A Bayesian approach to dynamic homology of morphological characters and the ancestral phenotype of jawed vertebrates

Phylogenetic analysis of morphological data proceeds from a fixed set of primary homology statements, the character-by-taxon matrix. However, there are cases where multiple conflicting homology statements can be justified from comparative anatomy. The upper jaw bones of placoderms have traditionally been considered homologous to the palatal vomer-dermopalatine series of osteichthyans. The discovery of ‘maxillate’ placoderms led to the alternative hypothesis that ‘core’ placoderm jaw bones are premaxillae and maxillae lacking external (facial) laminae. We introduce a BEAST2 package for simultaneous inference of homology and phylogeny, and find strong evidence for the latter hypothesis. Phenetic analysis of reconstructed ancestors suggests that maxillate placoderms are the most plesiomorphic known gnathostomes, and the shared cranial architecture of arthrodire placoderms, maxillate placoderms and osteichthyans is inherited. We suggest that the gnathostome ancestor possessed maxillae and premaxillae with facial and palatal laminae, and that these bones underwent divergent evolutionary trajectories in placoderms and osteichthyans.

Efficient implied alignment

Background Given a binary tree $\mathcal {T}$ T of n leaves, each leaf labeled by a string of length at most k, and a binary string alignment function ⊗, an implied alignment can be generated to describe the alignment of a dynamic homology for $\mathcal {T}$ T . This is done by first decorating each node of $\mathcal {T}$ T with an alignment context using ⊗, in a post-order traversal, then, during a subsequent pre-order traversal, inferring on which edges insertion and deletion events occurred using those internal node decorations. Results Previous descriptions of the implied alignment algorithm suggest a technique of “back-propagation” with time complexity $\mathcal {O}\left (k^{2} * n^{2}\right)$ O k 2 ∗ n 2 . Here we describe an implied alignment algorithm with complexity $\mathcal {O}\left (k * n^{2}\right)$ O k ∗ n 2 . For well-behaved data, such as molecular sequences, the runtime approaches the best-case complexity of Ω(k∗n). Conclusions The reduction in the time complexity of the algorithm dramatically improves both its utility in generating multiple sequence alignments and its heuristic utility.