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題名 共有物種數的無母數估計探討
A non-parametric estimate for the number of shared species作者 洪志叡 貢獻者 余清祥
洪志叡關鍵詞 生物多樣性
共有物種數
涵蓋機率
電腦模擬
Jackknife估計
Biodiversity
Number of share species
overage probability
Computer simulation
Jackknife estimated日期 2009 上傳時間 5-Sep-2013 15:11:43 (UTC+8) 摘要 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.參考文獻 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。 描述 碩士
國立政治大學
統計研究所
97354024
98資料來源 http://thesis.lib.nccu.edu.tw/record/#G0097354024 資料類型 thesis dc.contributor.advisor 余清祥 zh_TW dc.contributor.author (Authors) 洪志叡 zh_TW dc.creator (作者) 洪志叡 zh_TW dc.date (日期) 2009 en_US dc.date.accessioned 5-Sep-2013 15:11:43 (UTC+8) - dc.date.available 5-Sep-2013 15:11:43 (UTC+8) - dc.date.issued (上傳時間) 5-Sep-2013 15:11:43 (UTC+8) - dc.identifier (Other Identifiers) G0097354024 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/60436 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計研究所 zh_TW dc.description (描述) 97354024 zh_TW dc.description (描述) 98 zh_TW dc.description.abstract (摘要) 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。 zh_TW dc.description.abstract (摘要) 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. en_US dc.description.tableofcontents 第一章 緒論.................................1第二章 文獻回顧與模式簡介...................32.1 抽樣方法與模式假設......................32.2 符號定義................................42.3 未出現物種機率─Good估計式..............62.4 單一群落物種數估計......................72.4.1 物種數估計─Burnham and Overton估計式.72.4.2 物種數估計─Chao估計式................92.5 共有物種數估計─Chao估計式.............10第三章 研究方法............................143.1 未出現共有物種機率─Yue估計式..........143.2 共有物種數估計─Yue估計式..............153.3 未出現共有物種機率估計式...............173.4 共有物種估計式.........................17第四章 電腦模擬驗證........................194.1 未出現共有物種機率電腦模擬探討.........204.2 共有物種數電腦模擬探討.................224.3 模擬驗證變異數數值.....................27第五章 實際資料驗證........................315.1 資料簡介...............................315.2 四個實例之未出現共有物種機率探討.......335.3 四個實例之共有物種數探討...............365.4 四個實例之涵蓋機率探討.................40第六章 結論與建議..........................456.1 結論...................................456.2 建議...................................46參考文獻......................................48附錄..........................................50 zh_TW dc.format.extent 1575206 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0097354024 en_US dc.subject (關鍵詞) 生物多樣性 zh_TW dc.subject (關鍵詞) 共有物種數 zh_TW dc.subject (關鍵詞) 涵蓋機率 zh_TW dc.subject (關鍵詞) 電腦模擬 zh_TW dc.subject (關鍵詞) Jackknife估計 zh_TW dc.subject (關鍵詞) Biodiversity en_US dc.subject (關鍵詞) Number of share species en_US dc.subject (關鍵詞) overage probability en_US dc.subject (關鍵詞) Computer simulation en_US dc.subject (關鍵詞) Jackknife estimated en_US dc.title (題名) 共有物種數的無母數估計探討 zh_TW dc.title (題名) A non-parametric estimate for the number of shared species en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) 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。 zh_TW
