Results
The results of character information entropy (Fig. 2b) show that
characters with more states tend to have higher information entropy,
indicating those multi-state characters generally introduce more
information in systematic studies. Among characters with the same number
of states, the information entropy still varies a lot in most datasets.
Six matrices show consistent pattern in their joint information entropy
(Fig. 2c, only first 40 characters are shown). For the first few
characters, the joint information entropy increases fast to approximate
the source information entropy, which is the upper limit of joint
information entropy, and the majority of characters serve in channel
coding as they do not contribute to the source coding much. The curves
of joint information entropy shows that only a few characters are
required to distinguish each OTU (classification) and the majority of
characters in the matrices are for channel coding (systematics).
The mutual information across 6 matrices is also calculated (Fig. 2d) to
test the mutuality between characters. Due to the existence of missing
data, the diagonal line numbers showing mutuality between any character
and itself are not strictly its information entropy but are still
generally higher than other areas of the heatmaps. The distribution of
mutuality seems to have no pattern in most matrices. After reorder and
partition characters by anatomical structures (crania, pectoral girdle
and forelimb, pelvic girdle and hindlimb, axial bones, and others), some
parts exhibit relatively high mutuality, for example the forelimbs and
hindlimbs of Carnivoramorpha (Spaulding & Flynn 2012) show both higher
inter- and intra-mutuality than other anatomical structures.
The distributions of noise power in taxa domain and character domain are
shown in Figure 3a and 3b, respectively. The results show saturation in
channel capacity when increasing bandwidth, the number of characters
(Fig. 3c). Different character matrices reach the maximum channel
capacity when having 62.5% (multituberculata) to 89.7% (Diplodocidae)
of total characters.