The phrase "adjacency trees" is correct and usable in written English.
It can be used in contexts related to computer science, linguistics, or data structures, particularly when discussing hierarchical relationships or structures.
Example: "In our analysis, we utilized adjacency trees to represent the relationships between different nodes in the dataset."
Alternatives: "proximity trees" or "neighboring trees".
Solutions for one class may consist of several adjacency trees.
The backtracking procedure classically follows each cost on the chosen line in the recurrence formulas, creating adjacency trees from root to leaves.
The description of the method requires that we formally introduce the three kinds of trees we handle (species, gene and adjacency trees), as well as the definition of the optimization problem we propose (Section 2).
There are examples where temporal relationships defined by adjacency trees contradict the partial order of the nodes of one gene tree: see such an example in Figure S1 in Supplementary Material.
As adjacencies are pairs of genes, they follow the evolution of genes: if an adjacency AB descents from an adjacency CD, then A descents from C and B from D. So adjacency trees are defined given a set of reconciliated gene trees and have to follow their LCA reconciliations.
P X)= P Y) or X is the root of a gene tree, and either Y is also a root, or S(P(Y))≠ S Y) The cost of an adjacency forest is the sum of the costs of all adjacency trees.
An adjacency tree TA describes the descent pattern of adjacencies.
Together with the 'Adjacency Gain' (abbreviated Gain, which never labels the nodes of the trees as there is exactly one gain per adjacency tree), they are all the evolutionary events we consider.
Indeed an adjacency duplication means that two genes are duplicated together, while two nodes of an adjacency tree such that one is the descendant of the other and both are gene duplication events define a directed relation between the two duplications, even if they are not comparable from the gene trees (not in the same tree or not comparable in one tree).
Formally, every node N of an adjacency tree verifies If N is a leaf, then E (N )∈{ Extant,GLos,ALos,Break } and if N is an internal node, then E (N )∈{ Spec,GDup,ADup } If E (N )≠ Break, then there is a couple A (N )= XY of gene tree nodes X and Y (possibly from two different gene trees) such that S (N )= S (X )= S (Y ).
It requires that we rethink the process of viral origination and evolution, outside of the traditional molecular systematics interpretation of patterns of adjacency on trees, which treat large-scale similarity as evidence of inheritance from con-specific ancestors.
