A short proof that phylogenetic tree reconstruction by maximum likelihood is hard.

Area of Science:

• Computational evolutionary biology
• Phylogenetics
• Algorithm complexity

Background:

• Maximum likelihood is a cornerstone for inferring evolutionary trees.
• The computational complexity of maximum likelihood inference has been a long-standing question.
• Previous assumptions suggested intractability without formal proof.

Purpose of the Study:

• To formally prove that computing the maximum likelihood tree is NP-hard.
• To establish the theoretical computational limits of phylogenetic inference using maximum likelihood.
• To connect maximum likelihood with parsimony to demonstrate hardness.

Main Methods:

• Developed a novel proof strategy for computational complexity in phylogenetics.
• Exploited the established relationship between maximum likelihood and parsimony.
• Utilized established NP-hardness proof techniques adapted for phylogenetic models.

Main Results:

• Demonstrated that the problem of finding the maximum likelihood tree is NP-hard.
• Provided a concise and accessible proof of this computational intractability.
• Established a formal link between the complexity of likelihood and parsimony.

Conclusions:

• The inference of evolutionary trees under the maximum likelihood criterion is computationally intractable for large datasets.
• This NP-hardness result has significant implications for the development and application of phylogenetic algorithms.
• Understanding the complexity landscape is crucial for advancing evolutionary biology research.