Biology Reference
In-Depth Information
alleles (C, S, and R) approached their quasi-stationary values. This could be achieved
within 10,000 generations in most cases. The first few simulations have been repeated
three times with each parameter setting, using different random number arrays, but
since variation in the results was very small at a lattice size of 300 × 300 in all cases,
and each run took a long time to finish, we stopped producing replicate runs.
During the simulations we record and plot the time series of the eight different
genotype frequencies, from which the frequencies of the three functional alleles can
be calculated and plotted against time.
Evaluation of the Model Outputs
The simulation results are recorded as 10.000-generation time series of genotype fre-
quencies and spatial patterns of the genotypes. With regard to allele frequencies we
asked the following question: are the genes for cooperation (C) and QS (S and R) se-
lected for beyond their respective mutation-selection equilibria based on the metabolic
selection coefficients s C = (M C −M 0 )/M C , s S = (M S −M 0 )/M S and s R = (M R −M 0 )/M R, and
the (uniform) mutation rate μ. For example, relative frequencies of the cooperating al-
lele above its mutation-selection equilibrium q C
) indicate a net fitness
benefit of cooperation and thus positive selection for the C allele. q S and q R can be
calculated the same way.
= μ
/( s C
+ μ
DISCUSSION
Microorganisms display a wide range of social behaviors, such as swarming motil-
ity, virulence, biofilm formation, foraging, and “chemical warfare” [7-10, 21]. These
social behaviors involve cooperation and communication. Cooperation often takes the
form of a coordinated production and excretion of molecules like enzymes, toxins, and
virulence factors. In bacteria, this cooperative behavior is typically regulated by QS, a
chemical communication system in which cells produce diffusible molecules and can
assess the cell density by sensing the local concentration of these signaling molecules
[11, 12, 22, 23]. In fact, QS can be viewed itself as a cooperative behavior to optimize
other forms of social behavior. An important issue is the evolutionary stability of co-
operation because of its potential vulnerability to social cheating: the occurrence and
selection of individuals who gain the benefit of cooperation without paying their share
of the costs [2, 10]. We studied the evolution of cooperative behavior in bacteria (e.g.,
production of a public good) and of a QS system which coordinates this cooperative
behavior, using CA modeling. This approach allows a fairly precise evaluation of the
role played by the spatial population structure, because all bacterial interactions are
supposed to occur between neighboring cells.
Our results allow three main conclusions, which we discuss in turn.
1. Cooperation Only Evolves Under Conditions of Limited Dispersal
The simulations in which we analyzed the evolution of cooperation without QS sug-
gest that cooperation can only evolve when the degree of spatial mixing in the popula-
tion is low, which implies a high relatedness between neighboring cells. Our model
 
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