Danni Guo 1, Renkuan Guo 2, Guy F. Midgley 1 and A. G. Rebelo 1 
1 Kirstenbosch Research Center, South African National Biodiversity Institute, Private Bag X7, Claremont 7735, Cape Town, South Africa
2 Department of Statistical Sciences, Univ. of Cape Town, Private Bag, Rondebosch 7701, Cape Town, South Africa

Abstract. One of the major concerns today is global warming and climate change impacts, and how they are changing the distribution and behaviour of the plant species. For example, Proteas species in the Cape Floristic Region, South Africa, are very sensitive to climate change. In this paper, we first arguing and the random fuzzy error structure for spatial modelling accuracy and then 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 develop a bivariate partial differential  equation associated regression (PDEAR) model for investigating the impacts from rainfall and temperature on the Protea species. Under same the average biodiversity structure assumptions, we explore the future spatial change patterns of Protea species with future (average) predicted rainfall and temperature.  Our investigation shows that the global climate change impacts on distributional patterns of the endangered Protea species are significant.

Keywords: random fuzzy variable, bivariate partial differential equation associated regression model, Protea, South Africa, climate change, Cape Floristic Region

In: Wan, Y. et al. (eds) Proceeding of the 8th international symposium on spatial accuracy assessment in natural resources and environmental sciences, World Academic Union (Press).