Graph matching a skeletonized theoretical morphospace with a cladogram for gomphonemoid-cymbelloid diatoms (Bacillariophyta)

Abstract

A three-dimensional (3D) theoretical morphospace of gomphonemoid and cymbelloid diatoms was skeletonized using concepts from extended Reeb graph analysis and Morse theory. The resultant skeleton tree was matched to a cladogram of the same group of related taxa using adjacency matrices of the trees and ordinated with multidimensional scaling (MDS) of leaf nodes. From this, an unweighted path matrix based on the number of branches between leaf nodes was ordinated to determine degree of matched tree structures. A constrained MDS of the path matrix, weighted by ranked MDS leaf node groups as facets, was used to interpret taxon environmental tolerances and habitat preferences with respect to adaptive value. The methods developed herein provided a way to combine results from morphological and phylogenetic analyses and interpret those results with respect to an aspect of evolutionary process, namely, adaptation.