52 



The solution then seems to be not the accumulation of data matrices with only 

 phylogenetically informative characters (which may be impossible to determine), but of 

 matrices that represent a random sample of the universe of all possible characters. This is 

 based on the assumption that of the many possible signals influencing the form of a 

 character, the phylogenetic signal will be the strongest (otherwise, a systematic analysis 

 based upon phylogenetic principles would appear to be unrealizable). Thus, by taking a 

 random sample, the phylogenetically informative characters will hopefully predominate 

 and point towards the one true phylogeny. As well, in such a case (where the signal within 

 the data matrix closely approximates the true phylogeny), the various statistical tests 

 mentioned above will be more likely to be placing confidence intervals on how well we 

 have reconstructed the true phylogeny. 



A simple analogy involves a universe of (scattered) points that roughly indicate a square 

 in space. Through some biased sampling (which emulates the inclusion of increasing 

 numbers of non-phylogenetically determined characters), we could achieve data sets whose 

 underlying distributions are of a straight line and a circle respectively. [Note that this is 

 also possible under random sampling, but should be far less likely to occur. Likewise, 

 biased sampling could also indicate a square (e.g., sample only from the corner regions), 

 but, again, this is unlikely.] By employing tests based on each data matrix, or some sample 

 thereof, we cannot help but observe something along the lines of a line and a circle each 

 time. 



Although all of our current tests provide valuable information, they may be erroneously 

 focused. These tests indicate only the signal strength in our samples, with no indication 

 as to the accuracy of that signal. They are similarly hampered by being based, to varying 

 degrees, on the same tree constructing methods (and thus the same potential biases) that 

 were used to generate the cladogram under examination. As stressed by Sanderson (1989), 

 more tests that are independent of the various tree constructing methods are required. 

 Although it is unlikely to ever be developed, what we really require is a statistical test 

 measuring the randomness of our sample of characters, for it is presumably only with a 

 random sample that our data matrices will estimate the true phylogeny to various degrees 

 (which our current tests could then delineate). Unfortunately, even with such a test we 

 would be left with a discrepancy between what it really indicates (randomness of the 

 character set) and what we would interpret it to mean (the potential accuracy of the 

 character set in predicting the true phylogeny). Note that this desired test is subtly, but 

 meaningfully different from our current PTP and skewness tests. In a universe of characters 

 shaped largely by evolution, a random sample thereof should covary significantly, except 

 now this covariation would be primarily due to common descent with modification. The 

 characters need not be completely independent either (and in all likelihood they would 

 not be), merely a random sample. Without such a test for randomness, all that we are left 

 with is a critical examination of the characters used to achieve a given result, something 

 that has, unfortunately, become increasingly rare with the influx of statistics into cladistics. 

 The total evidence approach, where different data sets are combined into one larger data 

 set (see Kluge 1989; Kluge & Wolf 1993), is one step towards reducing the bias present 

 in our character sets. Disregarding potential problems such as how to combine characters 



