BACKGROUND:A multi-labeled tree, or MUL-tree, is a phylogenetic tree where two or more leaves share a label, e.g., a species name. A MUL-tree can imply multiple conflicting phylogenetic relationships for the same set of taxa, but can also contain conflict-free information that is of interest and yet is not obvious.RESULTS:We define the information content of a MUL-tree T as the set of all conflict-free quartet topologies implied by T, and define the maximal reduced form of T as the smallest tree that can be obtained from T by pruning leaves and contracting edges while retaining the same information content. We show that any two MUL-trees with the same information content exhibit the same reduced form. This introduces an equivalence relation among MUL-trees with potential applications to comparing MUL-trees. We present an efficient algorithm to reduce a MUL-tree to its maximally reduced form and evaluate its performance on empirical datasets in terms of both quality of the reduced tree and the degree of data reduction achieved.CONCLUSIONS:Our measure of conflict-free information content based on quartets is simple and topologically appealing. In the experiments, the maximally reduced form is often much smaller than the original tree, yet retains most of the taxa. The reduction algorithm is quadratic in the number of leaves and its complexity is unaffected by the multiplicity of leaf labels or the degree of the nodes.

Evolution is the unifying theory of biology. The importance of understanding evolution by those who study the origins, diversification and diversity life cannot be overstated. Because of its importance, in addition to a scientific study of evolution, many researchers have spent time studying the acceptance and the teaching of evolution. Phylogenetic Systematics is the field of study developed to understand the evolutionary history of organisms, traits, and genes. Tree-thinking is the term by which we identify concepts related to the evolutionary history of organisms. It is vital that those who undertake a study of biology be able to understand and interpret what information these phylogenies are meant to convey. In this project, we evaluated the current impact a traditional study of biology has on the misconceptions students hold by assessing tree-thinking in freshman biology students to those nearing the end of their studies. We found that the impact of studying biology was varied with some misconceptions changing significantly while others persisted. Despite the importance of tree-thinking no appropriately developed concept inventory exists to measure student understanding of these important concepts. We developed a concept inventory capable of filling this important need and provide evidence to support its use among undergraduate students. Finally, we developed and modified activities as well as courses based on best practices to improve teaching and learning of tree-thinking and organismal diversity. We accomplished this by focusing on two key questions. First, how do we best introduce students to tree-thinking and second does tree-thinking as a course theme enhance student understanding of not only tree-thinking but also organismal diversity. We found important evidence suggesting that introducing students to tree-thinking via building evolutionary trees was less successful than introducing the concept via tree interpretation and may have in fact introduced or strengthened a misconception. We also found evidence that infusing tree-thinking into an organismal diversity course not only enhances student understanding of tree-thinking but also helps them better learn organismal diversity.