Statistical and Biological Physics

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The Law of the Weakest

Maximilian Berr, Tobias Reichenbach, Martin Schottenloher and Erwin Frey

haende_web Up to 50 species extinct each day on earth. While this large number is supposedly due to human influence, a certain rate of species extinction is unavoidable. It reflects competition of different species as well as their (missing) ability to adapt to changing environments. Together with speciation (meaning the formation of new species) and selection it allows for evolutionary change. In the common understanding of Darwinian evolution, this change tends to increase fitness, as of two competing species the "stronger" one survives.

Here, we investigate what happens when three species display a form of cyclic competition ("rock-paper-scissors game"). We show an unexpected "law of the weakest": Not the fittest, but the weakest species survives, with the other two condemned to extinction. This behavior is intrinsically linked to the stochastic nature of ecological systems, where chance has an important role. Despite its stochastic origin, however, the "law of the weakest" is (for many interacting individuals) strict: Even if the differences between the three species are small, the weakest one survives for sure. These results may prove important for our understanding of ecosystems' evolution and designing of conservation strategies.