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.