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Phenotypic variation in fossil samples: modeling the consequences of time-averaging

Published online by Cambridge University Press:  08 February 2016

Gene Hunt
Gene Hunt*
Affiliation:
Committee on Evolutionary Biology, University of Chicago, Chicago, Illinois 60637
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Abstract

Fossil samples almost always accumulate on timescales much longer than the life spans of individual organisms. This time-averaging has the potential to inflate the variability of fossil samples because phenotypic changes may occur during the interval of sample accumulation. Although many have realized that this effect may increase the variance of fossil samples, only qualitative predictions have been possible thus far. In this paper, I assume a simple but general Markovian model of evolution to derive expressions that predict the effects of time-averaging on trait variance and covariance. For lineages evolving as an unbiased random walk, phenotypic variance in samples increases linearly with the duration of time-averaging, at a slope that is proportional to the evolutionary rate. Although based on a very simple model of specimen input into time-averaged samples, the expressions relating variance, time-averaging, and evolutionary rate prove to be robust or adaptable to more realistic assumptions.

The theoretical findings are applied to analyze variation in a set of samples of the deep-sea ostracode Poseidonamicus miocenicus that vary greatly in temporal acuity. The relationship between duration of time-averaging and morphological variance is used to estimate evolutionary rates of two morphological traits in these ostracodes. These rate estimates are similar to those calculated independently from differences between presumed ancestor-descendant pairs of populations. Consistent with other studies of variability and time-averaging, these data suggest that phenotypic variance tends to increase rather slowly with the duration of time-averaging, indicating that greatly inflated variance is expected only in samples that have accumulated over many tens of thousands of years.

Type
Articles
Information
Paleobiology , Volume 30 , Issue 3 , Summer 2004 , pp. 426 - 443
Copyright
Copyright © The Paleontological Society 

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References

Literature Cited

Baily, R. C., and Byrnes, J. 1990. A new, old method for assessing measurement error in both univariate and multivariate morphometric studies. Systematic Zoology 39:124–130.CrossRefGoogle Scholar
Bell, M. A., Sadagursky, M. S., and Baumgartner, J. V. 1987. Utility of lacustrine deposits for the study of variation within fossil samples. Palaios 2:455–466.CrossRefGoogle Scholar
Berggren, W. A., Hilgen, F. J., Langereis, C. G., Kent, D. V., Obradovich, J. D., Raffi, I., Raymo, M. E., and Shackleton, N. J. 1995a. Late Neogene chronology: new perspectives in high-resolution stratigraphy. Geological Society of America Bulletin 107:1272–1287.2.3.CO;2>CrossRefGoogle Scholar
Berggren, W. A., Kent, D. V., Swisher, C. C. I., and Aubrey, M.-P. 1995b. A revised Cenozoic geochronology and chronostratigraphy. Pp. 129–212in Berggren, W. A., Kent, D. V., Aubrey, M.-P., and Hardenbol, J., eds. Geochronology, time scales and global stratigraphic correlation. Society for Sedimentary Geology, Tulsa, Okla.Google 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
Bookstein, F. L., Gingerich, P. D., and Kluge, A. G. 1978. Hierarchical linear modeling of the tempo and mode of evolution. Paleobiology 4:120–134.CrossRefGoogle Scholar
Boyle, E. A. 1984. Sampling statistic limitation on benthic foraminifera chemical and isotopic data. Marine Geology 58:213–224.CrossRefGoogle Scholar
Bush, A., Powell, M. G., Arnold, W. S., Bert, T. M., and Daley, G. M. 2002. Time-averaging, evolution and morphological variation. Paleobiology 28:9–25.2.0.CO;2>CrossRefGoogle Scholar
Cronin, T. M., Raymo, M. E., and Kyle, K. P. 1996. Pliocene (3.2–2.4 Ma) ostracode faunal cycles and deep ocean circulation, North Atlantic Ocean. Geology 24:695–698.2.3.CO;2>CrossRefGoogle Scholar
Flessa, K. W., and Kowalewski, M. 1994. Shell survival and time-averaging in nearshore and shelf environments: estimates from the radiocarbon literature. Lethaia 27:153–165.CrossRefGoogle Scholar
Gingerich, P. D. 1993. Quantification and comparison of evolutionary rates. American Journal of Science 293-A:453–478.CrossRefGoogle Scholar
Haldane, J. B. S. 1949. Suggestions as to the quantitative measurement of rates of evolution. Evolution 3:51–56.CrossRefGoogle Scholar
Hansen, T. E., and Martins, E. P. 1996. Translating between microevolutionary process and macroevolutionary patterns: the correlation structure of interspecific data. Evolution 50:1404–1417.CrossRefGoogle ScholarPubMed
Hughes, N. C. 1990. Computer-aided restorations of a late Cambrian ceratopygid trilobite from Wales, and its phylogenetic implications. Palaeontology 33:429–445.Google Scholar
Hunt, G.In press. Phenotypic variance inflation in fossil samples: an empirical assessment. Paleobiology.Google Scholar
Hunt, G., and Chapman, R. E. 2001. Evaluating hypotheses of instar-groupings in arthropods: a maximum likelihood approach. Paleobiology 27:466–484.2.0.CO;2>CrossRefGoogle Scholar
Kendall, M. G., and Stuart, A. 1969. The advanced theory of statistics, Vol. 1. Distribution theory. Hafner, New York.Google Scholar
Kidwell, S. M. 1986. Models for fossil concentrations: paleobiological implications. Paleobiology 12:6–24.CrossRefGoogle Scholar
Kidwell, S. M. 1998. Time-averaging in the marine fossil record: overview of strategies and uncertainties. Geobios 30:977–995.CrossRefGoogle Scholar
Kidwell, S. M., and Aigner, T. 1985. Sedimentary dynamics of complex shell beds: implications for ecologic and evolutionary patterns. Pp. 382–395in Bayer, U. and Seilacher, A., eds. Sedimentary and evolutionary cycles. Springer, Berlin.CrossRefGoogle Scholar
Kidwell, S. M., and Behrensmeyer, A. K. 1993a. Summary: estimates of time-averaging. Pp. 301–302in Kidwell, and Behrensmeyer, 1993b.CrossRefGoogle Scholar
Kidwell, S. M., and Behrensmeyer, A. K. 1993b. Taphonomic approaches to time resolution in fossil assemblages. Short Courses in Paleontology No. 6. Paleontological Society, Knoxville, Tenn.CrossRefGoogle Scholar
Kidwell, S. M., and Flessa, K. W. 1996. The quality of the fossil record: populations, species, and communities. Annual Review of Earth and Planetary Sciences 24:433–464.CrossRefGoogle Scholar
Kidwell, S. M., and Holland, S. M. 2002. The quality of the fossil record: implications for evolutionary analysis. Annual Review of Ecology and Systematics 33:561–588.CrossRefGoogle Scholar
Kowalewski, M., and Bambach, R. K. 2003. The limits of paleontological resolution. Pp. 1–48in Harries, P. J. and Geary, D. H., eds. High resolution approaches in paleontology. Plenum/Kluwer, New York.Google Scholar
Kowalewski, M., Goodfriend, G. A., and Flessa, K. W. 1998. High-resolution estimates of temporal mixing within shell beds: the evils and virtues of time-averaging. Paleobiology 24:287–304.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
MacFadden, B. J. 1989. Dental character variation in paleo-populations and morphospecies of fossil horses and extant analogs. Pp. 128–141in Prothero, D. R. and Schoch, R. M., eds. The evolution of perissodactyls. Oxford University Press, New York.Google Scholar
Martin, R. E. 1999. Taphonomy: a process approach. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Martins, E. P. 1994. Estimating the rate of phenotypic evolution from comparative data. American Naturalist 144:193–209.CrossRefGoogle 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.CrossRefGoogle Scholar
Meldahl, K. H., Flessa, K. W., and Cutler, A. H. 1997. Time-averaging and postmortem skeletal survival in benthic fossil assemblages: quantitative comparisons among Holocene environments. Paleobiology 23:207–229.CrossRefGoogle Scholar
Olszewski, T. 1999. Taking advantage of time-averaging. Paleobiology 25:226–238.CrossRefGoogle Scholar
Pagel, M. 2002. Modelling the evolution of continuously varying characters on phylogenetic trees: the case of Hominid cranial capacity. Pp. 269–286in MacLeod, N. and Forey, P. L., eds. Morphology, shape and phylogeny. Taylor and Francis, London.CrossRefGoogle Scholar
Raup, D. M. 1977. Stochastic models in evolutionary paleobiology. Pp. 59–78in 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
Rohlf, F. J. 1998. tpsDig, Version 1.20. Stonybrook, NY.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
Sadler, P. M. 1981. Sediment accumulation rates and the completeness of stratigraphic sections. Journal of Geology 89:569–584.CrossRefGoogle Scholar
Schindel, D. E. 1980. Microstratigraphic sampling and the limits of paleontological sampling. Paleobiology 6:408–426.CrossRefGoogle Scholar
Sokal, R. R., and Rohlf, F. J. 1995. Biometry, 3d ed. W. H. Freeman, New York.Google Scholar
Turelli, M., Gillespie, J. H., and Lande, R. 1988. Rate tests for selection on quantitative characters during macroevolution and microevolution. Evolution 42:1085–1089.CrossRefGoogle ScholarPubMed
Van Valen, L. M. 1969. Variation genetics of extinct animals. American Naturalist 103(931):193–224.CrossRefGoogle Scholar
Walker, K. R., and Bambach, R. K. 1971. The significance of fossil assemblages from fine-grained sediments: time-averaged communities. Geological Society of America Abstracts with Programs 3:783–784.Google Scholar
Webster, M., and Hughes, N. C. 1999. Compaction-related deformation in Cambrian olenelloid trilobites and its implications for fossil morphometry. Journal of Paleontology 73:355–371.CrossRefGoogle Scholar
Wilson, M. V. H. 1988. Taphonomic processes: information loss and information gain. Geoscience Canada 15:131–148.Google Scholar