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Selected Publications are listed here.

See full publications in full CV and

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* indicates that I am also the corresponding author

Ladderpath &
Assembly tree of molecules

Nature is tinkering. We developed a method that we call the "ladderpath" to characterize the complexity of particular objects, which uncovers the hierarchical information that is shaped by evolution and selection. This method is general and is able to deal with amino acid and gene sequences, chemical molecules, network structures, etc.

We further found that, in intuition, complexity may refer to two distinct directions: one is how ordered the system is, and the other is how difficult to reproduce the system. Ladderpath helps us distinguish the two directions and gives a quantitative description, where we can see various applications in bioinformatics and linguistics.


Z. Zhang, C. Liu, Y. Zhu, L. Peng, W. Qiu, Q. Tang, H. Liu, K. Zhang, Z. Di, Y. Liu*. Evolutionary tinkering enriches the hierarchical and nested structures in amino acid sequences.
Physical Review Research, 6: 023215, 2024.

Y. Liu*, Z. Di, P. Gerlee. Ladderpath Approach: How Tinkering and Reuse Increase Complexity and Information. Entropy, 24(8):1082, 2022.

Y. Liu, C. Mathis, M. Bajczyk, S. Marshall, L. Wilbraham, L. Cronin, Exploring and Mapping Chemical Space with Molecular Assembly Trees, Science Advances, 7, eabj2465, 2021.


Origin of Life / autocatalytic set

All life on Earth, probably all life in general, is able to replicate itself. We provide a general model to explain how a set of non-self-replicating chemical reactions coupled together into a system which is able to self-replicate as a whole.

We find specific chemical systems that exhibit self-replication and show that these systems are common and emerge often. These results start to explain the origins of prebiotic evolution.

Animation (YouTube, Bilibili)

Y. Liu*, On the definition of a self-sustaining chemical reaction system and its role in heredity, Biology Direct, 15(15), 2020.  (Errata)

Y. Liu*, D. Hjerpe and T. Lundh, Side reactions do not completely disrupt linear self-replicating chemical reaction systems, Artificial Life 26(3): 327-337, 2020. (Full text)

Y. Liu*, and D. Sumpter, Mathematical modeling reveals spontaneous emergence of self-replication in chemical reaction systems, J. Biological Chemistry 293(49), 18854-18863, 2018.

Y. Liu*, and D. Sumpter, Is the golden ratio a universal constant for self-replication? PLOS ONE 13(7), e0200601, 2018.

Artificial Ecosystem

Community ecosystems at very different levels of biological organisation often have similar properties. We develop a bottom-up model of consumer–resource interactions, in the form of an artificial ecosystem "number soup", which reflects basic properties of many bacterial and other community ecologies. 


For example, 1) communities self-organise so that all available resources are fully consumed; 2) the evolved ecosystems are often "robust yet fragile", with keystone species required to prevent the whole system from collapsing; 3) a useful ecological concept---species loop---could be developed, which can be considered as a higher level unit of selection than individual species.

Y. Liu*, and D. Sumpter, Insights into resource consumption, cross-feeding, system collapse, stability and biodiversity from an artificial ecosystem, J. R. Soc. Interface, 14(126), 20160816, 2017.

Y. Liu*, The artificial ecosystem: number soup (part II), arXiv:1801.04916, 2018.

Other projects involved

Resonance algorithm

A new algorithm for the shortest path problem

Y. Liu*, et al., Complex & Intelligent Systems, 2022.


Biochemical cellular processes


Collective animal behaviour


Magnetic confinement fusion

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