Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-27T11:15:37.891Z Has data issue: false hasContentIssue false
  • English
  • Français

Likelihood tests of hypothesized durations: determining and accommodating biasing factors

Published online by Cambridge University Press:  08 February 2016

Peter J. Wagner
Peter J. Wagner*
Affiliation:
1400 South Lake Shore Drive, Department of Geology, Field Museum of Natural History, Chicago, Illinois 60605. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Paleobiologists frequently hypothesize that a taxon's duration (i.e., the true span from origination to extinction) exceeds its stratigraphic range (i.e., the span from first appearance to last appearance in the fossil record). One can test hypothesized duration by assessing the plausibility of the implicitly hypothesized gaps between origination and first appearance and / or between last appearance and extinction. Several tests assess the probability of not finding a taxon over some stratigraphic gap. Because the likelihood of a hypothesis given data reflects the probability of the data given that hypothesis, these probabilities also give the likelihood of a hypothesized duration. However, many probability / likelihood tests require simplifying assumptions about unknown sampling parameters such as the consistency of sampling over time, sampling intensities for unknown ancestors, and actual sampling intensities themselves.

This paper examines the effects of sampling parameters on probability / likelihood tests and presents methods for testing hypotheses about these unknowns while testing hypotheses about true durations. Two data sets are used here as examples. One analysis tests the origination times among Paleozoic gastropods implied by phylogenetic inferences. The other analysis tests the extinction times among Maastrichtian ammonites implied by different numbers of extinction events. In both cases, hypotheses positing many gaps in the fossil record become more likely after accommodating uncertainty about sampling. However, the increased likelihoods are insufficient to prevent these hypotheses from being rejected in favor of hypotheses positing fewer gaps. In both cases, the conclusions are identical to those derived by simple methods using simple models for unknown sampling parameters. Although numerous factors can exaggerate the implausibility of gaps, making these factors parts of testable hypotheses is possible. Thus, excessive assumptions about sampling parameters need not hinder empirical testing of hypothesized durations.

Type
Articles
Information
Paleobiology , Volume 26 , Issue 3 , Summer 2000 , pp. 431 - 449
Copyright
Copyright © The 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

Literature Cited

Alroy, J. 1998. Diachrony of mammalian appearance events: implications for biochronology. Geology 26:23–26.2.3.CO;2>CrossRefGoogle Scholar
Archibald, J. D. 1993. The importance of phylogenetic analysis for the assessment of species turnover: a case history of Paleocene mammals in North America. Paleobiology 19:1–27.CrossRefGoogle Scholar
Bottjer, D. J., and Jablonski, D. 1988. Paleoenvironmental patterns in the evolution of post-Paleozoic benthic marine invertebrates. Palaios 3:540–560.CrossRefGoogle Scholar
Burgman, M. A., Grimson, R. C., and Ferson, S. 1995. Inferring threat from scientific collections. Conservation Biology 9:923–928.CrossRefGoogle Scholar
Cheetham, A. H., and Jackson, J. B. C. 1995. Process from pattern: tests for selection versus random change in punctuated bryozoan speciation. Pp. 184–207in Erwin, D. H. and Anstey, R. L.New approaches for studying speciation in the fossil record. Columbia University Press, New York.Google Scholar
Cox, D. R., and Lewis, P. A. W. 1966. The statistical analysis of series of events. Meuthen, London.CrossRefGoogle Scholar
Edwards, A. W. F. 1992. Likelihood, expanded ed. Johns Hopkins University Press, Baltimore.CrossRefGoogle Scholar
Edwards, A. W. F., and Cavalli-Sforza, L. L. 1964. Reconstruction of evolutionary trees. Pp. 67–76in Heywood, J. H. and McNeil, J., eds. Phenetic and phylogenetic classification. Systematics Association, London.Google Scholar
Felsenstein, J. 1985. Phylogenies and the comparative method. American Naturalist 125:1–15.CrossRefGoogle Scholar
Foote, M. 1997. Estimating taxonomic durations and preservation probability. Paleobiology 23:278–300.CrossRefGoogle Scholar
Foote, M., and Raup, D. M. 1996. Fossil preservation and the stratigraphic ranges of taxa. Paleobiology 22:121–140.CrossRefGoogle ScholarPubMed
Foote, M., Hunter, J. P., Janis, C. M., and Sepkoski, J. J. Jr. 1999. Evolutionary and preservational constraints on the origins of major biologic groups: limiting divergence times of eutherian mammals. Science 283:1310–1314.CrossRefGoogle Scholar
Gingerich, P. D., and Uhen, M. D. 1998. Likelihood estimation of the time of origin of Cetacea and the time of divergence of Cetacea and Artiodactyla. Palaeontologica Electronica 1:45.Google Scholar
Goldman, N. 1993. Statistical tests of models of DNA substitution. Journal of Molecular Evolution 36:182–198.CrossRefGoogle ScholarPubMed
Holland, S. M. 1995. The stratigraphic distribution of fossils. Paleobiology 21:92–109.CrossRefGoogle Scholar
Huelsenbeck, J. P., and Rannala, B. 1997. Maximum likelihood estimation of topology and node times using stratigraphic data. Paleobiology 23:174–180.CrossRefGoogle Scholar
Kluge, A. G., and Farris, J. S. 1969. Quantitative phyletics and the evolution of anurans. Systematic Zoology 18:1–32.CrossRefGoogle Scholar
Macellari, C. E. 1986. Late Campanian–Maastrichtian ammonite fauna from Seymour Island (Antarctic Peninsula). Journal of Paleontology Memoir 18:1–55.Google Scholar
Marshall, C. R. 1990. Confidence intervals on stratigraphic ranges. Paleobiology 16:1–10.CrossRefGoogle Scholar
Marshall, C. R. 1994. Confidence intervals on stratigraphic ranges: partial relaxation of the assumption of randomly distributed fossil horizons. Paleobiology 20:459–469.CrossRefGoogle Scholar
Marshall, C. R. 1995a. Distinguishing between sudden and gradual extinctions in the fossil record: predicting the position of the iridium anomaly using the ammonite fossil record on Seymour Island, Antarctica. Geology 23:731–734.2.3.CO;2>CrossRefGoogle Scholar
Marshall, C. R. 1995b. Stratigraphy, the true order of species' originations and extinctions, and testing ancestor-descendant hypotheses among Caribbean bryozoans. Pp. 208–236in Erwin, D. H. and Anstey, R. L.New approaches for studying speciation in the fossil record. Columbia University Press, New York.Google Scholar
Marshall, C. R. 1997. Confidence intervals on stratigraphic ranges with nonrandom distributions of fossil horizons. Paleobiology 23:165–173.CrossRefGoogle Scholar
Marshall, C. R., and Ward, P. D. 1996. Sudden and gradual molluscan extinctions in the latest Cretaceous of the western European Tethys. Science 274:1360–1363.CrossRefGoogle ScholarPubMed
McKinney, M. L. 1986a. Biostratigraphic gap analysis. Geology 14:75–117.2.0.CO;2>CrossRefGoogle Scholar
McKinney, M. L. 1986b. How biostratigraphic gaps form. Journal of Geology 94:875–884.CrossRefGoogle Scholar
Norell, M. A. 1993. Tree-based approaches to understanding history: comments on ranks, rules, and the quality of the fossil record. American Journal of Science 293-A:407–417.CrossRefGoogle Scholar
Patterson, C. 1982. Morphological characters and homology. Pp. 21–74in Joysey, K. A. and Friday, A. E., eds. Problems of phylogenetic reconstruction. Academic Press, London.Google Scholar
Paul, C. R. C. 1982. The adequacy of the fossil record. Pp. 75–117in Joysey, K. A. and Friday, A. E., eds. Problems of phylogenetic reconstruction. Academic Press, London.Google Scholar
Paul, C. R. C. 1985. The adequacy of the fossil record revisited. Pp. 1–16in Cope, J. C. W. and Skelton, P. W., eds. Evolutionary case histories from the fossil record. Palaeontological Society, London.Google Scholar
Raftery, A. E., and Akman, V. E. 1986. Bayesian analysis of a Poisson process with a change-point. Biometrika 73:85–89.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
Rieppel, O. 1997. Falsificationist versus verificationist approaches to history. Journal of Vertebrate Paleontology 17A:71A.Google Scholar
Signor, P. W., and Lipps, J. H. 1982. Sampling bias, gradual extinction patterns and catastrophes in the fossil record. Geological Society of America Special Paper 190:291–296.CrossRefGoogle Scholar
Smith, A. B. 1994. Systematics and the fossil record: documenting evolutionary patterns. Blackwell Scientific, Oxford.CrossRefGoogle Scholar
Smith, A. F. M. 1975. A Bayesian approach to inference about a change-point in a sequence of random variables. Biometrika 62:410–416.CrossRefGoogle Scholar
Sober, E. 1988. Reconstructing the past. MIT Press, Cambridge.Google Scholar
Sokal, R. R., and Rohlf, F. J. 1981. Biometry, 2d ed.W. H. Freeman, New York.Google Scholar
Solow, A. R. 1993a. Inferring extinction from sighting data. Ecology 74:962–963.CrossRefGoogle Scholar
Solow, A. R. 1993b. Inferring extinction in a declining population. Journal of Mathematical Biology 32:79–82.CrossRefGoogle Scholar
Solow, A. R. 1996. Tests and confidence intervals for a common upper endpoint in fossil taxa. Paleobiology 22:406–410.CrossRefGoogle Scholar
Solow, A. R., and Smith, W. 1997. On fossil preservation and the stratigraphic ranges of taxa. Paleobiology 23:271–277.CrossRefGoogle Scholar
Springer, M. S. 1990. The effect of random range truncations on patterns of evolution in the fossil record. Paleobiology 16:512–520.CrossRefGoogle Scholar
Springer, M. S., and Lilje, A. 1988. Biostratigraphy and gap analysis: the expected sequence of biostratigraphic events. Journal of Geology 96:228–236.CrossRefGoogle Scholar
Strauss, D., and Sadler, P. M. 1989. Classical confidence intervals and Bayesian probability estimates for ends of local taxon ranges. Mathematical Geology 21:411–427.CrossRefGoogle Scholar
Wagner, P. J. 1995. Stratigraphic tests of cladistic hypotheses. Paleobiology 21:153–178.CrossRefGoogle Scholar
Wagner, P. J. 1998. A likelihood approach for estimating phylogenetic relationships among fossil taxa. Paleobiology 24:430–449.CrossRefGoogle Scholar
Wagner, P. J. 1999. Phylogenetics of Ordovician–Silurian Lophospiridae (Gastropoda: Murchisoniina): the importance of stratigraphic data. American Malacological Bulletin 15:1–31.Google Scholar