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中文論文名稱 破碎棲息地上捕食者與被捕食者的密度模型受到傳播消耗影響下的動態行為研究
英文論文名稱 Dynamics of Fragmented Patches Predator-Prey Population Models with Dispersal Costs
校院名稱 淡江大學
系所名稱(中) 數學學系碩士班
系所名稱(英) Department of Mathematics
學年度 103
學期 2
出版年 104
研究生中文姓名 余金衛
研究生英文姓名 Jin-Wei Yu
電子信箱 happyeat0625@yahoo.com.tw
學號 600190168
學位類別 碩士
語文別 中文
口試日期 2015-06-26
論文頁數 25頁
口試委員 指導教授-楊定揮
委員-許正雄
委員-楊智烜
中文關鍵字 破碎棲息地  被捕食者 
英文關鍵字 Fragmented Patches  Predator-Prey 
學科別分類 學科別自然科學數學
中文摘要 這篇論文我們研究在兩個或三個破碎環境下捕食者與被捕食者物種密度相互影響的傳播動態分析。在每個破碎棲息地上,擁有兩或三物種的雜食生態系。我們假設在兩物種時的捕食者和三物種時頂端捕食者和中間物種可以在破碎棲息地之間移動。在兩物種兩棲息地的情況下,我們已經研究出所有變數的動態行為,也找出來局部穩定的所有平衡點。甚至一些全域穩定的情況也找到理論判別出來。最後我們提出三物種兩棲息地和三物種三棲息地的數據分析。傳播消耗的影響我們則在生物多樣性下面去討論。
英文摘要 In this work, we consider the population-dispersal dynamics for predator-prey interactions in a two- or three-patchy environment. On each fragmented patch, there is a two-species predator-prey or three-species omnivory ecological system. It is assumed that the predator species of two-species models or the intermediate species and top predator of three-species models are mobile. For the 2-species-2-patch case, we have completely classi_ed all dynamics with respect to all parameters and have showed the local stability of all equilibria. Moreover, some global extinction results are verified analytically. Finally, numerical simulations of 3-species-two-patch and 3-species-3-patch model are performed. The the effect of dispersal rate with respect to the bio-diversity are discussed.
論文目次 Contents
1 Introduction 1
2 Theoretical Analysis of Predator-Prey Systems in Two Patches 3
2.1 Preliminary Results and Local Stability of Boundary Equilibria 5
2.2 Numerical Study of Global Stability of the EquilibraĒ2 and Ē* 10
3 Some Numerical Simulations of Three-Species Omnivory Model on Two-Patch and Three-Patch Habitat 11
3.1 Numerical Simulations of Three-Species Omnivory Model on Two-Patch Habitat 14
3.2 Numerical Simulations of Three-Species Omnivory Model on Three-Patch Habitat 20
3.2.1 Simulations of Three-Species Omnivory Model on Three-Patch Habitat with Linear Connection 20
3.2.2 Simulations of Three-Species Omnivory Model on Three-Patch Habitat with Complete Connection 21
4 Discussion and Biological Interpretations 23
References 24


List of Figures
2.1: The dynamics of (2.3)-(2.4) by parameters ayx and byx. 10
2.2: Time courses of numerical simulation of each species of (2.3)-(2.4) with parameters and dy1 = 0.1 in Table 2.1. 11
2.3: Time courses of numerical simulation of each species of (2.3)-(2.4) with parameters and dy1 = 0.5 in Table 2.1. 12
3.1: The asymptotical states of the isolated patches are presented with parameters in Table 3.1 15
3.2: The asymptotical states of whole systems with coupled patch 1 and patch 2 are calculated its corresponding bio-diversity indicator . 16
3.3: The asymptotical states of whole systems with coupled patch 1 and patch 2 are calculated its corresponding bio-diversity indicator I for another four cases. 17
3.4: The four cases of the Table 3.3 18
3.5: Another six cases of the Table 3.3 19
3.6: I as a function of symmetric dispersal rates m12 = m21 > 0 and n12 = n21 > 0 21
3.7: Sx ⊕ Sx ⊕ Sxy 23


List of Tables
2.1: Parmeters to simulate the global dynamics of (2.3)-(2.4) numerically. 11
3.1: Parameters of (3.5) with respect to asymptotical states for mij = nij = 0. 14
3.2: The indicator I of bio-diversity of (3.5) with mij > 0 and nij = 0 17
3.3: The indicator I of bio-diversity of (3.5) with mij > 0 and nij > 0 18
3.4: The indicator I of bio-diversity of (3.6)-(3.8) with mij > 0 and nij > 0 22

參考文獻 References
[1] R. Cressman and V. K rivan. Two-patch population models with adaptive dispersal: the effects of varying dispersal speeds. Journal of Mathematical Biology, 67(2):329-358, 2013.
[2] D. L. DeAngelis, G. S. K.Wolkowicz, Y. Lou, Y. Jiang, M. Novak, R. Svanback, M. S. Ara ujo, Y. Jo, and E. A. Cleary. The effect of travel loss on evolutionarily stable distributions of populations in space. The American naturalist, 178(1):15-29, July 2011.
[3] S.-B. Hsu, S. Ruan, and T.-H. Yang. Analysis of three species Lotka-Volterra food web models with omnivory. Journal of Mathematical Analysis and Applications, 426(2):659-687, 2015.
[4] R. Levins. Evolution in Changing Environments. Princeton University Press, Princeton, 1969.
[5] Y. Lou and C.-H. Wu. Global dynamics of a tritrophic model for two patches with cost of dispersal. SIAM Journal on Applied Mathematics, 71(5):1801-1820, 2011.
[6] M. L. McKinney. Urbanization, Biodiversity, and Conservation The impacts of urbanization on native species are poorly studied, but educating a highly urbanized human population about these impacts can greatly improve species conservation in all ecosystems. BioScience, 52(10):883-890, Oct. 2002.
[7] T. Namba, A. Umemoto, and E. Minami. The effects of habitat fragmentation on persistence of source-sink metapopulations in systems with predators and prey or apparent competitors. Theoretical Population Biology, 56(1):123-137, Aug. 1999.
[8] M. R. W. Rands, W. M. Adams, L. Bennun, S. H. M. Butchart, A. Clements, D. Coomes, A. Entwistle, I. Hodge, V. Kapos, J. P. W. Scharlemann, W. J. Sutherland, and B. Vira. Biodiversity Conservation: Challenges Beyond 2010. Science (New York, NY), 329(5997):1298-1303, Sept. 2010.
[9] S. P. D. Riley, R. M. Sauvajot, T. K. Fuller, E. C. York, D. A. Kamradt, C. Bromley, and R. K. Wayne. Effects of Urbanization and Habitat Fragmentation on Bobcats and Coyotes in Southern California. Conservation Biology, 17(2):566-576, Apr. 2003.
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