## Tuesday, October 24, 2017

### More on fitting & comparing basic diversification models using phytools

I have now added a function to fit a Yule (pure-birth) model to phytools, as well as an S3 logLik method. This allows us to fit both a birth-death model & a pure-birth model, and then compare them in a relatively straightforward way.

Here's an example using a phylogeny of darters from Near et al. (2011).

library(phytools)
invisible(ltt(rotateNodes(darter.tree,"all"),show.tree=TRUE,lwd=2,
xlab="time since the root"))
title(main="LTT plot for phylogeny of darters from Near et al. (2011)")

Let's fit our models. According to the study, there are actually 216 lineages in this clade, although the tree contains only 201 of these. We can now take this into account.

Yule<-fit.yule(multi2di(darter.tree),sampling.f=Ntip(darter.tree)/216)
Yule
##
## Fitted Yule model:
##
## ML(b/lambda) = 0.2289
## log(L) = 370.8404
##
## Assumed sampling fraction (rho) = 1
##
## R thinks it has converged.
BD<-fit.bd(multi2di(darter.tree),sampling.f=Ntip(darter.tree)/216)
BD
##
## Fitted birth-death model:
##
## ML(b/lambda) = 0.2362
## ML(d/mu) = 0.015
## log(L) = 370.8757
##
## Assumed sampling fraction (rho) = 1
##
## R thinks it has converged.
library(lmtest)
lrtest(Yule,BD)
## Likelihood ratio test
##
## Model 1: Yule
## Model 2: BD
##   #Df LogLik Df  Chisq Pr(>Chisq)
## 1   1 370.84
## 2   2 370.88  1 0.0706     0.7905

This tells us, of course, that we cannot reject the simpler Yule model.

Similarly:

aic<-setNames(c(AIC(Yule),AIC(BD)),c("Yule","birth-death"))
aic.w(aic)
##        Yule birth-death
##   0.7240612   0.2759388

shows that the majority of weight of evidence favors the Yule model for this tree.

Neat.