Global warming and climate changes are changing the environment and therefore changing the distribution and behaviour of the plant species. Plant species often move and change their distributions as they find their original habitats are no longer suitable to their needs. It is therefore important to establish a statistical model to catch up the movement and patterns of the endangered species in order to effectively manage environmental protection under the inevitable
biodiversity changes that are taking place. In this paper, we are focusing on the population category of rare Proteas that has an estimated population size from 1 to 10 per sample site, which is very small. We used the partial differential equation associated regression (PDEAR) model, which merges the partial differential equation theory, (statistical) linear model theory and random fuzzy variable theory together into a efficient small-sample oriented model, for the spatial pattern changing analysis. The regression component in a PDEAR model is in nature a special random fuzzy multivariate regression model. We developed a bivariate model for investigating the impacts from rainfall and temperature on the
Protea species in average sense in the population size of 1 to 10, in the Cape Floristic Region, from 1992 to 2002, South Africa. Under same the average biodiversity structure assumptions, we explore the future spatial change patterns of Protea species in the population size of 1 to 10 with future (average) predicted rainfall and temperature. The spatial distribution and patterns are clearly will help us to explore global climate changing impacts on endangered species.