兩個或以上群落間的比較, 稱為β 多樣性, 在生物多樣性的研究上已是一重要的課題; 其量度方式不乏以相對觀念描繪多樣性的相似度指標(Jaccard 出現指標、S□rensen 出現指標、Morisita 豐富指標等) , 亦有直接利用多樣性指標作測量(Shannon 指標、Simpson 指標等) 。
本文以Shannon 指標量度多個群落間的β 多樣性, 旨在將Schechtman and Wang (2004) 針對兩組樣本所發展出的二階段摺刀估計量( Two-Step Jackknife Estimator ) , 推廣到多組樣本, 並應用於Shannon 指標的估計。文中以三個群落為例, 探討其與最大概似估計量、Horvitz-Thompson 估計量在估計上的優劣, 除藉由理論推導大致說明外, 另配合電腦模擬結果加以解釋; 此外, 針對摺刀估計量及Horvitz-Thompson 估計量, 將特別討論兩者適用的時機, 不外乎樣本數的多寡、抽樣的比例及估計時權重的選擇。最後, 在實例分析中, 採用由美國康乃迪克大學,Chazdon, R.L. 教授所提供之森林資料, 分析比較不同型態森林及不同樹種的β 多樣性程度。

韓若平(2008), “Beta 多樣性的統計估計”, 清華大學統計所博士論文
Arvesen, J.N. (1969), “Jackknifing u-statistics”, The Annals of Mathematical Statistics, 40, 2076–2100.
Basharin, G.P. (1959), “On a statistical estimate for the entropy of a sequence of independent random variables”, Theory of Probability and Its Applications, 4, 333–336.
Brillinger, D.R. (1964), “The asymptotic behaviour of tukey’s general method of setting approximate confidence limits (the jackknife) when applied to maximum likelihood estimates”, Review of the International Statistical Institute, 32, 202–206.
Chao, A., Chazdon, R.L., Colwell, R.K., and Shen, T.-J. (2005), “A new statistical approach for assessing similarity of species composition with incidence and abundance data”, Ecology Letters, 8, 148–159.
Chao, A., Jost, L., Chiang, S.-C., Jiang, Y.-H., and Chazdon, R.L. (2008),“A two-stage probabilistic approach to multiple-community similarity indices”,Biometrics.
Chao, A. and Shen, T.-J. (2003), “Nonparametric estimation of shannon’s index of diversity when there are unseen species”, Environmental and Ecological Statistics, 10, 429–443.
Convention on Biological Diversity (1992).
Efron, B. (1979), “Bootstrap methods: Another look at the jackknife”, The Annals of Statistics, 7, 1–26.
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”, The Annals of Mathematical Statistics,12, 42–58.
Good, I.J. (1953), “The population frequencies of species and the estimation of population parameters”, Biometrica, 40, 237–264.
Hill, M.O. (1973), “Diversity and evenness: a unifying notation and its consequences”, Ecology, 54, 427–432.
Horvitz, D.G. and Thompson, D.J. (1952), “A generalization of sampling without replacement from a finite universe”, Journal of the American Statistical Association, 47, 663–685.
Jaccard, P. (1908), “Nouvelles recerches sur la distribution florale”, Bulletin de la Societe Vaudoise des Sciences Naturelles, 44, 223–270.
Jost, L. (2006), “Entropy and diversity”, Oikos, 113, 363–375.
Jost, L. (2007), “Partitioning diversity into independent alpha and beta components”,Ecology, 88, 2427–2439.
Lande, R. (1996), “Statistics and partitioning of species diversity and similarity　among multiple communities”, Oikos, 76, 39581.
Margalef, R. (1957), “La teor´ıa de la informaci´on en ecolog´ıa”, Memorias de　la Real Academia de Ciencias y Artes de Barcelona, 32, 373–449.
Morisita, M. (1959), “Measuring of interspecific association and similarity　between communities”, Memorias of the Faculty of Science, Kyushu University,　Series E, 3, 215–235.
Peet, R.K. (1974), “The measurement of species　diversity”, Annual Review　of Ecology and Systematics, 5, 285–307.
Pielou, E.C. (1975), Ecological Diversity, Wiley, New York.
Quenouille, M.H. (1949), “Approximate tests of correlation in time-series”,Journal of the Royal Statistical Society. Series B (Methodological), 11,68–84.
Quenouille, M.H. (1956), “Notes on bias in estimation”, Biometrika, 43, 353–360.
R´enyi, A. (1961), “On measures of entropy and information”, Proceedings of　the 4th Berkeley Symposium on Mathematics, Statistics and Probability,1, 547–561.
Schechtman, E. and Wang, S. (2004), “Jackknifing two sample statistics”,Journal of Statistical Planning and Inference, 119, 329–340.
Shannon, C.E. (1948), “The mathematical theory of communication”, Bell System Technical Journal, 27, 379–423, 623–656.
Simpson, E.H. (1949), “Measurement of diversity”, Nature, 163–688.
S□rensen, T. (1948), “A method of establishing groups of equal amplitude in plant sociology based on similarity of species content and its application to analyses of the vegetation on danish commons”, Biologiske Skrifter(Kongelige Danske Videnskabernes Selskab), 5, 1–34.
Tukey, J. (1958), “Bias and confidence in not quite large samples”, Annals of Mathematical Statistics, 29, 614.
Whittaker, R.H. (1960), “Vegetation of the siskiyou mountains, oregon and california”, Ecological Monograph, 30, 279–338.
Whittaker, R.H. (1972), “Evolution and measurement of species diversity”, Taxon,21, 213–251.
Wilson, M.V. and Shmida, A. (1984), “Measuring beta diversity with presence-absence data”, Ecology, 72, 1055–1064.
Zahl, S. (1977), “Jackknifing an index of diversity”, Ecology, 58, 907–913.