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Estimation of Animal Abundance Through Imperfectly Characterising Signatures

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Growth Curve and Structural Equation Modeling

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 132))

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Abstract

The problem of estimating population total of animals from imperfectly characterising animal signs poses a number of interesting statistical questions that are not addressed through conventional methods of estimating animal abundance. A case in point is the estimation of tiger population total from pugmark (footprint) measurements, which has been the traditional mode of tiger census in India for several decades. Usual methods based on distance sampling would not work well because, unlike dung produced by elephants or nests produced by birds, such signs are not produced at a steady rate. On the other hand, these signs may not carry as accurate and reliable characterising information as one expects from fingerprints. Is it still possible to estimate the population total precisely and accurately? If so, what should be the appropriate number of signs to be sampled? How can one cluster the signs so that each group of signs belongs to a distinct animal? Is good clustering a prerequisite for good estimation of population total? Is it possible to account for animals missed in the sample? In this article, we attempt to answer to these questions.

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References

  • Brochers DL, Buckland ST, Zucchini W (2002) Estimating animal abundance: closed populations. Springer, London

    Book  Google Scholar 

  • Calvin JA (1993) REML estimation in unbalanced multivariate variance components model using an EM algorithm. Biometrics 49:691–701

    Article  MATH  MathSciNet  Google Scholar 

  • Calvin JA, Dykstra RL (1995) REML estimation of covariance matrices with restricted parameter spaces. J Am Stat Assoc 90:321–329

    Article  MATH  MathSciNet  Google Scholar 

  • Champion FW (1929) Tiger tracks. J Bombay Nat Hist Soc 33:284–287

    Google Scholar 

  • Fowlkes EB, Gnanadesikan R, Kettering JR (1988) Variable selection in clustering. J Classif 5:205–228

    Article  Google Scholar 

  • Fraley C, Raftery AE (1998) How many clusters? Which clustering methods? Answers via model-based cluster analysis. Comput J 41:578–588

    Article  MATH  Google Scholar 

  • Fraley C, Raftery AE (2002) Model-based clustering, discriminant analysis, and density estimation. J Am Stat Assoc 97:611–631

    Article  MATH  MathSciNet  Google Scholar 

  • Gore AP, Paranjape SA, Rajgopala G, Kharshikar AV, Joshi NV, Watve MG, Gogate MG (1993) Tiger census: role of quantification. Curr Sci 64:711–714

    Google Scholar 

  • Hubert L, Arabie P (1985) Comparing partitions. J Classif 2:193–218

    Article  Google Scholar 

  • Karanth KU, Nichols JD, Seidenstricker J, Dinerstein E, Smith JLD, McDougal C, Johnsingh AJT, Chundawat RS, Thapar V (2003) Science deficiency in conservation practice: the monitoring of tiger populations in India. Anim Conserv 6:141–146

    Article  Google Scholar 

  • Karanth KU, Raghunandan S, Chundawat RS, Nichols JD, Samba Kumar N (2003) Estimation of tiger densities in the tropical dry forests of Panna, Central India, using photographic capture-recapture sampling. Anim Conserv 7:285–290

    Article  Google Scholar 

  • Karanth KU, Nichols JD, Kumar NS (2004) Photographic sampling of elusive mammals in tropical forests, in WL Thompson, ed., Sampling Rare and Elusive Species, Island Press, Covelo, CA, 229–247

    Google Scholar 

  • Kaufman L, Rousseeuw PJ (1990) Finding groups in data: an introduction to cluster analysis. Wiley Series in Probability and Mathematical Statistics. Wiley, New York

    Book  Google Scholar 

  • Liang SE, Buckland ST, Burn RW, Lambie D, Amphlet A (2003) Dung and nest surveys: estimating decay rates. J Appl Ecol 40:1102–1111

    Article  Google Scholar 

  • Mazoomdaar J (2005) Have you seen a tiger at Sariska since June? If yes, you’re the only one. The Indian Express, 21 January 2005 (http://www.indianexpress.com/res/web/pIe/archive_full_story.php?content_id=632809)

  • McLachlan GJ, Bean R, Peel D (2002) A mixture model-based approach to the clustering of microarray expression data. Bioinformatics 18:413–422

    Article  Google Scholar 

  • Milligan GW, Cooper MC (1985) An examination of procedures for determining the number of clusters in a data set. Psychometrika 50:159–179

    Article  Google Scholar 

  • Schliep A, Schönhuth A, Steinhoff C (2003) Using hidden Markov models to analyze gene expression time course data. Bioinformatics 19:(Suppl. 1) i255–i263

    Article  Google Scholar 

  • Sharma S, Jhala Y, Sawarkar VB (2005) Identification of individual tigers (Panthera tigris) from their pugmarks. J Zool 266:1–10

    Article  Google Scholar 

  • Smallwood KS, Fitzhugh EL (1993) A rigorous technique for identifying individual mountain lions (Felis concolor) by their tracks. Biol Conserv 65:51–59

    Article  Google Scholar 

  • Tibshirani R, Walther G, Hastie T (2001) Estimating the number of data clusters via the Gap statistic. J R Stat Soc Ser B 63:411–423

    Article  MATH  MathSciNet  Google Scholar 

  • Tiger Task Force, Government of India (2005) Joining the dots: the report of the tiger task force (http://projecttiger.nic.in/TTF2005/pdf/full_report.pdf9)

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Correspondence to Debasis Sengupta .

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Sengupta, D. (2015). Estimation of Animal Abundance Through Imperfectly Characterising Signatures. In: Dasgupta, R. (eds) Growth Curve and Structural Equation Modeling. Springer Proceedings in Mathematics & Statistics, vol 132. Springer, Cham. https://doi.org/10.1007/978-3-319-17329-0_4

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