Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-26T07:14:14.180Z Has data issue: false hasContentIssue false
  • English
  • Français

On the measurement of occupancy in ecology and paleontology

Published online by Cambridge University Press:  23 August 2016

Michael Foote
Michael Foote*
Affiliation:
Department of the Geophysical Sciences, University of Chicago, Chicago, Illinois 60637, U.S.A. E-mail:mfoote@uchicago.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract

Occupancy statistics in ecology and paleontology are biased upward by the fact that we generally do not have solid data on species that exist but are not found. The magnitude of this bias increases as the average occupancy probability decreases and as the number of sites sampled decreases. A maximum-likelihood method is developed to estimate the underlying distribution of occupancy probabilities of all species based only on the sample of observed species with nonzero occupancy. The method is based on determining the probability that the number of occupied sites will take on any specific value for a given occupancy probability, integrated over the entire distribution of occupancy probabilities. If the shape of the underlying distribution is well modeled, the resulting occupancy estimates circumvent the bias inherent in failing to observe some species and the fact that this bias depends on the number of sites. For occupancy data on marine animal genera drawn from the Paleobiology Database, the underlying distribution is reasonably approximated as a right-truncated log-normal, but the methods developed can be extended to any distribution. Examples are presented to illustrate some observations that are robust and others that need to be revised in light of this bias correction. The method is compared to a recently developed, distribution-free approach to the same problem.

Type
Methods in Paleobiology
Information
Paleobiology , Volume 42 , Issue 4 , November 2016 , pp. 707 - 729
Copyright
Copyright © 2016 The Paleontological Society. All rights reserved 

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. 2008. Dynamics of origination and extinction in the marine fossil record. Proceedings of the National Academy of Sciences USA 105:11536–11542.CrossRefGoogle ScholarPubMed
Alroy, J. 2010a. The shifting balance of diversity among major marine animal groups. Science 329:1191–1194.CrossRefGoogle ScholarPubMed
Alroy, J. 2010b. Geographical, environmental, and intrinsic biotic controls on Phanerozoic marine diversification. Palaeontology 53:1211–1235.CrossRefGoogle Scholar
Alroy, J., Aberhan, M., Bottjer, D. J., Foote, M., Fürsich, F. T., Harries, P. J., Hendy, A. J. W., Holland, S. M., Ivany, L. C., Kiessling, W., Kosnik, M. A., Marshall, C. R., McGowan, A. J., Miller, A. I., Olszewski, T. D., Patzkowsky, M. E., Peters, S. E., Villier, L., Wagner, P. J., Bonuso, N., Borkow, P. S., Brenneis, B., Clapham, M. E., Fall, L. M., Ferguson, C. A., Hanson, V. L., Krug, A. Z., Layou, K. M., Leckey, E. H., Nürnberg, S., Powers, C. M., Sessa, J. A., Simpson, C., Tomašových, A., and Visaggi, C. C.. 2008. Phanerozoic trends in the global diversity of marine invertebrates. Science 321:97–100.CrossRefGoogle ScholarPubMed
Brayard, A., Bucher, H., Escarguel, G., Fluteau, F., Bourquin, S., and Galfetti, T.. 2006. The Early Triassic ammonoid recovery: paleoclimatic significance of diversity gradients. Palaeogeography, Palaeoclimatology, Palaeoecology 239:374–395.CrossRefGoogle Scholar
Buzas, M. A., Koch, C. F., Culver, S. J., and Sohl, N. F.. 1982. On the distribution of species occurrence. Paleobiology 8:143–150.CrossRefGoogle Scholar
Chao, A. 1987. Estimating the population size for capture-recapture data with unequal catchability. Biometrics 43:783–791.CrossRefGoogle ScholarPubMed
Chao, A., and Jost, L.. 2012. Coverage-based rarefaction and extrapolation: standardizing samples by completeness rather than size. Ecology 93:2533–2547.CrossRefGoogle ScholarPubMed
Chao, A., Gotelli, N. J., Hsieh, T. C., Sander, E. L., Ma, K. H., Colwell, R. K., and Ellison, A. M. 2014. Rarefaction and extrapolation with Hill numbers: a framework for sampling and estimation in species diversity studies. Ecological Monographs 84:45–67.CrossRefGoogle Scholar
Chao, A., Hsieh, T. C., Chazdon, R. L., Colwell, R. K., and Gotelli, N. J.. 2015a. Unveiling the species-rank abundance distribution by generalizing the Good-Turing sampling coverage theory. Ecology 96:1189–1201.CrossRefGoogle ScholarPubMed
Chao, A., Hsieh, T. C., Chazdon, R. L., Colwell, R. K., and Gotelli, N. J.. 2015b. R code for JADE (Joint species-rank Abundance Distribution/Estimation) based on individual-based (abundance) and sampling-unit-based (incidence) data. Ecological Archives E096–107-S1.Google Scholar
Chen, Z.-Q., Kaiho, K., and George, A. D.. 2005. Early Triassic recovery of the brachiopod faunas from the end-Permian mass extinction: a global review. Palaeogeography, Palaeoclimatology, Palaeoecology 224:270–290.CrossRefGoogle Scholar
Clapham, M. E., Shen, S., and Bottjer, D. J.. 2009. The double mass extinction revisited: reassessing the severity, selectivity, and causes of the end-Guadalupian biotic crisis (Late Permian). Paleobiology 35:32–50.CrossRefGoogle Scholar
Colwell, R. K., Chao, A., Gotelli, N. J., Lin, S.-Y., Mao, C. X., Chazdon, R. L., and Longino, J. T.. 2012. Models and estimators linking individual-based and sample-based rarefaction, extrapolation and comparison of assemblages. Journal of Plant Ecology 5:3–21.CrossRefGoogle Scholar
Coull, B. A., and Agresti, A.. 1999. The use of mixed logit models to reflect heterogeneity in capture-recapture studies. Biometrics 55:294–301.CrossRefGoogle ScholarPubMed
Darroch, S. A. F., and Wagner, P. J.. 2015. Responses of beta diversity to pulses of Ordovician–Silurian mass extinction. Ecology 96:532–549.CrossRefGoogle ScholarPubMed
Dorazio, R. M., Royle, J. A., Söderström, B., and Glimskär, A.. 2006. Estimating species richness and accumulation by modeling species occurrence and detectability. Ecology 87:842–854.CrossRefGoogle ScholarPubMed
Edwards, A. W. F. 1991. Likelihood, expanded ed. Johns Hopkins University Press, Baltimore, Md.Google Scholar
Efron, B., and Tibshirani, R. J.. 1993. An introduction to the bootstrap. Chapman and Hall, New York.CrossRefGoogle Scholar
Erwin, D. H. 2001. Lessons from the past: biotic recoveries from mass extinctions. Proceedings of the National Academy of Sciences USA 98:5399–5403.CrossRefGoogle ScholarPubMed
Feller, W. 1971. An introduction to probability theory and its applications, Vol. 2, 2nd ed. Wiley, New York.Google Scholar
Ferguson, P. F. B., Conroy, M. J., and Hepinstall-Cymerman, J.. 2015. Occupancy models for data with false positive and false negative errors and heterogeneity across sites and surveys. Methods in Ecology and Evolution 6:1395–1406.CrossRefGoogle Scholar
Finnegan, S., Payne, J. L., and Wang, S. C.. 2008. The Red Queen revisited: reevaluating the age selectivity of Phanerozoic marine genus extinctions. Paleobiology 34:318–341.CrossRefGoogle Scholar
Finney, D. J. 1949. The truncated binomial distribution. Annals of Eugenics 14:319–328.CrossRefGoogle ScholarPubMed
Fisher, R. A. 1936. The effect of methods of ascertainment upon the estimation of frequencies. Annals of Eugenics 6:13–25.CrossRefGoogle Scholar
Fisher, R. A., Corbet, A. S., and Williams, C. B.. 1943. The relation between the number of species and the number of individuals in a random sample of an animal population. Journal of Animal Ecology 12:42–58.CrossRefGoogle Scholar
Foote, M. 1997. Estimating taxonomic durations and preservation probability. Paleobiology 23:278–300.CrossRefGoogle Scholar
Foote, M. 2007. Symmetric waxing and waning of marine invertebrate genera. Paleobiology 33:517–529.CrossRefGoogle Scholar
Foote, M. 2014. Environmental controls on geographic range size in marine animal genera. Paleobiology 40:440–458.CrossRefGoogle Scholar
Foote, M., and Miller, A. I.. 2013. Determinants of early survival in marine animal genera. Paleobiology 39:171–192.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., Crampton, J. S., Beu, A. G., Marshall, B. A., Cooper, R. A., Maxwell, P. A., and Matcham, I.. 2007. Rise and fall of species occupancy in Cenozoic fossil mollusks. Science 318:1131–1134.CrossRefGoogle ScholarPubMed
Foote, M., Ritterbush, K. A., and Miller, A. I.. 2016. Geographic ranges of genera and their constituent species: structure, evolutionary dynamics, and extinction resistance. Paleobiology 42:269–288.CrossRefGoogle Scholar
Good, I. J. 1953. The population frequencies of species and the estimation of population parameters. Biometrika 40:237–264.CrossRefGoogle Scholar
Gradstein, F. M., Ogg, J., Schmitz, M., and Ogg, G.. 2012. The geologic time scale 2012. Elsevier, Amsterdam.Google Scholar
Haldane, J. B. S. 1932. A method for investigating recessive characters in man. Journal of Genetics 26:251–255.CrossRefGoogle Scholar
Haldane, J. B. S. 1938. The estimation of the frequencies of recessive conditions in man. Annals of Eugenics 8:255–262.CrossRefGoogle Scholar
Hallam, A., and Wignall, P. B.. 1997. Mass extinctions and their aftermath. Oxford University Press, Oxford.CrossRefGoogle Scholar
Jablonski, D., Roy, K., and Valentine, J. W.. 2006. Out of the tropics: evolutionary dynamics of the latitudinal diversity gradient. Science 314:102–106.CrossRefGoogle ScholarPubMed
Jablonski, D., Belanger, C. L., Berke, S. K., Huang, S., Krug, A. Z., Roy, K., Tomasovych, A., and Valentine, J. W.. 2013. Out of the tropics, but how? Fossils, bridge species, and thermal ranges in the dynamics of the marine latitudinal diversity gradient. Proceedings of the National Academy of Sciences USA 110:10487–10494.CrossRefGoogle ScholarPubMed
Liow, L. H., and Stenseth, N. C.. 2007. The rise and fall of species: implications for macroevolutionary and macroecological studies. Proceedings of the Royal Society of London B 274:2745–2752.Google ScholarPubMed
Liow, L. H., Skaug, H. J., Ergon, T., and Schweder, T.. 2010. Global occurrence trajectories of microfossils: environmental volatility and the rise and fall of individual species. Paleobiology 36:224–252.CrossRefGoogle Scholar
MacKenzie, D. I., Nichols, J. D., Lachman, G. B., Droege, S., Royle, J. A., and Langtimm, C. A.. 2002. Estimating site occupancy rates when detection probabilities are less than one. Ecology 83:2248–2255.CrossRefGoogle Scholar
MacKenzie, D. I., Nichols, J. D., Hines, J. E., Knutson, M. G., and Franklin, A. B.. 2003. Estimating site occupancy, colonization, and local extinction when a species is detected imperfectly. Ecology 84:2200–2207.CrossRefGoogle Scholar
MacKenzie, D. I., Nichols, J. D., Royle, J. A., Pollock, K. H., Bailey, L. L., and Hines, J. E.. 2006. Occupancy estimation and modeling: inferring patterns and dynamics of species occurrence. Academic Press, Amsterdam.Google Scholar
McGill, B. J. 2003. Does Mother Nature really prefer rare species or are log-left-skewed SADs a sampling artefact? Ecology Letters 6:766–773.CrossRefGoogle Scholar
Miller, A. I. 1997. A new look at age and area: the geographic and environmental expansion of genera during the Ordovician Radiation. Paleobiology 23:410–419.CrossRefGoogle Scholar
Miller, A. I., and Foote, M.. 2003. Increased longevities of post-Paleozoic marine genera after mass extinctions. Science 302:1030–1032.CrossRefGoogle ScholarPubMed
Payne, J. L., and Finnegan, S.. 2007. The effect of geographic range on extinction risk during background and mass extinction. Proceedings of the National Academy of Sciences USA 104:10506–10511.CrossRefGoogle ScholarPubMed
Preston, F. W. 1948. The commonness, and rarity, of species. Ecology 29:254–283.CrossRefGoogle Scholar
R Development Core Team 2011. R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org.Google Scholar
Rabinowitz, D. 1981. Seven forms of rarity. Pp. 205–217 in H. Synge, ed. The biological aspects of rare plant conservation. Wiley, Chichester, U.K.Google Scholar
Rider, P. R. 1955. Truncated binomial and negative binomial distributions. Journal of the American Statistical Association 50:877–883.CrossRefGoogle Scholar
Royle, J. A., and Nichols, J. D.. 2003. Estimating abundance from repeated presence-absence data or point counts. Ecology 84:777–790.CrossRefGoogle Scholar
Schubert, J. K., and Bottjer, D. J.. 1995. Aftermath of the Permian–Triassic mass extinction event: paleoecology of Lower Triassic carbonates in the western USA. Palaeogeography, Palaeoclimatology, Palaeoecology 116:1–39.CrossRefGoogle Scholar
Slocomb, J., Stauffer, B., and Dickson, K. L.. 1977. On fitting the truncated lognormal distribution to species-abundance data using maximum likelihood estimation. Ecology 58:693–696.CrossRefGoogle Scholar
Solow, A. R., and Smith, W.. 1997. On fossil preservation and the stratigraphic ranges of taxa. Paleobiology 23:271–277.CrossRefGoogle Scholar
Stevens, G. C. 1989. The latitudinal gradient in geographic range: how so many species coexist in the tropics. American Naturalist 133:240–256.CrossRefGoogle Scholar
Wagner, P. J., and Marcot, J. D.. 2013. Modelling distributions of fossil sampling rates over time, space, and taxa: assessment and implications for macroevolutionary studies. Methods in Ecology and Evolution 4:703–713.CrossRefGoogle Scholar
Wagner, P. J., Kosnik, M. A., and Lidgard, S.. 2006. Abundance distributions imply elevated complexity in post-Paleozoic marine ecosystems. Science 314:1289–1292.CrossRefGoogle ScholarPubMed
Willig, M. R., Kaufman, D. M., and Stevens, R. D.. 2003. Latitudinal gradients of biodiversity: pattern, process, scale, and synthesis. Annual Review of Ecology, Evolution, and Systematics 34:273–309.CrossRefGoogle Scholar
Willis, J. C. 1926. Age and area. Quarterly Review of Biology 1:553–571.CrossRefGoogle Scholar