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Estimating taxonomic diversity, extinction rates, and speciation rates from fossil data using capture-recapture models

Published online by Cambridge University Press:  08 April 2016

James D. Nichols  and
Kenneth H. Pollock
James D. Nichols
Affiliation:
U.S. Fish and Wildlife Service, Migratory Bird Research, Patuxent Wildlife Research Center, Laurel, Maryland 20708
Kenneth H. Pollock
Affiliation:
North Carolina State University, Department of Statistics, Box 5457, Raleigh, North Carolina 27607
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Abstract

Methods currently used to estimate taxonomic extinction probabilities from fossil data generally assume that the probability of encountering a specimen in a particular stratum, given that the taxon was extant in the time period and location represented by the stratum, either equals 1.0 or else is a constant for all strata. Methods used to estimate taxonomic diversity (number of taxa) and speciation rate generally assume that encounter probabilities equal 1.0. We suspect that these assumptions are often false. Capture-recapture models were historically developed for estimation in the face of variable and unknown sampling probabilities. These models can thus be used to estimate parameters of interest from paleobiological data when encounter probabilities are unknown and variable over time. These models also permit estimation of sampling variances, and goodness-of-fit tests are available for assessing the fit of data to most models. Here we describe capture-recapture models which should be useful in paleobiological analyses and discuss the assumptions which underlie them. We illustrate these models with examples and discuss aspects of study design. We conclude that these models should prove useful in paleobiological analyses.

Type
Research Article
Information
Paleobiology , Volume 9 , Issue 2 , Spring 1983 , pp. 150 - 163
Copyright
Copyright © The Paleontological Society 

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References

Literature Cited

Arnason, A. N. and Baniuk, L. 1980. A computer system for mark-recapture analysis of open populations. J. Wildlife Manage. 44:325–332.Google Scholar
Balser, J. P. 1981. Confidence interval estimation and tests for temporary outmigration in tag-recapture studies. Unpublished Ph.D. thesis, Cornell Univ., Ithaca, N.Y.205 pp.Google Scholar
Begon, M. 1979. Investigating Animal Abundance: Capture-Recapture for Biologists. Univ. Park Press, Baltimore, Md.Google Scholar
Brownie, C, Anderson, D. R., Burnham, K. P., and Robson, D. S. 1978. Statistical inference from band recovery data: a handbook. U.S. Fish Wildlife Serv., Resour. Publ. 130.Google Scholar
Burnham, K. P. and Overton, W. S. 1978. Estimation of the size of a closed population when capture probabilities vary among animals. Biometrika. 65:625–633.Google Scholar
Burnham, K. P. and Overton, W. S. 1979. Robust estimation of population size when capture probabilities vary among animals. Ecology. 60:927–936.Google Scholar
Carothers, A.D. 1971. An examination and extension of Leslie's test of equal catchability. Biometrics. 27:615–630.CrossRefGoogle ScholarPubMed
Carothers, A. D. 1973. The effects of unequal catchability on Jolly-Seber estimates. Biometrics. 29:79–100.CrossRefGoogle Scholar
Cormack, R. M. 1968. The statistics of capture-recapture methods. Oceanogr. Marine Biol. Annu. Rev. 6:455–506.Google Scholar
Cormack, R. M. 1972. The logic of capture-recapture estimates. Biometrics. 28:337–343.Google Scholar
Cormack, R. M. 1973. Commonsense estimates from capture-recapture studies. Pp. 225–234. In: Bartlett, M. S. and Hiorns, R. W., eds. The Mathematical Theory of the Dynamics of Biological Populations. Academic Press, New York.Google Scholar
Cormack, R. M. 1979. Models for capture-recapture. Pp. 217–255. In: Cormack, R. M., Patil, G. P., and Robson, D. S., eds., Sampling Biological Populations. Statistical Ecology Series, vol. 5. International Cooperative Publ. House, Burtonsville, Md.Google Scholar
Crosbie, S. F. 1979. The mathematical modeling of capture-mark-recapture experiments on animal populations. Unpublished Ph.D. thesis. Univ. Otago, Dunedin, New Zealand. 383 pp.Google Scholar
Darroch, J. N. 1958. The multiple recapture census. I. Estimation of a closed population. Biometrika. 45:343–359.Google Scholar
Davies, R. G. 1971. Computer Programming in Quantitative Biology. Academic Press, London.Google Scholar
Gilbert, R. O. 1973. Approximations of the bias in the Jolly-Seber capture-recapture model. Biometrics. 29:501–526.CrossRefGoogle Scholar
Gray, H. L. and Shucany, W. R. 1972. The Generalized Jack-knife Statistic. Marcel Dekker, New York.Google Scholar
Jolly, G. M. 1965. Explicit estimates from capture-recapture data with both death and immigration-stochastic model. Biometrika. 52:225–247.Google Scholar
Jolly, G. M. 1979. A unified approach to mark-recapture stochastic models, exemplified by a constant survival rate model. Pp. 277–282. In: Cormack, R. M., Patil, G. P., and Robson, D. S., eds. Sampling Biological Populations. Statistical Ecology Series, vol. 5. International Cooperative Publ. House, Burtonsville, Md.Google Scholar
Jolly, G. M. 1982. Mark-recapture models with parameters constant in time. Biometrics. 38:301–321.Google Scholar
Keyfitz, N. 1968. Introduction to the Mathematics of Population. Addison-Wesley, Reading, Mass.Google Scholar
Kurtén, B. 1954. Population dynamics—a new method in paleontology. J. Paleontol. 28:286–292.Google Scholar
Leslie, P. H. 1958. Statistical appendix. J. Anim. Ecol. 27:84–86.Google Scholar
Leslie, P. H., Chitty, D., and Chitty, H. 1953. The estimation of population parameters from data obtained by means of the capture-recapture method. III. An example of the practical applications of the method. Biometrika. 40:137–169.Google Scholar
Lincoln, F. C. 1930. Calculating waterfowl abundance on the basis of banding returns. U.S. Dept. Agric., Circ. no. 118. 4 pp. Washington, D.C.Google Scholar
Moore, R. C. and Teichert, C., eds. 1953–1978. Treatise on Invertebrate Paleontology. Geol. Soc. Amer. and Univ. Kansas. Boulder, Colo., and Lawrence, Kans.Google Scholar
Nichols, J. D., Noon, B. R., Stokes, S. L., and Hines, J. E. 1981. Remarks on the use of mark-recapture methodology in estimating avian population size. Pp. 121–136. In: Ralph, C. J. and Scott, M. J., eds. Estimating the Numbers of Terrestrial Birds. Stud. Avian Biol. 6. Lawrence, Kansas.Google Scholar
Nichols, J. D. and Pollock, K. H. 1983. Estimation methodology in contemporary small mammal capture-recapture studies. J. Mammal. 64:253–260.Google Scholar
Nichols, J. D., Stokes, S. L., Hines, J. E., and Conroy, M. J. 1982. Additional comments on the assumption of homogeneous survival rates in modern bird banding estimation models. J. Wildlife Manage. 46:953–962.CrossRefGoogle Scholar
Otis, D. L., Burnham, K. P., White, G. C., and Anderson, D. R. 1978. Statistical inference from capture data on closed animal populations. Wildl. Monogr. 62.Google Scholar
Petersen, C. G. J. 1896. The yearly immigration of young plaice into limfjord from the German Sea. Rept. Danish Biol. Sta. for 1895. 6:1–77.Google Scholar
Pollock, K. H. 1981. Capture-recapture models: a review of current methods, assumptions and experimental design. Pp. 426–435. In: Ralph, C. J. and Scott, J. M., eds. Estimating the Numbers of Terrestrial Birds. Stud. Avian Biol. 6. Lawrence, Kansas.Google Scholar
Pollock, K. H. 1982. A capture-recapture sampling design robust to unequal catchability. J. Wildlife Manage. 46:752–757.CrossRefGoogle Scholar
Pollock, K. H. and Raveling, D. G. 1982. Assumptions of modern bird-banding models, with emphasis on heterogeneous survival rates. J. Wildlife Manage. 46:88–98.Google Scholar
Raup, D. M. 1975. Taxonomic survivorship curves and Van Valen's Law. Paleobiology. 1:82–96.Google Scholar
Raup, D. M. 1978. Cohort analysis of generic survivorship. Paleobiology. 4:1–15.Google Scholar
Raup, D. M. and Sepkoski, J. J. 1982. Mass extinctions in the marine fossil record. Science. 215:1501–1503.CrossRefGoogle ScholarPubMed
Robson, D. S. and Youngs, W. D. 1971. Statistical analysis of reported tag-recaptures in the harvest from an exploited population. BU-369–M. Biometrics Unit, Cornell Univ., Ithaca, N.Y.Google Scholar
Romer, A. S. 1966. Vertebrate paleontology. 3d ed.Univ. Chicago Press, Chicago.Google Scholar
Rosenzweig, M. L. and Duek, J. L. 1979. Species diversity and turnover in an Ordovician marine invertebrate assemblage. Pp. 109–119. In: Patil, G. P. and Rosenzweig, M. L., eds. Contemporary Quantitative Ecology and Related Ecometrics. Statistical Ecology Series, vol. 12. International Cooperative Publ. House, Burtonsville, Md.Google Scholar
Rosenzweig, M. L. and Taylor, J. A. 1980. Speciation and diversity in Ordovician invertebrates: filling niches quickly and carefully. Oikos. 35:236–243.CrossRefGoogle Scholar
Schankler, D. 1980. Faunal zonation of the Willwood Formation in the Central Bighorn Basin, Wyoming. Univ. Michigan Pap. Paleont. 24:99–114.Google Scholar
Seber, G. A. F. 1965. A note on the multiple-recapture census. Biometrika. 52:249–259.Google Scholar
Seber, G. A. F. 1970. Estimating time-specific survival and reporting rates for adult birds from band returns. Biometrika. 57:313–318.CrossRefGoogle Scholar
Seber, G. A. F. 1973. The Estimation of Animal Abundance and Related Parameters. Griffin, London.Google Scholar
Sepkoski, J. J. Jr. 1975. Stratigraphic biases in the analysis of taxonomic survivorship. Paleobiology. 1:343–355.CrossRefGoogle Scholar
Sepkoski, J. J. 1982. A compendium of fossil marine families. Milwaukee Publ. Mus. Contr. in Biology and Geology. Milwaukee, Wisc.Google Scholar
Simpson, G. G. 1953. The major features of evolution. Columbia Univ. Press, New York. 434 pp.Google Scholar
Sorgenfrei, T. 1958. Molluscan assemblages from the marine Middle Miocene of South Jutland and their environments. Geol. Surv. Denmark, 2d ser., no. 79.Copenhagen.CrossRefGoogle Scholar
Stanley, S. M. 1979. Macroevolution. Freeman, San Francisco.Google Scholar
Stanley, S. M. 1982. Macroevolution and the fossil record. Evolution. 36:460–473.Google Scholar
Van Valen, L. 1973. A new evolutionary law. Evol. Theory. 1:1–30.Google Scholar
White, E. G. 1971. A computer program for capture-recapture studies of animal populations: a fortran listing for the stochastic model of G. M. Jolly. Tussock Grasslands and Mountain Lands Inst. Spec. Publ. no. 8. Christchurch, N.Z.Google Scholar
White, G. C, Burnham, K. P., Otis, D. L., and Anderson, D. R. 1978. User's Manual for Program capture. Utah State Univ. Press, Logan, Utah.Google Scholar
White, G. C, Anderson, D. R., Burnham, K. P., and Otis, D. L. 1982. Capture-Recapture and Removal Methods for Sampling Closed Populations. LA-8787–NERP. Los Alamos National Laboratory. Los Alamos, New Mexico.Google Scholar