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Fitting and comparing models of phyletic evolution: random walks and beyond

Published online by Cambridge University Press:  08 April 2016

Gene Hunt
Gene Hunt*
Affiliation:
Department of Paleobiology, National Museum of Natural History, Smithsonian Institution, Washington, D.C. 20013-7012. E-mail: [email protected]
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Abstract

For almost 30 years, paleontologists have analyzed evolutionary sequences in terms of simple null models, most commonly random walks. Despite this long history, there has been little discussion of how model parameters may be estimated from real paleontological data. In this paper, I outline a likelihood-based framework for fitting and comparing models of phyletic evolution. Because of its usefulness and historical importance, I focus on a general form of the random walk model. The long-term dynamics of this model depend on just two parameters: the mean (μstep) and variance (σ2step) of the distribution of evolutionary transitions (or “steps”). The value of μstep determines the directionality of a sequence, and σ2step governs its volatility. Simulations show that these two parameters can be inferred reliably from paleontological data regardless of how completely the evolving lineage is sampled.

In addition to random walk models, suitable modification of the likelihood function permits consideration of a wide range of alternative evolutionary models. Candidate evolutionary models may be compared on equal footing using information statistics such as the Akaike Information Criterion (AIC). Two extensions to this method are developed: modeling stasis as an evolutionary mode, and assessing the homogeneity of dynamics across multiple evolutionary sequences. Within this framework, I reanalyze two well-known published data sets: tooth measurements from the Eocene mammal Cantius, and shell shape in the planktonic foraminifera Contusotruncana. These analyses support previous interpretations about evolutionary mode in size and shape variables in Cantius, and confirm the significantly directional nature of shell shape evolution in Contusotruncana. In addition, this model-fitting approach leads to a further insight about the geographic structure of evolutionary change in this foraminiferan lineage.

Type
Articles
Information
Paleobiology , Volume 32 , Issue 4 , Fall 2006 , pp. 578 - 601
Copyright
Copyright © The Paleontological Society 

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References

Literature Cited

Akaike, H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control 19:716–723.CrossRefGoogle Scholar
Alroy, J. 2000. Understanding the dynamics of trends within evolving lineages. Paleobiology 26:319–329.2.0.CO;2>CrossRefGoogle Scholar
Anderson, D. R., Burnham, K. P., and Thompson, W. L. 2000. Null hypothesis testing: problems, prevalence, and an alternative. Journal of Wildlife Management 64:912–923.CrossRefGoogle Scholar
Bookstein, F. L. 1987. Random walk and the existence of evolutionary rates. Paleobiology 13:446–464.CrossRefGoogle Scholar
Bookstein, F. L. 1988. Random walk and the biometrics of morphological characters. Evolutionary Biology 9:369–398.CrossRefGoogle Scholar
Bulmer, M. G. 1979. Principles of statistics. Dover, New York.Google Scholar
Chapelle, G., and Peck, L. S. 1999. Polar gigantism dictated by oxygen availability. Nature 399:114–115.Google Scholar
Clyde, W. C., and Gingerich, P. D. 1994. Rates of evolution in the dentition of early Eocene Cantius: comparison of size and shape. Paleobiology 20:506–522.Google Scholar
Connolly, S. R., and Miller, A. I. 2002. Global Ordovician faunal transitions in the marine benthos: ultimate causes. Paleobiology 28:26–40.2.0.CO;2>CrossRefGoogle Scholar
Cunningham, C. W., Omland, K. E., and Oakley, T. H. 1998. Reconstructing ancestral character states: a critical reappraisal. Trends in Ecology and Evolution 13:361–366.CrossRefGoogle Scholar
Davis, S. J. M. 1981. The effects of temperature change and domestication on the body size of Late Pleistocene to Holocene mammals of Israel. Paleobiology 7:101–114.Google Scholar
Edwards, A. W. F. 1992. Likelihood. Johns Hopkins University Press, Baltimore.Google Scholar
Felsenstein, J. 1985. Phylogenies and the comparative method. American Naturalist 125:1–15.Google Scholar
Finkel, Z. V., Katz, M. E., Wright, J. D., Schofield, O. M. E., and Falkowski, P. G. 2005. Climatically driven macroevolutionary patterns in the size of marine diatoms over the Cenozoic. Proceedings of the National Academy of Sciences USA 102:8927–8932.Google Scholar
Foote, M. 2003. Origination and extinction through the Phanerozoic: a new approach. Journal of Geology 111:125–148.CrossRefGoogle Scholar
Foote, M. 2005. Pulsed origination and extinction in the marine realm. Paleobiology 31:6–20.2.0.CO;2>CrossRefGoogle Scholar
Garland, T., and Ives, A. R. 2000. Using the past to predict the present: confidence intervals for regression equations in phylogenetic comparative methods. American Naturalist 155:346–364.Google Scholar
Gingerich, P. D. 1976. Paleontology and phylogeny: patterns of evolution at the species level. American Journal of Science 276:1–28.Google Scholar
Gingerich, P. D. 1993. Quantification and comparison of evolutionary rates. American Journal of Science 293-A:453–478.Google Scholar
Gould, S. J. 2002. The structure of evolutionary theory. Belknap Press of Harvard University Press, Cambridge.Google Scholar
Gould, S. J., and Eldredge, N. 1977. Punctuated equilibria: the tempo and mode of evolution reconsidered. Paleobiology 3:115–151.Google Scholar
Hallam, A. 1968. Morphology, palaeoecology and evolution of the genus Gryphaea in the British Lias. Philosophical Transactions of the Royal Society of London B 254:91–128.Google Scholar
Hansen, T. F., and Martins, E. P. 1996. Translating between microevolutionary process and macroevolutionary patterns: the correlation structure of interspecific data. Evolution 50:1404–1417.Google Scholar
Hunt, G. 2004. Phenotypic variation in fossil samples: modeling the consequences of time-averaging. Paleobiology 30:426–443.2.0.CO;2>CrossRefGoogle Scholar
Hunt, G., and Roy, K. 2006. Climate change, body size evolution, and Cope's Rule in deep-sea ostracodes. Proceedings of the National Academy of Sciences USA 103:1347–1352.Google Scholar
Hurvich, C. M., and Tsai, C.-L. 1989. Regression and time series model selection in small samples. Biometrika 76:297–307.CrossRefGoogle Scholar
Johnson, J. B., and Omland, K. S. 2004. Model selection in ecology and evolution. Trends in Ecology and Evolution 19:101–108.Google Scholar
Kaiho, K. 1999. Evolution in the test size of deep-sea benthic foraminifera during the past 120 m.y. Marine Micropaleontology 37:53–65.Google Scholar
Kalinowski, S. T., and Taper, M. L. 2005. Likelihood-based confidence intervals of relative fitness for a common experimental design. Canadian Journal of Fisheries and Aquatic Science 62:693–699.CrossRefGoogle Scholar
Kinnison, M. T., and Hendry, A. P. 2001. The pace of modern life II: from rates of contemporary microevolution to pattern and process. Genetica 112-113:145–164.CrossRefGoogle Scholar
Kucera, M., and Malmgren, B. A. 1998. Differences between evolution of mean form and evolution of new morphotypes: an example from Late Cretaceous planktonic foraminifera. Paleobiology 24:49–63.CrossRefGoogle Scholar
Le, C. T. 1992. Fundamentals of biostatistical inference. Marcel Dekker, New York.Google Scholar
Lynch, M. 1990. The rate of morphological evolution in mammals from the standpoint of the neutral expectation. American Naturalist 136:727–741.CrossRefGoogle Scholar
Lynch, M., and Walsh, B. 1998. Genetics and analysis of quantitative traits. Sinauer, Sunderland, Mass.Google Scholar
MacLeod, N. 1991. Punctuated anagenesis and the importance of stratigraphy to paleobiology. Paleobiology 17:167–188.Google Scholar
Malmgren, B. A., Berggren, W. A., and Lohmann, G. P. 1983. Evidence for puncuated gradualism in the Late Neogene Globorotalia tumida lineage of planktonic foraminifera. Paleobiology 9:377–389.Google Scholar
Martins, E. P. 1994. Estimating the rate of phenotypic evolution from comparative data. American Naturalist 144:193–209.Google Scholar
Martins, E. P. 1999. Estimation of ancestral states of continuous characters: a computer simulation study. Systematic Biology 48:642–650.Google Scholar
Martins, E. P., and Hansen, T. F. 1997. Phylogenies and the comparative method: a general approach to incorporating phylogenetic information into the analysis of interspecific data. American Naturalist 149:646–667.Google Scholar
McClain, C. R., and Rex, M. A. 2001. The relationship between dissolved oxygen concentration and maximum size in deep-sea turrid gastropods: an application of quantile regression. Marine Biology 139:681–685.Google Scholar
McKinney, M. 1985. Distinguishing patterns of evolution from patterns of depostion. Journal of Paleontology 59:561–567.Google Scholar
Pagel, M. 2002. Modelling the evolution of continuously varying characters on phylogenetic trees: the case of Hominid cranial capacity. Pp. 269–286 in MacLeod, N. and Forey, P. L., eds. Morphology, shape and phylogeny. Taylor and Francis, London.CrossRefGoogle Scholar
Posada, D., and Buckley, T. R. 2004. Model selection and model averaging in phylogenetics: advantages of Akaike Information Criterion and Bayesian approaches over likelihood ratio tests. Systematic Biology 53:793–808.Google Scholar
R Development Core Team. 2005. R: A language and environment for statistical computing, Version 2. 1.1. R Foundation for Statistical Computing, Vienna.Google Scholar
Raup, D. M. 1977. Stochastic models in evolutionary paleobiology. Pp. 59–78 in Hallam, A., ed. Patterns of evolution as illustrated by the fossil record. Elsevier, Amsterdam.CrossRefGoogle Scholar
Raup, D. M., and Crick, R. E. 1981. Evolution of single characters in the Jurassic ammonite Kosmoceras . Paleobiology 7:200–215.CrossRefGoogle Scholar
Raup, D. M., and Gould, S. J. 1974. Stochastic simulation and evolution of morphology—towards a nomothetic paleontology. Systematic Zoology 23:305–322.CrossRefGoogle Scholar
Roopnarine, P. D. 2001. The description and classification of evolutionary mode: a computational approach. Paleobiology 27:446–465.Google Scholar
Roopnarine, P. D. 2003. Analysis of rates of morphologic evolution. Annual Review of Ecology and Systematics 34:605–632.Google Scholar
Roopnarine, P. D., Byars, G., and Fitzgerald, P. 1999. Anagenetic evolution, stratophenetic patterns, and random walk models. Paleobiology 25:41–57.Google Scholar
Schmidt, D. N., Thierstein, H. R., Bollman, J., and Schiebel, R. 2004. Abiotic forcing of plankton evolution in the Cenozoic. Science 303:207–210.Google Scholar
Schroeder, M. 1991. Fractals, chaos, power laws. W. H. Freeman, New York.Google Scholar
Sheets, H. D., and Mitchell, C. E. 2001a. Uncorrelated change produces the apparent dependence of evolutionary rate on interval. Paleobiology 27:429–445.Google Scholar
Sheets, H. D., and Mitchell, C. E. 2001b. Why the null matters: statistical tests, random walks and evolution. Genetica 112– 113:105–125.Google Scholar
Smith, F., Betancourt, J. L., and Brown, J. H. 1995. Evolution of body size in the woodrat over the past 25,000 years of climate change. Science 270:2012–2014.Google Scholar
Sokal, R. R., and Rohlf, F. J. 1995. Biometry: the principles and practice of statistics in biological research, 3d ed. W. H. Freeman, New York.Google Scholar
Trueman, A. E. 1922. The use of Gryphaea in the correlation of the lower Lias. Geological Magazine 59:256–268.Google Scholar