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NCTS Summer Course on Mathematical Biology
10:00 - 12:00; 14:00 - 17:00, August 27 - September 4, 2018
Lecture Room B, 4th Floor, The 3rd General Building, NTHU

Yu-Yun Chen (Department of Natural Resources and Environmental Studies, National Dong Hwa University)
Chueh-Hsin Chang (Tunghai University)
Je-Chiang Tsai (National Tsing Hua University)

Sze-Bi Hsu (National Tsing Hua University)
Feng-Bin Wang (Chang Gung University)

一、 課程背景與目的:
In this summer course, we focus on the interplay between mathematical approaches and
forest ecology. This course begins with mathematical materials necessary for understanding
of ecology, and then some forest ecology problems will be introduced by ecologists.
二、 課程講者:
三、 課程之大綱:
Mathematical Theory
1. Existence of two species traveling waves (TW) of competition-diffusion
systems (Review some idea of Kan-on's 1995 paper)
2. Stability of TW (Basic materials on Sturm-Liouville theorem and idea of spectral
3. Existence of three species TW (Bifurcation theory)
4. Weakly interaction between TW (Shin-Ichiro Ei's approach).
Forest Ecology Theory
Plants are sessile organisms that do not move as quickly and freely as animals when
resource in their habitat becomes scarce. Thus plants may be under great pressure of
competition for common resources. Although G. Gause predicted competitive exclusion and
mono-dominance under intense competition, terrestrial systems are rarely monocultures.
This provokes the discussion of mechanisms permitting species coexistence in these
ecosystems and the forming of such geographical difference in diversity. Several
hypotheses proposed mechanisms that may reduce competition strength and promotes
species coexistence. Among them, niche differentiation hypothesis, theory of storage effect,
intermediate disturbance hypothesis, and enemy hypothesis obtain most attention. Recent
studies have suggested that other inter-specific interactions, such facilitation effect between
species, may also play an important role in species coexistence. New aspect and empirical
data allows new discussion beyond the regime of species competition. In this course, we
will examine cases related to the above important ecological theories and discuss on
formulating models to investigate the ecological questions.

Contact: tsaijc.math at gmail.com

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