Bayesian analysis for morphological data!!!

[David Marjanovic <david.marjanovic@gmx.at>]

At last someone explains how to do that!

John J. Wiens, James W. Fetzner, Jr., Christopher L. Parkinson & Tod W. 
Reeder: Hylid Frog Phylogeny and Sampling Strategies for Speciose Clades, 
Systematic Biology 54(5), 778 -- 807 (October 2005)

>From page 781:

"Morphological data [in addition to several genes] were coded as binary 
and multistate characters and were analyzed using parsimony and Bayesian 
methods. Multistate characters involving quantitative variation along a 
single axis (length or extent of ossification of a structure, number of a 
meristic character) were ordered. Given that the states of these 
characters were delimited based on the assumption that similarity in trait 
values is informative, we believe it is only logical to use this 
assumption in ordering the states. The alternative is to assume that 
similarity in quantitative trait values is not informative, in which case 
many taxa would have to be given a unique state for these characters 
(because most taxa will not be identical), the states would be unordered, 
and these characters would therefore be largely uninformative."

Meristic characters appear to be the number of something (like sacral 
vertebrae). Not ordering these would mean that you can go from, say, 1 
sacral vertebra to 10 in one step (and back in another one).

p. 781f:

"Bayesian analyses were performed using MrBayes version 3.0b4 [...]. 
Analyses of the morphological data used two replicate searches of 10.0 x 
10^6 generations each, sampling every 1,000 generations, with four chains 
and default priors (i.e., equal state frequencies; uniform shape 
parameter; all topologies equally likely a priori; branch lengths 
unconstrained:exponential). [...] The phylogeny was estimated from the 
majority-rule consensus of post-burn-in trees pooled from the two 
replicates. [...]
  Bayesian analysis of the morphological data was performed using the 
maximum likelihood model for discrete morphological character data (Markov 
_k_ or Mk) developed by Lewis (2001). The data were modeled under the 
assumption that only characters that varied among taxa were included 
(i.e., coding = variable; see Lewis (2001)). Analyses were performed both 
including and excluding a parameter for variation in rates of change among 
characters (using the gamma distribution; Yang, 1993, 1994). We then 
compared the fit of these models to our data using the Bayes factor 
(following Nylander et al., 2004). The Bayes factor (B10) represents the 
ratio of the model likelihoods of the two models under consideration. 
Values of [...] [2 ln B10] were calculated (i.e., two times the difference 
between the harmonic means of the log-likelihoods (post burn-in) of the 
two models) and values > 10 were considered to be very strong evidence 
favoring one model over the other (Kass and Raftery, 1995). The harmonic 
mean of the log-likelihoods was calculated using the _sump_ command in 
MrBayes, based on the pooled likelihood scores of the post-burn-in trees 
from the two replicate searches for each model. These analyses strongly 
favored the Mk + Gamma model (Mk-v of Lewis (2001), lnL = -3,723.62) over 
the Mk model (lnL = -3,850.67), with a Bayes factor of 254.10. Only 
results from the former analysis are presented."

Er, yeah. Erm. I don't quite get all of this, but it looks like a very 
promising approach for the future, and maybe for the present. Note that 
the Gamma parameter does not require input on which characters evolve 
faster than which others.

p. 786:

"_Results_

_Morphological Data_

  Parsimony and Bayesian analyses gave similar results for most analyses 
in this study, and differences generally involved branches only weakly 
supported by one or both methods. Given that we expect model-based methods 
to provide phylogenetic estimates that are as accurate or more accurate 
than those from parsimony (e.g., all data sets show demonstrably poor fit 
to the simple model of character change assumed by equally weighted 
parsimony), and in order to conserve space and paper, we present and 
describe trees from the Bayesian analyses only (for all types of data). 
However, we indicate congruent support from parsimony bootstrapping on all 
trees, and describe many parsimony results in the text."

As an aside, the (fully resolved!!!) morphological tree is, to the 
authors' own surprise, thoroughly weird. The traditional classification 
(morphology-based) is much more similar to the molecular tree and to the 
combined tree (which the authors prefer). I guess the reason is the 
unfavorable ratio of taxa (79) to morphological + life history + 
chromosomal characters (144). Compare the theropod analysis in The 
Dinosauria -- 75 taxa, 638 characters (and a few impressive plesiomorphies 
nevertheless). Way to go. -- Besides, the number of 144 characters is IMHO 
artificially inflated. Consider characters 35 and 36: "Tympanic annulus: 
(0) absent, (1) present", "Tympanic annulus: (0) separate from crista 
parotica, (1) fused to crista parotica". Why not fuse these into an 
unordered multistate character? "Tympanic annulus: (0) absent, (1) 
separate from crista parotica, (2) fused to it"? There are several more 
such pairs, like 137 and 138 or 25 and 26 (...which might also be 
correlated with 24). The authors themselves only identify probable 
correlation among characters that are probably adaptations for climbing 
and convergence of a specialized tadpole type (coded as several 
characters) between an ingroup and an outgroup taxon.

I won't bore you with the outcome, except to mention that most 
leptodactylids aren't leptodactylids. And next I'll read

Paul O. Lewis: A Likelihood Approach to Estimating Phylogeny from Discrete 
Morphological Character Data, Systematic Biology 50(6), November 2001

Oh, and the main message of Wiens et al.: Don't be afraid of missing data. 
:-)

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