CAFCA - Manual

We consider the bacteriophage T7 data generated by Hillis et al.(1992).. The characters in this data set are all binary and represent variable restriction enzyme cleavage sites. As in Charleston's (1995) example for his Spectrum program 198 characters from that data set are used here --- the four sites in which the relevant site was deleted in one or more of the lineages are left out.

The true tree for the nine lineages is shown below. This true tree is recovered from the data by Spectrum, a program that implements phylogenetic inference through the Hadamard conjugation, or spectral analysis (Hendy and Penny, 1993). PAUP through its standard parsimony approach also finds this one tree for the T7 data using exhaustive search. CAFCA as well finds this one tree as the MPC whether PMS, SMS, or TTSP are used. When we compare CAFCA and spectral analysis as implemented in, e.g., Spectrum by Charleston (1995), we notice that they agree in what they consider to represent primary data. From the binary data matrix spectral analysis derives a list of binary partitions (bipartitions) of the taxa concerned. These partitions correspond with partial monothetic sets in CAFCA's sense. Spectral analysis considers all possible partitions and associates these with their frequency of occurence, thus building a so-called spectrum of partitions. CAFCA only considers the partitions according to a particular set definition (PMS, SMS, TTSP, etc...). All other possible partitions are not included in CAFCA's list of sets and thus correspond with zero frequency entries in the partition spectrum. By means of the Hadamard conjugate spectral analysis transforms these observed frequencies of partitions to expected frequencies under a particular evolutionary model. The latter partitions are used to infer a phylogenetic tree. In this particular example it appears that the phylogenetic signal present in the data is that strong that even methods that take the observed partitions instead of the expected ones as their primary data can find the one and only true tree.

When instead of the normal data matrix (with 198 characters) the monothetic sets weighted according to the number of their corresponding character states (with a minimum weight of one even if there is not a single separate state supporting the set) are used as characters, PAUP will find the true tree by exhaustive search from all the sets listed in table 3.18.

	zero is ancestral	sets	cladograms	MPC
PMS	yes	41	100	1
	no	59	546	1
SMS	yes	127	14176	1
	no	288	241920	?
TTSP	yes	163	22320	1
	no	218	69570	?
TTSP (N&P)	yes	111	2430	1
	no	269	249750	?

Table 3.18: Number of sets and corresponding cladograms and MPC's found by CAFCA when applying different options in the analysis of the T7 data.

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© M. Zandee 1996