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Measuring rates of phenotypic evolution and the inseparability of tempo and mode

Published online by Cambridge University Press:  08 February 2016

Gene Hunt
Gene Hunt*
Affiliation:
Department of Paleobiology, National Museum of Natural History, Smithsonian Institution, Washington, D.C. 20560. E-mail: hunte@si.edu
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Abstract

Rates of phenotypic evolution are central to many issues in paleontology, but traditional rate metrics such as darwins or haldanes are seldom used because of their strong dependence on interval length. In this paper, I argue that rates are usefully thought of as model parameters that relate magnitudes of evolutionary divergence to elapsed time. Starting with models of directional evolution, random walks, and stasis, I derive for each a reasonable rate metric. These metrics can be linked to existing approaches in evolutionary biology, and simulations show that they can be estimated accurately at any temporal resolution via maximum likelihood, but only when that metric's underlying model is true.

The estimation of generational rates of a random walk under realistic paleontological conditions is compared with simulations to that of a prominent alternative approach, Gingerich's LRI (log-rate, log-interval) method. Generational rates are estimated poorly by LRI; they often reflect sampling error more than the actual pace of change. Further simulations show that under some realistic conditions, it is simply not possible to infer generational rates from coarsely sampled populations.

These modeling results indicate a complex dependence between evolutionary mode and the measurement of evolutionary rates, and that there is unlikely to be a rate metric that works well for all traits and time scales. Compilations of paleontological and phylogenetic data indicate that all of the three rate metrics derived here show some relationship with interval length. Although there is no perfect rate metric, at present the most practical choices derive from the parameters of the stasis and random walk models. The latter, called the step variance, is particularly promising as a rate metric in paleontology and comparative biology.

Type
Featured Article
Information
Paleobiology , Volume 38 , Issue 3 , Summer 2012 , pp. 351 - 373
Copyright
Copyright © The Paleontological Society 

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References

Literature Cited

Ackerly, D. 2009. Conservatism and diversification of plant functional traits: Evolutionary rates versus phylogenetic signal. Proceedings of the National Academy of Sciences USA 106:19699–19706.CrossRefGoogle ScholarPubMed
Alfaro, M. E., Santini, F., Brock, C., Alamillo, H., Dornburg, A., Rabosky, D. L., Carnevale, G., and Harmon, L. J. 2009. Nine exceptional radiations plus high turnover explain species diversity in jawed vertebrates. Proceedings of the National Academy of Sciences USA 106:13410–13414.CrossRefGoogle ScholarPubMed
Alroy, J. 2008. Dynamics of origination and extinction in the marine fossil record. Proceedings of the National Academy of Sciences of the United States of America 105:11536–11542.CrossRefGoogle ScholarPubMed
Alroy, J. 2010. Fair sampling of taxonomic richness and unbiased estimation of origination and extinction rates. Pp. 55–80in Alroy and Hunt 2010.Google Scholar
Alroy, J., and Hunt, G., eds. 2010. Quantitative methods in paleobiology. Paleontological Society Papers 16. Paleontological Society, New Haven, Conn.Google Scholar
Arnold, S. J., Pfrender, M. E., and Jones, A. G. 2001. The adaptive landscape as a conceptual bridge between micro- and macroevolution. Genetica 112–113:9–32.CrossRefGoogle Scholar
Bookstein, F. L. 1987. Random walk and the existence of evolutionary rates. Paleobiology 13:446–464.CrossRefGoogle Scholar
Brusatte, S. L., Montanari, S., Yi, H. Y., and Norell, M. A. 2011. Phylogenetic corrections for morphological disparity analysis: new methodology and case studies. Paleobiology 37:1–22.CrossRefGoogle Scholar
Burnham, K. P. and Anderson, D. R. 2010. Model selection and multimodel inference. Springer, New York.Google Scholar
Bush, A. 2000. Evolution within demes: stasis as a hierarchical phenomenon. Geological Society of America, Abstracts with Programs 32:445.Google Scholar
Cheetham, A. H., Jackson, J. B. C., and Hayek, L-A. C. 1993. Quantitative genetics of bryozoan phenotypic evolution. I. Rate tests for random change versus selection in differentiation of living species. Evolution 47:1526–1538.CrossRefGoogle ScholarPubMed
Cheetham, A. H., Jackson, J. B. C., and Hayek, L-A. C. 1994. Quantitative genetics of bryozoan phenotypic evolution. II. Analysis of selection and random change in fossil species using reconstructed genetic parameters. Evolution 48:360–375.CrossRefGoogle ScholarPubMed
Ciampaglio, C. N., Kemp, M., and McShea, D. W. 2001. Detecting changes in morphospace occupation patterns in the fossil record: characterization and analysis of measures of disparity. Paleobiology 27:695–715.2.0.CO;2>CrossRefGoogle 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.CrossRefGoogle Scholar
Eldredge, N., and Gould, S. J. 1972. Punctuated equilibria: an alternative to phyletic gradualism. Pp. 82–115inSchopf, T. J. M., ed. Models in paleobiology. Freeman, Cooper, San Francisco.Google Scholar
Eldredge, N., Thompson, J. N., Brakefield, P. M., Gavrilets, S., Jablonski, D., Jackson, J. B. C., Lenski, R. E., Lieberman, B. S., McPeek, M. A., and Miller, W. I. 2005. The dynamics of evolutionary stasis. Paleobiology 31(Suppl. to No. 2):133–145.CrossRefGoogle Scholar
Erwin, D. H., and Anstey, R. L. 1995. Speciation in the fossil record. Pp. 11–38inErwin, D. H. and Anstey, R. L., eds. New approaches to speciation in the fossil record. Columbia University Press, New York.Google Scholar
Erwin, D. H., Laflamme, M., Tweedt, S. M., Sperling, E. A., Pisani, D., and Peterson, K. J. 2011. The Cambrian conundrum: early divergence and later ecological success in the early history of animals. Science 334:1091–1097.CrossRefGoogle ScholarPubMed
Estes, S., and Arnold, S. J. 2007. Resolving the paradox of stasis: models with stabilizing selection explain evolutionary divergence on all timescales. American Naturalist 169:227–244.CrossRefGoogle ScholarPubMed
Felsenstein, J. 1985. Phylogenies and the comparative method. American Naturalist 125:1–15.CrossRefGoogle Scholar
Foote, M. 1991. Analysis of morphological data. Pp. 59–86inGilinsky, N. L. and Signor, P. W., eds. Analytical paleobiology. Paleontological Society, Knoxville, Tennessee.Google Scholar
Foote, M. 2000. Origination and extinction components of taxonomic diversity: general problems. InErwin, D. H. and Wing, S. L., eds. Deep time: Paleobiology's perspective. Paleobiology. 26(Suppl. to No. 4):74–102.CrossRefGoogle Scholar
Foote, M. 2003. Origination and extinction through the Phanerozoic: a new approach. Journal of Geology 111:125–148.CrossRefGoogle Scholar
Geary, D. H., Hunt, G., Magyar, I., and Schreiber, H. 2010. The paradox of gradualism: phyletic evolution in two lineages of lymnocardiid bivalves (Lake Pannon, central Europe). Paleobiology 36:592–614.CrossRefGoogle Scholar
Gingerich, P. D. 1983. Rates of evolution: effects of time and temporal scaling. Science 222:159–161.CrossRefGoogle ScholarPubMed
Gingerich, P. D. 1985. Species in the fossil record: concepts, trends, and transitions. Paleobiology 11:27–41.CrossRefGoogle Scholar
Gingerich, P. D. 1993. Quantification and comparison of evolutionary rates. American Journal of Science 293-A:453–478.CrossRefGoogle Scholar
Gingerich, P. D. 2001. Rates of evolution on the time scale of evolutionary process. Genetica 112–113:127–144.CrossRefGoogle Scholar
Gingerich, P. D. 2009. Rates of evolution. Annual Review of Ecology, Evolution, and Systematics 40:657–675.CrossRefGoogle Scholar
Gould, S. J. 1984. Smooth curve of evolutionary rate: a psychological and mathematical artifact. Science 226:994–995.CrossRefGoogle 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.CrossRefGoogle Scholar
Haldane, J. B. S. 1949. Suggestions as to the quantitative measurement of rates of evolution. Evolution 3:51–56.CrossRefGoogle Scholar
Hannisdal, B. 2006. Phenotypic evolution in the fossil record: numerical experiments. Journal of Geology 114:133–153.CrossRefGoogle Scholar
Hansen, T. F. 1997. Stabilizing selection and the comparative analysis of adaptation. Evolution 51:1341–1351.CrossRefGoogle ScholarPubMed
Harmon, L. J., Weir, J., Brock, C., Glor, R., Challenger, W., and Hunt, G. 2009. geiger: analysis of evolutionary diversification, R package, Version 1.3–1.Google Scholar
Harmon, L. J., Losos, J. B., Davies, T. J., Gillespie, R. G., Gittleman, J. L., Jennings, W. B., Kozak, K. H., McPeek, M. A., Moreno-Roark, F., Near, T. J., Purvis, A., Ricklefs, R. E., Schluter, D., Schulte, J. A., Seehausen, O., Sidlauskas, B. L., Torres-Carvajal, O., Weir, J. T., and Mooers, A. O. 2010. Early bursts of body size and shape evolution are rare in comparative data. Evolution 64:2385–2396.Google ScholarPubMed
Hendry, A. P., and Kinnison, M. T. 1999. The pace of modern life: measuring rates of contemporary microevolution. Evolution 53:1637–1653.CrossRefGoogle ScholarPubMed
Hersch, E. I., and Phillips, P. C. 2004. Power and potential bias in field studies of natural selection. Evolution 58:479–485.Google ScholarPubMed
Hunt, G. 2006. Fitting and comparing models of phyletic evolution: random walks and beyond. Paleobiology 32:578–601.CrossRefGoogle Scholar
Hunt, G. 2007. The relative importance of directional change, random walks, and stasis in the evolution of fossil lineages. Proceedings of the National Academy of Sciences USA 104:18404–18408.CrossRefGoogle ScholarPubMed
Hunt, G. 2008a. Evolutionary patterns within fossil lineages: model-based assessment of modes, rates, punctuations and process. InKelley, P. H. and Bambach, R. K., eds. From evolution to geobiology: research questions driving paleontology at the start of a new century. Paleontological Society Papers 14:117–131Paleontological Society, Pittsburgh.CrossRefGoogle Scholar
Hunt, G. 2008b. Gradual or pulsed evolution: when should punctuational explanations be preferred? Paleobiology 34:360–377.CrossRefGoogle Scholar
Hunt, G. 2011. paleoTS: Modeling evolution in paleontological time-series, R package, Version 0.4-1.Google Scholar
Hunt, G., and Carrano, M. T. 2010. Models and methods for analyzing phenotypic evolution in lineages and clades Pp. 245–269in Alroy and Hunt 2010.Google Scholar
Jablonski, D., and Bottjer, D. J. 1990. Onshore-offshore trends in marine invertebrate evolution. Pp. 21–75inAllmon, W. D. and Ross, R. M., eds. Causes of evolution: a paleontological perspective. University of Chicago Press, Chicago.Google Scholar
Kendall, M. G., and Stuart, A. 1969. The advanced theory of statistics, Vol. 1. Distribution theory. Hafner, New York.Google Scholar
Kingsolver, J. G., and Pfennig, D. W. 2007. Patterns and power of phenotypic selection in nature. BioScience 57:561–572.CrossRefGoogle Scholar
Kingsolver, J. G., Hoekstra, H. E., Hoekstra, J. M., Berrigan, D., Vignieri, S. N., Hill, C. E., Hoang, A., Gilbert, P., and Beerli, P. 2001. The strength of phenotypic selection in natural populations. American Naturalist 157:245–261.CrossRefGoogle ScholarPubMed
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
Knapczyk, F. N., and Conner, J. K. 2007. Estimates of the average strength of natural selection are not inflated by sampling error or publication bias. American Naturalist 170:501–508.CrossRefGoogle ScholarPubMed
Lande, R. 1976. Natural selection and random genetic drift in phenotypic evolution. Evolution 30:314–334.CrossRefGoogle ScholarPubMed
Lande, R., and Arnold, S. J. 1983. The measurement of selection on correlated characters. Evolution 37:1210–1226.CrossRefGoogle ScholarPubMed
Liow, L. H., and Nichols, J. D. 2010. Estimating rates and probabilities of origination and extinctionusing taxonomic occurrence data: capture-mark-recapture (CMR) approaches. Pp. 81–94in Alroy and Hunt 2010.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
Marshall, C. R. 2006. Explaining the Cambrian “explosion” of animals. Annual Review of Earth and Planetary Sciences 34:355–384.CrossRefGoogle Scholar
Mousseau, T. A., and Roff, D. A. 1987. Natural selection and the heritability of fitness components. Heredity 59:181–197.CrossRefGoogle ScholarPubMed
Nee, S. 2004. Extinct meets extant: simple models in paleontology and molecular phylogenetics. Paleobiology 30:172–178.2.0.CO;2>CrossRefGoogle Scholar
O'Meara, B. C., Ané, C. c., Sanderson, M. J., and Wainwright, P. C. 2006. Testing for different rates of continuous trait evolution using likelihood. Evolution 60:922–933.Google ScholarPubMed
Pagel, M. 1998. Inferring evolutionary processes from phylogenies. Zoologica Scripta 26:331–348.CrossRefGoogle Scholar
Polly, P. D. 2002. Phylogenetic tests for differences in shape and the importance of divergence times: Eldredge's enigma explored. Pp. 220–246inMacLeod, N. and Forey, P. L., eds. Morphology, shape and phylogeny. Taylor and Francis, London.CrossRefGoogle Scholar
Rabosky, D. L. 2009. Heritability of extinction rates links diversification patterns in molecular phylogenies and fossils. Systematic Biology 58:629–640.CrossRefGoogle ScholarPubMed
Roopnarine, P. D. 2003. Analysis of rates of morphologic evolution. Annual Review of Ecology and Systematics 34:605–632.CrossRefGoogle Scholar
Roy, K., and Foote, M. 1997. Morphological approaches to measuring biodiversity. Trends in Ecology and Evolution 12:277–281.CrossRefGoogle ScholarPubMed
Sheets, H. D., and Mitchell, C. E. 2001a. Uncorrelated change produces the apparent dependence of evolutionary rate on interval. Paleobiology 27:429–445.2.0.CO;2>CrossRefGoogle 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
Simpson, G. G. 1944. Tempo and mode in evolution. Columbia University Press, New York.Google Scholar
Smith, F. A., Elliott, S. M., and Lyons, S. K. 2010. Methane emissions from extinct megafauna. Nature Geoscience 3:374–375.CrossRefGoogle Scholar
Stanley, S. M. 1985. Rates of evolution. Paleobiology 11:13–26.CrossRefGoogle Scholar
Thomas, G. H., Meiri, S., and Phillimore, A. B. 2009. Body size diversification in Anolis: novel environment and island effects. Evolution 63:2017–2030.CrossRefGoogle ScholarPubMed
Uyeda, J. C., Hansen, T. F., Arnold, S. J., and Pienaar, J. 2011. The million-year wait for macroevolutionary bursts. Proceedings of the National Academy of Sciences USA 108:15908–15913.CrossRefGoogle ScholarPubMed
Wang, S. C. 2010. Principles of statistical inference: likelihood and the Bayesian paradigm. Pp. 1–18in Alroy and Hunt 2010.Google Scholar