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Convegno della Società Italiana di Statistica

SIS 2015: Theoretical and Applied Statistics pp 61–70Cite as

Bayesian Estimation of Gini-Simpson’s Index Under Mainland-Island Community Structure

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 274))

Abstract

The mainland-island community structure is an ecological transposition of a popular model in population genetics in which a fixed number of subpopulations (islands) are connected, through differing immigration rates, to a single metapopulation (mainland) where diversity is generated through speciation. It has been recently shown that a large class of neutral models with this particular structure converges in the large population limit to the Hierarchical Dirichlet process. This finding provides the analogous, in the multipopulation setting, of the Ewens sampling formula for the single population neutral hypothesis. Here we apply some recent results for conditional moments of diversity measures under Gibbs-type priors to derive a Bayesian nonparametric estimator of Gini-Simpson’s index under the Hubbell Unified Neutral Theory of Biodiversity and Biogeography. Potential applications are also illustrated.

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References

  1. Cerquetti, A.: Marginals of multivariate Gibbs distributions with applications in Bayesian species sampling. Electr. J. Stat. 169, 321–354 (2013)

    MathSciNet  MATH  Google Scholar 

  2. Cerquetti, A.: Bayesian nonparametric estimation of Tsallis diversity indices under Gnedin-Pitman priors (2014). arXiv:1404.3441v2 [math.ST]

  3. Chao, A., Jost, L., Hsieh, T.C., Ma, K.H., Sherwin, W.B., Rollins, L.A.: Expected Shannon entropy and Shannon differentiation between subpopulations for neutral genes under the finite island model. Plos One 10, 1–2 (2015)

    Google Scholar 

  4. Etienne, R.S.: A new sampling formula for neutral biodiversity. Ecol. Lett. 7, 321–354 (2005)

    Google Scholar 

  5. Etienne, R.S.: A neutral sampling formula for multiple samples and an ’exact’ test of neutrality. Ecol. Lett. 10, 608–618 (2007)

    Article  Google Scholar 

  6. Etienne, R.S.: Maximum likelihood estimation of neutral model parameters for multiple samples with different degrees of dispersal limitation. J. Theor. Biol. 257, 510–514 (2009)

    Article  MathSciNet  Google Scholar 

  7. Etienne, R.S., Olff, H.: A novel genealogical approach to neutral biodiversity. Ecol. Lett. 8, 253–260 (2004)

    Article  Google Scholar 

  8. Ewens, W.J.: The sampling theory of selectively neutral alleles. Theoret. Popul. Biol. 3, 87–112 (1972)

    Article  MathSciNet  Google Scholar 

  9. Favaro, S., Lijoi, A., Mena, R.H., Prünster, I.: Bayesian non-parametric inference for species variety with a two-parameter Poisson-Dirichlet process prior. J. R. Stat. Soc. B. 71, 993–1008 (2009)

    Article  MathSciNet  Google Scholar 

  10. Favaro, S., Lijoi, A., Prünster, I.: Conditional formulae for Gibbs-type exchangeable random partitions. Ann. Appl. Probab. 23, 1721–1754 (2013)

    Article  MathSciNet  Google Scholar 

  11. Ferguson, T.S.: A Bayesian analysis of some nonparametric problems. Ann. Stat. 1, 209–230 (1973)

    Article  MathSciNet  Google Scholar 

  12. Gini, C.W.: Variabilita e mutabilita. Studi Economico-Giuridici della R. Università di. Cagliari 3, 3–159 (1912)

    Google Scholar 

  13. Gnedin, A., Pitman, J.: Exchangeable Gibbs partitions and Stirling triangles. J. Math. Sci. 138(3), 5674–5685 (2006)

    Article  MathSciNet  Google Scholar 

  14. Harris, K., Parsons, T. L., Ijaz, U. Z., Lahti, L., Holmes, I., Quince, C. Linking statistical and ecological theory: Hubbell’s unified neutral theory of biodiversity as a hierarchical Dirichlet process. Proceedings of the IEEE, Issue: 99(2015)

    Google Scholar 

  15. Hubbell, S.P.: The Unified Neutral Theory of Biodiversity and Biogeography. Princeton University Press, Princeton (2001)

    Google Scholar 

  16. Jabot, F., Chave, J.: Analyzing tropical forest tree species abundance distributions using a nonneutral model and through approximate Bayesian inference. Am. Nat. 178(2), 38–47 (2011)

    Article  Google Scholar 

  17. Jost, L.: Partitioning diversity into independent alpha and beta components. Ecology 88, 2427–2439 (2007)

    Article  Google Scholar 

  18. Kimura, M.: Evolutionary rate at the molecular level. Nature 217, 624–626 (1968)

    Article  Google Scholar 

  19. Kingman, J.F.C.: Random discrete distributions. J. R. Stat. Soc. B 37, 1–22 (1975)

    MathSciNet  MATH  Google Scholar 

  20. MacArthur, R.H., Wilson, E.O.: The Theory of Island Biogeography. Princeton University Press, Princeton (1967)

    Google Scholar 

  21. Patil, G.P., Taille, C.: Diversity as a concept and its measurement. J. Am. Stat. Assoc. 77, 548–561 (1982)

    Article  MathSciNet  Google Scholar 

  22. Pitman, J.: Poisson-Kingman partitions. In: Goldstein, D.R. (ed.) Science and Statistics: A Festschrift for Terry Speed. LN Monograph Series, vol. 40, pp. 1–34. IMS, Hayward (2003)

    Google Scholar 

  23. Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 (1948)

    Article  MathSciNet  Google Scholar 

  24. Simpson, E.H.: Measurement of diversity. Nature 163, 688 (1949)

    Article  Google Scholar 

  25. Teh, Y.W., Jordan, M.I., Beal, M.J., Blei, D.M.: Hierarchical Dirichlet processes. J. Am. Stat. Assoc. 101, 1566–1581 (2006)

    Article  MathSciNet  Google Scholar 

  26. Tsallis, C.: Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys. 52, 479–487 (1988)

    Article  MathSciNet  Google Scholar 

  27. Watterson, G.A.: Heterosis or neutrality? Genetics 88, 405–417 (1977)

    MathSciNet  Google Scholar 

  28. Xing, E.P., Sohn, K., Jordan, M.I., Teh, Y.W.: Bayesian Multi-Population Haplotype Inference via a Hierarchical Dirichlet Process Mixture. Proceedings of the 23rd International Conference on Machine Learning (2006)

    Google Scholar 

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Authors and Affiliations

  1. MEMOTEF, Sapienza Università di Roma, Via del Castro Laurenziano, 9, 00161, Roma, Italy

    Annalisa Cerquetti

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  1. Annalisa Cerquetti
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Correspondence to Annalisa Cerquetti .

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Editors and Affiliations

  1. Department of Economics, University of Foggia, Foggia, Italy

    Corrado Crocetta

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Cerquetti, A. (2019). Bayesian Estimation of Gini-Simpson’s Index Under Mainland-Island Community Structure. In: Crocetta, C. (eds) Theoretical and Applied Statistics. SIS 2015. Springer Proceedings in Mathematics & Statistics, vol 274. Springer, Cham. https://doi.org/10.1007/978-3-030-05420-5_7

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