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研究生:洪志叡
論文名稱:共有物種數的無母數估計探討
論文名稱(外文):A non-parametric estimate for the number of shared species
指導教授:余清祥余清祥引用關係
學位類別:碩士
校院名稱:國立政治大學
系所名稱:統計研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2010
畢業學年度:98
語文別:中文
論文頁數:110
中文關鍵詞:生物多樣性共有物種數涵蓋機率電腦模擬Jackknife估計
外文關鍵詞:BiodiversityNumber of share speciesoverage probabilityComputer simulationJackknife estimated
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在生態學、生物學、和比較文學的研究中,物種個數通常是評估生物多樣性的重要指標,單一群落物種數的估計已有非常豐富的相關研究。較為知名者包括Good (1953)提出未出現物種的機率,作為估計物種數的參考,往後Good的想法被大量延伸,推演出不少新的估計方法,像是Burnham and Overton (1978)的Jackknife估計法,Chao and Lee (1992)利用涵蓋機率的估計。相對而言,兩群落共有物種數的研究較少,現有研究中較為知名的有Chao et al. (2000)的估計式。
本研究延伸Good想法,探討Jackknife估計法在兩群落的應用,以出現一次的共有物種(一階Jackknife估計),推估未出現共有物種機率,並且仿造Burnham and Overton的想法,建立共有物種數的估計值及變異數。本文除了以電腦模擬,也使用實例(包括:金庸武俠小說、台灣野生水鳥、巴拿馬螃蟹和巴洛科羅拉多森林)檢驗本文的Jackknife估計法,利用涵蓋機率角度發現抽出某特定比例樣本時,估計值涵蓋母體共有物種數之機率值達到九成以上,且也與Chao提出的估計值比較。

The number of species is frequently used to measure the biodiversity of a population in ecology, biology, and comparative literature. There are quite a lot of studies related to estimating the number of species. Among these studies, Good (1953) proposed a famous estimate (Turing’s estimate) for the probability of unseen species. Subsequently, many methods have been proposed for estimating the number of species based on Good’s idea. For example, the Jackknife estimator by Burnham and Overton (1978) and sample coverage probability by Chao and Lee (1992) are two famous estimates for the number of species. In contrast, there are not many studies for the number of shared species in two communities, and Chao et al. (2000) is probably the only one.
This article extends Good’s idea and the Jackknife method to estimate the number of shared species in two communities. Similar to Burnham and Overton, we establish the estimate and its estimated variance, based on the number of species appearing exactly once. We also use computer simulation and real data sets (Jin-Yong martial arts novels, Taiwan wild birds, Panama crustacean, and Barro Colorado Island forest) to evaluate the proposed method. We found that the coverage probability for confidence interval covering the true number of shared species is more than 90%. In addition, we compare the proposed method with Chao’s method.

第一章 緒論.................................1
第二章 文獻回顧與模式簡介...................3
2.1 抽樣方法與模式假設......................3
2.2 符號定義................................4
2.3 未出現物種機率─Good估計式..............6
2.4 單一群落物種數估計......................7
2.4.1 物種數估計─Burnham and Overton估計式.7
2.4.2 物種數估計─Chao估計式................9
2.5 共有物種數估計─Chao估計式.............10
第三章 研究方法............................14
3.1 未出現共有物種機率─Yue估計式..........14
3.2 共有物種數估計─Yue估計式..............15
3.3 未出現共有物種機率估計式...............17
3.4 共有物種估計式.........................17
第四章 電腦模擬驗證........................19
4.1 未出現共有物種機率電腦模擬探討.........20
4.2 共有物種數電腦模擬探討.................22
4.3 模擬驗證變異數數值.....................27
第五章 實際資料驗證........................31
5.1 資料簡介...............................31
5.2 四個實例之未出現共有物種機率探討.......33
5.3 四個實例之共有物種數探討...............36
5.4 四個實例之涵蓋機率探討.................40
第六章 結論與建議..........................45
6.1 結論...................................45
6.2 建議...................................46
參考文獻......................................48
附錄..........................................50


英文部份:
Bunge, J. and Fitzpatrick, M. (1993). Estimating the number of species: A review. Journal of the American Statistical Association, 88, pp. 364-373.
Burnham, P. K. and Overton, S. W. (1978). Estimation of the size of a closed population when capture probabilities vary among animals. Biometrika, 65, pp. 625-633.
Chao, A. and Lee, S-M. (1992). Estimating the number of classes via sample coverage. Journal of American Statistical Association, 87, pp. 210-217.
Chao, A., Ma, M.C., and Yang, M.C.K. (1993). Stopping rule and estimation for recapture debugging with unequal detection rates. Biometrika, 80, pp. 193-201.
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, pp. 227-246.
Chao, A., Pan, H. Y., and Chiang, S. C. (2008). The Petersen-Lincoln estimator and its extension to estimate the size of a shared population. Biometrical Journal, 50, pp. 957-970.
Clayton, M. K. and Frees, E. W. (1987). Nonparametric estimation of the probability of discovering a new species. Journal of the American Statistical Association, 82, pp. 305-311.
Good, I. J. (1953). The population frequencies of species and the estimation of population parameters. Biometrika, 40, pp. 237-264.
Good, I. J. and Toulmin, G. H. (1956). The number of new species, and the increase in population coverage, when a Sample is increased. Biometrika, 43, pp. 45-63.
Efron, B. and Thisted, R. (1976). Estimation the number of unseen species: How many words did Shakespeare now? Biometrika, 63, pp. 435-447.
Efron, B. and Tibshirani, R. J. (1993). An introduction to the bootstrap. New York: Chapman & Hall.
Esty, W. W. (1983). A normal limit law for a nonparametric estimator of the coverage of a random sample. The Annals of Statistics, 11, pp. 905-912.
Esty, W. W. (1986). The efficiency of Good's nonparametric coverage estimator. The Annals of Statistics, 14, pp. 1257-1260.
Mao, C. X. and Lindsay, B. G. (2002). A Poisson model for the coverage problem with a genomic application. Biometrika, 89, pp. 669-681.
Otis, D., Burnham, K. P., White, G., and Anderson, D. R. (1978). Statistical inference from capture data on closed animal populations. Wildlife Monograph, 62, Washington, D.C.: The Wildlife Soc.
Quenouille, M. H. (1949). Approximate tests of correlation in time-series. Journal of the Royal Statistical Society. Series B, 11, pp. 68-84.
Quenouille, M. H. (1956). Notes on bias in estimation. Biometrika, 43, pp. 353-360.
Schucany, W. R., Gray, H. L., and Owen, D. B. (1971). On bias Reduction in Estimation. Journal of the American Statistical Association, 66, pp. 524-533.
Sharot, T. (1976). The generalized jackknife: finite samples and subsample sizes. Journal of the American Statistical Association, 71, pp. 451-454.
Yue, C. J. (2009). Sequential sampling in the search new shared species. , Technical report, Department of Statistics, National Chengchi University.

中文部份:
余清祥(1998),統計在紅樓夢的應用,國立政治大學學報,第76期,頁303-327。
趙蓮菊(1995),種類知多少,數學傳播,第74期,頁1-6。

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