## Mussels organise themselves like molecules in materials

Mussels within mussel beds form a pattern resembling the way molecules and atoms are organised in materials such as bronze, steel or rubber. This means it is possible to explain their behaviour on the basis of the same mathematical model.

### Patterns in dynamic systems

Ecologists and mathematicians at the Royal Netherlands Institute for Sea Research (NIOZ) and the universities of Utrecht and Leiden revealed their findings in *Proceedings of the National Academy of Science* (PNAS) on 1 July. Mathematicians Arjen Doelman and Vivi Rottschäfer from Leiden University, who were involved in the project, are specialists in describing pattern formation in dynamic systems.

### Bronze, steel and rubber

Mussels organise themselves into a pattern known as ‘phase separation’: molecules and atoms of different types separate out to form spatial patterns. Phase separation is a physical process which gives alloys such as bronze and steel, and polymers such as rubber, their robustness. It can be described by means of a mathematical model (the Cahn-Hilliard model).

### Animal behaviour

Ecologists are familiar with the phenomenon of aggregation and pattern formation by animals in motion, but until now they based this fascinating phenomenon of self-organisation on the spatial differences in the growth or death of organisms, rather than on the behaviour of the animals themselves.

### Mathematical models

Professor Arjen Doelman, mathematician at Leiden University, who was involved in the project together with colleague Vivi Rottschäfer, is rarely surprised by such wonders of nature. He believes that the same mathematical models can be applied to many different natural phenomena. His own PhD research, which was inspired by the desire to understand water currents, later proved to be significant for the understanding of superconductivity. And a mathematical description of a chemical reaction was recorded in the same way by an ecologist 20 years later.

### Cross pollination at its best

Doelman: ‘This type of research is cross pollination at its best. We discover a new mathematical angle, and ecologists are able to look at nature in a different way.’ He also found it ‘really fascinating to observe’ the speed and the precision with which the mussels formed the pattern.

### Desertification

Doelman often works with ecologists, and one example of his studies is the relation between vegetation patterns and desertification. He is also fascinated by phytoplankton, that organise themselves in mysterious concentrations. Doelman: ‘As phytoplankton absorb 50% of CO2 in the atmosphere, they have a crucial role in climates. It's therefore very important that we fully understand what is going on here.'

(9* July 2013)*

### Article

*Phase separation explains a new class of self-organized spatial patterns in ecological systems.
*Quan-Xing Liu, Arjen Doelman, Vivi Rottschäfer, Monique de Jager, Peter M.J. Herman, Max Rietkerk, Johan van de Koppel.

PNAS July 2013.

### See also

Fundamentals of Science is one of the six key themes for research at Leiden University.