在生態學及生物學的研究中，「物種個數」(Number of Species)通常是「生物多樣性」(Species Diversity)的重要測量值，物種個數的多寡、分布與多樣性有相當的關聯。「物種」的概念不侷限於生物，舉凡網路搜尋引擎(Search Engine)使用的關鍵字詞、圖書館分類的數目種類、國際疾病代碼等，都可視為物種。 本文著眼於寫作風格的比較，研究中國知名小說「紅樓夢」，主要探討前八十回與後四十回是否為同一個作者，以估計物種個數的觀點作為寫作風格的比較標準，並以金庸的武俠小說為對照組，驗證分析的結果。本文除了使用除了Efron and Thisted的隨機模型，也考慮藉由區塊抽樣估計母體種類數之Jackknife、Bootstrap、Chao(1992)等估計方法。研究發現Efron and Thisted的模型的估計量容易呈現不穩定的震盪，可能會有無法收歛的問題；而Bootstrap、Jackknife與Chao(1992)則會有高估母體種類數的現象。利用涵蓋機率的概念發現Jackknife與Chao皆在抽出特定比例的樣本數時，估計值涵蓋母體種類數之機率值非常接近1。 / The number of species is frequently used to measure the species diversity of a population in studying ecology and biology. There are such relationships between numbers of species and its diversities. The idea of species diversity is not restricted to biology, it receives more applications in recent years. For example, the applications also include key words in search engines, classification's numbers in a library, and disease types in Measuring health. This article studies the well-known Chinese novel “The Dream of Red Chamber”, and the goal is to study whether the first 80 and last 40 chapters are from the same author. In particular, methods related the number of species are used to evaluate the goal of study. Also, some Chinese martial novels, by the famous writer Jin Yong, are used as the control group for the methods used. Methods considered in this study include Efron and Thisted’s Model, Jackknife, Bootstrap, estimation method from Chao (1992). We found that Efron and Thisted’s estimates tend to be less stable and slow in convergence. On the other hand, the estimates of Jackknife, Bootstrap, and Chao are likely to be over-biased. However, after some modifications, we found that the Jackknife and Chao’s estimates can be used to provide reliable predictions for the number of species of a finite population, given that part of the population is observed.

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.