# 6.S: Beyond Brownian Motion (Summary)

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In this chapter, I have described a few models that represent alternatives to Brownian motion, which is still the dominant model of trait evolution used in the literature. These examples really represent the beginnings of a whole set of models that one might fit to biological data. The best applications of this type of approach, I think, are in testing particular biologically motivated hypotheses using comparative data.

## Section 6.9: Footnotes

1: Pagel's original models were initially focused on discrete characters, but - as he later pointed out - apply equally well to continuous characters.

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## References

Alfaro, M. E. 2013. Key evolutionary innovations. in J. B. Losos, D. A. Baum, D. J. Futuyma, H. E. Hoekstra, R. E. Lenski, A. J. Moore, C. L. Peichel, D. Schluter, and M. C. Whitlock, eds. The Princeton guide to evolution. Princeton University Press, Princeton.

Blomberg, S. P., T. Garland Jr, and A. R. Ives. 2003. Testing for phylogenetic signal in comparative data: Behavioral traits are more labile. Evolution 57:717–745.

Boettiger, C., G. Coop, and P. Ralph. 2012. Is your phylogeny informative? Measuring the power of comparative methods. Evolution 66:2240–2251.

Bokma, F. 2008. Detection of “punctuated equilibrium” by Bayesian estimation of speciation and extinction rates, ancestral character states, and rates of anagenetic and cladogenetic evolution on a molecular phylogeny. Evolution 62:2718–2726. Blackwell Publishing Inc.

Eastman, J. M., M. E. Alfaro, P. Joyce, A. L. Hipp, and L. J. Harmon. 2011. A novel comparative method for identifying shifts in the rate of character evolution on trees. Evolution 65:3578–3589.

Garland, T., Jr. 1992. Rate tests for phenotypic evolution using phylogenetically independent contrasts. Am. Nat. 140:509–519.

Goldberg, E. E., and B. Igić. 2012. Tempo and mode in plant breeding system evolution. Evolution 66:3701–3709. Wiley Online Library.

Grant, P. R., and B. R. Grant. 2002. Unpredictable evolution in a 30-year study of Darwin’s finches. Science 296:707–711.

Grant, P. R., and R. B. Grant. 2011. How and why species multiply: The radiation of Darwin’s finches. Princeton University Press.

Hansen, T. F., and E. P. Martins. 1996. Translating between microevolutionary process and macroevolutionary patterns: The correlation structure of interspecific data. Evolution 50:1404–1417.

Harmon, L. J., J. B. Losos, T. Jonathan Davies, R. G. Gillespie, J. L. Gittleman, W. Bryan Jennings, K. H. Kozak, M. A. McPeek, F. Moreno-Roark, T. J. Near, and Others. 2010. Early bursts of body size and shape evolution are rare in comparative data. Evolution 64:2385–2396.

Hunter, J. P. 1998. Key innovations and the ecology of macroevolution. Trends Ecol. Evol. 13:31–36.

Lande, R. 1976. Natural selection and random genetic drift in phenotypic evolution. Evolution 30:314–334.

O’Meara, B. C., C. Ané, M. J. Sanderson, and P. C. Wainwright. 2006. Testing for different rates of continuous trait evolution using likelihood. Evolution 60:922–933.

Pagel, M. 1999a. Inferring the historical patterns of biological evolution. Nature 401:877–884.

Pagel, M. 1999b. The maximum likelihood approach to reconstructing ancestral character states of discrete characters on phylogenies. Syst. Biol. 48:612–622.

Pennell, M. W., and L. J. Harmon. 2013. An integrative view of phylogenetic comparative methods: Connections to population genetics, community ecology, and paleobiology. Ann. N. Y. Acad. Sci. 1289:90–105.

Revell, L. J. 2013. Two new graphical methods for mapping trait evolution on phylogenies. Methods Ecol. Evol. 4:754–759.

Revell, L. J., L. J. Harmon, and D. C. Collar. 2008. Phylogenetic signal, evolutionary process, and rate. Syst. Biol. 57:591–601.

Simpson, G. G. 1945. Tempo and mode in evolution. Trans. N. Y. Acad. Sci. 8:45–60.

Thomas, G. H., R. P. Freckleton, and T. Székely. 2006. Comparative analyses of the influence of developmental mode on phenotypic diversification rates in shorebirds. Proc. Biol. Sci. 273:1619–1624.

Uyeda, J. C., and L. J. Harmon. 2014. A novel bayesian method for inferring and interpreting the dynamics of adaptive landscapes from phylogenetic comparative data. Syst. Biol. 63:902–918. sysbio.oxfordjournals.org.

Yoder, J. B., E. Clancey, S. Des Roches, J. M. Eastman, L. Gentry, W. Godsoe, T. J. Hagey, D. Jochimsen, B. P. Oswald, J. Robertson, and Others. 2010. Ecological opportunity and the origin of adaptive radiations. J. Evol. Biol. 23:1581–1596. Blackwell Publishing Ltd.

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