How to express two kinds of basic transition in evolution of ecosystems: Application of exterior algebra in theoretic ecology

摘要

An evolution process of ecosystems consists of many transitions, the final target of these transitions, no matter if structure of the ecosystem alters, have to concern with function changed.Functional variation, as external behaviour, exhibits final effect of the transitions. Therefore, quantitative relationship between structure of the ecosystems and their function is significant for revealing internal mechanism of the transitions. With the introduction of Exterior algebra,such relation can be explained reasonably. In fact, evolution of ecosystem implies the animate part to adapt its environmental variation, sometimes, the animate part can adjust its state configuration of structural elements to achieve the target, and this is the most general phenomena. However, structural reform is necessary if the configuration adjustment can not keep prevailing structure consistent with changed environmental condition. The exterior product model describes these transition processes according to different situations, structure fixed and structure reformed, in this paper.