Random walk as a null model for high-dimensional morphometrics of fossil series: Geometrical considerations

Paleobiology

Volumn 39, Issue 1, 2012, Pages 52-74

  Bookstein, Fred L ^a,b  

^a UNIVERSITY OF VIENNA   (Austria)

^b UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DATA SET; EVOLUTIONARY BIOLOGY; FOSSIL RECORD; GAUSSIAN METHOD; GEOMETRY; HYPOTHESIS TESTING; MORPHOMETRY; PALEOBIOLOGY; RANDOM WALK METHOD;

EID: 84872155696     PISSN: 00948373     EISSN: None     Source Type: Journal    
DOI: 10.1666/0094-8373-39.1.52     Document Type: Article

References (45)

1. Aguirre, W. E., and M. A. Bell. 2012. Twenty years of body shape evolution in a threespine stickleback population adapting to a lake environment. Biological Journal of the Linnean Society 105:817-831.
2. Bell, M. A. 2001. Lateral plate evolution in the threespine stickleback: getting nowhere fast. Genetica 112-113:445-461.
3. Berg, H. C. 1993. Random walks in biology, 2nd ed. Princeton University Press, Princeton, N.J.
4. Bingham, N. H., and R. A. Doney. 1988. On higher-dimensional analogues of the Arc-sine Law. Journal of Applied Probability 25:120-131.
5. Blackith, R. E., and R. A. Reyment. 1971. Multivariate morphometrics. Academic Press.
6. Bookstein, F. L. 1987. Random walk and the existence of evolutionary rates. Paleobiology 13:446-464.
7. -1988. Random walk and the biometrics of morphological characters. Evolutionary Biology 23:369-398.
8. Codling, E. A., M. J. Plank, and S. Benhamou. 2008. Random walk models in biology. Journal of the Royal Society Interface 5:813-834. (Pubitemid 351882159)
9. Dean, D., L. Marcus, and F. L. Bookstein. 1996. Chi-square test of biological space curve affinities. Pp. 235-261 in L. F. Marcus, M. Corti, A. Loy, G. J. P. Naylor, and D. E. Slice, eds. Advances in morphometrics. NATO ASI Series A, Life Sciences, Vol. 284. Plenum, New York.
10. Dryden, I. M., and K. V. Mardia. 1998. Statistical shape analysis. Wiley, Chichester, U.K.
11. Einstein, A. 1905. U ber die von molekularischen Theorie der Warme geforderte Bewegung von ruhenden Flüssigkeiten suspendierten Teilchen (Investigations on the theory of Brownian movement). Annalen der Physik 17:549-560. Edited R. Fürth, translated by A. D. Cowper. Dover Books, 1956.
12. Feller, W. 1968. An introduction to probability theory and its applications, Vol. 1, 3rd ed. Wiley, Chichester, U.K.
13. Felsenstein, J. 1988. Phylogenies and quantitative characters. Annual Review of Ecology and Systematics 19:445-471.
14. -2004. Inferring phylogenies. Sinauer, Sunderland, Mass.
15. Fisk, P. R. 1970. A note on a characterization of the multivariate normal distribution. Annals of Mathematical Statistics 41:486-494.
16. Gingerich, P. D. 1993. Quantification and comparison of evolutionary rates. American Journal of Science 293A:453-478.
17. Gould, S. J. 1989. Wonderful life: The Burgess Shale and the nature of history. W. W. Norton, New York.
18. Gould, S. J., and N. Eldredge. 1977. Punctuated equilibria: The tempo and mode of evolution reconsidered. Paleobiology 3:115-151.
19. Gower, J. C. 1966. Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika 53:325-338.
20. Gunz, P., P. Mitteroecker, A. Stadlmayr, G. W. Weber, H. Seidler, and F. L. Bookstein. 2009. The origins of modern human diversity: multi-wave and multi-pathway migration during Late Pleistocene. Proceedings of the National Academy of Sciences USA 106:6094-6098.
21. Hannisdal, B. 2006. Phenotypic evolution in the fossil record: numerical experiments. Journal of Geology 114:133-153.
22. -2007. Inferring phenotypic evolution in the fossil record by Bayesian inversion. Paleobiology 33:98-115.
23. Hunt, G. 2006. Fitting and comparing models of phyletic evolution: random walks and beyond. Paleobiology 32:578-601. (Pubitemid 44873478)
24. -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.
25. Kahneman, D. 2011. Thinking, fast and slow. Farrar Straus Giroux, New York.
26. Kendall, D. G. 1984. Shape manifolds, Procrustean metrics and complex projective spaces. Bulletin of the London Mathematical Society 16:81-121.
27. Kimura, M. 1983. The neutral theory of molecular evolution. Cambridge University Press, Cambridge.
28. Lande, R. 1979. Quantitative genetic analysis of multivariate evolution, applied to brain:body size allometry. Evolution 33:402-426.
29. Lynch, M., and W. G. Hill. 1986. Phenotypic evolution by neutral mutation. Evolution 40:915-935.
30. Mardia, K. V., F. L. Bookstein, J. T. Kent, and C. R. Meyer. 2006. Intrinsic random fields and image deformations. Journal of Mathematical Imaging and Vision 26:59-71. (Pubitemid 44832620)
31. Mitteroecker, P., and F. L. Bookstein. 2009. The ontogenetic trajectory of the phenotypic covariance matrix, with examples from craniofacial shape in rats and humans. Evolution 63:727-737.
32. Nei, M. 2007. The new mutation theory of phenotypic evolution. Proceedings of the National Academy of Sciences USA 104:12235-12242. (Pubitemid 47206121)
33. Pearson, K., and A. Lee. 1903. On the laws of inheritance in man. I. Inheritance of physical characters. Biometrika 2:357-462.
34. Perrin, J. 1909. Mouvement Brownien et ŕealit́e moĺeculaire. Annales de Chimie et de Physique XVIII:5-113.
35. -1923. Atoms, 2nd ed. Translated by D. L. Hamnick. Constable, London.
36. Podani, J., and I. Mikĺ os. 2002. Resemblance coefficients and the horseshoe effect in principal coordinates analysis. Ecology 83:3331-3343. (Pubitemid 36524649)
37. Polly, P. D. 2008. Developmental dynamics and G-matrices: can morphometric spaces be used to model phenotypic evolution Evolutionary Biology 35:83-96.
38. Raup, D. M. 1977. Stochastic models in evolutionary palaeobiology. Pp. 59-78 in A. Hallam, ed. Patterns of evolution as illustrated by the fossil record. Elsevier, Amsterdam.
39. Reyment, R. A. 1991. Multidimensional palaeobiology. Pergamon, Oxford.
40. Roopnarine, P. D. 2003. Analysis of rates of morphologic evolution. Annual Review of Ecology, Evolution, and Systematics 34:605-632. (Pubitemid 38171432)
41. Rudnick, J., and G. Gaspari. 2004. Elements of the random walk: an introduction for advanced students and researchers. Cambridge University Press, Cambridge.
42. Sheets, H. D., and C. E. Mitchell. 2001. Why the null matters: statistical tests, random walks, and evolution. Genetica 112-113:105-125. (Pubitemid 34119656)
43. Torgerson, W. 1958. Theory and methods of scaling. Wiley, Chichester, U.K.
44. Wartenberg, D., S. Ferson, and F. J. Rohlf. 1987. Putting things in order: a critique of detrended correspondence analysis. American Naturalist 129:434-448.
45. Wood, A. R., M. L. Zelditch, A. N. Rountrey, T. P. Eiting, H. D. Sheets, and P. D. Gingerich. 2007. Multivariate stasis in the dental morphology of the Paleocene-Eocene condylarth Ectocion. Paleobiology 33:248-260. (Pubitemid 47008296)