Biology Reference
In-Depth Information
Figure 4.
The evolution of QS in a population with the cooperating C allele fixed
.
Parameters as in
Figure 3, with n
e
= 6 and D = 0.2. The simulation was started from the “All-Blunt” initial state.
(2) Cooperation is Relatively Cheap (m
C
= 10.0).
The right column in Figure 3 shows the simulation results for less costly cooperation.
Just as in the case of costly cooperation, QS alleles are selected in a large part of the
parameter space and boost the frequency of cooperators in the population (compare
with Figure 1, right column). In particular, QS enables the maintenance of cooperative
behavior at higher levels of population mixing. At low quorum thresholds (n
q
= 2 and
n
q
= 3) and a low rate of diffusion, the QS machinery is too expensive because suf-
ficiently often neighborhoods will contain a quorum of unconditional cooperators, and
the QS alleles are not selected. When the rate of spatial mixing increases, the predict-
ability of the local population composition goes down, and QS becomes profitable. At
higher quorum thresholds (n
q
≥ 4), we see again that if the population (almost) exclu-
sively consists of (potential) cooperators, QS is selected because its machinery allows
cells to avoid cooperating when the number of unconditionally cooperating neighbors
is already equal to or higher than the quorum. The resulting cooperating population
consists of a dynamical coexistence of fully QS (“Honest”) genotypes, uncondition-
ally cooperators (“Blunt” types), and signaling unconditionally cooperators (“Vains”).
The Effect of Decreasing the Reward of Cooperation
At a lower cooperation reward of r = 0.5 neither cooperation nor QS evolves: the pop-
ulation becomes almost completely uniform “Ignorant” within the entire parameter
space. This result is somewhat surprising, given that at r = 0.5, successful QS coopera-
tors like the “Honest” genotype should still enjoy a substantial fitness advantage com-
pared to the “Ignorant.” The total metabolic burden of an “Honest” individual after
getting the cooperation reward is 133.0 * 0.5 = 66.5, whereas the “Ignorant” carries a
burden of 100.0 units, that is the cooperator should have a fitness advantage of about
34% over the parasite. It cannot use it to the full, however, because nearby parasites
may take the advantage as well without paying the costs, and those parasites which are
successful in doing so carry an even lower (50.0 units) metabolic burden. Apparently a
minimum threshold measure of fitness reward is necessary for cooperation to become
an option. With the quorum threshold fixed at n
q
= 3 and diffusion at D = 0.0, we
looked for the critical value of the fitness reward by increasing r from 0.5 to 0.9, and
found it to be rc = 0.8. This means that the kind of exploitable, broadcasted cooperation,
