Hi William.
Why would you suspect phytools? ;)
I didn't figure this out for you, but I did eliminate some possibilities.
It does not seem to be due to phytools::fastBM. You can replace fastBM
with phytools:sim.corrs or geiger:sim.char as follows:
var<-sim.char(Bigtrees[[i]],par=1,root=0)[,,1]
## or
var<-sim.corrs(Bigtrees[[i]],matrix(1,1,1))
## and
var1<-sim.char(subtrees[[i]],par=1,root=0)[,,1]
## or
var1<-sim.corrs(subtrees[[i]],matrix(1,1,1))
and the result is the same. (Note that all three use different methods
for simulation.)
Neither does it seem to be due to phytools::phylosig. You can replace
phylosig with geiger::fitContinuous as follows:
maxlambda<-phytools:::maxLambda(subtrees[[i]])
sig_sub[i]<-fitContinuous(subtrees[[i]],var[subtrees[[i]]$tip.label],
model="lambda",bounds=list(lambda=c(0,maxlambda)))$opt$lambda
sig[i]<-fitContinuous(subtrees[[i]],var1,model="lambda",
bounds=list(lambda=c(0,maxlambda)))$opt$lambda
and the result is unchanged. (Note that we need to compute the maximum
value of lambda for which the likelihood function is defined otherwise
fitContinuous by default bounds optimization on [0,1].)
What I also observed is that the variances are unequal, as you report,
but not in a particular direction. That is, sometimes sig_sub has a
higher variance, and sometimes sig does.
If I had to guess, I would hazard that perhaps the distribution of
lambda (even after you make it symmetric) is leptokurtic which is why
var.test is significant due to idiosyncratic differences in the variance
of lambda, even though the values were obtained by the same process.
(Invariably lamb_sub and lamb fail a normality test, so this seems like
a distinct possibility.)
All the best, Liam
Liam J. Revell, Associate Professor of Biology
University of Massachusetts Boston
web: http://faculty.umb.edu/liam.revell/
email: liam.rev...@umb.edu
blog: http://blog.phytools.org
On 10/20/2017 1:32 AM, William Gelnaw wrote:
Hi all,
I've been investigating the use of Pagel's lambda and run into a problem
comparing trees that have a low speciation rate and no extinction with
trees that have a high speciation rate and lots of extinction. I'm
comparing phylogenetic signal in two characters. In the first, I simulate
a character under Brownian evolution over a 200 taxon tree and then prune
it down to 100 taxa. The second character was evolved over the pruned-down
tree. I then estimated Pagel's lambda for both characters on the
pruned-down tree. Doing this 500 times, I found that the error rate in the
estimate of lambda was not the same for the two methods of generating the
data. The difference was small but statistically significant. To my
understanding though, there shouldn't be a difference. The rate of
evolution is the same in both cases and the tree topology and branch
lengths are identical. If the characters are evolving in a Brownian way,
shouldn't there be, on average, no difference between the characters with
respect to phylogenetic signal? Could this be an artifact of using fastBM
to simulate the characters? Is there another function that I should be
using to simulate a character evolving under Brownian motion?
Here's the script I'm using:
library(phytools)
library(TreeSim)
library(adephylo)
age<-2
lambda <- 2.0
mu <- 0.5
frac <-0.6
sample_size<-100
smalltrees<-list()
Bigtrees<-sim.bd.taxa.age(200,500,lambda,mu,frac,age)
## using sim.bd.taxa.age to get an ultrametric tree with known age
subtrees<-list()
sig<-vector()
sig_sub<-vector()
for (i in 1:500){
var<-fastBM(Bigtrees[[i]],nsim=1)
tips_to_drop<-sample(1:200, 200-sample_size, replace=FALSE)
subtrees[[i]]<-drop.tip(Bigtrees[[i]], tips_to_drop)
var1<-fastBM(subtrees[[i]],nsim=1)
sig_sub[i]<-phylosig(subtrees[[i]],var,method="lambda")$lambda
sig[i]<-phylosig(subtrees[[i]],var1,method="lambda")$lambda}
lamb<-(2-sig)
## reflected the data around lambda=1 so that standard deviation has a
symmetric distribution
lamb<-c(lamb,sig)
lamb_sub<-(2-sig_sub)
lamb_sub<-c(lamb_sub,sig_sub)
var.test(lamb,lamb_sub)
Best regards,
- Will Gelnaw
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