We are a dynamic research group led by Prof Cang Hui, a SARChI Chair in Mathematical and Theoretical Physical Biosciences. We work at 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. As ecological processes are highly complex and adaptive, we rely on the simplicity of mathematical language to build models and theoretical frameworks. Nature never fails to amaze us. Scientific research endeavours to measure natural objects, quantify structures, and ultimately identify the mechanisms governing these structures. Our research has thus focused on formulating and modelling the complexity of biodiversity patterns and biotic interactions. Besides mathematical ecology and modelling, our studies have spanned into population ecology, community ecology, network ecology, evolutionary ecology, macroecology and global change biology, as well as invasion biology. See Ecological and Evolutionary Modelling (2018 Springer) for selected topics of our theoretical modelling, Invasion Dynamics (2017 Oxford University Press) for our syntheses on hypotheses, models and theories of invasion science, and Invading Ecological Networks (2022 Cambridge University Press) for “an atlas of possibilities” on the concept of open adaptive networks.