Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chen FC, Li WH (2001) Genomic divergences between humans and other hominoids and the effective population size of the common ancestor of humans and chimpanzees. Am J Hum Genet 68: 444–456. doi:10.1086/318206
Degnan JH, Rosenberg NA (2006) Discordance of species trees with their most likely gene trees. PLoS Genet 2: 762–768. doi:10.1371/journal.pgen.0020068
Donnelly P, Tavare S (1995) Coalescents and genealogical structure under neutrality. Annu Rev Genet 29: 401–421. doi:10.1146/annurev.ge.29.120195.002153
Doyle JJ (1992) Gene trees and species trees—molecular systematics as one-character taxonomy. Syst Bot 17: 144–163. doi:10.2307/2419070
Edwards SV, Beerli P (2000) Perspective: Gene divergence, population divergence, and the variance in coalescence time in phylogeographic studies. Evol Int J Org Evol 54: 1839–1854
Edwards SV, Liu L, Pearl DK (2007) High-resolution species trees without concatenation. Proc Natl Acad Sci USA 104: 5936–5941. doi:10.1073/pnas.0607004104
Felsenstein J (2004) Inferring phylogenies. Sinauer Associates, Sunderland
Hudson RR (1991) Gene genealogies and the coalescent process. Oxford Surv Evol Biol 1–44
Jennings WB, Edwards SV (2005) Speciational history of Australian grass finches (Poephila) inferred from thirty gene trees. Evol Int J Org Evol 59: 2033–2047
Kingman JFC (1982) On the genealogy of large populations. Stoch Proc Appl 13: 235–248. doi:10.1016/0304-4149(82)90011-4
Kingman JFC (2000) Origins of the coalescent: 1974–1982. Genetics 156: 1461–1463
Kubatko LS, Degnan JH (2007) Inconsistency of phylogenetic estimates from concatenated data under coalescence. Syst Biol 56: 17–24. doi:10.1080/10635150601146041
Liu L, Pearl DK (2007) Species trees from gene trees: reconstructing Bayesian posterior distributions of a species phylogeny using estimated gene tree distributions. Syst Biol 56: 504–514. doi:10.1080/10635150701429982
Maddison WP (1997) Gene trees in species trees. Syst Biol 46: 523–536. doi:10.2307/2413694
Maddison WP, Knowles LL (2006) Inferring phylogeny despite incomplete lineage sorting. Syst Biol 55: 21–30. doi:10.1080/10635150500354928
Mossel E, Roch S (2007) Incomplete lineage sorting: consistent phylogeny estimation from multiple Loci. arXiv:0710.0262v2 [q-bio.PE]
Nielsen R et al (1998) Maximum-likelihood estimation of population divergence times and population phylogeny in models without mutation. Evol Int J Org Evol 52: 669–677. doi:10.2307/2411262
Page RDM (1998) GeneTree: comparing gene and species phylogenies using reconciled trees. Bioinformatics 14: 819–820. doi:10.1093/bioinformatics/14.9.819
Page RDM, Charleson MA (1997) From gene to organismal phylogeny: reconciled trees and the gene tree species tree problem. Mol Phylogenet Evol 7: 231–240. doi:10.1006/mpev.1996.0390
Rannala B, Yang ZH (2003) Bayes estimation of species divergence times and ancestral population sizes using DNA sequences from multiple loci. Genetics 164: 1645–1656
Rosenberg NA, Tao R (2008) Discordance of species trees with their most likely gene trees: the case of five taxa. Syst Biol 57: 131–140. doi:10.1080/10635150801905535
Takahata N (1989) Gene genealogy in 3 related populations—consistency probability between gene and population trees. Genetics 122: 957–966
Takahata N, Satta Y, Klein J (1995) Divergence time and population-size in the lineage leading to modern humans. Theor Popul Biol 48: 198–221. doi:10.1006/tpbi.1995.1026
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liu, L., Yu, L. & Pearl, D.K. Maximum tree: a consistent estimator of the species tree. J. Math. Biol. 60, 95–106 (2010). https://doi.org/10.1007/s00285-009-0260-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00285-009-0260-0