具階段性生活史之物種的反應擴散模型的行波解

Traveling wave solutions for a stage structure model

施智皓(Zhi-Hao Shi)

指導教授 ： 陳俊全

國立臺灣大學/理學院/應用數學科學研究所/碩士(2022年)

https://doi.org/10.6342/NTU202200261

摘要

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。

關鍵字

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

並列摘要

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.

並列關鍵字

traveling wave solution ； stage-structured species ； competitive Lotka- Volterra model ； speed selection mechanism ； critical competition coefficient

參考文獻

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).