Phylogenetic network analysis as a parsimony optimization problem

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.

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.

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.