Nature never fails to amaze us. My continuous interest is to apply mathematics in the field of ecology for a deeper and more fundamental understanding of emerging ecological patterns. This will not only enhance our understanding in the natural sciences but also challenge the development of mathematics. Scientific research, from my perspective, endeavours to measure natural objects, to quantify patterns and structures from these measurements, and ultimately to identify the mechanisms governing these patterns and structures. This is equal to unveiling (i) what patterns exist in nature, (ii) how such patterns emerge, and (iii) why nature organizes itself in such a way. My research, thus, focuses in three specific areas. First, spatial patterns caused by organism-environment feedback and biotic interactions, such as the consequence of niche construction, the origin of altruism (e.g. the evolution of cooperation), spatial complexity (e.g. from the Allee effect, overcrowding, competition, or predation), and the evolutionary processes (e.g. allopatric speciation). Second, the scaling patterns of species distribution and biodiversity, specifically, macroecological patterns such as the occupancy frequency distribution of species ranges in a community and the non-random aggregated patterns of species distribution and association. Finally, estimating rates of spread from a dispersal kernel. These three areas of research all serve to clarify the relationship among patterns, scales and dynamics in ecological systems.