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Environmental and Ecological Statistics

, Volume 25, Issue 4, pp 495–522 | Cite as

Estimation of abundance from presence–absence maps using cluster models

  • Richard Huggins
  • Wen-Han Hwang
  • Jakub Stoklosa
Article

Abstract

A presence–absence map consists of indicators of the occurrence or nonoccurrence of a given species in each cell over a grid, without counting the number of individuals in a cell once it is known it is occupied. They are commonly used to estimate the distribution of a species, but our interest is in using these data to estimate the abundance of the species. In practice, certain types of species (in particular flora types) may be spatially clustered. For example, some plant communities will naturally group together according to similar environmental characteristics within a given area. To estimate abundance, we develop an approach based on clustered negative binomial models with unknown cluster sizes. Our approach uses working clusters of cells to construct an estimator which we show is consistent. We also introduce a new concept called super-clustering used to estimate components of the standard errors and interval estimators. A simulation study is conducted to examine the performance of the estimators and they are applied to real data.

Keywords

Abundance Clustering Negative binomial Presence–absence map 

Notes

Acknowledgements

We are grateful to the Associate Editor and a referee for providing helpful comments and constructive suggestions, especially for indicating the use of jackknife standard error. The BCI forest dynamics research project was founded by S.P. Hubbell and R.B. Foster and is now managed by R. Condit, S. Lao, and R. Perez under the Center for Tropical Forest Science and the Smithsonian Tropical Research in Panama. Numerous organizations have provided funding, principally the U.S. National Science Foundation, and hundreds of field workers have contributed to this project. This work was supported by the Ministry of Science & Technology of Taiwan.

Supplementary material

10651_2018_415_MOESM1_ESM.pdf (160 kb)
Supplementary material 1 (pdf 160 KB)

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Richard Huggins
    • 1
  • Wen-Han Hwang
    • 2
  • Jakub Stoklosa
    • 3
  1. 1.Department of Mathematics and StatisticsThe University of MelbourneMelbourneAustralia
  2. 2.Institute of StatisticsNational Chung Hsing UniversityTaichungTaiwan
  3. 3.School of Mathematics and Statistics and Evolution and Ecology Research CentreThe University of New South WalesSydneyAustralia

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