本篇文章主要提出於出現與否地圖透過估計物種發生率，並將發生率帶入斯皮爾曼相關係數以檢驗物種共現性的方法，同時比較了二項分配方法、Veech 方法及 t 檢定。二項分配方法和 Veech 方法可以直接應用於出現與否地圖，而另外兩種方法則需透過核估計法來估計物種出現在各個格子的發生率，再進行皮爾森相關係數和斯皮爾曼相關係數檢定。本篇文章透過模擬研究及實際資料比較這四種方法的表現，整體來說，我們推薦當某一物種發生率在 10% 以下，且與另一物種之發生率差距達40% 以上時，可以使用斯皮爾曼相關係數，其型一誤差會最接近顯著水準，且檢定力會是最高的。實際資料分析我們使用的是宜蘭福山植物園區的資料，該資料為點過程資料，所以我們會先將資料轉換為出現與否地圖後再進行分析。我們總共挑選了 8 個物種進行兩兩配對並作檢定，可以發現物種間都呈現正相關或負相關。

This research introduces a method for testing species co-occurrence by incorporating species presence rates into the Spearman rank correlation coefficient on presenceabsence maps. We compare this method with binomial distribution methods, the Veech method, and t-tests. While the binomial distribution method and Veech method can be directly applied to presence-absence maps, the other two tests require estimating the species presence rate in each grid cell by kernel estimation before conducting t-tests or Spearman rank correlation coefficient tests. Through simulation studies and real data analysis, we evaluate the performance of these four methods. Our recommendation is to employ the Spearman rank correlation coefficient when the occurrence rate of one species is below 10% and the occurrence rate of other species exceeds it by 40%. This is because it yields the closest type I error rate to the significance level and the highest testing power. For our analysis of real data, we utilized data from the Fushan Botanical Garden in Yilan. Since the data is a point pattern process, we converted it into presence-absence data before analysis. We selected 8 species for pairwise testing and observed either positive or negative correlations among them.

目錄
圖目錄 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II
表目錄 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .III
第一章 緒論 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  1
第二章 研究方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
第一節 機率方法 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
第一小節 二項分配方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
第二小節 Veech 方法 . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . 7
第二節 t 檢定方法 . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 9
第一小節 皮爾森相關係數 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
第二小節 斯皮爾曼相關係數. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
第三章 模擬研究. . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . 13
第四章 實例分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . 23
第五章 結論 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
參考文獻 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

圖目錄
1.1 點型態資料轉換出現與否資料 . . . . . . . . . . . . . . . . . . . . . . . 3
3.1 λ(x, y) ∝ 1 生成的出現與否資料 . . . . . . . . . . . . . . . . . . . . . 14
3.2 λ(x, y) ∝ x 生成的出現與否資料 . . . . . . . . . . . . . . . . . . . . . 14
3.3 λ(x, y) ∝ x + y 生成的出現與否資料 . . . . . . . . . . . . . . . . . . 15
3.4 λ(x, y) ∝ 21 − x 生成的出現與否資料 . . . . . . . . . . . . . . . . . . 15
3.5 λ(x, y) ∝ 41 − x − y 生成的出現與否資料 . . . . . . . . . . . . . . . . 15
4.1 福山植物園八種樹種之出現與否資料 . . . . . . . . . . . . . . . . . . . 24
4.2 福山植物園等高圖 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

表目錄
2.1 兩物種出現與否所對應之格點個數觀察值 . . . . . . . . . . . . . . . . 5
2.2 在兩物種分布為獨立的情況下 Oi 與 Ei 個數示意表格 . . . . . . . . . 5
2.3 斯皮爾曼排序示意表格 . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 斯皮爾曼計算示意表格 . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.1 雙尾檢定下四種方法之型一誤差 (粗體為最接近顯著水準 0.05) . . . . 16
3.2 右尾檢定下四種方法之型一誤差 (粗體為最接近顯著水準 0.05) . . . . 17
3.3 左尾檢定下四種方法之型一誤差 (粗體為最接近顯著水準 0.05) . . . . 18
3.4 強正相關及弱正相關下之檢定力 (粗體為該發生率下最高檢定力) . . . 19
3.5 強負相關和弱負相關下之檢定力 (粗體為該發生率下最高檢定力) . . . 21
4.1 福山植物園物種個數、存在格數和出現率 . . . . . . . . . . . . . . . . 25
4.2 物種間獨立性雙尾檢定之 P 值 (物種名稱下方為發生率) . . . . . . . . 26
4.3 檢測福山植物園八種物種間正負相關之 P 值 (物種名稱下方為發生率) 28

[1] Arita, H. T., Christen, A., Rodríguez, P., and Soberón, J. (2012). The presence–
absence matrix reloaded: the use and interpretation of range–diversity plots. Global
Ecology and Biogeography, 21(2):282–292.
[2] Arita, H. T., Christen, J. A., Rodríguez, P., and Soberón, J. (2008). Species diversity and distribution in presence-absence matrices: mathematical relationships and
biological implications. The American Naturalist, 172(4):519–532.
[3] Blanchet, F. G., Cazelles, K., and Gravel, D. (2020). Co-occurrence is not evidence
of ecological interactions. Ecology Letters, 23(7):1050–1063.
[4] Carstensen, D. W. and Olesen, J. M. (2009). Wallacea and its nectarivorous birds:
nestedness and modules. Journal of Biogeography, 36(8):1540–1550.
[5] Cazelles, K., Araújo, M. B., Mouquet, N., and Gravel, D. (2016). A theory for
species co-occurrence in interaction networks. Theoretical Ecology, 9:39–48.
[6] Chang, Y., Rakshit, S., Huang, C., and Wu, W. (2023). Probabilistic approaches
for investigating species co-occurrence from presence-absence maps. Peerj, 11.
[7] Cressie, N. (2015). Statistics for spatial data. John Wiley & Sons.
[8] Dormann, C. F., Bobrowski, M., Dehling, D. M., Harris, D. J., Hartig, F., Lischke,
H., Moretti, M. D., Pagel, J., Pinkert, S., Schleuning, M., et al. (2018). Biotic
interactions in species distribution modelling: 10 questions to guide interpretation
and avoid false conclusions. Global ecology and biogeography, 27(9):1004–1016.
[9] Gotelli, N. J. (2000). Null model analysis of species co-occurrence patterns. Ecology,
81(9):2606–2621.
[10] Gotelli, N. J. and Ulrich, W. (2010). The empirical bayes approach as a tool to
identify non-random species associations. Oecologia, 162:463–477.
[11] Griffith, D. M., Veech, J. A., and Marsh, C. J. (2016). Cooccur: probabilistic
species co-occurrence analysis in Ｒ. Journal of Statistical Software, 69:1–17.
[12] Patterson, B. D. and Atmar, W. (1986). Nested subsets and the structure of insular
mammalian faunas and archipelagos. Biological journal of the Linnean society, 28(1-
2):65–82.
[13] Pitta, E., Giokas, S., and Sfenthourakis, S. (2012). Significant pairwise cooccurrence patterns are not the rule in the majority of biotic communities. Diversity,
4(2):179–193.
[14] Sanderson, J. G. (2000). Testing ecological patterns. American Scientist, 88(4):332.
[15] Sanderson, J. G., Diamond, J. M., and Pimm, S. L. (2009). Pairwise co-existence
of bismarck and solomon landbird species. Evolutionary Ecology Research, 11(5):771–
786.
[16] Schober, P., Boer, C., and Schwarte, L. (2018). Correlation coefficients: Appropriate use and interpretation. Anesthesia and Analgesia, 126(5):1763–1768.
[17] Sfenthourakis, S., Giokas, S., and Tzanatos, E. (2004). From sampling stations to
archipelagos: investigating aspects of the assemblage of insular biota. Global Ecology
and Biogeography, 13(1):23–35.
[18] Sfenthourakis, S., Tzanatos, E., and Giokas, S. (2006). Species co-occurrence: the
case of congeneric species and a causal approach to patterns of species association.
Global Ecology and Biogeography, 15(1):39–49.
[19] Spearman, C. (1987). The proof and measurement of association between two
things. The American journal of psychology, 100(3/4):441–471.
[20] Ulrich, W., Almeida-Neto, M., and Gotelli, N. J. (2009). A consumer’s guide to
nestedness analysis. Oikos, 118(1):3–17.
[21] Ulrich, W. and Gotelli, N. J. (2013). Pattern detection in null model analysis.
Oikos, 122(1):2–18.
[22] Veech, J. A. (2006). A probability-based analysis of temporal and spatial cooccurrence in grassland birds. Journal of Biogeography, 33(12):2145–2153.
[23] Veech, J. A. (2013). A probabilistic model for analysing species co-occurrence.
Global Ecology and Biogeography, 22(2):252–260.
[24] Veech, J. A. (2014). The pairwise approach to analysing species co-occurrence.
Journal of Biogeography, 6(41):1029–1035.
[25] Wright, D. H. and Reeves, J. H. (1992). On the meaning and measurement of
nestedness of species assemblages. Oecologia, 92:416–428.