Phylogenetic network analysis as a parsimony optimization problem

Abstract

Background: Many problems in comparative biology are, or are thought to be, best expressed as phylogenetic "networks" as opposed to trees. In trees, vertices may have only a single parent (ancestor), while networks allow for multiple parent vertices. There are two main interpretive types of networks, "softwired" and "hardwired." The parsimony cost of hardwired networks is based on all changes over all edges, hence must be greater than or equal to the best tree cost contained ("displayed") by the network. This is in contrast to softwired, where each character follows the lowest parsimony cost tree displayed by the network, resulting in costs which are less than or equal to the best display tree. Neither situation is ideal since hard-wired networks are not generally biologically attractive (since individual heritable characters can have more than one parent) and softwired networks can be trivially optimized (containing the best tree for each character). Furthermore, given the alternate cost scenarios of trees and these two flavors of networks, hypothesis testing among these explanatory scenarios is impossible. Results: A network cost adjustment (penalty) is proposed to allow phylogenetic trees and soft-wired phylogenetic networks to compete equally on a parsimony optimality basis. This cost is demonstrated for several real and simulated datasets. In each case, the favored graph representation (tree or network) matched expectation or simulation scenario. Conclusions: The softwired network cost regime proposed here presents a quantitative criterion for an optimality-based search procedure where trees and networks can participate in hypothesis testing simultaneously.

On the quirks of maximum parsimony and likelihood on phylogenetic networks

“…In particular, several related complexity questions have been settled (Fischer et al, 2015;Jin et al, 2009;Nguyen et al, 2007) and exact algorithms and heuristics (Fischer et al, 2015;Wheeler, 2012, 2014) to tackle this problem have been proposed. In contrast, the big parsimony problem has so far only been mentioned in one article (Wheeler, 2015), where formal proofs were omitted. Yet, the big problem is exactly what is ultimately of interest to evolutionary biologists who wish to reconstruct a rooted phylogenetic network from molecular data under a parsimony framework.…”

Comparing and displaying phylogenetic trees using edge union networks

“…We can see then that the arc removal step is of a higher complexity than any of the Table 1: Input tree data sets used in complexity analysis. The D50, D200, and D600 sets are simulations (Ford and Wheeler, 2016), the remainder are empirical Wheeler, 1999, 2001;Svenson and Whiting, 2004;Wheeler, 2007;Grazia et al, 2008;Benson et al, 2013;Wheeler, 2015;Wheeler and Whiteley, 2015;Ford and Wheeler, 2016;Wheeler et al, 2017…”

“…The data were taken from 20 analyses based on a variety of real and simulated datasets using anatomical, molecular and linguistic information (Giribet and Wheeler, , ; Svenson and Whiting, ; Wheeler, ; Benson et al., ; Wheeler, ; Wheeler and Whiteley, ; Ford and Wheeler, ; Wheeler et al., ; Table ).…”

“… The D50, D200 and D600 sets are simulations (Ford and Wheeler, ), the remainder are empirical (Giribet and Wheeler, , ; Svenson and Whiting, ; Wheeler, , ; Grazia et al., ; Benson et al., ; Wheeler and Whiteley, ; Ford and Wheeler, ; Wheeler et al., ). …”

Rooting Phylogenies and the Tree of Life While Minimizing Ad Hoc and Auxiliary Assumptions

“…In the presence of reticulations, single or multiple origins can lead to a network structure that finally resolves into leaves. [19][20][21][22] A network of this kind implies the existence of explicit convergent and divergent relationships in the historical statements, with changes occurring simultaneously in some regions of the network ("parallelisms" or "convergences"). It also implies the existence of symmetry-joining events.…”