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Species diversity by pattern formation

Our earth exhibits an enormous diversity of animal and plant species. This richness is essential for the viability of ecological systems. It comes with a complex network of interactions that occur between the different species, such as predator-prey relationships or symbiotic dependences. Conceptual explanations of species diversity therefore quickly run into fundamental problems. Why does, among two competing species, not one outcompete the other in the long run, be it due to higher fitness or random events?

Bacteria offer the possibility to study ecological systems on a micrometer scale. The number of such microorganisms as well as their different species is by far higher than that of macroscopic living beings. Moreover, experiments can be carried out under controlled laboratory conditions. Indeed, biologists from Yale and Stanford have recently performed experiments regarding species diversity employing three bacterial strains. One of those produces a poison that kills a second, sensitive strain. However, the third strain is resistant to the toxin. As it reproduces faster that the poison-producing one, but slower than the sensitive strain, cyclic dominance arises. As in the game rock-paper-scissors, each strain outperforms another but is itself beaten by the remaining one. The experiments have shown that all three bacterial strains coexist when they can spatially separate. On a Petri dish, temporally dependent patterns of regions where different strains dominate form.

 

Figure: (a) Species diversity in a coral reef. (b) Schematic of the interactions of three bacterial strains that cyclically dominate each other. A poison producing strain can kill a sensitive one which, however, grows quicker than a third, resistant strain, which in turn reproduces faster than the poisonous one. (c) Theoretically computed spiral pattern formation of three species in cyclic competition.

What happens when bacteria can migrate on the Petri dish? Which influence does bacteria's mobility have on pattern formation and species diversity? In our work we have investigated these questions employing a theoretical model. By a combination of numerical computer simulations and mathematical descriptions we could identify a critical threshold of mobility. Below the threshold, i.e., when bacteria's mobility is not too high, spiral patterns form, in which the three strains "chase" each other in a cyclic manner. Above the threshold patterns can no longer form. The diversity is lost, and solely one strain survives. Interestingly, it is the one that, in a certain sense, is "weakest".

Our work has shown that mobility can destroy species diversity, and quantified this phenomenon. In collaboration with the Chair of Biological Physics at the LMU M√ľnchen we are currently devising experiments with bacteria to validate these theoretical results. Therefrom, we expect novel insights into ecological pattern formation and species diversity.

Tobias Reichenbach
Education

Since 2008
Postdoctoral Research at Rockefeller University, New York

2005 - 2008
Doctoral Thesis,
Supervisor: Prof. Erwin Frey, LMU

1999 - 2004
Diploma in Physics, Leipzig Universität

Selected Publications

T. Reichenbach, T. Franosch, E. Frey (2006): "Exclusion Processes with Internal States", Phys. Rev. Lett. 97, 050603

T. Reichenbach, M. Mobilia, E. Frey (2007): "Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games", Nature 448, 1046-1049

T. Reichenbach, E. Frey (2008): "Instability of Spatial Patterns and Its Ambiguous Impact on Species Diversity", Phys. Rev. Lett. 101, 058102