First, let me post another type of data set that I believe would fall
into the class of compatibility analyses. Atchley and Fitch (1993,MBE)
studied the divergence of inbred mouse strains, and studied the
hypothesis that "observed patterns of genetic divergence among these
24 strains can be explained by the segregation of residual
heterozygosity arising from a small population of highly heterozygous
mice". They used the concept of loss parsimony, which I believe
(please correct me if I'm wrong) is a bit more stringent than
compatibility. I, at least, found their arguments for using this
approach quite persuasive. An oversimplification of their analysis
is that traditional parsimony and loss parsimony fit the data
equally well, so keep the "simpler" model. I will also add that the
pedigree of these mice was known because of controlled mating. In any
case, this is a novel paper that's worth a look.
Second, let me suggest an application where compatibility analysis is
desirable. This is the problem of studying recombination in intra-
specific samples of DNA. Ignoring the effect of back mutations, all
individual sites within a block of DNA that has not undergone a
recombination event should be compatible with the same tree. Analyses
based on this "fact" are useful, although not completely rigorous,
approaches for studying recombination. (See Stephens (1985) Mol. Biol.
Evol. and Leicht et al. (1995) Genetics for applications to gene
conversion and recombination.)
