Biology Reference
In-Depth Information
(2) Cooperation is Relatively Cheap (m
c
= 10)
Qualitatively the same trends are apparent when cooperation is less costly (Figure
1, right column). Cooperation is maintained over a broader range of diffusion rates,
compared to the case of costly cooperation. Clearly, with less costly cooperation, oc-
casional futile cooperation attempts (when the number of cooperators in a neighbor-
hood is less than the quorum) are less deleterious. With increasing quorum threshold
the scope for parasitism by non-cooperators becomes smaller and as a consequence a
larger fraction of the population will consist of cooperators, as long as neighborhoods
sufficiently often contain at least a quorum of cooperators. Above a certain level of
population mixing this is no longer the case, and then cooperation does not evolve.
The Evolution of Cooperation and Quorum Sensing
In the next series of simulations we allow cooperation and QS to evolve simultaneous-
ly, and allowing mutations at all three loci from inactive to functional and vice versa
with probability μ = 10
−4
. Figure 2 shows as an example the evolution of the genotype
and allele frequencies in a run of the simulation model with a high cost of cooperation
and a relatively cheap QS system (m
C
= 30.0, m
S
= 3.0, m
R
= 1.0), medium quorum
threshold (n
e
= 3), high cooperation reward (r = 0.9), and no diffusion (D = 0.0).
Figure 2.
Details of a single QS-enabled simulation.
Parameters as in Figure 1, except for μ
s
= μ
r
= 10
−
4
; m
c
= 30.0, n
e
= 3, and D = 0.0. Time evolution of A.: genotype frequencies; B.: genotype
distribution; C.: allele frequencies. D.: The spatial pattern of genotypes at T = 10.000.
The fi rst invading genotype is the “Blunt” one (Csr) which cooperates uncondi-
tionally but lacks QS. However, as soon as the “Blunt” type reaches a high frequency
