Efficient Generation of Uniform Samples from Phylogenetic Trees

Abstract

Abstract. In this paper, we introduce new algorithms for selecting taxon (leaf) samples from large phylogenetic trees, uniformly at random, under certain biologically relevant constraints on the taxa. All the algorithms run in polynomial time and have been implemented. The algorithms have direct applications to the evaluation of phylogenetic tree and supertree construction methods using biologically curated data. We also relate one of the sampling problems to the well-known clique problem on undirected graphs. From this, we obtain an interesting new class of graphs for which many open problems exist.

Pairwise compatibility graphs

“…However, we could not find any such graph. Thus the question-"whether or not all graphs are pairwise compatibility graphs" still remains as an open problem [3].…”

“…Lin et al proved that a class of graphs similar to PCG, known as "phylogenetic k-root graphs" are chordal graphs [7]. However, PCGs are neither a subset of chordal graphs nor are they disjoint from that class [3]. In the following theorem we show that a restricted set of PCGs that includes phylogenetic k-root graphs are chordal graphs.…”

“…Usually phylogenetic relationships are expressed as a tree, known as phylogenetic tree. Dealing with a sampling problem in a phylogenetic tree Kearney et al introduced the concept of pairwise compatibility graphs [3]. They showed that "the clique problem" is polynomially solvable for pairwise compatibility graphs if the pairwise compatibility tree construction problem can be solved in polynomial time.…”

New Constraints on Generation of Uniform Random Samples from Evolutionary Trees

“…There are also a wide variety of methods for supertree construction including matrix representation of parsimony (MRP), BUILD, and quartet methods. Kearney, Munro, and Phillips [1] introduce three nontrivial constraints for the sampling process and solve them. We, in this paper, by using different better approaches, improve the runtime of their algorithms.…”

“…The approach involves generating a topology on the taxa using model, then generating a sequence label for the root and evolving the sequence along the paths in the tree to obtain a label for each leaf [1]. Efficiency and performance of the algorithm depends on how close the inferred tree and the target tree are.…”