Information in morphological characters

Abstract

The construction of morphological character matrices is central to paleontological systematic study, which extracts paleontological information from fossils. Although the word information has been repeatedly mentioned in a wide array of paleontological systematic studies, its meaning has rarely been clarified nor specifically defined. It is important, however, to establish a standard to measure paleontological information because fossils are hardly complete, rendering the recognition of homologous and homoplastic structures difficult. Here, based on information theory, we show the deep connections between paleontological systematic study and communication system engineering. Information is defined as the decrease of uncertainty and it is the information in morphological characters that allows distinguishing operational taxonomic units (OTUs) and reconstructing evolutionary history. We propose that concepts in communication system engineering such as source coding and channel coding, correspond to the construction of diagnostic features and the entire character matrices in paleontological studies. The two coding strategies should be distinguished following typical communication system engineering, because they serve dual purposes. With character matrices from six different vertebrate groups, we analyzed their information properties including source entropy, mutual information, and channel capacity. Estimation of channel capacity shows character saturation of all matrices in transmitting paleontological information, indicating that, due to the presence of noise, oversampling characters not only increases the burden in character scoring, but also may decrease quality of matrices. We further test the use of information entropy, which measures how informative a variable is, as a character weighting criterion in parsimony-based systematic studies. The results show high consistency with existing knowledge with both good resolution and interpretability.

Keywords: character weighting; information theory; morphology; systematics.

FIGURE 1

(a) Typical communication system modified from Shannon (1948); (b) Paleontological systematic studies in abstract

FIGURE 2

(a) Information entropy distribution of a binary variable; (b) information entropy of characters in different morphological character matrices, x‐axis: number of character states, y‐axis: average information entropy; (c) joint information entropy in different morphological character matrices, only first 40 characters are shown to save space; (d) mutual information distribution heat map in different morphological character matrices, orange: high mutual information, blue: low mutual information, anatomical parts abbreviations, C: crania, F: forelimb and pectoral girdle, H: hindlimb and pelvic girdle, A: axial elements, O: others

FIGURE 3

(a) noise power distribution in taxa domain; (b) noise power distribution in character domain; (c) channel capacity and bandwidth in character matrices

FIGURE 4

Tree results of Ceratopsia. (a) Equal weighting; (b) implied weighting (k = 3); (c) implied weighting (k = 12); (d) information entropy weighting. Colored columns on the right side of trees represent OTUs and their color gradients correspond to the taxa order in the original character matrix