Phase separation explains a new class of self-organized spatial patterns in ecological systems

作者：Liu Quan Xing^*; Doelman Arjen; Rottschafer Vivi; de Jager Monique; Herman Peter M J; Rietkerk Max; van de Koppel Johan

来源：Proceedings of the National Academy of Sciences, 2013, 110(29): 11905-11910.

DOI：10.1073/pnas.1222339110

• mussels
• mathematical model
• spatial self-organization
• animal a ggregation

The origin of regular spatial patterns in ecological systems has long fascinated researchers. Turing%26apos;s activator-inhibitor principle is considered the central paradigm to explain such patterns. According to this principle, local activation combined with long-range inhibition of growth and survival is an essential prerequisite for pattern formation. Here, we show that the physical principle of phase separation, solely based on density-dependent movement by organisms, represents an alternative class of self-organized pattern formation in ecology. Using experiments with self-organizing mussel beds, we derive an empirical relation between the speed of animal movement and local animal density. By incorporating this relation in a partial differential equation, we demonstrate that this model corresponds mathematically to the wellknown Cahn-Hilliard equation for phase separation in physics. Finally, we show that the predicted patterns match those found both in field observations and in our experiments. Our results reveal a principle for ecological self-organization, where phase separation rather than activation and inhibition processes drives spatial pattern formation.

• 出版日期2013-7-16