Cyclical Competition Of Three Species Favors Weakest As Victor

So maybe our definition of "weak" and "strong" is the problem. Eg., individual tigers are "stronger" than individual lions, but a group of lions will kill off a group of tigers, because the lions work together, while tigers are loners.

http://www.sciencedaily.com/releases/2009/02/090213115127.htm

ScienceDaily (Feb. 24, 2009) — The extinction of species is a consequence of their inability to adapt to new environmental conditions, and also of their competition with other species. Besides selection and the appearance of new species, the possibility of adaptation is also one of the driving forces behind evolution. According to the interpretation that has been familiar since Darwin, these processes increase the “fitness” of the species overall, since, of two competing species, only the fittest would survive.

I would say "adaptation" is the consequence of "selection".

LMU researchers have now simulated the progression of a cyclic competition of three species. It means that each participant is superior to one other species, but will be beaten by a third interaction partner. “In this kind of cyclical concurrence, the weakest species proves the winner almost without exception,” reports Professor Erwin Frey, who headed the study. “The two stronger species, on the other hand, die out, as experiments with bacteria have already shown.
...
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.
...
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.
...
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.”