2010) and also called the ACDC
model (acceleratingdecelerating; Blomberg et al. 2003). Set by the a
rate parameter, EB
fits a model where the rate of evolution increases or decreases exponentially through time, under the model r[t] = r[0] * exp(a * t), where r[0]
is the
initial rate, a
is the rate change parameter, and t
is time. The maximum bound is set to 0.000001
, representing a decelerating rate of evolution. The minimum bound is set to log(10^5)/depth of the tree.
rate_trend is a diffusion model with linear trend in rates through time (toward larger or smaller rates). Used to be denominated the "trend"
model, which is still accepted by fitContinuous
for backward compatibility. Default bounds are slope = c(min = 100, max = 100)
lambda is one of the Pagel (1999) models that fits the extent to which the phylogeny predicts covariance among trait values for species. The model effectively transforms the tree:
values of lambda
near 0 cause the phylogeny to become more starlike, and a lambda
value of 1 recovers the BM
model. Default
bounds are lambda = c(min = exp(500), max = 1
kappa is a punctuational (speciational) model of trait evolution (Pagel 1999), where character divergence is related to the number of speciation events between two species. Note that if
there are speciation events that are missing from the given phylogeny (due to extinction or incomplete sampling), interpretation under the kappa
model may be difficult. Considered as a tree
transformation, the model raises all branch lengths to an estimated power (kappa
). Default bounds are kappa = c(min = exp(500), max = 1)
delta is a timedependent model of trait evolution (Pagel 1999). The delta
model is similar to ACDC
insofar as the delta
model fits the relative contributions of
early versus late evolution in the tree to the covariance of species trait values. Where delta
is greater than 1, recent evolution has been relatively fast; if delta
is less
than 1, recent evolution has been comparatively slow. Intrepreted as a tree transformation, the model raises all node depths to an estimated power (delta
). Default bounds are delta = c(min = exp(500), max = 3)
mean_trend is a model of trait evolution with a directional drift or trend component (i.e., toward smaller or larger values through time). This model is sensible only for nonultrametric trees, as the likelihood surface is entirely flat with respect to the slope of the trend if the tree is ultrametric. The model used to be denominated the "drift"
model, which is still accepted by fitContinuous
for backward compatibility. Default bounds are drift = c(min = 100, max = 100)
white is a white
noise (nonphylogenetic) model, which assumes data come from a single normal distribution with no covariance structure among species. The variance parameter sigsq
takes the same bounds defined under the BM
model
fitContinuous
returns a list with the following four elements:
lik 
is the function used to compute the model likelihood. The returned function ( 
bnd 
is a matrix of the used bounds for the relevant parameters estimated in the model. Warnings will be issued if any parameter estimates occur at the supplied (or default) parameter bounds 
res 
is a matrix of results from optimization. Rownames of the 
opt 
is a list of the primary results: estimates of the parameters, the maximumlikelihood estimate ( 
To speed the likelihood search, one may set an environment variable to make use of parallel processing, used by mclapply
. To set the environment variable, use options(mc.cores=INTEGER)
, where INTEGER
is the number of available cores. Alternatively, the mc.cores
variable may be preset upon the initiation of an R session (see Startup
for details).
LJ Harmon, W Challenger, and JM Eastman
Blomberg SP, T Garland, and AR Ives. 2003. Testing for phylogenetic signal in comparative data: behavioral traits are more labile. Evolution 57:717745.
Butler MA and AA King, 2004. Phylogenetic comparative analysis: a modeling approach for adaptive evolution. American Naturalist 164:683695.
Felsenstein J. 1973. Maximum likelihood estimation of evolutionary trees from continuous characters. American Journal of Human Genetics 25:471492.
Harmon LJ et al. 2010. Early bursts of body size and shape evolution are rare in comparative data. Evolution 64:23852396.
Pagel M. 1999. Inferring the historical patterns of biological evolution. Nature 401:877884
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83  geo=get(data(geospiza))
tmp=treedata(geo$phy, geo$dat)
phy=tmp$phy
dat=tmp$data
# STORE RESULTS
brownFit < fitContinuous(phy, dat[,"wingL"], SE=NA, control=list(niter=50), ncores=2)
# PRINT RESULTS
print(names(brownFit))
print(brownFit)
# COMPUTE LIKELIHOOD
flik=brownFit$lik
print(argn(flik))
# CREATE a FUNCTION to COMPARE MODELS
fitGeospiza=function(trait=c("wingL","tarsusL","culmenL","beakD","gonysW")){
trait=match.arg(trait, c("wingL","tarsusL","culmenL","beakD","gonysW"))
# define set of models to compare
models=c("BM", "OU", "EB", "white")
summaries=c("diffusion", "OrnsteinUhlenbeck", "early burst", "white noise")
## ESTIMATING measurement error ##
aic.se=numeric(length(models))
lnl.se=numeric(length(models))
for(m in 1:length(models)){
cat("\n\n\n\n\t*** ", paste(toupper(summaries[m]),": fitting ", sep=""), models[m],
" with SE *** \n", sep="")
tmp=fitContinuous(phy,dat[,trait],SE=NA, model=models[m],
bounds=list(SE=c(0,0.5)), ncores=2)
print(tmp)
aic.se[m]=tmp$opt$aicc
lnl.se[m]=tmp$opt$lnL
}
## ASSUMING no measurement error ##
aic=numeric(length(models))
lnl=numeric(length(models))
for(m in 1:length(models)){
cat("\n\n\n\n\t*** ", paste(toupper(summaries[m]),": fitting ", sep=""), models[m],
" *** \n", sep="")
tmp=fitContinuous(phy,dat[,trait],SE=0,model=models[m], ncores=2)
print(tmp)
aic[m]=tmp$opt$aicc
lnl[m]=tmp$opt$lnL
}
## COMPARE AIC ##
names(aic.se)<names(lnl.se)<names(aic)<names(lnl)<models
delta_aic<function(x) xx[which(x==min(x))]
# no measurement error
daic=delta_aic(aic)
cat("\n\n\n\t\t\t\t*** MODEL COMPARISON: ",trait," *** \n",sep="")
cat("\tdeltaAIC values for models assuming no measurement error
\t\t\t\t zero indicates the best model\n\n")
print(daic, digits=2)
# measurement error
daic.se=delta_aic(aic.se)
cat("\n\n\n\n\t\t\t\t*** MODEL COMPARISON: ",trait," ***\n",sep="")
cat("\t\t deltaAIC values for models estimating SE
\t\t\t\t zero indicates the best model\n\n")
print(daic.se, digits=2)
cat("\n\n\n")
res_aicc=rbind(aic, aic.se, daic, daic.se)
rownames(res_aicc)=c("AICc","AICc_SE","dAICc", "dAICc_SE")
return(res_aicc)
}
# COMPARE MODELS for WING LENGTH
res=fitGeospiza("wingL")
print(res)

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