Mortal Enemies Form Powerful Alliances

Mortal enemies form powerful alliances, discovered György Szabó (Research Institute for Technical Physics and Materials Science, Budapest, szabo@mfa.kfki.hu, 36-1275-4991) and Tamás Czárán (Hungarian Academy of Sciences) in a simulation of biochemical war among nine competing bacterial strains.

The study was inspired by recent discoveries of bacteria that excrete toxins affective against their microbial cousins. The researchers began by hypothesizing that there exist three types of related bacteria: toxin producing Killers (K); Resistants (R) carrying genetic factors that protect them from a given toxin; and Sensitives (S) that neither produce toxins nor carry resistance factors. A population of S-type bacteria are clearly at the mercy of K, but K-type can be overrun by R which do not expend precious resources creating toxins. S-type can in turn out-compete the R bacteria because they do not shoulder the burden of producing toxins or resistance factors. This is a biological version of the "rock-paper-scissors" game well known in various natural populations.

The researchers were surprised by the consequences when they complicated things by imagining that bacteria could produce two distinct toxins and could carry their corresponding resistance factors. The hypothesis leads to nine types of related bacteria with various combinations of K, R, and S characteristics (KK, KR, KS, RS, RR, etc.). Under some circumstances, trios of the very worst enemies form alliances that eliminate any of the other six species they encounter, essentially as a side effect of their vicious rock-paper-scissors game.

For example, the alliance KK-RR-SS, is one of three stable combinations in which each strain entirely dominates one ally and is entirely dominated by the other. While an invading RS species could out-compete the RR strain, it is susceptible to attack by the KK strain and is overrun by the SS strain. Similar troubles threaten any other invading strain, and it is this multi-level attack that protects the alliance from all other bacteria.

The researchers were also startled to find that varying the rate of bacterial mutation in their model could dramatically affect the balance of power on a bacterial battleground. At low mutation rates, one of the three stable alliances will eventually wipe out all non-alliance bacteria, with each alliance equally likely to win the day.

Above a certain critical mutation rate, bacteria change identities frequently enough (e.g. KK turns into KR) that alliances break down, and all nine strains are present in equal proportions. Changing the mutation rate, therefore, can lead to a phase change as the system jumps from a soup of all nine bacteria to a stable, cyclic alliance of mortal enemies.

The complexity of even this simple system suggests that population dynamics in nature is much richer than predicted by previous models based on equations initially developed to study simple systems of predators and their prey. (G. Szabó and T. Czárán, Physical Review E, June 2001; text at Physics News Select.)