Minimizing the Average Distance to a Closest Leaf in a Phylogenetic Tree

Abstract

When performing an analysis on a collection of molecular sequences, it can be convenient to reduce the number of sequences under consideration while maintaining some characteristic of a larger collection of sequences. For example, one may wish to select a subset of high-quality sequences that represent the diversity of a larger collection of sequences. One may also wish to specialize a large database of characterized "reference sequences" to a smaller subset that is as close as possible on average to a collection of "query sequences" of interest. Such a representative subset can be useful whenever one wishes to find a set of reference sequences that is appropriate to use for comparative analysis of environmentally derived sequences, such as for selecting "reference tree" sequences for phylogenetic placement of metagenomic reads. In this article, we formalize these problems in terms of the minimization of the Average Distance to the Closest Leaf (ADCL) and investigate algorithms to perform the relevant minimization. We show that the greedy algorithm is not effective, show that a variant of the Partitioning Around Medoids (PAM) heuristic gets stuck in local minima, and develop an exact dynamic programming approach. Using this exact program we note that the performance of PAM appears to be good for simulated trees, and is faster than the exact algorithm for small trees. On the other hand, the exact program gives solutions for all numbers of leaves less than or equal to the given desired number of leaves, whereas PAM only gives a solution for the prespecified number of leaves. Via application to real data, we show that the ADCL criterion chooses chimeric sequences less often than random subsets, whereas the maximization of phylogenetic diversity chooses them more often than random. These algorithms have been implemented in publicly available software.

HIV-1 Superinfection Occurs Less Frequently Than Initial Infection in a Cohort of High-Risk Kenyan Women

“…An amplicon-specific profile HMM was created from an alignment of representative sequences from multiple subtypes. For each subject and amplicon, 20 reference sequences were selected by placing 454 reads on a tree of candidate reference sequences [34] and minimizing the average distance to the closest leaf [35]. These reference sequences, representatives from subtypes common to the region, and 454 reads were aligned to the HMM using hmmalign [36] and non-consensus columns removed.…”

Choosing Subsamples for Sequencing Studies by Minimizing the Average Distance to the Closest Leaf

“…Let H be the set of n haplotypes, and let X be the selected k -element subset of H . The objective is then to find X such that the branch-length distance from a randomly chosen haplotype in H to its closest neighboring haplotype in X is minimized over all possible k -element subsets of H ( Matsen et al 2013 ). Note that because the haplotypes in X are also in H , each of these haplotypes is its own closest neighbor, and we can equivalently consider either H or .…”

“…In a detailed study of ADCL, Matsen et al (2013) demonstrated that unlike when choosing the subset that maximizes PD, the greedy algorithm need not give rise to the globally optimal ADCL solution. It is therefore necessary to produce alternative algorithms that seek to minimize ADCL.…”

“… Matsen et al (2013) described two algorithms that, for a given set of haplotypes, seek to produce the subset of size k that minimizes ADCL. The first approach leverages similarities between the problem of minimizing ADCL and the technique known as k-medoids clustering ( Kaufman and Rousseeuw 1987 ).…”

“…PD can be viewed as emphasizing diversity in the internal reference panel rather than representativeness . To determine whether an alternative focused on identifying the most representative subsample for use as the internal reference panel is preferable, we adapted another method borrowed from phylogenetic studies ( Matsen et al 2013 ): minimizing the average distance to the closest leaf (ADCL), an approach that identifies reference haplotypes based on their genetic proximity to the rest of the sample haplotypes. We compare the imputation accuracy of the maximum-PD, minimum-ADCL, and random reference panels on both simulated data and data from the 1000 Genomes Project, and find that the minimum-ADCL panel consistently provides higher imputation accuracy, irrespective of changes to parameters such as reference panel size, marker density, and sequence length.…”