Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-25T22:52:57.007Z Has data issue: false hasContentIssue false
  • English
  • Français

Mathematical models of temporal mixing in the fossil record

Published online by Cambridge University Press:  17 July 2017

Alan H. Cutler
Alan H. Cutler*
Affiliation:
Department of Paleobiology, National Museum of Natural History, Smithsonian Institution, Washington, D.C. 20560
Get access Rights & Permissions [Opens in a new window]

Extract

In December 1969 officials from the U.S. Selective Service System conducted a draft lottery to establish the order in which nineteen-year-old men were to be called for military service. Three hundred sixty-six capsules, one for each possible birthday, were placed in a large wooden box. As the capsules for each month were added to the box, the contents of the box were mixed. Once all 366 capsules were in the box, it was shaken several times and emptied into a deep bowl. Capsules were then drawn from the bowl to determine the draft number corresponding to each date. Observers were satisfied that the capsules had been thoroughly mixed, but, as it turned out, the results were anything but random. The Spearman rank correlation between birth date and draft number was significant at the.001 level – men with December birthdays had a significantly higher probability of being called than did those with January birthdays (Fienberg, 1971).

Type
Research Article
Information
Short Courses in Paleontology , Volume 6: Taphonomic Approaches to Time Resolution in Fossil Assemblages , 1993 , pp. 169 - 187
Copyright
Copyright © 1993 Paleontological Society 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Berger, W.H., and Heath, G.R. 1968. Vertical mixing in pelagic sediments. Journal of Marine Research, 26:134–143.Google Scholar
Berger, W.H., Johnson, R.F., and Killingley, J.S. 1977. ‘Unmixing’ of the deep-sea record and the deglacial melt water spike. Nature, 269:661–663.Google Scholar
Boudreau, B.P. 1986a. Mathematics of tracer mixing in sediments: I. spatially-dependent, diffusive mixing. American Journal of Science, 286:161–198.Google Scholar
Boudreau, B.P. 1986b. Mathematics of tracer mixing in sediments: II. nonlocal mixing and biological conveyor-belt phenomena. American Journal of Science, 286:199–238.Google Scholar
Boudreau, B.P., and Imboden, D.M. 1987. Mathematics of tracer mixing in sediments: III. the theory of nonlocal within sediments. American Journal of Science, 287:693–719.Google Scholar
Bromley, R.G. 1990. Trace fossils: biology and taphonomy. Unwin Hyman, London, 280p.Google Scholar
Causton, D.R. 1987. A Biologist's Advanced Mathematics. Allen & Unwin, London, 326p.Google Scholar
Christensen, E.R., and Goetz, R.H. 1987. Historical fluxes of particle-bound pollutants from deconvolved sedimentary records. Environmental Science & Technology, 21:1088–1096.Google Scholar
Christensen, E.R., and Osuna, J.L. 1989. Atmospheric fluxes of lead, zinc, and cadmium from frequency domain deconvolution of sedimentary records. Journal of Geophysical Research, 94:14585–14597.Google Scholar
Christensen, E.R., and Klein, R.J. 1991. “Unmixing” of 137Cs, Pb, Zn, and Cd records in lake sediments. Environmental Science & Technology, 25:1627–1637.Google Scholar
Cutler, A.H. 1990. Avoiding stratigraphic disorder: sampling strategies for shallow marine strata. Geological Society of America, Abstracts with Programs, 22:A81.Google Scholar
Cutler, A.H., 1991. Processes of hardpart breakdown and models of stratigraphic disorder in shallow marine environments. Unpublished Ph.D. dissertation, University of Arizona, Tucson, Arizona, 256p.Google Scholar
Cutler, A.H., and Flessa, K. W. 1990. Fossils out of sequence: computer simulations and strategies for dealing with stratigraphic disorder. Palaios, 5:227–235.Google Scholar
Dubois, L.G. and Prell, W.L. 1988. Effects of carbonate dissolution on the radiocarbon age structure of sediment mixed layers. Deep-Sea Research, 35:1875–1885.CrossRefGoogle Scholar
Flessa, K.W., Cutler, A.H., Meldahl, K.H., and Fürsich, F.T. 1989. Taphonomic processes and stratigraphic disorder. Abstracts, 28th International Geological Congress, I:493–494.Google Scholar
Flessa, K.W., Cutler, A.H., and Meldahl, K.H., in press, Time and taphonomy: quantitative estimates of time-averaging and stratigraphic disorder in a shallow marine habitat. Paleobiology.Google Scholar
Fienberg, S.E., 1971. Randomization and social affairs: the 1970 draft lottery. Science, 171:255–261.Google Scholar
Fienberg, S.E., Cutler, A.H., and Meldahl, K.H., in press. Time and taphonomy: quantitative estimates of time-averaging and stratigraphic disorder in a shallow marine habitat. Paleobiology.Google Scholar
Goldberg, E.D., and Koide, M. 1962. Geochronological studies of deep sea sediments by the ionium/thorium method. Geochimica Cosmochimica Acta, 26:417–450.Google Scholar
Guinasso, N.L. Jr., and Schink, D.R. 1975. Quantitative estimates of biological mixing rates in abyssal sediments. Journal of Geophysical Research, 80:3032–3043.Google Scholar
Hanor, J.S., and Marshall, N.F. 1971. Mixing of sediment by organisms, p. 127–135. In: Perkins, B. F. (ed.), Trace Fossils: a field guide to selected localities in Pennsylvanian, Permian, Cretaceous, and Tertiary rocks of Texas, and related papers. Louisiana State University, Miscellaneous Publication 71.Google Scholar
Kim, K.H., and Burnett, W.C. 1988. Accumulation and biological mixing of Peru margin sediments. Marine Geology, 80:181–194.Google Scholar
McCave, I.N. 1988. Biological pumping upwards of the coarse fraction of deep sea sediments. Journal of Sedimentary Petrology, 58:148–158.Google Scholar
Officer, C.B. and Lynch, D.R. 1983. Determination of mixing parameters from tracer distributions in deep-sea sediment cores. Marine Geology, 52: 59–74.Google Scholar
Peng, T.H., Broecker, W.S., Kipphut, G., and Shackelton, N.J. 1977. Benthic mixing in deep-sea cores as determined by 14C dating and its implication regarding climate stratigraphy and the fate of fossil fuel CO2 , p.355–373. In: Anderson, N.R. and Malahoff, A. (eds.), The fate of fossil fuel CO2 in the oceans. Plenum Press, New York.CrossRefGoogle Scholar
Rosato, A., Strandburg, K.J., Prinz, F., and Swendsen, R.H. 1987. Why the Brazil nuts are on top: size segregation of particulate matter by shaking. Physical Review Letters, 58:1038–1040.Google Scholar
Schiffelbein, P. 1985. Extracting the benthic mixing impulse response function: a constrained deconvolution technique. Marine Geology, 64:313–336.Google Scholar
Wheatcroft, R.A. 1990. Preservation potential of sedimentary event layers. Geology, 18:843–845.Google Scholar
Wheatcroft, R.A., and Jumars, P.A. 1987. Statistical re-analysis for size dependency in deep-sea mixing. Marine Geology, 77:157–163.Google Scholar
Wheatcroft, R.A., Jumars, P.A., Smith, C.R., and Nowell, A.R.M. 1990. A mechanistic view of the particulate biodiffusion coefficient: step lengths, rest periods and transport direction. Journal of Marine Research, 48:177–207.Google Scholar