# 11.S: Fitting Birth-Death Models (Summary)

- Page ID
- 21647

In this chapter, I described how to estimate parameters from birth-death models using data on species diversity and ages, and how to use patterns of tree balance to test hypotheses about changing birth and death rates. I also described how to calculate the likelihood for birth-death models on trees, which leads directly to both ML and Bayesian methods for estimating birth and death rates. In the next chapter, we will explore elaborations on birth-death models, and discuss models that go beyond constant-rates birth-death models to analyze the diversity of life on Earth.

## References

Blum, M. G. B., and O. François. 2006. Which random processes describe the tree of life? A large-scale study of phylogenetic tree imbalance. Syst. Biol. 55:685–691.

Blum, M. G. B., O. François, and S. Janson. 2006. The mean, variance and limiting distribution of two statistics sensitive to phylogenetic tree balance. Ann. Appl. Probab. 16:2195–2214. Institute of Mathematical Statistics.

Bortolussi, N., E. Durand, M. Blum, and O. François. 2006. ApTreeshape: Statistical analysis of phylogenetic tree shape. Bioinformatics 22:363–364.

Coyne, J. A., and H. A. Orr. 2004. Speciation. Sinauer, New York.

Drummond, C. S., R. J. Eastwood, S. T. S. Miotto, and C. E. Hughes. 2012. Multiple continental radiations and correlates of diversification in Lupinus (Leguminosae): Testing for key innovation with incomplete taxon sampling. Syst. Biol. 61:443–460. academic.oup.com.

FitzJohn, R. G., W. P. Maddison, and S. P. Otto. 2009. Estimating trait-dependent speciation and extinction rates from incompletely resolved phylogenies. Syst. Biol. 58:595–611. sysbio.oxfordjournals.org.

Gould, S. J., D. M. Raup, J. J. Sepkoski, T. J. M. Schopf, and D. S. Simberloff. 1977. The shape of evolution: A comparison of real and random clades. Paleobiology 3:23–40. Cambridge University Press.

Harding, E. F. 1971. The probabilities of rooted tree-shapes generated by random bifurcation. Adv. Appl. Probab. 3:44–77. Cambridge University Press.

Hedges, B. S., and S. Kumar. 2009. The timetree of life. Oxford University Press, Oxford.

Höhna, S. 2014. Likelihood inference of non-constant diversification rates with incomplete taxon sampling. PLoS One 9:e84184.

Höhna, S., M. R. May, and B. R. Moore. 2016. TESS: An R package for efficiently simulating phylogenetic trees and performing Bayesian inference of lineage diversification rates. Bioinformatics 32:789–791.

Höhna, S., T. Stadler, F. Ronquist, and T. Britton. 2011. Inferring speciation and extinction rates under different sampling schemes. Mol. Biol. Evol. 28:2577–2589.

Hughes, C., and R. Eastwood. 2006. Island radiation on a continental scale: Exceptional rates of plant diversification after uplift of the Andes. Proc. Natl. Acad. Sci. U. S. A. 103:10334–10339.

Hutter, C. R., S. M. Lambert, and J. J. Wiens. 2017. Rapid diversification and time explain amphibian richness at different scales in the tropical Andes, Earth’s most biodiverse hotspot. Am. Nat. 190:828–843.

Maddison, W. P., P. E. Midford, S. P. Otto, and T. Oakley. 2007. Estimating a binary character’s effect on speciation and extinction. Syst. Biol. 56:701–710. Oxford University Press.

Madriñán, S., A. J. Cortés, and J. E. Richardson. 2013. Páramo is the world’s fastest evolving and coolest biodiversity hotspot. Front. Genet. 4:192.

Magallon, S., and M. J. Sanderson. 2001. Absolute diversification rates in angiosperm clades. Evolution 55:1762–1780.

McConway, K. J., and H. J. Sims. 2004. A likelihood-based method for testing for nonstochastic variation of diversification rates in phylogenies. Evolution 58:12–23.

Miller, E. C., and J. J. Wiens. 2017. Extinction and time help drive the marine-terrestrial biodiversity gradient: Is the ocean a deathtrap? Ecol. Lett. 20:911–921.

Mooers, A. O., and S. B. Heard. 1997. Inferring evolutionary process from phylogenetic tree shape. Q. Rev. Biol. 72:31–54.

Mora, C., D. P. Tittensor, S. Adl, A. G. B. Simpson, and B. Worm. 2011. How many species are there on earth and in the ocean? PLoS Biol. 9:e1001127. Public Library of Science.

Morlon, H., T. L. Parsons, and J. B. Plotkin. 2011. Reconciling molecular phylogenies with the fossil record. Proc. Natl. Acad. Sci. U. S. A. 108:16327–16332. National Academy of Sciences.

Nee, S. 2006. Birth-Death models in macroevolution. Annu. Rev. Ecol. Evol. Syst. 37:1–17. Annual Reviews.

Nee, S., R. M. May, and P. H. Harvey. 1994. The reconstructed evolutionary process. Philos. Trans. R. Soc. Lond. B Biol. Sci. 344:305–311.

Paradis, E. 2012. Shift in diversification in sister-clade comparisons: A more powerful test. Evolution 66:288–295. Wiley Online Library.

Rabosky, D. L., S. C. Donnellan, A. L. Talaba, and I. J. Lovette. 2007. Exceptional among-lineage variation in diversification rates during the radiation of Australia’s most diverse vertebrate clade. Proc. Biol. Sci. 274:2915–2923.

Raup, D. M. 1985. Mathematical models of cladogenesis. Paleobiology 11:42–52.

Raup, D. M., and S. J. Gould. 1974. Stochastic simulation and evolution of morphology: Towards a nomothetic paleontology. Syst. Biol. 23:305–322. Oxford University Press.

Raup, D. M., S. J. Gould, T. J. M. Schopf, and D. S. Simberloff. 1973. Stochastic models of phylogeny and the evolution of diversity. J. Geol. 81:525–542.

Rohatgi, V. K. 1976. An introduction to probability theory and mathematical statistics. Wiley.

Slowinski, J. B., and C. Guyer. 1993. Testing whether certain traits have caused amplified diversification: An improved method based on a model of random speciation and extinction. Am. Nat. 142:1019–1024.

Stadler, T. 2013a. How can we improve accuracy of macroevolutionary rate estimates? Syst. Biol. 62:321–329.

Stadler, T. 2013b. Recovering speciation and extinction dynamics based on phylogenies. J. Evol. Biol. 26:1203–1219.

Stadler, T., and J. Smrckova. 2016. Estimating shifts in diversification rates based on higher-level phylogenies. Biol. Lett. 12:20160273. The Royal Society.

Strathmann, R. R., and M. Slatkin. 1983. The improbability of animal phyla with few species. Paleobiology. cambridge.org.

Vamosi, S. M., and J. C. Vamosi. 2005. Endless tests: Guidelines for analysing non-nested sister-group comparisons. Evol. Ecol. Res. 7:567–579. Evolutionary Ecology, Ltd.

Yule, G. U. 1925. A mathematical theory of evolution, based on the conclusions of dr. J. C. Willis, FRS. Philos. Trans. R. Soc. Lond. B Biol. Sci. 213:21–87. The Royal Society.