Structural properties of distance-bounded phylogenetic reconciliation

TL;DR

This paper investigates the structural properties of distance-bounded phylogenetic reconciliation, focusing on cases where the maximum distance for host switching is 3 or 4, revealing bounded cycle conditions that aid understanding of reconciliation complexity.

Contribution

It provides a structural analysis of reconciliation with fixed maximum distances, identifying bounded cycle conditions that simplify the problem for certain cases.

Findings

Bounded-size cycles suffice for checking acyclicity in reconciliations.

Structural properties are characterized for cases d=3 and d=4.

Results highlight conditions under which reconciliation remains computationally manageable.

Abstract

Phylogenetic reconciliation seeks to explain host-symbiont co-evolution by mapping parasite trees onto host trees through events such as cospeciation, duplication, host switching, and loss. Finding an optimal reconciliation that ensures time feasibility is computationally hard when timing information is incomplete, and the complexity remains open when host switches are restricted by a fixed maximum distance $d$. While the case $d=2$ is known to be polynomial, larger values are unresolved. In this paper, we study the cases $d=3$ and $d=4$. We show that although arbitrarily large cycles may occur, it suffices to check only bounded-size cycles (we provide a complete list), provided the reconciliation satisfies acyclicity (i.e., time-feasibility) in a stronger sense. These results do not resolve the general complexity, but highlight structural properties that advance the understanding of distance-bounded reconciliations.