26 



can also be determined by simply arranging the lengths derived from the random data sets 

 in ascending order and counting off to the appropriate percentile (L.R. Linton pers. 

 comm.). 



A serious limitation of the PTP statistic is that it will consistently underestimate the 

 departure of the data from randomness with the low number of randomizations typically 

 employed in phylogenetic PTP analyses (Källersjö et al. 1992). Therefore, Källersjö et al. 

 (1992) have derived two more accurate, albeit slightly conservative measures (a" and a:*) 

 for such instances from the standardized Z-scores of the sample of random solutions. 

 However, bearing the conservative natures of all these statistics in mind, Källersjö et al. 

 (1992) recommend using the smallest value obtained from any of the PTP statistic (which 

 they refer to as a), a\ or a*. 



Strictly speaking, a PTP test is not sensitive to hierarchical structure in the data set, but 

 merely to patterns of association (Alroy 1994). The tacit assumption then is that the 

 character covariation that the PTP test is sensitive to is due solely to common ancestry, 

 and not to other correlative factors such as character non-independence. Together, this 

 leads to the PTP test being an extremely forgiving and occasionally erroneous test 

 (Källersjö et al. 1992; Novacek 1993). Therefore, it appears that a significant result is not 

 so telling with respect to the PTP test as opposed to a non-significant result. 

 Another limitation of the PTP test is that it only operates at the level of the solution as a 

 whole, and not for subgroups of interest within it. Although Faith (1991) has suggested 

 an analogous procedure for this latter goal, this topology-dependent PTP test (T-PTP test) 

 is limited to very small data sets for practical reasons. This is because the idea behind a 

 posteriori T-PTP tests for the monophyly of a given clade is to determine how likely it is 

 to form any clade with a similar number of members, and not how likely it is to form 

 that one particular clade of interest. Thus, in order to a posteriori determine whether there 

 is statistical support for a monophyletic Monachinae for instance, we need test not only 

 the monachines, but all clades of nine taxa, for which, for the 19 phocids examined here, 

 there are 92,378 such combinations. It is possible to correct for, rather than test all these 

 possible combinations (see Faith 1991 ), but for the example given here, a significant result 

 (at the 0.05 level) would still require a P value on the order of 10 7 . 

 The lack of a PTP subroutine in any computer package to date makes use of the PTP test 

 rather labour intensive. Thus, only the minimally suggested number of data sets, 100 (99 

 permutated plus the original), were analyzed. The permutated data sets were created using 

 the SEQBOOT program of PHYLIP (version 3.52c) (Felsenstein 1993), and subsequently 

 converted to PAUP's NEXUS format to be analyzed using the heuristic search option as 

 detailed above. All three measures of significance - a\ a", and a* - were determined for 

 this analysis. As we make no pretense as to the independence of our characters, we will 

 interpret the results of this analysis in terms of character covariation only, and not 

 hierarchical structure. 



Skewness (Fitch 1979) 



Skewness tests derive from Fitch's (1979) simple observation that distributions of tree 

 length for most phylogenetic data sets possess long left-hand tails (i.e., are left-skewed). 



