遷徙的競爭種群之全局動態

Abstract

在這篇論文中，我們回顧了幾篇文獻資料是關於生態數學裡，Lotka - Volterra模型以及有關物種的補丁模型(Patch model)的動態現象。關於多個物種互動的補丁模型，我們研究 S. A. Gourley 和 Y. Kuang 在2005年提出的兩個尚未解決的問題，這是探討遷徙率如何影響兩競爭物種的補丁模型的動態，與其物種的成長率分佈有關。據推測，在一個高度遷徙的環境中，物種的制勝策略取決於在某個單一補丁的成長率。也就是說，物種在其中一個補丁具有最大的成長率就獲勝。另一方面，在足夠小的遷徙率下可能會出現全局穩定的共存態。雖然我們還沒有解決這兩種全局動態的猜想，但在這些問題上已有更好的了解。

In this thesis, we review the investigations of dynamics for Lotka Volterra models and patch models in mathematical ecology. We study two open questions posed by Gourley and Kuang in 2005, which are concerned with how dispersal rates affect the competition in two-species patch model with various spatial distribution of their growth rate. It was conjectured that, in a high dispersal environment, the winning strategy for species depends on the growth rate in a single patch. That is, the species which has the greatest growth rate will win. On the other hand, the system may have a globally asymptotically stable positive equilibrium for a small enough dispersal rate. We have not solved the conjectures, but have better understanding on these issues.