Biology Reference
In-Depth Information
The n
q
= 4, 5, and 6 cases are similar to the n
q
= 3 case, except for two important
aspects. One is that, due to the high quorum threshold, the system becomes more
sensitive to spatial mixing. For n
q
= 4, the upper limit of the diffusion parameter that
still allows the cooperation and QS alleles to persist is D = 0.5; for n
q
= 5 it is D =
0.2, and for n
q
= 6 cooperation is only maintained in the absence of spatial mixing (D
= 0). Above these D values, successfully cooperating clumps (neighborhoods with n
q
or more cooperators) are disintegrated by too intensive mixing, at a rate faster than
they are built by interactions. Second, at zero diffusion (D = 0.0), for n
q
= 4, 5, and
6, cooperators increase in abundance and they tend to lose one or both components
of the QS system, unlike in the n
q
= 3 simulation. The reason for the loss of the
communication device is that cooperators become so common, that QS is no longer
needed to fi nd out whether there is a suffi cient number of cooperators present in
the immediate neighborhood. Constitutively cooperating genotypes like “Blunt” and
“Vain” increase in frequency because they do not pay the (complete) cost of QS. At
n
q
= 4 the “Honest” type is maintained at about 30%, because QS is still suffi ciently
often useful, with almost 30% of the population consisting of non-cooperators. Here
most of the non-cooperating strains are of the “Liar” type: in neighborhoods with
fewer than n
q
= 4 “Honest” individuals, their signaling helps to persuade the latter
to cooperate. At n
q
= 5 and n
q
= 6 with zero diffusion, the simulations bring an inter-
esting strategic aspect of QS to the light. Although almost 100% of the population
is cooperating, the fully QS “Honest” type is maintained at some 30-50% of the
population. This is at fi rst sight surprising, since the presence in local neighborhoods
of a quorum of cooperators is practically guaranteed. However, here QS appears
to function as a mechanism to avoid expression of the cooperative behavior when
already a suffi cient number of unconditionally cooperating (“Blunt”) neighbors are
producing the public good. Clearly, when less then n
q
cells in a neighborhood are
producing the quorum signal molecule, “Honest” types will not cooperate, thus sav-
ing the cost of cooperation while frequently enjoying the cooperation benefi t thanks
to their unconditionally cooperating neighbors. This explains the fairly high fre-
quency of signaling unconditional cooperators (“Vains”). By enhancing the local
concentration of the quorum signal they induce “Honest” cells to cooperate, thereby
enhancing the likelihood that a quorum of cooperators is reached. Actually, in situ-
ations where cooperation is so attractive that the C allele is (almost) fi xed, the three
cooperating types: “Honest”, “Blunt,” and “Vain” display a cyclic interaction pattern
(Blunt>Vain>Honest>Blunt) reminiscent of the RSP game [20, 21]. A population of
“Blunt” is invaded by “Honest” because as explained above“Honest” parasitizes on
the unconditional cooperation by the “Blunts”. Conversely, an “Honest” population
is invaded by “Blunt” and by “Vain”, because they do not pay (part of) the costs of
the QS machinery, and “Vain” invades a polymorphic (“Honest”, “Blunt”) popula-
tion, enhancing the likelihood of a quorum of actual cooperators by inducing “Hon-
est” cells. Figure 4 shows the evolutionary dynamics of such a population with the
cooperating C allele fi xed.
