Maximum tree: A consistent estimator of the species tree

Liang Liu, Lili Yu, Dennis K. Pearl

Research output: Contribution to journalArticlepeer-review

58 Scopus citations


We propose a model based approach to use multiple gene trees to estimate the species tree. The coalescent process requires that gene divergences occur earlier than species divergences when there is any polymorphism in the ancestral species. Under this scenario, speciation times are restricted to be smaller than the corresponding gene split times. The maximum tree (MT) is the tree with the largest possible speciation times in the space of species trees restricted by available gene trees. If all populations have the same population size, the MT is the maximum likelihood estimate of the species tree. It can be shown the MT is a consistent estimator of the species tree even when the MT is built upon the estimates of the true gene trees if the gene tree estimates are statistically consistent. The MT converges in probability to the true species tree at an exponential rate.

Original languageEnglish (US)
Pages (from-to)95-106
Number of pages12
JournalJournal of Mathematical Biology
Issue number1
StatePublished - Sep 1 2010

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


Dive into the research topics of 'Maximum tree: A consistent estimator of the species tree'. Together they form a unique fingerprint.

Cite this