Recently global climate change has been a critical issue for survivability of the whole life system on the globe. Monitoring and prediction of population and community stabilities are an urgent issue as a prerequisite for achieving sustainability of ecosystems. Example cases of population/community dynamics are presented during the course of invasion, eruption and establishment. Based on model applications population growth patterns are reported, showing the break points during the course of invasion and eruption. Community structure properties are additionally revealed in responding to various sources of natural and anthropogenic disturbances according to species abundance distributions. The responding patterns of communities were observed including a few dominant taxa in natural conditions and rapid decrease in species richness under stressful conditions of disturbances. Feasibility of mathematical models in population/community monitoring and management are further discussed in the presentation.