27 



Hillis & Huelsenbeck (1992) suggest that this phenomenon, which indicates the presence 

 of relatively few solutions around the most parsimonious solution, derives from an 

 increased amount of correlation between characters. Therefore, like the PTP test, 

 interpreting a significant left-hand skew to mean significant phylogenetic signal requires 

 the assumption that the indicated correlation derives primarily from common ancestry. So, 

 once again, a non-significant result is more revealing than a significant one (Hillis & 

 Huelsenbeck 1992), although a distribution with a significant left-hand skew does 

 apparently increase the probability that parsimony will correctly identify the actual 

 phylogeny (Huelsenbeck 1991a). 



Hillis & Huelsenbeck (1992) also suggested that a significant left-skew for the whole 

 solution may only be an artifact of a particularly strongly indicated subgroup. Therefore, 

 a tree length distribution of all solutions, but with the relationships of this one subgroup 

 constrained, should produce a non-significant skew. Presumably, this is due to the left- 

 hand tail of a left-skewed distribution being composed primarily of solutions containing 

 the indicated subgroup as a clade (but with different combinations of relationships 

 internally). 



Despite the work of Huelsenbeck (1991a) and Hillis & Huelsenbeck (1992), the use of 

 skewness (as measured by the g, statistic) as an indicator of phylogenetic signal is also 

 not without its problems. Skewness analyses will occasionally give an erroneous outcome 

 due to being influenced more strongly by character state frequency (which in turn affects 

 the pattern of branching) than by correlation between characters, as well as being 

 insensitive to character number (Källersjö et al. 1992). However, this last point is countered 

 by the question of whether support should be measured by the absolute [as in simply 

 tallying the number of synapomorphies, and as Källersjö et al. (1992) apparently feel it 

 should be] or the relative number of characters (as in the bootstrap) supporting a node. 

 Källersjö et al. (1992) also question whether the limited random sample of all possible 

 solutions that skewness statistics are based on for studies with more than 10 taxa can 

 accurately estimate the distribution of all possible solutions, or even sufficiently sample 

 from the attenuated left-hand tail of the distribution. However, Hillis & Huelsenbeck 

 (1992) demonstrate that a random sample of only 10,000 trees does produce a statistically 

 accurate sample, regardless of the number of taxa. 



In all but two cases (see below), skewness statistics, g l5 were obtained from a random 

 sample of 1,000,000 trees generated using the RANDOM TREES subroutine of PAUP, 

 and all were compared to critical values published for a given number of taxa and 

 characters (both binary and four-state) by Hillis & Huelsenbeck (1992). Although 

 molecular simulations were used to achieve these critical values, they should, at the very 

 least, give a rough indicator of the level of significance. For those cases when the exact 

 values for either taxa or character number were not present, the next higher category was 

 used, producing a more conservative estimate of the level of significance. However, all 

 skewness results here should be regarded as extremely tenuous as the RANDOM TREES 

 subroutine of PAUP (version 3.1.1) contains major bugs that inhibit the analysis of 

 (inversely) weighted data matrices. 



For the "constrained" skewness analysis, the strongly supported subgroup in question 

 (hereafter referred to as the "anti-Phocini" clade) was held to be all taxa excluding 



