研究某一地區的生物多樣性（biodiversity），必須從各方面對這個地區的物種與環境加以評估，利用有效的統計方法，透過模式將之量化，此量化之值稱為生物多樣性指標（biodiversity index）。本研究主題主要分成兩部份，第一部份是將傳統文獻上量測兩群落之相似指標推廣到三個群落。第二部份是將相似指標的估計量應用於連續型資料。
在評估生物多樣性時，常遇到的困難是一個地區不僅只有兩個群落，由收集的資料亦顯示許多地區含有三個群落或是四個群落，目前的方法除了Morisita相似指標外，其他相似指標僅能分析兩個群落。因此，本文先定義三個群落裡的共同種，分別為至少在兩個群落存在的「廣義共同種」，及於三個群落都存在的「狹義共同種」，嘗試將Jaccard與Sørensen豐富型相似指標推廣到三個群落，突破過去「兩兩比較」的方法，並將指標應用在熱帶雨林演替（tropical rainforest succession）、原生物種的普世性（protozoa ubiquity）兩筆資料分析，再討論兩個群落及三個群落相似指標的表現。在熱帶雨林演替的研究，本文建議使用架構於狹義共同種的三群落相似指標解釋熱帶雨林演替過程。在原生物種分佈研究，透過兩個群落及三個群落相似度比較，可知原生物種分布情形。此外，亦在各種假設下，模擬本文所提出的方法，探討本文所提出三種群落估計量的表現。
微生物是否到處都存在（普世性）是生態界倍受關心的議題。一般而言，收集到的資料其物種豐富度均非以個體數表示，因此過去以出現個體之頻率為分析的方法無法使用並須加以修正。本文將Jaccard與Sørensen豐富型相似指標推廣應用於此型資料，並針對Horn熵相似指標（1966）以兩樣本摺刀法降低偏誤。本文利用Jaccard豐富型相似指標與Horn熵相似指標，透過真菌類解釋真核生物分佈，結論為真核生物的相似性將隨著空間距離變化而改變，因此普世性的証據不足。最後經由電腦模擬，本文所提出的估計量均可改善樣本裡未出現物種的影響。

參考文獻
Arvesen, J.N. (1969) Jackknifing U-statistics. The Annals of Mathematical Statistics, 40, 2076-2100.
Bohannan, B. J. M. and Hughes, J.B. (2003) New approaches to analyzing microbial diversity data. Current Opinion in Microbiology 6, 282 - 287.
Bray, J. R. and Curtis, J. T. (1957). An ordination of the upland forest assemblages of southern Wisconsin. Ecological Monograph 27, 328-349.
Chao, A. and Lee, S-M. (1992). Estimating the number of classes via sample coverage. Journal of American Statistical Association 87, 210-217.
Chao, A., Hwang, W. H., Chen, Y. C., and Kuo C. Y. (2000). Estimating the number of shared species in two communities. Statistica Sinica 10, 227-246.
Chao, A. and Shen, T. J. (2003). User’s guide for program SPADE (Species Prediction And Diversity Estimation), at web site: http:// chao.stat.nthu.edu.tw..
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., Chazdon, R. L., Colwell, R. K. and Shen, T.-J.(2006). Abundance-based similarity indices and their estimation when there are unseen species in samples. Biometrics 62, 361-371.
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. To appear in Biometrics.
Chazdon, R. L., Colwell, R. K., Denslow, J. S. and Guariguata, M. R. (1998). Statistical method for estimating species richness of woody regeneration in primary and secondary rain forests of NE Costa Rica. In: Forest Biodiversity Research, Monitoring and Modeling: Conceptual Background and Old World Case Studies. (eds. Dallmeier , F. & Comiskey, J.). Parthenon Publishing, Paris, 285-309.
Colwell, R. K. and Coddington, J. A. (1994). Estimating terrestrial biodiversity through extrapolation. Philosophical Transactions of the Royal Society of London B – Biological Science 345, 101-118.
Colwell, R. K. (1994-2004). EstimateS: Statistical estimation of species richness and shared species from samples. URL http://viceroy.eeb.uconn.edu/estimates. Persistent URL http://purl.oclc.org/estimates.
Danovaro, R., Luna, G. M., Dell’Anno, A., and Pietrangeli, B. (2006) Comparison of two fingerprinting techniques, terminal restriction fragment length polymorphism and automated ribosomal intergenic spacer analysis, for determination of bacterial diversity in aquatic environments. Applied and Environmental Microbiology 72, 5982-5989.
Dunbar, J., Ticknor, L. O., and Kuske, C. R. (2000) Assessment of microbial diversity in four southwestern United States soils by 16S rRNA gene terminal restriction fragment analysis. Applied and Environmental Microbiology 66, 2943-2950.
Efron, B. (1979). Bootstrap methods: Another look at the jackknife. Annals of Statistics 7, 1-26.
Efron, B. (1981). Nonparametric standard errors and confidence intervals. Canadian Journal of Statistics 9, 139-172.
Erkanli, A. (1994). Laplace approximations for posterior expectations when the mode occurs at the boundary of the parameter space. Journal of the American Statistical Association 89, 250-258.
Erkanli, A. (1997). Boundary-mode approximations for posterior expectations. Journal of Statistical Planning and Inference 58, 217-239.
Fisher, B. L. (1999). Improving inventory efficiency: a case study of leaf-litter ant diversity in Madagascar. Ecological Applications 9, 714-731.
Foissner, W. (1997).Global Soil Ciliate（Protozoa, Ciliphora）Diversity: a probability-based approach using large sample collections from Africa, Australia and Antarctica, Biodiversity and Conservation 6, 1627-1638.
Foissner, W. (2006). Biogeography and dispersal of microorganisms: a review emphasizing protists. Acta Protozoologica 45, 111-136.
Gans, J., Wolinsky, M., and Dunbar, J. (2005) Computational improvements reveal great bacterial diversity and high metal toxicity in soil. Science 309,1387-1390.
Good, I. J. (1953). The population frequence of species and the estimation of population parameters. Biometrika 40,237-264.
Gower, J. C. (1985). Measures of similarity, dissimilarity and distance. In Enclopedia of Statistical Sciences, 5 (S. Kotz and N. L. Johnson, eds), 397-405. New York: Wiley.
Goutis, C. and Casella, G. (1999). Explaining the saddlepoint approximation. The American Statistician 53, 216-224.
Green, J. L., Holmes, A. J., Westoby, M., Oliver, I., Briscoe, D., Dangerfield, M., Gillings, M., and Beattie, A. J. (2004) Spatial scaling of microbial eukaryote diversity, Nature 432, 747-750.
Harte, J., Kinzig, A., and Green, J.L. (1999) Self-similarity in the distribution and abundance of species. Science 284, 334-336.
Heltshe, J. F., and Forrester, N. E. (1983) Estimating diversity using quadrat sampling. Biometrics 39, 1073-1076.
Horn, H. S. (1966). Measurement of overlap in comparative ecological studies. The American Natural 100, 419-424.
Hurlbert, S. H. (1978). The measurement of niche overlap and some relatives. Ecology 59, 67-77.
Huggins, R. M. (2001). A note on the difficulties associated with the analysis of capture-recapture experiments with heterogeneous capture probabilities. Statistics and Probability Letters 54, 147-152.
Huggins, R. M. (2002). A parametric empirical Bayes approach to the analysis of capture-recapture experiments. Australian and New Zealand Journal of Statistics 44, 55-62.
Hughes, J. B., Hellman , J. J., Ricketts , T. H., and Bohannan, B. J. M. (2001) Counting the uncountable: statistical approaches to estimating microbial diversity. Applied and Environmental Microbiology 67, 4399-4406.
Jaccard, P. (1908). Nouvelles recerches sur la distribution florale. Bull. Soc. Vaudoise Sci. Nat. 44, 223-270.
Janson, S. and Vegelius, J. (1981). Measures of ecological association. Oecologia 49, 371-376.
Janzen, D. H. (1973). Sweep samples of tropical foliage insects: description of study sites, with data on species abundances and size distribution. Ecology 54, 659-686.
Krebs, C. J. (1999). Ecological Methodology, 2nd edition. NewYork: Harper & Row.
Lamont, B. B. and Grant, K. J. (1979). A comparison of twenty-one measures of site dissimilarity. In multivariate methods in ecological work, eds. Orloci, L., Rao, C. R. and Stiteler , W. M., Fairland, Maryland: International co-operative publishing house,101-206.
Lehmann, E. L. (1998) Theory of point estimation. 2nd edition. Springer.
Lennon, J. J., Koleff, P., Greenwood, J. J. D., and Gaston, K. J. (2001). The geographical structure of British bird distributions: diversity, spatial turnover and scale. Journal of Animal Ecology 70, 966–979.
Liu, W. T., Marsh, T. L., Cheng, H., and Forney, L. J. (1997) Characterization of microbial diversity by determining terminal restriction fragment length polymorphisms of genes encoding 16S rRNA. Applied and Environmental Microbiology 63, 4516-4522.
Li, P. C. (2005). Species estimation and similarity indices in quadrate sampling. Ph. D. dissertation, National Tsing-Hua University, Hsin-Chu, Taiwan.
Longino, J. T., Coddington, J. and Colwell, R. K. (2002). The ant fauna of a tropical rain forest: estimating species richness three different ways. Ecology 83, 689-702.
Magurran, A. E. (2004). Measuring Biological Diversity. Oxford: Blackwell.
Miller, R. G. (1974) The jackknife – a review. Biometrika 61, 1-15.
Morisita, M. (1959) Measuring of interspecific association and similarity between communities. Memorias of the Faculty of Science, Kyushu University, Series E, 3, 215-235.
Plotkin, J. B., and Muller-Landau, H. C. (2002) Sampling the species composition of a landscape. Ecology 83, 3344-3356.
Quenouille, M. (1949)Approximate tests of correlation in time series. Journal of the Royal Statistical Society, Series B 11, 68-84.
Quenouulle, M. (1956) Notes on bias in estimation. Biometrika, 43, 353-360.
Ricklefs, R. E. and Lau, M. (1980). Bias and dispersion of overlap indices: results of some Monte Carlo simulations. Ecology 61, 1019-1024.
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.
Sloan,W. T., Woodcock , S., Lunn, M., Head, I. M., and Curtis, T. P.(2007) Modeling taxa-abundance distributions in microbial communities using environmental sequence data. Microbial Ecology 53, 443-455.
Sørensen, 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
Venter, J. C., Remington, K., Heidelberg, J. F., Halpern, A. L., Rusch, D., Eisen, J. A., Wu, D., Paulsen, I., Nelson, K. E., Nelson, W., Fouts, D. E., Levy, S., Knap, A. H., Lomas, M. W., Nealson, K., White, O., Peterson, J., Hoffman, J., Parsons, R., Baden-Tillson, H., Pfannkoch, C., Rogers, Y. H., and Smith, H. O.(2004) Environmental genome shotgun sequencing of the Sargasso Sea. Science 304, 66-74.
Whittaker, R.H. (1972) Evolution and measurement of species diversity. Taxon 21, 213-251.
Wilson, E. O. (1992) The Diversity of Life. Belknap Press of Harvard Unirersity Press. Cambridge. MA.
Wolda, H. (1981). Similarity indices, sample size and diversity. Oecologia 50, 296-302.
Wolda, H. (1983). Diversity, diversity indices and tropical cockroaches. Oecologia 58, 290-298.
Woodcock, S., Curtis, T. P., Head, I. M., Lunn, M., and Sloan, W. T. (2006) Taxa–area relationships for microbes: the unsampled and the unseen. Ecology Letters 9, 805-812.
Zahl, S. (1977) Jackknifing an index of diversity. Ecoology 58, 907-913.