Determining species tree topologies from clade probabilities under the coalescent

Area of Science:

• Phylogenetics and Evolutionary Biology
• Computational Biology
• Statistical Genetics

Background:

• Estimating species trees from gene trees is crucial for understanding evolutionary relationships.
• Current methods like greedy consensus algorithms can be statistically inconsistent under the multispecies coalescent model.
• The theoretical possibility of reconstructing species trees from clade probabilities remains an open question.

Purpose of the Study:

• To investigate whether species tree topology can be theoretically reconstructed from clade probabilities derived from gene trees.
• To identify features of the species tree reflected in clade probabilities under the multispecies coalescent model.
• To explore the utility of linear invariants for inferring species tree topology.

Main Methods:

• Analysis of clade probabilities generated by the multispecies coalescent model.
• Investigation of the relationship between gene tree clades and species tree clades based on probability thresholds.
• Theoretical and computational study of linear invariants of clade probabilities.

Main Results:

• Clades with probabilities greater than 1/3 in gene trees are shown to accurately reflect clades in the species tree.
• Linear invariants of clade probabilities provide insights into the species tree's clade structure.
• For species trees with generic edge lengths, these invariants can uniquely identify the species tree topology.

Conclusions:

• Clade probabilities contain sufficient information to fully determine the species tree topology.
• The findings support the theoretical possibility of species tree reconstruction from clade probabilities.
• This research suggests new avenues for developing statistically consistent phylogenetic inference methods.