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:

陳毓昀副教授(東華大學自然資源與環境學系)

張覺心助理教授(東海大學應用數學系)

蔡志強教授(清華大學數學系)

 

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

analysis)

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.