Medians seek the corners, and other conjectures

Area of Science:

• Computational Biology
• Phylogenetics
• Genomics

Background:

• Median construction is fundamental to gene-order phylogeny methods.
• Median problem solutions are often non-unique and can differ significantly.
• Medians may converge to input orders, limiting phylogenetic information.

Purpose of the Study:

• To investigate the tendency of breakpoint medians to approach input genomes.
• To analyze the behavior of median solutions with increasing gene order randomness and gene number.
• To explore alternate solutions and their distances in gene-order median problems.

Main Methods:

• Conjectural analysis of breakpoint medians for circular unichromosomal genomes (unsigned and signed cases).
• Simulations to confirm conjectures regarding median behavior.
• Extension of findings to medians involving more than three genomes.

Main Results:

• Breakpoint medians tend to approach one of the input genomes ('corners') as genomes become more random and larger.
• Alternate solutions also approach other input genomes, leading to large average distances between solutions.
• Simulations confirm these tendencies and extend them to multiple genomes.

Conclusions:

• The tendency of medians to approach input genomes introduces biases in phylogenetic analysis.
• A reconsideration of the median's role in gene-order phylogeny is prompted.
• A small proportion of median solutions avoid this 'corner' tendency and are close to each other, suggesting a focused search strategy.