The Binary Perfect Phylogeny with Persistent characters

TL;DR

This paper introduces a generalized model for binary perfect phylogenies allowing for a specific back mutation, and develops an exact algorithm for reconstructing near perfect phylogenies with persistent characters.

Contribution

It formulates the Persistent Perfect Phylogeny problem as a special case of incomplete phylogeny with missing data and provides a graph-based exact solution method.

Findings

The problem can be reduced to an edge-colored graph problem.

An exponential-time algorithm in characters and polynomial in species is developed.

The approach effectively handles missing data in phylogenetic reconstruction.

Abstract

The binary perfect phylogeny model is too restrictive to model biological events such as back mutations. In this paper we consider a natural generalization of the model that allows a special type of back mutation. We investigate the problem of reconstructing a near perfect phylogeny over a binary set of characters where characters are persistent: characters can be gained and lost at most once. Based on this notion, we define the problem of the Persistent Perfect Phylogeny (referred as P-PP). We restate the P-PP problem as a special case of the Incomplete Directed Perfect Phylogeny, called Incomplete Perfect Phylogeny with Persistent Completion, (refereed as IP-PP), where the instance is an incomplete binary matrix M having some missing entries, denoted by symbol ?, that must be determined (or completed) as 0 or 1 so that M admits a binary perfect phylogeny. We show that the IP-PP problem can be reduced to a problem over an edge colored graph since the completion of each column of the input matrix can be represented by a graph operation. Based on this graph formulation, we develop an exact algorithm for solving the P-PP problem that is exponential in the number of characters and polynomial in the number of species.