同功群間捕食數學模型之分析

Mathematical analysis on a Droop model with intraguild predation.

何怡慧(Yi-Hui Ho)

指導教授 ： 許世壁

國立清華大學/理學院/數學系/碩士(2016年)

摘要

本論文主要探討兩個物種儲存內能競爭單一資源的數學模型，其中一個物種可以作為一個同功群間捕食者(intraguild predator)，它也吃其他的物種。我們利用 uniform persistence 的定理去證明在一些合適的條件下，這兩個物種共存是可能的，我們的數值模擬也證實了理論結果。值得注意的是，在參考文獻[18]或[19]中，已經證明在典型沒有捕食功能的模型中，物種會競爭排斥，也就是說，對資源濃度需求量最低的物種會單獨存活，而其他物種終將滅絕。從我們的研究中，同功群間捕食(intraguild predation)可促進物種共存的可能性。

關鍵字

同功群間捕食 ； 物種競爭

並列摘要

In this thesis, we investigate a mathematical model of two species competing in a chemostat for one resource that is stored internally, where one of the species can act as an intraguild predator that also feeds on the other species. We utilize theory of uniform persistence to prove that coexistence is possible under some suitable conditions, and our numerical simulations also confirm theoretical results.
It is worth noting that Smith and Waltman proved that competitive exclusion holds for the classical model without predation, that is, the species that can grow at the lowest nutrient concentration will win the competition. From our study, intraguild predation may promote the possibility of coexistence.

並列關鍵字

competition ； internal storage ； intraguild predation ； uniform persistence

參考文獻

[17] H. L. Smith, Monotone Dynamical Systems:An Introduction to the Theory of Competitive and Cooperative Systems, Math. Surveys Monogr 41, American Mathematical Society, Providence, RI, 1995.

[19] H. L. Smith and P. E.Waltman, The Theory of the Chemostat, Cambridge Univ. Press, 1995.

[1] Polis, G. A. et al., The ecology and evolution of intraguild predation: po-tential competitiors that eat each other, Annu. Rew. Ecol. Syst. 20 (1989),pp. 297-330.

[2] Arim, M. and Marquet, P. A., Intraguild predation: a widespread inter-action related to species biology, Ecol. Lett. Syst. 7 (2004), pp. 557-564.

[3] R. D. Holt and G. A. Polis, A theoretical framework for intraguild predation, American Naturalist 149(1997), pp. 746-764.