本篇研究針對兩物種的有無地圖進行相關性分析，先使用卡方檢定檢驗兩物種是否無相關性，若有相關性的話，接著在二項分配假設之下使用三種P-value檢驗兩物種為正或負相關。在模擬中，比較卡方檢定以及三種P-value的檢驗結果，計算它們拒絕虛無假設的比例，也就是第一型誤差或檢定力。最後利用本篇提出的方法，並使用巴拿馬科羅拉多島嶼的樹木資料以及臺灣陽明山的白蟻資料，去檢驗物種間的相關性，發現不同物種間會存在正、負相關性。

In this study, we use presence-absence maps to test whether the distributions of two species are correlated or not. First, the Chi-squared test is used to determine the distributions of two species are uncorrelated or not. If they are correlated, then we compute three types of P-values under Binomial distribution assumption to test the significance of positive or negative correlation. The performance of the Chi-squared test and these three types of P-values is illustrated in the simulation. The type I errors and powers are shown by computing the proportions of rejecting the null hypothesis of non-correlation. The proposed method is applied to the tree data of the Barro Colorado Island of Panama and the termite data of Yangmingshan in Taiwan. The positive and negative correlations are found among some species in these two real data.

目錄
第一章緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
第二章研究方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
第三章模擬研究. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
第一節均勻分布——隨機(Uniform–Random) . . . . . . . . . . . . . . . . . . . 8
第二節非均勻分布——正相關(Inhomogeneous–Positive Correlation) . . . . . 9
第一小節兩物種豐富度相近. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
第二小節固定其中一物種強度函數. . . . . . . . . . . . . . . . . . . . . . . . 10
第三節非均勻分布——負相關(Inhomogeneous–Negative Correlation) . . . . 11
第一小節兩物種豐富度相近. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
第二小節固定其中一物種強度函數. . . . . . . . . . . . . . . . . . . . . . . . 12
第四章實例分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
第一節巴羅科羅拉多島嶼樹木資料(Tree Data of Barro Colorado Island) . . 13
第二節臺灣陽明山白蟻資料(Termite Data of Yangmingshan in Taiwan). . . 19
第五章結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
圖目錄
1.1 點過程分布圖轉換成有無矩陣及有無地圖的過程. . . . . . . . . . . . 2
2.1 A 及B 兩物種的有無矩陣示意圖. . . . . . . . . . . . . . . . . . . . . 4
4.1 有無地圖合併四個方格形成新有無地圖示意圖. . . . . . . . . . . . . . 19
4.2 天母區域四種白蟻有無地圖. . . . . . . . . . . . . . . . . . . . . . . . 23
4.3 天母土白蟻100 × 2 有無地圖合併成50 × 1 有無地圖的合併過程. . . . 24
表目錄
2.1 兩物種方格數觀察值之關係. . . . . . . . . . . . . . . . . . . . . . . . 5
3.1 物種均勻分布的模擬結果–卡方檢定. . . . . . . . . . . . . . . . . . . . 8
3.2 物種正相關分布的模擬結果—兩物種豐富度相近. . . . . . . . . . . . 9
3.3 物種正相關分布的模擬結果—固定其中一物種強度函數. . . . . . . . 10
3.4 物種負相關分布的模擬結果—兩物種豐富度相近. . . . . . . . . . . . 11
3.5 物種負相關分布的模擬結果—固定其中一物種強度函數. . . . . . . . 12
4.1 巴羅科羅拉多島嶼中九種樹木的發生率. . . . . . . . . . . . . . . . . . 14
4.2 九種樹木在50 × 100 有無地圖上的相關性檢定結果-1 . . . . . . . . . . 15
4.3 九種樹木在50 × 100 有無地圖上的相關性檢定結果-2 . . . . . . . . . . 16
4.4 九種樹木在100 × 200 有無地圖上的相關性檢定結果-1 . . . . . . . . . 17
4.5 九種樹木在100 × 200 有無地圖上的相關性檢定結果-2 . . . . . . . . . 18
4.6 天母四種白蟻的發生率. . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.7 阿里磅四種白蟻的發生率. . . . . . . . . . . . . . . . . . . . . . . . . 20
4.8 大屯溪四種白蟻的發生率. . . . . . . . . . . . . . . . . . . . . . . . . 21
4.9 倒照湖四種白蟻的發生率. . . . . . . . . . . . . . . . . . . . . . . . . 21
4.10 紗帽山四種白蟻的發生率. . . . . . . . . . . . . . . . . . . . . . . . . 22
4.11 陽峰四種白蟻的發生率. . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.12 陽明山四種白蟻的發生率. . . . . . . . . . . . . . . . . . . . . . . . . 22
4.13 白蟻在100 × 2 有無地圖上的相關性檢定結果–天母區域. . . . . . . . 25
4.14 白蟻在50 × 1 有無地圖上的相關性檢定結果–天母區域. . . . . . . . . 25
4.15 白蟻在100 × 2 有無地圖上的相關性檢定結果–阿里磅區域. . . . . . . 26
4.16 白蟻在50 × 1 有無地圖上的相關性檢定結果–阿里磅區域. . . . . . . . 26
4.17 白蟻在100 × 12 有無地圖上的相關性檢定結果–陽明山全區. . . . . . . 27
4.18 白蟻在50 × 6 有無地圖上的相關性檢定結果–陽明山全區. . . . . . . . 28

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