The Law of the Weakest
Not only the fittest will prevail
Ecosystems are composed of a large number of different species, which interact and compete with one another for scarce resources. This competition between species in turn affects the probability with which the individual can reproduce and survive – a matter of life and death, as it were. All of these processes are also largely probabilistic and lead to fluctuations that ultimately lead to the extinction of species. We know that up to 50 species become extinct every day on Earth, which at this high rate can be attributed to the influence of man.
Yet, the phenomenon of extinction of species itself cannot be avoided altogether – and is still only barely understood. Theoretical ecologists and biophysicists are therefore intensively researching conditions and mechanisms that affect the biodiversity of Earth. Cyclic dominance is a particularly interesting constellation of species competing with each other. It means that each participant is superior to one other interaction partner, but will be beaten by a third. In ecosystems, this would be three subpopulations – in the simplified model – which dominate in turn. In fact, communities of subpopulations following such rules have been identiﬁed in numerous ecosystems, ranging from coral reef invertebrates to lizards in the inner Coast Range of California.
Such cyclical interaction is also familiarly termed “rock-paper-scissors” interaction. This is where the rock blunts the scissors, which cut the paper, which in turn wraps around the rock. Together, these non-hierarchical relationships form a cyclical motion. “The game can help describe the diversity of species,” explains Frey. “The background is a branch of mathematics called game theory, and in this case evolutionary game theory. It helps analyze systems that involve multiple actors whose interactions are similar to those in parlor games.”
Using game theory, one can also study the collective development of populations. In their study, the scientists working with Frey developed elaborate computer simulations in order to calculate the probabilities with which species in cyclical competition will survive. The games started off with three species coexisting in the systems, and ran until two species became extinct – with the third being the only remaining survivors. “What we saw was that in large populations, the weakest species would – with very high probability – come out as the victor,” says Frey.
This “law of the weakest” even held true when the difference between the competing species was slight. “This result was just as unexpected for us,” reports Frey. “But it shows once more that chance plays a big part in the dynamics of an ecosystem. Incidentally, in experiments that were conducted a couple of years ago on bacterial colonies, in order to study cyclical competition, there was one clear result: The weakest of the three species emerged victorious from the competition.”
The project was supported by the cluster of excellence “Nanoinitiative Munich (NIM)”, of which Professor Erwin Frey is a principal investigator. (suwe)
“Zero-one survival behavior of cyclically competing species”,
Maximilian Berr, Tobias Reichenbach, Martin Schottenloher, and Erwin Frey,
Physical Review Letters, 13 February 2009
Professor Dr. Erwin Frey
Arnold Sommerfeld Center for Theoretical Physics, LMU Munich
Tel.: ++49 (0) 89 / 2180 – 4537
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