近年来以理论模型方法为主，综合应用种群生态学、数学模型、统计物理学等方法，对生态系统的空间自组织机理及其生态功能进行了系列研究。利用这些交叉学科的方法，迄今共发表32篇科研论文，论文已经被国际同行引用700多次。在国际一流期刊发表多篇论文，例如《自然-通讯》(Nature Communiations)、《美国科学院院刊》(PNAS)、《生命物理学评论》(Phys. Life Rev.)、《英国皇家协会会刊B》(Proc. Roy. Soc. B)、《英国皇家协会会刊-交叉学科》(J. R. Soc. Interface)、《美国自然博物学》(Am. Nat)、《物理评论 E》(Phys. Rev. E)。研究成果被美国科学院Simon Levin院士，Sharon Glotzer院士，Nigel Goldenfeld 院士，英国爱丁堡皇家科学院Michael Cates院士，Philip Maini院士，匈牙利科学院、欧洲科学院Tamas Vicsek院士，Jonathan Sherratt教授等国际著名学者高度评价和引用。
Simulation mussel beds with GPU
Theoretical models highlight that spatial self-organized patterns can have important emergent effects on the functioning of ecosystems, for instance by increasing productivity and affecting the vulnerability to catastrophic shifts. However, most theoretical studies presume idealized homogeneous conditions, which are rarely met in real ecosystems. Using self-organized mussel beds as a case study, we reveal that spatial heterogeneity resulting from the large-scale effects of mussels on their environment, significantly alters the emergent properties predicted by idealized self-organization models that use homogeneous conditions (see Liu et al 2014, J. Roy. Soc. Interface).
Ecosystem functioning of Mussel beds
Theory predicts that self-organized pattern formation has important implications by affecting vulnerability to disturbances and increasing production. Whether these emergent effects depend on the presumed underlying mechanisms is an often ignored question. Here, we show that two models using very different mechanisms for pattern formation in mussel beds are equally able to explain the observed spatial patterns (Liu et al 2012, Proc. R. Soc. B). Interestingly, they predict a strikingly contrasting effect of these spatial patterns on ecosystem vulnerability and production. This study provides a cautionary warning against predictions of the implications of spatial self-organization, when the underling mechanisms are incompletely understood, and not based on experimental study.
Phase separation principle in mussel patterning
Using mussels as expriment, we demonstrate that the physical principle of phase separation (which is well-known and widely used in physics, but absent in the ecological literature) is able to explain spatial pattern formation in ecological systems (Liu et al, 2013 PNAS). Specifically, we show that aggregation of mussels into labyrinth-like patterns closely follows the mathematical principle for phase separation as outlined by Cahn and Hilliard in 1958.
Until now, the general model used for explaining the underlying regular, self-organized spatial patterns in ecology has been Turing's activator-inhibitor principle, with birth and death processes as the driving ecological process of pattern formation. The phase separation principle, as identified in our work, is solely based on movement and therefore has a behavioral basis. Hence, our study identifies a new, fundamentally different process underlying ecological pattern formation.
Multiple-scale patterns in ecosystems
Many ecosystems display complex spatial patterning at multiple spatial scales, particularly on mussel beds, seagrass, and coral reefs ecosystems. Using a theoretical model, we reveal the underlying mechanisms of the nested patterns development in mussel beds (Nature Communications, 2014 (5) 5234, doi: 10.1038/ncomms6234).
"This novel model analysis reveals that the interaction between these behavioural and ecosystem-level mechanisms increases mussel bed resilience, enables persistence under deteriorating conditions and makes them less prone to catastrophic collapse. Our analysis highlights that interactions between different forms of self-organization at multiple spatial scales may enhance the intrinsic ability of ecosystems to withstand both natural and human-induced disturbances." is coming from the abstract of paper.
- Heping Jiang, Yongli Song, Quan-Xing Liu, Yuan Yuan, Spatiotemporal dynamics of the diffusive mussel-algae model near Turing-Hopf bifurcation, SIAM Journal on Applied Dynamical Systems (SIADS), 2017. in revision.
- Quan-Xing Liu, Max Rietkerk, Peter M.J. Herman, Theunis Piersma, John M. Fryxell, Johan van de Koppel, Bridging physics and biology, Physics of Life Review, 2016 (19) 142-146.
- Quan-Xing Liu, Max Rietkerk, Peter M.J. Herman, Theunis Piersma, John M. Fryxell, Johan van de Koppel, Phase separation driven by density-dependent movement: a novel mechanism for ecological patterns, Physics of Life Review, 2016 (19) 107-121, doi: 10.1016/j.plrev.2016.07.009. (IF=8.615)
- Quan-Xing Liu, Peter M.J. Herman, Wolf Mooij, Jef Huisman, Marten Scheffer, Han Olff and Johan van de Koppel, Pattern formation at multiple spatial scales drives the resilience of mussel bed ecosystems, Nature Communications, 2014 (5) 5234, doi: 10.1038/ncomms6234.
- Quan-Xing Liu, Ellen Weerman, Rohit Gupta, Peter M.J. Herman, Han Olff and Johan van de Koppel, Biogenic gradients in algal density affects the emergent properties of spatially self-organized mussel beds, J. R. Soc. Interface, 2014 (11) 20140089.
- Quan-Xing Liu, Arjen Doelman, Vivi Rottschafer, Monique de Jager, Peter M.J. Herman, Max Rietkerk, Johan van de Koppel, Phase separation explains a new class of self-organized spatial patterns in ecological systems, PNAS, 2013 (110) 11905-11910.
- Quan-Xing Liu, Ellen Weerman, Peter Herman, Han Olff, and Johan van de Koppel, Alternate mechanisms alter the emergent properties of self-organization in mussel beds. Proc. Roy. Soc. B, 2012 (279) 2744-2753.
- Rong-Hua Wang, Zhen Jin, Quan-Xing Liu, Johan van de Koppel, and David Alnoso, Emergent effects of stochasticity and environmental transmission for outbreak periodicity in avian influenza epidemics, PloS One 2012 (6) e28873.
- Ellen J. Weerman, Johan van de Koppel, Maarten B. Eppinga, Francesc Montserrat, Quan-Xing Liu, Peter M.J. Herman, Spatial Self-Organization on Intertidal Mudflats through Biophysical Stress Divergence, American Naturalists 2010 (175) E15-E32
- Rong-Hua Wang, Quan-Xing Liu, Gui-Quan Sun, Zhen Jin and Johan van de Koppel, Nonlinear dynamics and pattern bifurcation in a model for spatial patterns in Young Mussel Beds, J. R. Soc. Interface, 2009 (6) 705-718.