10.S: Introduction to birth-death models (Summary)

Last updated
Save as PDF

Page ID: 21809

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

In this chapter, I introduced birth-death models and summarized their basic mathematical properties. Birth-death models predict patterns of species diversity over time intervals, and can also be used to model the growth of phylogenetic trees. We can visualize these patterns by measuring tree balance and creating lineage-through-time (LTT) plots.

References

Bailey, N. T. J. 1964. The elements of stochastic processes with applications to the natural sciences. John Wiley & Sons.

Bell, C. D., D. E. Soltis, and P. S. Soltis. 2005. The age of the angiosperms: A molecular timescale without a clock. Evolution 59:1245–1258.

Colless, D. H. 1982. Review of phylogenetics: The theory and practice of phylogenetic systematics. Syst. Zool.

Crepet, W. L., and K. J. Niklas. 2009. Darwin’s second “abominable mystery”: Why are there so many angiosperm species? Am. J. Bot. Botanical Soc America.

Davies, T. J., T. G. Barraclough, M. W. Chase, P. S. Soltis, D. E. Soltis, and V. Savolainen. 2004. Darwin’s abominable mystery: Insights from a supertree of the angiosperms. Proc. Natl. Acad. Sci. U. S. A. 101:1904–1909.

Farris, J. S. 1976. Expected asymmetry of phylogenetic trees. Syst. Zool. 25:196–198. [Oxford University Press, Society of Systematic Biologists, Taylor & Francis, Ltd.].

Felsenstein, J. 2004. Inferring phylogenies. Sinauer Associates, Inc., Sunderland, MA.

Foote, M., J. P. Hunter, C. M. Janis, and J. J. Sepkoski Jr. 1999. Evolutionary and preservational constraints on origins of biologic groups: Divergence times of eutherian mammals. Science 283:1310–1314.

Hedges, S. B., J. Dudley, and S. Kumar. 2006. TimeTree: A public knowledge-base of divergence times among organisms. Bioinformatics 22:2971–2972.

Kot, M. 2001. Stochastic birth and death processes. Pp. 25–42 in M. Kot, ed. Elements of mathematical ecology. Cambridge University Press, Cambridge.

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

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

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. 2011. Simulating trees with a fixed number of extant species. Syst. Biol. 60:676–684.