My research team is working on the interface between mathematics and biology. Our interests lie in proposing models and theories for explaining emerging patterns in whole-organism biology, namely ecology. Ecology studies biodiversity in its variety and complexity. Due to their non-random nature, ecological processes are highly complex and adaptive. In order to quantify emergent ecological patterns and to investigate their hidden mechanisms, we need to rely on the simplicity of mathematical language. Our research focus is to develop novel and apply available methods in mathematics, statistics and theoretical physics for unlocking the mechanisms behind realistic patterns. Nature never fails to amaze us. Scientific research 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 and dynamic complexity caused by organism-environment feedbacks and biotic interactions. Second, the scaling patterns of biodiversity, with the emphasis on the profound effect of spatial scales on macroecological and community assemblage patterns. Finally, using biological invasions, as a natural experiment, to study how species sharpen their weaponries and how the recipient systems respond. These three areas of research all serve to clarify the interactions among patterns, scales and dynamics in the ever-evolving ecological systems. The recent research theme has been focused on how patterns related to the heterogeneity of species distributions, the hierarchy of biological networks and the size of adaptive traits, change with spatial and temporal scales. Using scale as a thread, the proposed research weaves the kaleidoscope of biological patterns into a cohesive whole.