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研究生:施智皓
研究生(外文):Zhi-Hao Shi
論文名稱:具階段性生活史之物種的反應擴散模型的行波解
論文名稱(外文):Traveling wave solutions for a stage structure model
指導教授:陳俊全陳俊全引用關係
指導教授(外文):Chiun-Chuan Chen
口試委員:夏俊雄王振男
口試委員(外文):Chun-Hsiung HsiaJenn-Nan Wang
口試日期:2022-01-20
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:應用數學科學研究所
學門:數學及統計學門
學類:其他數學及統計學類
論文種類:學術論文
論文出版年:2022
畢業學年度:110
語文別:英文
論文頁數:43
中文關鍵詞:行波解階段性生活史競爭型洛特卡-沃爾泰拉方程式速度選擇機制臨界競爭係數
外文關鍵詞:traveling wave solutionstage-structured speciescompetitive Lotka- Volterra modelspeed selection mechanismcritical competition coefficient
DOI:10.6342/NTU202200261
相關次數:
  • 被引用被引用:0
  • 點閱點閱:163
  • 評分評分:
  • 下載下載:27
  • 收藏至我的研究室書目清單書目收藏:0
自然界中存在大量的物種生活史具有不同的生長階段(例如:青蛙與蝌蚪、蝴蝶與毛毛蟲等等),特別是大約有近45-60%的昆蟲都具有階段性的生長史,而階段性的生長史可能意味著成體和幼體佔據不同的生態區位。為了從反應擴散方程的角度解釋這個現象,我們藉由Alhasanat 和Ou在2019年發展的上下解技巧證明了其行波解非線性速度選擇的條件,其生態含意是: 在此給定情形下,階段性生活史的物種總是更能夠加速其入侵弱勢物種的速度。在論文的最後,我們給出了比較階段性的生長史和簡單生長史競爭優勢的判據。
About 45-60% species of insects have stage-structured life history, which means a large proportion of insects have totally different ecological niches at different life stages (e.g. frog and tadpole, butterfly and caterpillar). To explain this phenomenon from a reaction diffusion model, in this thesis, we use Alhasanat and Ou's subsolution technique to get some explicit conditions for nonlinear speed selection and biological implications: in some situation, structured species speed up their invasive processes more often than unstructured species. At the end of this thesis, we define the notion of critical competition coefficient and have developed a criterion to compare their advantages in strong-weak type competition.
1 Modeling and main questions 1
1.1 When can a stage structured species take advantage of unstructured one? 1
1.2 Modeling and a generalization of reproduction number R0 2
1.2.1 Previous modeling of a stage-structured model with diffusion and R0 as a characteristic of its asymptotic behavior 2
1.2.2 Diffusive staged structured Lotka-Volterra model 4
1.2.3 Generalized fitness and reproduction number structured LV model 5
2 Previous results of speed selection mechanism 6
2.1 A general theory for linear determinacy of cooperative systems 6
2.2 Some previous studies in nonlinear speed selection of a LV model 9
3 Model with stage structure and its traveling wave solution 11
3.1 Equal ratio solution of uniform competition effect (without interspecific competition) 11
3.2 Speed selection mechanism of a diffusive stage-structured model 14
3.3 Speed selection mechanism of a diffusive stage-structured competitive Lotka-Volterra model (Main result) 16
3.3.1 Linear speed selection 17
3.3.2 Non-linear speed selection 22
4 Numerical simulations and ecological implications 32
4.1 Critical competition coefficient between linear and nonlinear speed selection 32
4.2 Conclusion 34
Appendices 36
A Proof and numerical method 37
A.1 Asymptotic behavior of the wave profile near (0,0,0) 37
A.2 Newton method on measuring the traveling wave speed 39
Ahmad Alhasanat and Chunhua Ou. “Minimal-speed selection of traveling waves to the Lotka–Volterra competition model”. In: Journal of differential equations 266.11 (2019), pp. 7357–7378.
Ahmad Alhasanat and Chunhua Ou. “Stability of Traveling Waves to the Lotka-Volterra Competition Model”. In: Complexity 2019 (2019).
Yousef Alqawasmeh and Frithjof Lutscher. “Persistence and spread of stage structured populations in heterogeneous landscapes”. In: Journal of mathematical biology 78.5 (2019), pp. 1485–1527.
Xavier Belles. “MicroRNAs and the evolution of insect metamorphosis”. In: Annual Review of Entomology 62 (2017), pp. 111–125.
Xavier Belles. “Origin and evolution of insect metamorphosis”. In: eLS (2011).
SM Bouguima and FZ Mehlia. “Asymptotic behavior of an age-structured population model with diffusion”. In: J. Appl. Anal. Comput 2 (2012), pp. 351–362.
Deniz F Erezyilmaz. “Imperfect eggs and oviform nymphs: a history of ideas about the origins of insect metamorphosis”. In: Integrative and Comparative Biology 46.6 (2006), pp. 795–807.
Jian Fang, Yijun Lou, and JianhongWu. “Can pathogen spread keep pace with its host invasion?” In: SIAM Journal on Applied Mathematics 76.4 (2016), pp. 1633–1657.
Peter Hammond. “Species Inventory”. In: Global Biodiversity: Status of the Earth’s Living Resources. Ed. by Brian Groombridge. Dordrecht: Springer Netherlands, 1992, pp. 17–39. isbn: 978-94-011-2282-5. doi: 10.1007/978-94-011-2282-5_4. url: https://doi.org/10.1007/978-94-011-2282-5_4.
Yuzo Hosono. “The minimal speed of traveling fronts for a diffusive Lotka-Volterra competition model”. In: Bulletin of Mathematical Biology 60.3 (1998),pp. 435–448.
Qihua Huang and Yuxiang Zhang. “Spread rates of a juvenile-adult population in constant and temporally variable environments”. In: Theoretical Ecology 14.1 (2021), pp. 145–160.
Wenzhang Huang and Maoan Han. “Non-linear determinacy of minimum wave speed for a Lotka–Volterra competition model”. In: Journal of Differential Equations 251.6 (2011), pp. 1549–1561.
Jarmila Kukalova-Peck. “Origin and evolution of insect wings and their relation to metamorphosis, as documented by the fossil record”. In: Journal of Morphology 156.1 (1978), pp. 53–125.
Shengqiang Liu, Lansun Chen, and Ravi Agarwal. “Recent progress on stage structured population dynamics”. In: Mathematical and Computer Modelling 36.11-13 (2002), pp. 1319–1360.
VHW Rudolf and Kevin D Lafferty. “Stage structure alters how complexity affects stability of ecological networks”. In: Ecology letters 14.1 (2011), pp. 75–79.
Sebastian Schreiber and Volker HW Rudolf. “Crossing habitat boundaries: coupling dynamics of ecosystems through complex life cycles”. In: Ecology letters 11.6 (2008), pp. 576–587.
James W Truman and Lynn M Riddiford. “The evolution of insect metamorphosis: a developmental and endocrine view”. In: Philosophical Transactions of the Royal Society B 374.1783 (2019), p. 20190070.
Hans FWeinberger, Mark A Lewis, and Bingtuan Li. “Analysis of linear determinacy for spread in cooperative models”. In: Journal of Mathematical Biology 45.3 (2002), pp. 183–218.
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