The mathematics of microbial cooperation
Production of certain enzymes by individual cells can suffice to confer antibiotic resistance on an entire bacterial colony. The colony as a whole continues to grow rapidly in the presence of the antibiotic, but the public-spirited benefactors – the producer cells -- will grow more slowly than their non-cooperative neighbors. “If the cooperators die out, the whole population suffers,” says Anna Melbinger, one of the authors of the study. “However, the evolutionary advantage gained by the colony can outweigh the disadvantage suffered by cooperator cells.”
The detailed mechanisms that allow such a situation to emerge have so far remained obscure. Frey’s group has developed a mathematical model to simulate bacterial population dynamics under various conditions. Beginning with a collection of independently evolving colonies whose growth rates depend on the fraction of cooperators they contain, the researchers observed the fate of cooperators as populations go through repeated cycles of merging and random fragmentation.
Analysis of this model revealed two different mechanisms that facilitate the establishment of cooperation in bacterial populations. On the one hand, fragmentation can by chance produce colonies in which cooperators are not effectively exploited by non-cooperating cheaters. “If the proportion of cooperators becomes large enough, the non-cooperating bacteria can even be driven to extinction,” says Jonas Cremer.
In the second scenario colonies that include cooperators grow more rapidly than others that have fewer “public-spirited” members, even when the initial number of cooperators is low. Here, it turns out that a single spontaneous mutation that confers a socially useful trait may be sufficient to establish a whole population of cooperators.
The overall conclusion that emerges from the study is that cooperative behavior can become stably established in populations when colonies are repeatedly forced to split and evolve in isolation. “As we have now demonstrated mathematically, individual microbial cells that acquire a cooperative trait as the result of random genetic alterations actually have a chance of establishing cooperative behavior in whole populations,” says Frey. (CR/suwe)
Growth dynamics and the evolution of cooperation in microbial populations
Jonas Cremer, Anna Melbinger & Erwin Frey,
Scientific Reports online, 2, 281 (21. February 2012)
Prof. Dr. Erwin Frey
Institute for Statistical and Biological Physics, LMU
Phone: +49 89 2180 4538