Social conflict drives the evolutionary divergence ofquorum sensingAvigdor Eldar1

Department of Molecular Microbiology and Biotechnology, Faculty of Life Sciences, Tel Aviv University, Tel Aviv 69978, Israel

Edited by Raghavendra Gadagkar, Indian Institute of Science, Bangalore, India, and approved June 22, 2011 (received for review March 16, 2011)

In microbial “quorum sensing” (QS) communication systems,microbes produce and respond to a signaling molecule, enablinga cooperative response at high cell densities. Many species of bac-teria show fast, intraspecific, evolutionary divergence of their QSpathway specificity—signaling molecules activate cognate recep-tors in the same strain but fail to activate, and sometimes inhibit,those of other strains. Despite many molecular studies, it hasremained unclear how a signaling molecule and receptor can co-evolve, what maintains diversity, and what drives the evolutionof cross-inhibition. Here I use mathematical analysis to show thatwhenQS controls the productionof extracellular enzymes—“publicgoods”—diversification can readilyevolve.Coevolution ispositivelyselected by cycles of alternating “cheating” receptormutations and“cheating immunity” signaling mutations. The maintenance of di-versity and the evolution of cross-inhibition between strains arefacilitated by facultative cheating between the competing strains.My results suggest a role for complex social strategies in the long-term evolution of QS systems. More generally, my model of QS di-vergence suggests a form of kin recognition where different kintypes coexist in unstructured populations.

bacterial communication | diversifying selection | microbiology |sociobiology

Cooperative behavior in bacteria is guided in many cases byquorum sensing (QS) signaling where a response is produced

only once a secreted signal’s level is sufficient to activate its cog-nate receptor (1). Multiple bacterial species show intraspecificdivergence of their QS systems, where signals from one strain canactivate their own receptor but fail to activate and sometimes in-hibit a receptor from a different strain (2–7). This divergenceseems to be under strong selection, as implied by the functionaldivergence and is also corroborated by rapid sequence divergence(8–9), the signatures of diversifying selection (10–11), and thespread of divergent QS systems through horizontal gene transfer(3, 12). These observations provoke two related questions: Howdoes this divergence evolve in the first place, and what are theselective advantages that maintain it? Moreover, in some of thesystems, a signaling molecule from one strain inhibits a divergedreceptor from receiving its own signal (2, 7, 12). It is unclearwhether the same evolutionary forces that drive divergence candrive the evolution of cross-inhibition.The cross-inhibition between diverging strains in some of these

species and the ecological coexistence of divergent strains inothers (13) imply a possible intraspecific social role for this di-vergence. Therefore, to understand QS diversification, one has toconsider it in a social context. It has been shown in numerousspecies that QS controls the production of secreted substances(e.g., exoproteases, surfactants, and antibiotics; seeSIText, section1 for further discussion). From a social perspective these can becharacterized as “public goods”—costly actions to the individualthat benefit the whole population (SI Text, section 1). As such, QSwas shown both theoretically (14–16) and experimentally (17–20)to be susceptible to invasion by QS mutants that act as “cheaters”and exploit the public goods produced by a functioning QS strain.Such cheating can be repressed by mechanisms that increase re-latedness and lead to preferential assortment of cooperators and

cheaters through structured populations (21–24). Recent experi-mental work in fruiting body and biofilm formation has sug-gested that cheating can also be evolutionarily counteracted bymechanism-specific strategies (25–34). Nevertheless, there is littlemechanistic understanding of these types of interactions and theirlong-term evolutionary impact remains unclear.

ModelI sought to understand whether social evolution can explain thedivergence of quorum sensing systems. To this end, I constructeda general model of a quorum sensing system guiding public goodsproduction (Fig. 1A and SI Text, sections 2 and 3 for mathematicaldetails). I assumed that a QS system is composed of three genesencoding a signaling molecule (or the synthase producing it)denoted as S, a receptor (denoted asR), and a public good productwhose expression is regulated by the signal–receptor complex. Iassume that the public good is a secreted enzyme whose product isa usable nutrient (generalizations to other public goods are dis-cussed in SI Text, section 1). I assume that the growth rate of thebacteria is dependent on the usable nutrient and that enzymeproduction carries a cost that reduces the growth rate. In addition Iassume a density-dependent cell death that leads to a logistic formof growth equation. In such a model, enzyme production by thewild type benefits a nonproducingmutant strain. Themutant straindoes not pay the production cost and therefore has a higher growthrate than the wild type and will act as a cheater. As expected fromthis model, a strain with no QS system can cheat the wild type (SIText, section 2).To understand the evolution of divergent specificities in QS

pathways, I extended the model to include two divergent allelesof receptor (R1, R2) and signal (S1, S2). I assume that a singlemutation allows the transition between the two alleles of a givengene. I also assume that R1 interacts only with S1 and R2 onlywith S2 (Fig. 1B; this assumption can be relaxed, see below). Istart with a population composed of bacteria expressing the S1signal and the R1 receptor and examine the evolution of a pop-ulation of diverged individuals expressing the R2–S2 pair.Cooperation through public goods can be maintained only in

a structured population, where the population is divided intomultiple subpopulations with higher relatedness than total pop-ulation average (21, 24) (e.g., bacterial growth on surface is morestructured than in liquid). I therefore analyzed the competitionbetween various strains in a population evolving through bot-tlenecks—a simple type of structured population that has beenexperimentally demonstrated to maintain cooperation (17, 21,22, 35). I assume multiple subpopulations (demes) where in eachround N lineages seed each subpopulation and then grow to-gether for a given time. After the growth phase, bacteria are

Author contributions: A.E. designed research, performed research, contributed newreagents/analytic tools, analyzed data, and wrote the paper.

The author declares no conflict of interest.

This article is a PNAS Direct Submission.1E-mail: avigdore@tau.ac.il.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1102923108/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1102923108 PNAS | August 16, 2011 | vol. 108 | no. 33 | 13635–13640

EVOLU

TION

resampled, either from the same subpopulation (local competi-tion) or from the whole population (global competition), to seedthe next growth cycle of new subpopulations. The asymptoticdistribution of the various genotypes involved in the competitioncan be either simulated or analytically derived (see SI Text,section 6 for mathematical analysis).

ResultsTwo problems confine the selection of the divergent QS systemR2S2. First, the receptor and signal alleles have to evolve se-quentially, so their coevolution has to occur through an in-termediate strain with a mutation in either the receptor (R2S1) orthe signal (R1S2), but not both (Fig. 2A). These two intermediatestrains will have a nonfunctional QS system. Second, onceformed, the divergent QS strain (R2S2) has to compete with themore prevalent original strain (R1S1).The relative fitness of amutant in a social trait such as QS has to

be judged by its interaction with its parental strain. I thereforesimulated the invasion of all possible mutations of receptor andsignaling molecule during coevolution into their respective pa-rental strain. The results are striking: Divergence is positively se-lected through a nonfunctional intermediate. This process occursthrough the evolutionary trajectory where the receptor mutatesfirst and then the signaling molecule coevolves (Fig. 2).

Divergence Is Positively Selected by Rounds of Cheating andImmunity to Cheating. To understand why the pathway in whichthe receptor mutates first and the signaling molecule follows isselected I first analyzed the two steps of this process in an un-structured, well-mixed, environment (Fig. 2 B–D). The receptor-mutated intermediate strain (R2S1) is insensitive to neither its ownsignal nor its parental strain’s (R1S1) signal (Fig. 2B, Upper) andwill therefore invade into its parental strain by cheating (Fig. 2C,solid black line). Furthermore, the signal produced by the in-termediate strain (R2S1) induces the quorum response of the pa-rental cooperator strain, which may lead to increased exploitation

(SI Text, section 4). Like other obligate cheaters in well-mixedenvironments, R2S1 rise in frequency will eventually lead toa population collapse (Fig. 2D, solid black line). Its success istherefore transient, but provides a window of opportunity for theoccurrence of a second mutation that will restore the QS system.Restoration of QS cooperativity to strain R2S1 can occur by

either reversion of the receptor to the original QS system, R1S1(Fig. 2A, step 3), or divergence of the signal to the novel QSsystem, R2S2 (Fig. 2A, step 2). Reversion is unfavorable, how-ever, because the revertant strain remains sensitive to cheatingby strain R2S1 and will therefore decrease in frequency whenmixed with it (Fig. 2 C and D, gray dashed lines). In a sharpcontrast, the novel cooperator (R2S2) retains its initial frequencywhen mixed with strain R2S1 (Fig. 2C, solid gray line). The novelcooperator is therefore immune to the cheating of R2S1. Im-munity arises because the signal of strain R2S2 induces thequorum response of itself and of its ancestor R2S1, as both havethe novel receptor R2 (Fig. 2B, Lower). Therefore, both strainswill produce the enzyme to the same extent, sharing both itsbenefit and production cost. As the signal of the “immune” co-operator (R2S2) leads to public goods production by both strains,the total cell density of the mixed population increases mono-tonically with the frequency of R2S2 in the population (Fig. 2D,solid gray line and SI Text, section 5).I reasoned that due to its immunity to cheating and its global

benefit to the population, the diverged QS strain (R2S2) wouldperform better than the original QS strain (R1S1) when eachstrain competes with the intermediate strain R2S1 in a structuredpopulation (18–20). I analyzed the two competitions in thebottlenecked growth model for various bottleneck sizes (Fig. 2Eand SI Text, section 6). I find that the frequency of the originalcooperator (R1S1) diminishes with increasing bottleneck size. Insharp contrast, the immune cooperator (R2S2) frequency is in-dependent of bottleneck size and under conditions of globalcompetition will asymptotically outcompete the cheater inter-mediate strain for any bottleneck size.Immunity to cheating also explains why the evolutionary

pathway where the signaling molecule changes first (“lame” in-termediate) is not selected. The original quorum sensing strain,R1S1 is immune to the cheating of the mutant R1S2 in the sameway R2S2 is immune to R2S1. Therefore, R1S2 is nonbeneficial ina well-mixed population and counterselected in a structuredpopulation by R1S1.

Facultative Cheating Underlies the Maintenance of Divergence andthe Evolution of Cross-Inhibition. My model suggests that di-versification of QS systems can occur by sequential evolution ofan obligate cheater and immune cooperator. The long-termmaintenance of diversity also depends on the interaction be-tween the novel cooperator R2S2 and the still-prevalent originalQS system, R1S1. I find that both R2S2 and R1S1 can invadea territory dominated by the other strain to reach an equalabundance (Fig. 3A). This dynamic can be understood as follows:At low initial cell densities, before any quorum response is ac-tivated, the strains are equivalent and grow at the same rate (Fig.3A, gray area). Once the predominant strain (R1S1 in Fig. 3A)reaches a high density, it will activate its quorum response andproduce the public goods. The invading strain’s density is still lowand because it is insensitive to the signal of the dominant strain,it will not participate in public goods production and thereforeincreases its relative frequency (Fig. 3A, pink area). Finally,when the cell density of the invading strain becomes high enoughto activate its own quorum response, it will participate in enzymeproduction (Fig. 3A, green area). The invading strain thereforeperforms a facultative cheating strategy (36), exploiting the in-vaded strain at low frequencies and cooperating in public goodsproduction at high frequencies. This strategy leads to a negative

Public goods

QS ReceptorR1

Complex nutrient

Usable nutrient

QS SignalS1

Growth

Co

st

Benefit

A B

R1

R2

S1

S2

Fig. 1. A model for the divergence of QS systems. (A) I assume QS to controlthe production of public goods. A signalingmolecule is secreted out of the celland accumulates in the environment. A cellular receptor is activated by thesignaling molecule at high cell densities and leads to the production of publicgoods: anexo-enzyme thatmetabolizes a complexnutrient intoausable form.Enzyme production carries a growth cost to the producing cell, but usablenutrient brings benefit to the whole community. SeeMaterials and Methodsand SI Text, section 2 for further discussion and model equations. (B) Forsimplicity, I assume that both receptor and signal have two alleleswith specificand orthogonal interaction (i.e., each receptor is completely specific to itscognate signal) and that a single mutation allows transition between corre-sponding alleles. In SI Text, section 7 I show how diversification can evolve inthe presence of null alleles of receptor, signal, and public goods enzyme or ifreceptor and signal alleles are not fully orthogonal.

13636 | www.pnas.org/cgi/doi/10.1073/pnas.1102923108 Eldar

frequency-dependent selection and coexistence of both cooper-ators with a high steady-state yield of public goods.Many of the diverging QS systems display patterns of cross-

inhibition of a receptor by a noncognate signal (2, 7, 10) (Fig.3B). The evolution of cross-inhibition can be explained by mymodel as an eavesdropping strategy of the inhibited strain thatis used for cheating the inhibiting strain. In the presence of thecompeting inhibiting strain, the inhibited strain will contributeless to public goods production than either its ancestral (non-inhibited) strain or the inhibiting strain and will therefore invadeinto the population (Fig. 3 B and C). This facultative cheatingstrategy cannot be eliminated by structured population modelsthat eliminate obligate cheaters (Fig. 3E and SI Text, section 8),as all of the strains perform equally when alone. Cross-inhibitioncan easily evolve into mutual cross-inhibition of the QS pathways.This evolutionary path may eventually lead to complete mutualexclusion between strains and, under a low level of recom-bination, to speciation, as was proposed for Staphylococci (37).

Divergence of QS Can Occur Under More Complex Scenarios. I have sofar neglected the effects of other types of cheaters on the evolu-tionary divergence of QS. In fact, I expect most mutations inreceptor or signaling genes to yield effective null mutations. Thereceptor null mutants (and also the public goods enzyme null

mutant) will act as obligate cheaters in public goods production.The signal null mutant will act as a cheater by saving the cost ofsignal production (which is most likely smaller than that of publicgoods production) (17, 19, 20). To examine the effect of suchmutants on the evolution of a novel receptor–signal pair, I simu-lated the effect of these null mutants on the evolution of the novelreceptor (SI Text, section 7). I find that both types of mutants re-duce the total level of public goods in the population, but do notprevent the positive selection of a divergent pair. I emphasize thatthe cost of signaling is not directly affecting the evolutionarypathway leading to QS divergence, as all strains on this pathwayproduce a signal (either S1 or S2) and therefore pay the cost ofsignaling. Only the relevance of the signal changes under varioussocial contexts.The situation where a single mutation in the receptor and

signaling genes will lead to complete orthogonality (full in-teraction with the mutated partner and no interaction with thenonmutated partner) is an extreme case. I find that divergencecan occur by smaller mutational steps where the receptor mu-tation reduces its affinity to the original signal (but does noteliminate it) and the novel signal mutant increases the signal’saffinity to the mutated receptor. Such small steps still lead to

B

Benefit

Cost Intra-strain

Inter-strain

signaling

Public goods

R1S

1

Public goods

R2S

1

R2S

2R

2S

1

1

2

3

R1S1 vs R2S1 LocalR2S2 vs R2S1 LocalR1S1 vs R2S1 GlobalR2S2 vs R2S1 Global

Bottleneck size

Co

op

era

to

r f

re

qu

en

cy

Original ‘Naïve’ QS

12

3

Novel ‘Immune’ QS

E

To

ta

l c

ell d

en

sity

Time (AU)

C

In

va

de

r f

re

qu

en

cy

R2S1 invasion into R1S1

R2S2 invasion into R2S1

R1S1 invasion into R2S1

1

2

3

X Y Y invades XX YY does not

invade X

A

D

R1S1

R1S2

R2S1

R2S2

‘Cheater’Intermediate

‘Lame’Intermediate

Fig. 2. Coevolution of receptor and signaling molecule during divergence is positively selected. (A) The original QS system R1S1 (‘Naive’) can evolve into thenovel QS system R2S2 (‘Immune’) through one of two intermediates. I find that the evolutionary trajectory through the receptor-modified intermediate (R2S1,‘cheater’) is positively selected at both steps but the one through the signal-modified intermediate (R1S2, ‘lame’) is not (SI Text, section 5). (B) Scheme ofcontribution to public goods and communication during the two evolutionary steps (compare circled numbers to those in A). Shown are the two competingstrains, the signaling relations between them, and the contribution to public goods production (red) and benefit (green). (Upper) Competition between theoriginal QS system (R1S1) and the intermediate cheater strain (R2S1). Only R1S1 produces public goods. (Lower) Competition between the intermediate cheaterstrain (R2S1) and the novel QS system (R2S2). R2S2 signal induces public goods production by both itself and the intermediate strain R2S1 and is thereforeimmune to cheating by R2S1. (C and D) Results of invasion simulations of R2S1 into R1S1 (black line), R2S2 into R2S1 (gray solid line), and R1S1 into R2S1 (graydashed line) in well-mixed conditions. Invading strain initial frequency is 2%. (C) Frequency of invading strain as a function of time. (D) Total cell density asa function of time. I note that the immune cooperator (R2S2) frequency remains constant but the production of public goods leads to a higher total celldensity compared with a pure cheater (R2S1) population. Inset in D is as in C. (E) The immune cooperator outcompetes its ancestor in a structured population.Shown are the asymptotic frequencies as a function of bottleneck size of naive (R1S1, orange) and diverged immune (R2S2, cyan) QS strains when separatelycompeted with the intermediate cheater strain (R2S1). Each pair of strains undergoes cycles of growth and population bottlenecks, as explained in Materialsand Methods and SI Text, section 6. Whereas the naive cooperator frequency is quickly reduced when bottleneck size increases, the immune cooperator’s levelremains maximal for any bottleneck size.

Eldar PNAS | August 16, 2011 | vol. 108 | no. 33 | 13637

EVOLU

TION

cheating and immunity (SI Text, section 7) and are most likelymore realistic than large mutational jumps (8).Finally, a secreted substance can lead to a higher benefit to the

secreting cell than to a nonsecreting, cheater, cell. This relationcan lead to a snowdrift type of social interaction, where cheatersinvade to coexistence with the cooperators but do not eliminatethem. Such a scenario was recently demonstrated for the deg-radation of sucrose by the yeast’s invertase (38). In SI Text,section 7 I demonstrate that QS diversification can also occur ifthe QS-regulated enzyme leads to snowdrift dynamics.

DiscussionQS Evolution as an Intraspecific Diversification Mechanism. Treatedat the level of the single genotype, the fitness landscape of di-vergent QS is that of equally fit peaks separated by unfit valleys,where at least two mutations are needed to shift from one peakto the other. Here I demonstrated how social interaction canturn this rugged landscape into an “evolutionary ratchet” processthat strongly selects for divergence without any form of an armsrace with other species or strains—the usual mechanism invokedto explain diversification. In contrast to the common view ofcheating (36), here a cheater is a necessary evolutionary in-termediate in the evolution of social interactions.

QS Diversity Is a Unique Form of Kin Recognition. The mode of ac-tion of the divergent QS systems in bacteria bears resemblance tothe phenomenon of kin recognition as characterized in otherspecies (39–40). Whereas kin recognition may help raise the level

of cooperation in a population, the maintenance of kin diversityby selection for cooperation alone is highly debated (41–45).Two characteristics distinguish my model for QS divergencefrom other such models. First, most of the previous models areinspired by a “matching” kin-recognition mechanism (“the arm-pit effect”) and assume the existence of a single locus for kinrecognition, coding for a displayed tag. My model dissects an-other plausible kin-recognition type where two separate loci codefor tag display (signal) and tag recognition (receptor). I showhow in the context of a public-goods cooperation, rapid transi-tion between tag types is selected without reducing the level ofcooperation in the population. The evolutionary dynamics ofcheating and immunity may explain the switch from one tag toanother also in cooperative systems with direct cooperation.Second, the underlying population dynamics in all of the

previously described kin-recognition models are those of positivefrequency-dependent selection—the majority kin (as long as it iscooperative) will be selected for in a well-mixed population, as ithas a higher chance of obtaining cooperation than the minoritykin (41). The divergent QS systems, on the other hand, displaya negative frequency-dependent selection in a well-mixed pop-ulation. This dependence is a consequence of the public goodsnature of cooperation—kin recognition establishes the decisionto cooperate, but all neighboring bacteria are beneficiaries ofcooperation. Negative frequency-dependent selection, however,comes with a price; the diversity of alternative QS systems doesnot increase the level of cooperativity in the population. Thisresult is true because an obligate cheater will always benefit from

Ce

ll d

en

sity

E

As

ym

pto

tic

fre

qu

en

cy

Time (AU)

Bottleneck size

Public goods

No Quorum

A

Pu

blic

go

od

s

Pro

du

ctio

n p

er c

ell

Ce

ll d

en

sity

Time (AU)

Public goods

R1

R2

S1

S2

R1

in

B

D

C

Fig. 3. Maintenance of diversity and evolution of cross-inhibition. (A) Divergent QS systems act as facultative cheaters. A minority strain (cyan) activates itsquorum response later than a majority strain and therefore facultatively exploits the majority strain. Shown are cell densities of each strain (Upper) and thelevel of public goods produced by single cells from each strain (Lower). The facultative cheating domain is colored pink and cooperation (arbitrarily defined athalf-maximum production rate) is green. (Right) Graphs show convergence of strain frequencies to 50% at later times. (Inset) A scheme of public goodsproduction and communication in the competition between divergent strains. (B–E) The evolution of cross-inhibition. (B) The QS diversification model can beextended by assuming that one of the receptors (R1

in, orange) can mutate to a novel form (R1in, deep orange) that is inhibited by a divergent signal (cyan). (C)

A scheme of signaling and public goods contribution in the three-way competition between the two divergent strains and the one with cross-inhibitedreceptor. (D) Cross-inhibition is beneficial for the inhibited strain. A strain with a receptor that is inhibited by a divergent strain can invade into its parentalpopulation that is fully orthogonal to the divergent strain. Initial conditions of the divergent strains are their steady-state level when mixed without the cross-inhibited strain. The cross-inhibited strain’s initial density is 1% of the other strains. (E) Cross-inhibition is selected in structured populations. Shown are thefrequencies of the three strains described in C as a function of bottleneck size for a three-way competition analysis in a population going through cycles ofgrowth and bottleneck phases, similar to Fig. 2E. The strain with the cross-inhibited receptor (dashed deep orange line) is selected over its ancestral or-thogonal strain (solid orange line). The nonmonotonicity of the frequencies at low bottleneck sizes is discussed in SI Text, section 8.

13638 | www.pnas.org/cgi/doi/10.1073/pnas.1102923108 Eldar

the cooperation of others, irrespective of its tag, which is unlikethe case of kin discrimination by reciprocal cooperation (see SIText, section 9 for further discussion).

Limits of Diversification. If QS diversification is so strongly se-lected, why is it not found in all species? Multiple factors mayconfine this divergence. One limit is the availability of divergentsignaling molecules. Perhaps this limit is the main reason why QSdivergence has been mostly (but not exclusively) (6, 7) observedin Gram-positive bacteria. The peptide signaling molecule familyused by Gram-positive bacteria for signaling probably encom-passes greater potential molecular variability than that of acylhomoserine lactones (AHL) often used by Gram-negative bac-teria (14). Other constraints on QS divergence include the du-ration of intermediate obligate cheater (R2S1) survival and thepopulation size it reaches. Finally, this evolutionary mechanismrequires that the principal use of QS is for social regulation ofpublic goods. It is known that QS may serve other functions (46)or impact the behavior of single cells in a nonsocial manner (14,47) (SI Text, section 1).My results may help to explain some of the social strategies

observed during fruiting body development in bacteria andamoebas (25–31, 34). Specifically, immunity by signaling inductioncan explain the emergence of a novel immune cooperator froma cheater strain in Myxococcus xanthus (29) (SI Text, section 1).Immunity by induction can also help explain the restoration ofQS-dependent growth to a lasR cheatermutant by a secondary rhlIoverexpression mutation (48). Further understanding of the evo-lutionofQS systemsmayhelppredict the evolutionof resistance toQS inhibitory drugs (49) and enable synthetic biologists (50) torationally design strains with superior cheating strategies to in-terfere with pathogenic bacterial cooperation (51, 52).

Materials and MethodsBasic Model for Quorum Sensing. I used the following equations to describethe time-dependent density of M strains (n1, n2, . . . , nM), the signalingmolecules they produce (S1, S2,. . ., SM), the exo-enzyme (E), and the usablenutrient (Pd):

dni

dt¼

�Pd

Pd þ 1ð1− rfðRactive

i =KrxÞÞ−ntot − γn

�ni ; i ¼ 1; 2; . . . ;M [1]

dSidt

¼ βSðni − SiÞ; i ¼ 1; 2; . . .M [2]

dEdt

¼X

f�Ractivei

�ηi − βEE [3]

dPddt

¼ Jpd +VmaxE− βpd

PdPd þ 1

ntot ; [4]

where the enzyme activation function fðRactivei Þ (which is also reflected in the

growth cost term) is of the form f(x) = xm and the level of active receptor iscalculated from the equation

Ractivej ¼

Xi

ðKacij SiÞ=

�KRS þ

Xi

ðKacij SiÞ þ

Xi

ðKinij SiÞ

�

¼ Kac S!=ðKRS þ Kac S

!þ Kin S!Þ: [5]

The values used in all figures for the above equations are, r = 0.1, γn = 0.01,βS = 0.1, βE = 0.2, JPd ¼ 0:05, Vmax = 20, βPd ¼ 100, m = 1, and KRS = 0.025.Initial conditions of all variables but the cell densities are set to 0 (except forFig. 3D, where they are set as described in the legend). Initial cell densitiesdepend on the specific simulation. The competition matrices are

Kac ¼�1 10 0

�

for “naive” cooperator vs. the intermediate cheater and

K ¼�1 01 0

�

for immune cooperator vs. the intermediate cheater (Fig. 2 C–E), and

Kac ¼�1 00 1

�

for two strains with divergent QS systems (Fig. 3A). For the case of cross-inhibition I use three species with

Kac ¼0@1 0 0

0 1 10 1 1

1AKin ¼

0@0 0 1

0 0 00 0 0

1A

(Fig. 3 D and E). All simulations were done using the MATLAB (Mathworks)ordinary differential equation solver and self-written routines.

Selection for Cooperation Through Population Bottlenecks. I mathematicallygeneralized the experimental selection scheme used by refs. 17 and 21 toa general bottleneck size. I used a semianalytical approach to solve thechange in cooperator fraction under different types of selection when theintermediate cheater strain (R2S1) competes with one of the cooperators(naive R1S1 or immune R2S2). A full description and analysis of this compu-tation is given in SI Text, section 6. Briefly, I assume an infinite number ofsubpopulations where bacteria grow separately. I simulate a growth cycle oftime τ that is initiated by N bacterial lineages (N being the bottleneck size),where each lineage can be either a cooperator or a cheater. After growth,new N lineages are reselected for growth from a Poisson distribution on thebasis of the relative frequency of cooperators and cheaters in a single sub-population (local competition) or in the general population (global com-petition). Analytical methods were used to demonstrate that the immunecooperator will outcompete the intermediate cheater strain in all bottlenecksizes. Numerical values for global competition are obtained after 500 cyclesof growth. For the three-way competition shown in Fig. 3E, I repeated thesame simulations but now analyzed all ðN× ðN− 1ÞÞ=2 possible states andmixed them according to their Poisson distribution in every cycle.

ACKNOWLEDGMENTS. I thank Roy Kishony, Uri Gophna, Kevin Foster,Michael Elowitz, Shaul Pollak, and Peter Reuven for insightful suggestions.This work was funded by a Human Frontier Science Program career devel-opment grant, by the Israel Science Foundation, and by a Marie Curie in-ternational reintegration grant.

1. Waters CM, Bassler BL (2005) Quorum sensing: Cell-to-cell communication in bacteria.Annu Rev Cell Dev Biol 21:319–346.

2. Ji G, Beavis R, Novick RP (1997) Bacterial interference caused by autoinducing peptidevariants. Science 276:2027–2030.

3. Whatmore AM, Barcus VA, Dowson CG (1999) Genetic diversity of the streptococcalcompetence (com) gene locus. J Bacteriol 181:3144–3154.

4. Tran L-SP, Nagai T, Itoh Y (2000) Divergent structure of the ComQXPA quorum-sensing components: Molecular basis of strain-specific communication mechanism inBacillus subtilis. Mol Microbiol 37:1159–1171.

5. Slamti L, Lereclus D (2005) Specificity and polymorphism of the PlcR-PapR quorum-sensing system in the Bacillus cereus group. J Bacteriol 187:1182–1187.

6. Chatterjee A, et al. (2005) Comparative analysis of two classes of quorum-sensingsignaling systems that control production of extracellular proteins and secondarymetabolites in Erwinia carotovora subspecies. J Bacteriol 187:8026–8038.

7. Morohoshi T, Kato M, Fukamachi K, Kato N, Ikeda T (2008) N-acylhomoserine lactoneregulates violacein production in Chromobacterium violaceum type strain ATCC12472. FEMS Microbiol Lett 279:124–130.

8. Tortosa P, et al. (2001) Specificity and genetic polymorphism of the Bacillus compe-

tence quorum-sensing system. J Bacteriol 183:451–460.9. Dufour P, et al. (2002) High genetic variability of the agr locus in Staphylococcus

species. J Bacteriol 184:1180–1186.10. Ansaldi M, Dubnau D (2004) Diversifying selection at the Bacillus quorum-sensing

locus and determinants of modification specificity during synthesis of the ComX

pheromone. J Bacteriol 186:15–21.11. Ichihara H, Kuma K-i, Toh H (2006) Positive selection in the ComC-ComD system of

streptococcal species. J Bacteriol 188:6429–6434.12. Ansaldi M, Marolt D, Stebe T, Mandic-Mulec I, Dubnau D (2002) Specific activation of

the Bacillus quorum-sensing systems by isoprenylated pheromone variants. Mol Mi-

crobiol 44:1561–1573.13. Stefanic P, Mandic-Mulec I (2009) Social interactions and distribution of Bacillus

subtilis pherotypes at microscale. J Bacteriol 191:1756–1764.14. Hense BA, et al. (2007) Does efficiency sensing unify diffusion and quorum sensing?

Nat Rev Microbiol 5:230–239.

Eldar PNAS | August 16, 2011 | vol. 108 | no. 33 | 13639

EVOLU

TION

15. Czárán T, Hoekstra RF (2009) Microbial communication, cooperation and cheating:Quorum sensing drives the evolution of cooperation in bacteria. PLoS ONE 4:e6655.

16. Keller L, Surette MG (2006) Communication in bacteria: An ecological and evolu-tionary perspective. Nat Rev Microbiol 4:249–258.

17. Diggle SP, Griffin AS, Campbell GS, West SA (2007) Cooperation and conflict inquorum-sensing bacterial populations. Nature 450:411–414.

18. Venturi V, Bertani I, Kerényi Á, Netotea S, Pongor S (2010) Co-swarming and localcollapse: Quorum sensing conveys resilience to bacterial communities by localizingcheater mutants in Pseudomonas aeruginosa. PLoS ONE 5:e9998.

19. Rumbaugh KP, et al. (2009) Quorum sensing and the social evolution of bacterialvirulence. Curr Biol 19:341–345.

20. Wilder CN, Diggle SP, Schuster M (2011) Cooperation and cheating in Pseudomonasaeruginosa: The roles of the las, rhl and pqs quorum-sensing systems. ISME J, 10.1038/ismej.2011.13.

21. Griffin AS, West SA, Buckling A (2004) Cooperation and competition in pathogenicbacteria. Nature 430:1024–1027.

22. Chuang JS, Rivoire O, Leibler S (2009) Simpson’s paradox in a synthetic microbialsystem. Science 323:272–275.

23. Kreft J-U (2004) Biofilms promote altruism. Microbiology 150:2751–2760.24. Hamilton WD (1964) The genetical evolution of social behaviour. I. J Theor Biol 7:

1–16.25. Santorelli LA, et al. (2008) Facultative cheater mutants reveal the genetic complexity

of cooperation in social amoebae. Nature 451:1107–1110.26. Strassmann JE, Zhu Y, Queller DC (2000) Altruism and social cheating in the social

amoeba Dictyostelium discoideum. Nature 408:965–967.27. Fiegna F, Velicer GJ (2005) Exploitative and hierarchical antagonism in a cooperative

bacterium. PLoS Biol 3:e370.28. Fiegna F, Velicer GJ (2003) Competitive fates of bacterial social parasites: Persistence

and self-induced extinction of Myxococcus xanthus cheaters. Proc Biol Sci 270:1527–1534.

29. Fiegna F, Yu Y-TN, Kadam SV, Velicer GJ (2006) Evolution of an obligate social cheaterto a superior cooperator. Nature 441:310–314.

30. Velicer GJ, Yu YT (2003) Evolution of novel cooperative swarming in the bacteriumMyxococcus xanthus. Nature 425:75–78.

31. Khare A, et al. (2009) Cheater-resistance is not futile. Nature 461:980–982.32. Rainey PB, Rainey K (2003) Evolution of cooperation and conflict in experimental

bacterial populations. Nature 425:72–74.33. Zhang Q-G, Buckling A, Ellis RJ, Godfray HCJ (2009) Coevolution between cooperators

and cheats in a microbial system. Evolution 63:2248–2256.

34. Parkinson K, Buttery NJ, Wolf JB, Thompson CRL (2011) A simple mechanism forcomplex social behavior. PLoS Biol 9:e1001039.

35. Brockhurst MA (2007) Population bottlenecks promote cooperation in bacterial bio-films. PLoS ONE 2:e634.

36. Travisano M, Velicer GJ (2004) Strategies of microbial cheater control. Trends Mi-crobiol 12:72–78.

37. Wright JS, 3rd, et al. (2005) The agr radiation: An early event in the evolution ofstaphylococci. J Bacteriol 187:5585–5594.

38. Gore J, Youk H, van Oudenaarden A (2009) Snowdrift game dynamics and facultativecheating in yeast. Nature 459:253–256.

39. Mehdiabadi NJ, et al. (2006) Social evolution: Kin preference in a social microbe.Nature 442:881–882.

40. Giron D, Dunn DW, Hardy ICW, Strand MR (2004) Aggression by polyembryonic waspsoldiers correlates with kinship but not resource competition. Nature 430:676–679.

41. Crozier R (1986) Genetic clonal recognition abilities in marine invertebrates must bemaintained by selection for something else. Evolution 40:1100–1101.

42. Grafen A (1990) Do animals really recognize kin? Anim Behav 39:42–54.43. Rousset F, Roze D (2007) Constraints on the origin and maintenance of genetic kin

recognition. Evolution 61:2320–2330.44. Jansen VA, van Baalen M (2006) Altruism through beard chromodynamics. Nature

440:663–666.45. Antal T, Ohtsuki H, Wakeley J, Taylor PD, Nowak MA (2009) Evolution of cooperation

by phenotypic similarity. Proc Natl Acad Sci USA 106:8597–8600.46. Nadell CD, Xavier JB, Levin SA, Foster KR (2008) The evolution of quorum sensing in

bacterial biofilms. PLoS Biol 6:e14.47. Redfield RJ (2002) Is quorum sensing a side effect of diffusion sensing? Trends Mi-

crobiol 10:365–370.48. Sandoz KM, Mitzimberg SM, Schuster M (2007) Social cheating in Pseudomonas

aeruginosa quorum sensing. Proc Natl Acad Sci USA 104:15876–15881.49. Defoirdt T, Boon N, Bossier P (2010) Can bacteria evolve resistance to quorum sensing

disruption? PLoS Pathog 6:e1000989.50. Brenner K, You L, Arnold FH (2008) Engineering microbial consortia: A new frontier in

synthetic biology. Trends Biotechnol 26:483–489.51. Duan F, March JC (2010) Engineered bacterial communication prevents Vibrio chol-

erae virulence in an infant mouse model. Proc Natl Acad Sci USA 107:11260–11264.52. Brown SP, West SA, Diggle SP, Griffin AS (2009) Social evolution in micro-organisms

and a Trojan horse approach to medical intervention strategies. Philos Trans R SocLond B Biol Sci 364:3157–3168.

13640 | www.pnas.org/cgi/doi/10.1073/pnas.1102923108 Eldar

Supporting InformationEldar 10.1073/pnas.1102923108SI TextThe aim of this section is to describe and analyze the mathe-matical model I use and to extend the discussion on the generalityand impact of this unique evolutionary divergence mode. Belowis a short summary of each of the sections, to help the readerfocus on the material of interest.

i) Section 1 discusses the generality of my model of publicgoods regulation by quorum sensing. I bring examples forknown secreted public goods in multiple QS systems anddiscuss other types of public goods and other functions ofQS systems that are not related to public goods production.I also discuss the potential divergence of signals that do notmeasure “cell density” per se.

ii) Section 2 describes the development of the model, its ra-tionale, and the way it is simplified into Eqs. 1–5 of Materi-als and Methods and used in the main text. I define theinteraction matrices for various types of strain relations.

iii) Section 3 analyzes the steady-state behavior of a singlecooperator strain and of two diverged cooperator strains.I show that the behavior of the system depends on a di-mensionless factor that compares the rate of nutrient pro-duction by the enzyme and its rate of consumption throughgrowth. Stability analysis of the coexistent steady-statesolution of two strains shows that it is stable under allconditions.

iv) In section 4 I discuss the cost of signaling and its relation tothe model. I claim that as all strains on the pathwayfor diversification produce a signal, its cost is not impor-tant for the process. I also discuss the difference betweenobligate cheater and inducer cheater with a functional sig-naling allele.

v) In section 5 I elaborate on the immunity of the novel co-operator to the intermediate cheater strain. I analyticallydemonstrate that in homogenous conditions the two strainsmaintain their frequency in the population and discuss theadvantage of the induction to both strains in terms of totalyield of the mixed population. I also discuss the inability ofstrain R1S2 to invade into the original wild-type QS system,R1S1.

vi) In section 6 I describe and analyze the bottleneck selectionassay between cooperator and cheater. I analytically solvethe problem for bottleneck sizes of one and two lineagesand semianalytically show how to extend the analysis tolarger bottleneck sizes. I specifically prove the advantagesof the immune novel cooperator over the naive originalcooperator in this competition.

vii) In section 7 I demonstrate that diversification still holdsunder more general models that extend the basic modelin four important manners: (i) relaxing the assumption offull orthogonality between novel and original communica-tion pathways, (ii) adding null alleles to receptor/signal/enzyme, (iii) assuming a positive feedback of receptor ac-tivity on receptor and signal expression levels, and (iv) as-suming that the public goods have a greater benefit to theproducer, leading to snowdrift dynamics.

viii) In section 8 I analyze the consequences of asymmetricinteractions between strains. I first discuss the conse-quences of population structure on the evolution ofcross-inhibition. I then show that asymmetric cross-activation can be a direct outcome of divergence and tobenefit the signaling strain. I discuss the resulting arms

race between strains and why it can lead to mutualcross-inhibition.

ix) In section 9 I compare previously described models for kinrecognition with the kin-recognition system described in thetext. Two main differences are emphasized: the use of twoloci by the kin-recognition system and the decoupling ofrecognition and cooperation.

1. Quorum Sensing and Public Goods Production.A basic assumptionof my model is that quorum sensing is controlling the productionof “public goods”—products or behavioral strategies that benefitalso cells whose QS system is nonfunctional. In this section Idiscuss the prevalence of public goods production under QScontrol and compare it with other functions of quorum sensing.1.1. Quorum sensing and the regulation of secreted enzymes. As Imention in the main text, regulation of secretion is one of themajor roles of quorum sensing. In fact, a recent review hassuggested that the main use of the quorum sensing signal is toserve as a “cheaper” proxy to the fate of the more costly secretedmolecules (“efficiency sensing”) (1). Table S1 provides a set ofexamples for QS-dependent secreted molecules, including ex-amples from the six known divergent quorum sensing systems.1.2. Other types of public goods. Many other types of cooperation inbacteria can be regarded as producing public goods. This ob-servation is not surprising, given the relatively simple ways bywhich bacteria can interact and the relative lack of direct cell–cell interactions in bacteria (but cf. refs. 2–4 for examples ofdirect contact interactions with obvious or presumed social im-pact). Here are two important types of public goods, which donot involve the secretion of molecules by the cells. Both of thesetypes can lead to evolution of divergent QS systems in a similarmanner to what is presented in the main text:

a) Removal of public bad: Enzymes that intracellularly de-grade toxins help other cells by continuously removing thetoxin from the environment. An example of this behavior isthe formation of satellite colonies sensitive to beta-lactamantibiotics next to a colony expressing the beta-lactamaseresistance gene (which is expressed in the periplasm). Inote that it is not clear whether there is any advantagefor regulating these types of anti–public-bad enzymes byQS, as the public-bad presence may be independent ofdensity. If toxin is constitutive, then a QS regulation isnot likely.

b) Restrictive growth: Under various conditions, cooperatingcells may favor a mode of growth that restricts their growthrate to avoid reduced yield (5) or to prevent disruption ofspatial architectures (6). The public good here is the growthpotential, which cells are choosing not to consume at max-imal possible rate. It is not known whether quorum sensingactually regulates such a behavior, but there has been verylittle work in this direction.

c) Altruistic “suicide”: In the case where part of the popula-tion “decides” to dedicate its behavior toward the benefit ofother cells and not toward reproduction, it is effectivelycreating a public good. This behavior may not always leadto secretion of specific molecules. For example, in the pro-duction of a fruiting body, the stalk cells are altruistic sui-cides. Many fruiting body cheaters are strains that do notinvest in stalk cells. Here the public good is the work doneby the altruists toward the rest of the community. Thereare various extracellular signaling pathways working during

Eldar www.pnas.org/cgi/content/short/1102923108 1 of 20

fruiting body development in both bacteria and amoebasand recent work indicates that some of the social mutantsin amoebas are related to signaling (7).

d) Symbiosis: The production of a material that benefits a sym-biosis partner that in turn benefits the community is anindirect public good. The best studied case is the symbiosisbetween the bacteria Vibrio fischeri and the Hawaiian bob-tail squid, Euprymna scolopes. Here, QS drives the expres-sion of the lux enzymes that catalyze the production oflight, helping the squid. The squid, in return, provides foodand a controlled environment for the bacteria. It was shownthat both QS and lux mutants are outcompeted by wild typewhen competing in juvenile squids (8, 9). Also, “dark”strains were never isolated from squid-hosted bacterial pop-ulations (10). It is not clear yet what is the mechanism ofselection, although it may involve both a benefit to lightproducers and punishment to light nonproducers (the luxgene reduces reactive oxygen species introduced by thesquid) (8). In both cases, a highly structured populationimposed by the squid is probably an important part of theselection against dark cheaters. There are no reports ondiversification of signal in the V. fischeri lux system.

1.3. Divergence under “nonquorum” signals. The simple model ofquorum sensing described here assumes that signal production isconstitutive and therefore that the activation of quorum response isdensity dependent. In other cases, signaling may be regulated andactivation may depend not only on density but also on othercharacteristics of the population. I emphasize that the modeldiscussed in this paper is valid also for this extended type of sig-naling. The important criterion is the regulation of public goodsand not the conditions under which public goods are produced.Nonquorum signals may be specifically important in complexbehaviors, such as fruiting body formation and biofilm formation.1.4. Quorum signal as a public good.The QS signal is costly to produceand leads to a benefit to all receiving cells; therefore it is a publicgood. However, this public good cannot lead to the divergence ofthe quorum sensing system. From the perspective of the quorumsensing system, signal is a “club good” (11)—it can be used onlyby cells with an appropriate receptor and therefore cells witha divergent receptor will not be able to be cheaters (see nextsection). See more discussion on the cost of signaling in SI Text,section 4.1.5. Functions of quorum sensing that are not related to public goods.Multiple functions of quorum sensing do not follow the definitionof public goods. In general, these functions can be divided intotwo categories:

a) Single-cell use: It has been postulated that QS has actuallyevolved as a mechanism for probing the environment bysingle cells (“diffusion sensing”) (12). Relevant biologicalexamples are the invasion of bacteria into host cells andother cases where environment is highly compartmental-ized. Whereas it is highly controversial whether this viewis correct (and the subject of this paper—QS diversification—is most likely a proof to the contrary of this view), it mayvery well be that in some species diffusion sensing or “con-finement sensing” is the main function of a QS system.

b) Private goods and club goods: Many other QS functionsmay lead to the benefit of sensing cells only, either becausethey do not impact non-QS cells (“private goods”) or be-cause only QS cells can take advantage of their utility (clubgoods). Here are examples for the two types:i) Private goods: Certain species of bacteria will use QS toregulate the dispersal of complex structures, like bio-films. In this case non-QS cells will simply not dis-perse and will not be able to enjoy the benefits ofdispersal. Another example is the utilization of QS

for genetic transmission as occurs in various cases, bothat the level of the bacteria (genetic competence sys-tems) and at the level of various selfish genetic systems(conjugation, etc.).

ii) Club goods: Many species of bacteria produce a cou-pled set of products—a secreted product and a cell-autonomous product that is necessary for the utiliza-tion of the secreted product. If both products are underthe control of QS, then QS mutants will not be able touse the product secreted by others. This form of clubgoods includes siderophore–receptor pairs—if both areunder QS control, then a QS null strain will not be ableto use the siderophore. Another example is antibiotic-resistance pairs. Here, the QS null mutant cells may bekilled by the QS-active cells.

Note that whereas QS-regulated club goods seem to be a goodmechanism for preventing the cheating of quorum sensing sys-tems, they have a major drawback—they also prevent the abilityto act as a facultative cheater on the secreted product—to enjoyit when it is produced by other strains at low cell densities. Thisdrawback is most likely the reason why both siderophore re-ceptors and immunity genes have additional modes of regulationapart from QS.

2. A Mathematical Model for QS System Interaction. As describedin the main text, I assume that a quorum sensing signalingpathway regulates the production of a public good—an exo-enzyme in this case—whose production is costly, but is necessaryfor growth. Specifically, I assume that the exo-enzyme (E) cat-alyzes the cleavage of a complex nutrient (P) (e.g., a sugarpolymer) into a transportable form (Pd) (e.g., a sugar monomer).I assume that the level of complex nutrient is constant. Othervariables I use in the model are the receptor level (R), the signallevel (S), the receptor–signal complex ([RS]), and cell density(n). To formulate a model of such a system I make a set ofspecific assumptions. The nature of my hypothesis is such that itwill most likely be true in many other models of public goodscontrolled by quorum sensing, as long as QS null mutants caninvade the wild type. Some of these extensions are further ex-plored in SI Text, sections 7 and 8.2.1. A model for a single strain. The specific assumptions I make hereare as follows:

i) Growth is dependent (through a Holling’s type II term) onthe nutrient levels.

ii) A fraction r of the growth potential is diverted from growthto enzyme production in the quorum responding cell at themaximal production level.

iii) Cells may die in a density-dependent manner (logisticgrowth) or, in low probability, spontaneously.

iv) Enzyme production is a function of a signal molecule boundreceptor.

v) Complex nutrient levels are large compared with the affinityof the exo-enzyme.

vi) Signal molecule productions and receptor production areconstitutive.

These assumptions fit the following set of equations:

d~ndt

¼�αn

~pd~pd þ KG

ð1− rf ð½RS�ÞÞ− βn~n−~γn

�~n Cell density [S1]

d~Sdt

¼ PS~n− ~βS~S− ~nðkþR~S− k− ½RS�Þ Signal [S2]

Eldar www.pnas.org/cgi/content/short/1102923108 2 of 20

I further assume that the quorum response function f([RS]) isa monotonous increasing function with maximum of 1.I can now simplify the set of equations and the number of

parameters by normalizing some of the parameters and assumingseveral simplifying assumptions. The only parameters that differbetween the strains in the system are those of the quorum re-sponse, f([RS]), which I do not normalize and describe explicitlyin the following subsection. Simplifying assumptions include thefollowing:

Timescale: This is set by the maximal growth rate, αn = 1.Population density is measured by units of αnβn

; n¼ βnαn

~n:Signal molecule concentration is measured in units of

PS=βS; S ¼~S

PS=βS:

Enzyme levels are measured by units of PE=βn;E ¼~E

PE=βn:

I assume that the interaction between signal molecule andreceptor happens on amuch faster timescale than others, so it is inquasi-steady state, and that the levels of receptor are constant.This assumption implies a Michaelis–Menten relationship be-

tween [RS] and S: ½RS� ¼ SKRS þ S

:

Nutrient concentration is normalized by their growth saturation

value; Pd ¼~Pd

KPd

:

These assumptions and normalizations lead to the following setof equations:

dndt

¼�

Pd

Pd þ 1

�1− rf

�S

KRSþS

��− n− γn

�n Cell density [S7]

dsdt

¼ βSðn− SÞ Signal [S8]

dEdt

¼ f�

SKRSþS

�n− βEE Enzyme [S9]

dPd

dt¼ JPd þ VmaxE− βPd

Pd

Pd þ 1n Nutrient; [S10]

where the remaining parameters are appropriately normalized:�γn ¼ ~γn

αn; βS ¼

~βSαn; βE ¼

~βEαn

; JPd ¼~JPd

KPdαn;Vmax ¼

~VmaxPEβnαnKPd

;

βPd¼

~βPdKPd βn

�: For the quorum response form, I use f(x) = xm.

The initial levels of all variables except for cell density are set tozero.

I note here that the expression of the QS system constitutesa physiological positive feedback—the more cells there are, moreQS signal and public goods are made and there is more potentialfor growth. This feedback may lead to threshold dependenceon parameters. This positive feedback is not directly related tothe molecular positive feedback often found in QS systems—the quorum response activating the expression of signal andreceptor.2.2. The effect of multiple strains with varying signals on receptor activity.To analyze the interaction between different strains, I need todefine the type of interactions between various signals andreceptors. To allow for inhibiting interactions as well as activatingones, I assume that a QS receptor has two states, active proneðRac

i Þ and inactive prone ðRini Þ: I assume a simple form of com-

petition for the two states of the receptor:

Raci þ Sj ↔ Rac

i Sj [S11]

Rini þ Sj ↔ Rin

i Sj [S12]

Rini ↔ Rac

i : [S13]

It can be easily shown that this leads to a quasi-steady state of theactive receptor–signal molecule complex of the form

Ractivej ¼ Rtot

j

∑iKacij Si�

KRS þ∑iKacij Si þ∑iK

inij Si�

¼ Rtotj

KacS�KRS þ KacSþ K inS

�; [S14]

where Kac and Kin are the two matrices that define activatory andinhibitory interactions of the strains through the signals. Someexamples for the matrices defining the relations discussed in thepaper are as follows:

i) R1S1 strain vs. R2S2 strain (facultative cheaters):

Kac ¼�1 00 1

�

ii) R1S1 strain vs. R0S0 strain (obligate cheater, complete):

Kac ¼�1 00 0

�

iii) R1S1 strain vs. R2S1 strain (obligate cheater, signal pro-

ducer): Kac ¼�1 10 0

�

iv) R2S1 strain vs. R2S2 strain (strain 2 is an immune cooperator

activating strain 1): Kac ¼�0 10 1

�

v) Asymmetric cross-inhibition is represented by K in ¼�0 10 0

�; whereas the symmetric one is represented by

K in ¼�0 11 0

�:

In SI Text, section 7, I consider the effects of a nonorthogonalcross-activation term on the evolution of divergence. In this case,all zeros in the matrices shown in examples ii–iv should be re-placed with 0 < ρ < 1.2.3. Competition between two strains. To analyze the competitionbetween two strains, I use the same equations as in the single-strain model (Eqs. S7–S10), but dedicate specific equations tothe cell density and signal of each strain. This method results inthe equations presented Materials and Methods in the main text:

dRdt

¼ PR − kþR~Sþ k− ½RS�− βRR Receptor [S3]

d½RS�dt

¼ kþR~S− k− ½RS� Receptor-signal complex [S4]

d~Edt

¼ PEf ð½RS�Þ~n− ~βE~E Enzyme [S5]

d~Pd

dt¼ ~JPd þ ~Vmax~E− ~βPd

~Pd

~Pd þ KPd

n Nutrient [S6]

Eldar www.pnas.org/cgi/content/short/1102923108 3 of 20

dnidt

¼�

Pd

Pd þ 1�1− rf

�Ractivei

��− ntot − γn

�ni; i ¼ 1; 2; . . . ;N

[S15]

dSidt

¼ βSðni − SiÞ; i ¼ 1; 2; . . . ;N [S16]

dEdt

¼X

f�Ractivei

�ni − βEE [S17]

dPd

dt¼ JPd þ VmaxE− βPd

Pd

Pd þ 1ntot: [S18]

Two additional variables whose time evolution is useful to followwhen considering social invasion patterns are ntot = n1 + n2 and

s ¼ n1n2: I can easily find that

dntotdt

¼�

Pd

Pd þ 1�1− rf

�Ractive1

��− ntot − γn

�ntot

þ rPd

Pd þ 1�f�Ractive2

�− f�Ractive1

��n2 [S19]

dsdt

¼ n− 22

�n1dn2dt

− n2dn1dt

¼ r

Pd

Pd þ 1�f�Ractive2

�− f�Ractive1

��s:

[S20]

Therefore, total cell density behaves as a single strain with anadditional term for the difference in produced public goodsbetween the strains. The change in relative frequency of the twostrains is directly proportional to their public goods productiondifference due to its impact on the growth rate. Therefore, anysteady state will be reached only when both strains produce thesame level of public goods. This result is intuitively clear, as onlythen cost and benefit will be balanced in the same way.Note that the density-dependent death is proportional to ntot

as is commonly used in logistic growth models. The reason forassuming density-dependent death is to keep the steady-statedynamic. In models of growth by expansion [like the x–y expansionof swarming models (13) or the z expansion of biofilm models(14, 15)], this term is most likely unnecessary.2.4. A QS null mutant is a cheater in the model. A basic aspect ofa public goods model is that a strain that is not producing thepublic goods will be deficient on its own, but will be able to invadea community of a wild-type public goods-producing population.This process, however, will lead to a reduction in the finalpopulation fitness as public goods levels are diminished. Thisresult is demonstrated for the model presented in Eqs. S15–S18in Fig. S1; see the Fig. S1 legend for details.Interaction between obligate cheater (strain 2) and cooperator

(strain 1) is described by the interaction matrix Kac ¼�1 00 0

�: I

can easily see that the cheater will invade the population fromEq. S20. As cheaters do not contribute to public goods pro-duction, I find that

dsdt

¼ − rPd

Pd þ 1f�Ractive1

�s< 0 [S21]

and therefore cooperator levels will always decrease.

3. Steady-State Analysis. 3.1. Single strain.A steady-state cell densityand signaling level will be achieved as long as the level of usablenutrient, Pd, is either constant or high enough to sustain maximal

growth. Three different limiting factors will lead to a differentbehavior:

i) Growth-limited regime: Nutrient production by the exo-enzyme is larger than its maximal consumption (Pd ≫ 1).

ii) Enzyme-limiting regime: Enzyme levels are such that theydo not allow maximal growth.

iii) Signal-limiting regime: Signaling does not lead to maximalproduction of enzyme.

3.1.1. Case 1—growth limited. If Pd ≫ 1, the quasi–steady-stateequations for cell density are reduced to

0 ¼��

1− rf�

SKRS þ S

��− n− γn

�n [S22]

0 ¼ βSðn− SÞ; [S23]

which yield

n ¼�1− rf

�n

KRS þ n

��− γn ðor n ¼ 0Þ: [S24]

If n > KRX (i.e., signal is saturating the receptor), I find that n =1 − r − γn. In this case, the cells reach the highest possible densityof enzyme-producing cells.To attain this approximation, the enzyme production rate

needs to be high enough to maintain Pd ≫ 1, which implies thatthe Pd formation rate is faster than its use (Eq. S18):

VmaxE> βPdn: [S25]

Using Eqs. S7–S10 in steady state, I find that this result isequivalent to

ζ ≡Vmax

βPdβE

> 1: [S26]

3.1.2. Case 2—enzyme-limited growth. If Pd < 1, growth is re-stricted by the enzymatic conversion rate, and I can calculate thesteady state from Eqs. S7–S10:

n ¼ ζ

�1− rf

�n

KRS þ n

��f�

nKRS þ n

�− γn: [S27]

Again, if n > KRS, I find

n ¼ ζð1− rÞ− γn: [S28]

The two cases demonstrate that the critical parameter that deter-mines the nature of quasi-steady state if signaling is saturated is

ζ ¼ Vmax

βPdβE

¼~Vmax

�PE

βE

�

~βPd

: [S29]

This dimensional parameter represents the relative level of nutrientproduction and consumption in steady state. The second criticalparameter is KRS, which allows efficient utilization of the signal. Inan ideal scenario, enzyme production will be tuned such that itsvalue is optimal for growth, which depends on the exact level ofenzyme cost. Under most scenarios this level will be close to ζ = 1,which is the level chosen for the simulations in the main text.Note that in the above analysis I neglected the constant usable

nutrient production term JPd : In the simulations I performed, Iassume this term to have a small, but nonzero, level. This as-sumption implies that there is a lower limit to cell density, even if

Eldar www.pnas.org/cgi/content/short/1102923108 4 of 20

no enzyme is produced, thereby setting a nonzero fitness toa cheater-only population.

3.1.3. Case 3—signal-limited growth. What happens if signaldoes not saturate the receptor and enzyme’s production is notmaximal? I assume f(x) = x. If KRS > n, I find

n ≅ ζ

�1− r

nKRS þ n

�n

KRS þ n− γn⇒1

≅ ζ

�1− r

y1þ y

�1

1þ yn

KRS≅ζð1− rÞKRS

− 1:[S30]

If KRS > ζ(1 − r), then this result will not yield a positive steadystate and cell density will approach 0. If ζ(1 − r) ≫ KRS, then thesignal becomes saturated. The signal-limited situation occurstherefore only in a small region of parameter space where ζ ∼KRS. Fig. S2 shows the steady-state level of cells for the differentvalues of ζ, KRS.3.2. Competing strains. I consider here the case of two competingstrains with functional and divergent QS systems having the sameparameters. It is clear that as both strains have equivalent QSsystems, the steady state is symmetric (assuming a unique steadystate):

n1 ¼ n2 ¼ ntot2: [S31]

If I use this relation in Eqs. S15–S18 and assume a steady state, Ifind the exact two solutions found for the single-strain steady

state, but now withntot2

appearing in the expression for f:

Case 1: ntot ¼

0B@1− rf

0B@

ntot2

KRS þ ntot2

1CA1CA− γn [S32]

Case 2: ntot ¼ Vmax

βPdβE

0B@1− rf

0B@

ntot2

KRS þ ntot2

1CA1CAf

0B@

ntot2

KRS þ ntot2

1CA− γn:

[S33]

In both cases, if signal levels are sufficiently high to saturate thereceptors, then the steady-state levels of the mixed culture areclose to the one for the pure culture. In case 1, it may actually beslightly higher, as enzymes are overproduced by the single strainand enzyme cost is slightly reduced in the mixed population. Asimilar scenario was recently suggested in an experimental co-operative system (16).

3.2.1. Stability analysis. To address the stability and uniquenessof the equal-concentration steady state, Eq. S31, I analyze the

relative levels of n1, n2. I define s ¼ n1n2: Using Eq. S20, I find that

if n1 > n2, the time derivative of s follows

dsdt

¼ rPd

Pd þ 1�f�Ractive2

�− f�Ractive1

��s< 0: [S34]

This result is true because R is a monotonic increasing functionof n and f is a monotonic increasing function of R. The inequalityimplies that the relative frequency of n2 increases when it is ina minority and decreases when in a majority, implying that thesteady-state n1 = n2 is stable.

4. A Note on the Cost of Signaling. A quorum-sensing signal is byitself a type of public good and it was experimentally shown thata signal-deleted strain will be able to invade into a wild-type

population in both natural and synthetic contexts (17, 18). Al-though true in general, the cost of signaling does not affect thediversification of quorum-sensing systems. This is so because allrelevant strains (R1S1, R2S1, R2S2, and R1S2) contain a secretedsignal and therefore pay the cost of signaling. The differencebetween the strains is only in the effectiveness of the signal ina specific social context, not its cost.

It is worthwhile to note few related complications:

i) An extended model has to include also null alleles of re-ceptor, signal, and enzyme. In SI Text, section 7 I show thatsuch an extension does not interfere with either the evolu-tion of an intermediate cheater or the evolution of an im-mune cooperator.

ii) In natural quorum-sensing systems, the cost of quorum re-sponse is larger than the cost of signal production, as wasshown in Pseudomonas aeruginosa (17). This result impliesthat signal allele mutants are more weakly selected. In fact,a recent paper demonstrated conditions under which recep-tor null mutants are easily selected and signaling null mu-tants are not selected at all (19).

iii) Also, as noted in ref. 17, if a positive feedback on signalingis established through the quorum response, then most ofthe signaling cost is actually included in the cost of quorumresponse. It is only the constitutive signal production thatis not included. Whereas QS cannot diverge if the constitu-tive signal is the only public good in the system (SI Text,section 1), QS divergence can be selected if QS directs theproduction of signal (forming a positive feedback on signalproduction).

Finally, it is worth noting that the strain R2S1 is botha “cheater” and a “liar”. It better exploits cooperators, by in-ducing them to produce the enzyme. This additional function canbe seen in the longer invasion of the strain R0S1 compared witha full QS mutant R0S0 in Fig. S3 (0 refers to a null mutant). It iseasy to understand why “induction” is not a significant contri-bution to cheating—when inducer–cheater levels are low, theeffect of the signal they produce is insignificant. If they are high,then there are no cells to induce. Therefore, an inducer–cheaterwill have a marginal advantage over a “silent” cheater only forintermediate occupancy. This outcome might be balanced off bythe cost of constitutive signal production. If the signal is underpositive feedback through the quorum response, than this effectwill be even smaller (17) as the cheater strain is producing onlylow levels of signal.

5. Immunity to Cheating by Cooperation Induction. As explained inthe main text, the novel cooperator, R2S2, is immune to thecheating of its ancestor, R2S1, by inducing its quorum response. Ishow that the immune cooperator strategy is neutral in a mixturewith the ancestor: Its frequency does not change with time. I alsoshow that the community benefits from it, as some public good isproduced by both strains and therefore the total cell densityreached is higher than in a pure cheater (R2S1) population. Ifurther discuss these properties and some of their consequencesin this section.5.1. The immune cooperator phenotype in homogenous conditions. Iconsider the mathematical implication of competition betweenthe immune cooperator, R2S2, and the intermediate strain R2S1.This competition can be analyzed using Eqs. S15–S20 with the

activation matrix Kacij ¼

�1 01 0

�: As the receptors in both

strains are the same, both depend on f ðRactive1 Þ ¼ f ðRactive

2 Þ: I find

Eldar www.pnas.org/cgi/content/short/1102923108 5 of 20

dntotdt

¼�

Pd

Pd þ 1�1− rf

�Ractive1

��− ntot − γn

�ntot [S35]

d�n2n1

�

dt∝ f�Ractive2

�− f�Ractive1

� ¼ 0 [S36]

dS1dt

¼ βSðsntot − SÞ [S37]

dEdt

¼ f�Ractive1

�ntot − βEE [S38]

dPd

dt¼ VmaxE− βPd

Pd

Pd þ 1ntot: [S39]

The first characteristic of the immune cooperator is an immediate

consequence of Eq. S36; asdsdt

¼ 0, the initial fraction of the

immune cooperator will remain constant along growth. Thisbasic result stems from the fact that both cost and benefit areshared by the two strains and therefore the cooperator strain hasno selective advantage or disadvantage. Therefore, in homoge-nous conditions, the immune cooperator is able to invade intothe cheater only by neutral drift. However, I note that Eqs. S35–S39 are equivalent to Eqs. S7–S10 for the single-strain dynamicswith the only difference that signal production is s times lower.This result implies that the strains will reach a nonzero steadystate with a total density

ηtot ≅ ζð1− rÞ− γn ζ< 1 [S40]

ηtot ≅ ð1− rÞ− γn ζ > 1; [S41]

but with ζ ¼ Vmax

βPdβE

s: Therefore, the higher the immune cooper-

ator’s abundance is, the higher will be the total cell density, as itinduces more benefits to the population as a whole. As I show inSI Text, section 6, the two conditions needed for the fixationof the immune cooperator in a structured population when incompetition with the intermediate cheater are the constancy offrequency and the monotonous increase in the total cell densitywith the cooperator’s frequency in unstructured populations. AsI show above, both of these conditions are met.I note here that the immune cooperator’s advantage is mainly

apparent once it reaches a quorum. Therefore, there will typi-cally be an almost-neutral phase in the evolution of the co-operator, where a single mutant cell is sufficiently multiplied tostart activating the quorum response. This effect will be morepronounced in a quorum-sensing model with a threshold be-havior of quorum response, as the cell gets very little benefitbefore its density/number is sufficiently high. However, the sizeof a quorum in real-life context can be fairly small (depending onthe geometry and diffusion characteristics of the signal), so this“almost-neutral” drift phase may not be very large.

6. Comparing Cooperation Maintenance of Naive and Immune Co-operator Strains Under Population Bottlenecks. Previously, Griffinet al. (20) and similarly Chuang et al. (18) used a simple ex-perimental assay to assess the maintenance of cooperation underfour different ecological regimes involving low and high re-latedness in cooperativity and local and global competition be-tween lineages. The experimental procedure they devised issimple and useful for getting simple insight into the social in-

teraction between strains. In this section, I generalize this ap-proach to arbitrary levels of relatedness.I use this assay to show that the immune cooperator, R2S2, will

always be fixed when mixed with the intermediate cheater strainR2S1 irrespective of the level of relatedness. Therefore, it willalways do better than the naive cooperator, R1S1, when com-peting with the intermediate strain, R2S1.The assay I simulate is the following (Fig. S4 A and B, adapted

from ref. 21): I assume there are a very large number, M, ofpopulations (e.g., different tubes):

i) For Ns number of strains, I initiate the M populations, byrandomly choosing N cells (bottleneck size) from the differ-ent strains with equal probability. That is, I initially assumethat the abundance of all strains is equal.

ii) Growth: Each population develops according to Eqs. S10–S13 for a time τ.

iii) Selection:a) Local competition: N cells are randomly chosen from

each grown population and seed the next cycle of growthin this population.

b) Global competition: All M populations are mixed to-gether. Each population is reseeded by N randomlydrawn cells from the population mixture.

iv) Cycle back to stage ii.

The characteristic parameter I am interested in is the as-ymptotic frequency of the different strains in the population.Specifically, I am interested in the outcome of this selectionscheme for the competition between two strains: a cooperator anda cheater. I denote the frequency of cooperators in this assay as F(N) [the frequency of cheaters is therefore 1 − F(N)]. Fora population with bottleneck size N, I can calculate this value onthe basis of a (N + 1) × 2 matrix nij representing the density ofcooperators (j = 1) and cheaters (j = 2) in a mixed populationafter growth for a time τ, when seeded with i = 0, 1, . . . , Ncooperator cells. (Note that cooperator levels at i = 0 andcheater levels at i = N are identically zero, reducing the numberof free variables to 2N.) I can express these parameters using thefunctions ntot(x), 0 < fc(x) < 1, the total cell density and thefrequency of cooperators at the end of the growth phase whenthe initial frequency is x:

ni1 ¼ ntot

�iN

�fc

�iN

�; ni2 ¼ ntot

�iN

��1− fc

�iN

��: [S42]

The invasion of the cheater strain implies that the cooperatorfrequency always decreases with time during growth; therefore forx ≠ 1 I find the relation

fcðxÞ ≤ x: [S43]

Equality is true for the immune cooperator (SI Text, section 5),whereas a naive cooperator will follow the strong inequality.In the following sections I analyze the asymptotic frequency of

cooperators for local (Fl) and global (Fg) selection types. I firstdiscuss the simple cases n = 1, 2 used by ref. 20, and I thenderive a general formula for arbitrary N and use it to show thatthe immune cooperator’s frequency is always maximal for thespecific competition type (1 for global and 1

2 for local compe-tition) irrespective of bottleneck size, whereas the frequency ofthe naive cooperator will always go below 1 for a large enoughbottleneck size during global competition.6.1. Local competition. n = 1. In local competition each populationis seeded by its population from the previous culture. For the casen= 1, this simply means that populations of cheaters will be keptas cheaters and populations of cooperators as cooperators, im-

Eldar www.pnas.org/cgi/content/short/1102923108 6 of 20

plying that on average it will always be equal to the initialdrawing probability, Fl(0) = 0.5.

n = 2. Each test tube is initiated with two random cells andgrown for a time τ. There are now three types of cultures, twopure and one mixed. If a test tube is pure it will remain pure,whereas if it is a mix, it will diverge into a series of pure andmixed test tubes with ratios that depend on the relative fre-quencies of pairs chosen from the mixed population. One canshow that the number of mixed tubes will always go down withtime (Nmix, Ncoop, and Ncheat denote the fractions of mixed tubes,pure cooperator tubes, and pure cheaters tubes):

Nmixðkþ 1Þ ¼ 2n11n12ðn11 þ n12Þ2

NmixðkÞ⇒ NmixðkÞ

¼ Nmixð0Þ

2n11n12ðn11 þ n12Þ2

!k

[S44]

Ncoopðkþ 1Þ ¼ NcoopðkÞ þ n211ðn11 þ n12Þ2

NmixðkÞ [S45]

Ncheatðkþ 1Þ ¼ NcheatðkÞ þ n212ðn11 þ n12Þ2

NmixðkÞ: [S46]

One can show that these relations imply that at the limit

Ncoopð∞Þ ¼ Ncoopð0Þ þ n211�n211 þ n212

�Nmixð0Þ: [S47]

In the above design, the initial levels areNmix(0)= 0.5,Ncheat(0)=0.25, Ncoop(0) = 0.25 and I find

Flð2Þ ¼ Ncð∞Þ ¼ 0:25þ n211�n211 þ n212

�Nmixð0Þ: [S48]

For the naive cooperator I typically get n11 ≪ n12, implying thatFNaivel ð2Þ ∼ 0:25. For the immune cooperator, I find

Fimmunel ð2Þ ¼ 0:5.General N.Again, pure cooperators and cheaters will always be

maintained whereas mixed tubes will be eliminated. I defineMk asthe fraction of tubes initiated from k cooperators and find thatthe change in this fraction from one iteration to the next dependson a transition matrix Rk→r, which defines the chances of getting rcooperators after a growth experiment that was initiated with kcooperators:

Mrðiþ 1Þ ¼ ∑Nk¼0MkðiÞPk→r ; Pk→r ¼

�N

r

�ρrð1− ρÞN − r ;

ρ ¼ nk1nk1 þ nk2

:

[S49]

Or, in a shorter notation

M!ðiþ 1Þ ¼ RM

!ðiÞ; [S50]

where R is the transition matrix and M is the vector offractions.What do I know about Rk→r? That both cheater and co-

operator pure states are attractors,

Re0 ¼ e0; e0 ¼ ð10 . . . 0ÞT [S51]

ReM ¼ eM; eM ¼ ð10 . . . 0ÞT : [S52]

This condition implies that the matrix R has an eigenvalue of 1with degeneracy of 2. As none of the other mixed states is anattractor—pure states will always form from any intermediatemixed state—the other eigenvalues must be <1:

R ¼ UλU − 1 ¼ U

0BBBBBB@

1 . . . 0λ1

⋮ λ2

⋱0 . . . 1

1CCCCCCAU − 1; λi < 1

for i ¼ 1; . . . ;M − 1:

[S53]

Therefore, at infinite iterations, I find the asymptotic fraction ofcooperators:

FlðNÞ ¼ MðiÞji→∞ ¼ RiMð1Þ

¼ U

0BBBB@

1 . . . 00

⋮ 0⋱

0 . . . 1

1CCCCAU − 1Mð1Þ ¼ R∞Mð1Þ:

[S54]

U is composed of the right eigenvectors of R,

U ¼1 00 0. . . A . . .0 1

0BB@

1CCA, and can easily show that

R∞ ¼

0BB@

z00 z01 z0M

0 0 0. . . . . . . . . . . .zM0 zM1 zMM

1CCA; [S55]

where zij are the components of U−1. Therefore, the two vectorszN = zcoop, z0 = zcheat are the two left eigenvectors with eigen-value 1 of the transition matrix P that satisfy the conditionsz00 = 1, zNN = 1, and zNi + z0i = 1.For the immune cooperator I find ρ ¼ ni1

ðni1 þ ni2Þ ¼iN ′ as

the initial fraction does not change. Therefore,

Pk→r ¼�Nr

��kN

�r�1−

kN

�N − r

: One can show that in this case,

the eigenvalue for the cooperator is zNi = i/N. Therefore, thenumber of cooperators will be

FlðNÞ ¼�12

�NXN0

iN

�Ni

�¼ 0:5: [S56]

I find that the fraction of immune species will always remainconstant in the population under local competition selection. Theexact value of Fl(N) for the naive cooperator depends on thedetails of the competition; however, it is lower bounded by theinitial fraction of cooperator-only tubes and will typically be of

the same order, FlðNÞ ∼�12

�N

:

6.2. Global competition. n = 1. In global competition, each pop-ulation is initiated with a single strain and grown for a time τ.

Eldar www.pnas.org/cgi/content/short/1102923108 7 of 20

Populations are then mixed and plated together. Single lineagesare then picked and grown again. All populations are pure, dueto the bottleneck of 1. The ratio of pure cooperator populationto pure cheater populations increases from cycle to cycle by theirrelative cell density. If M(k) is the fraction of populations of

cooperators, thenMðkþ 1Þ

1−Mðkþ 1Þ ¼n01n12

MðkÞ1−MðkÞ. As I assume that

cooperators are superior to cheaters, I easily find that Fg(1) = M(∞) = 1. This result is, of course, the case for both the naiveand the immune cooperator, as their behavior when unmixed isthe same.

n = 2. In this scenario, each population is initiated with tworandomly chosen strains and grown for a time τ. Populations arethen mixed together. Pairs of cells are chosen randomly from themix to seed the next round of growth. If rcoop, rcheat are thefractions of cooperating and cheating cells found after platingthe mixed test tubes, I find the relations

rcoopðiþ 1Þ ∝ n21r2coopðiÞ þ 2n11rcoopðiÞrcheatðiÞ

rcheatðiþ 1Þ ∝ n02r2cheatðiÞ þ 2n12rcoopðiÞrcheatðiÞ:As rcoop(i) + rcheat(i) = 1 for all i, I find

rcoopðiþ 1Þ ¼ n21r2coopðiÞ þ 2n11rcoopðiÞrcheatðiÞn21r2coopðiÞ þ n02r2cheatðiÞ þ 2ðn12 þ n11ÞrcoopðiÞrcheatðiÞ

:

[S57]

The limits of this relation can be found by a fixed-point analysisof the above relation. It is easy to see that the two extremes(rcoop = 0, 1) are always fixed points of the above relations.In addition, there would be an intermediate single fixed point,rstcoop, if

0< rstcoop ¼�2n12 − n212n11 − n02

þ 1�− 1

< 1: [S58]

This will yield a solution between 0 and 1 only if

�2n11n02

− 1��

2n12n21

− 1�> 0: [S59]

The stability of the fixed points can be derived from graphicalanalysis of the iteration function that governs the recurrencerelation, Eq. S58 (Fig. S4 C–G),

f ðsÞ ¼ n21sþ 2n11ð1− sÞn21s2 þ n02ð1− sÞ2 þ 2ðn12 þ n11Þsð1− sÞs; [S60]

and its derivatives at the extremes,

f ′ð0Þ ¼ 2n11n02

; f ′ð1Þ ¼ 2n12n21

: [S61]

I find that the following conditions will lead to the following fixedpoints (Fig. S4 C and D):

a) f′ð1Þ< 1 and f′ð0Þ> 1: 100% cooperatorsb) f′ð1Þ> 1 and f′ð0Þ< 1: 100% cheatersc) f′ð1Þ> 1 and f′ð0Þ> 1: Intermediate stable stated) f′ð1Þ< 1 and f′ð0Þ< 1: Bistable extremes.

What will be these values for the two types of cooperators? Forthe immune cooperator

n022

< n11 ¼ n12 <n212, as I assume that

a mix of cooperator and cheater will do better than a cheater

only and worse than a cooperator only. This result implies thatcondition 2 will always hold and the selection will converge tocooperators only. For the naive cheater the conditions met willdepend on the exact parameters.

General N. In a similar manner to what I did in the case n= 2, Ican show that the result of selection with a bottleneck N willdepend on the fixed points of the recursion function f(s) andtheir stability, where

f ðsÞ ¼∑N

k¼0

�Nk

�nk1skð1− sÞN − k

∑Nk¼0

�Nk

�ðnk1 þ nk2Þskð1− sÞN − k

: [S62]

The shape of the recursion function will generally depend on theparameters nk1, nk2. In the following, I generally prove two re-lations:

a) The immune cooperator has a single stable fixed point forits recursion function, s = 1.

b) For the naive cooperator s=1will always becomeanunstablefixed point of the recursion function for large enough N.

Proofs of the two relations are as follows:

a) For the immune cooperator, however, this proof has a fairlysimple form and I can generally show that for 0 < s < 1, f(s)> s. To this end, I use Eq. S43 and define

ntotðkÞ ¼ nk1 þ nk2; nk1 ¼ kNntotðkÞ: [S63]

I can therefore rewrite Eq. S63 in this case as

f ðsÞ ¼∑N

k¼0

�Nk

�kNntotðkÞskð1− sÞN − k

∑Nk¼0

�Nk

�ntotðkÞskð1− sÞN − k

¼ 1N

kntotðkÞntotðkÞ

> s

¼ ∑Nk¼0

�Nk

�kNskð1− sÞN − k¼ 1

N�k: [S64]

As ntot(k) is an increasing function of k, I can easily show therelation between the averages:

kntotðkÞ− ntotðkÞ�k ¼ ðk− �kÞ�ntotðkÞ− ntotðkÞ�

¼ ðk− �kÞðntotðkÞ− ntotð�kÞÞ þ ðk− �kÞ�ntotð�kÞ− ntotðkÞ�

¼ ðk− �kÞðntotðkÞ− ntotð�kÞÞ> 0:[S65]

The last expression on the right is always positive because of themonotonicity of the function ntot. I have therefore proved thatthe recursion function f(s) is always larger than s, and this im-plies that the recurrence relation si+1 = f(si) will always havea single limit at s = 1: The immune cooperator will always befixed in the population, irrespective of bottleneck size! Fig. S4 Eand F shows the shape of f(s) for naive and immune cooperatorsfor values of n = 1, 2, 4, 8, 16, and 30. From these graphs I cansee the striking qualitative difference between the two cooper-ators. The naive cooperator gains a single stable fixed pointbetween 0 and 1 above a certain bottleneck size. This fixed pointapproaches 0 as N increases. The immune cooperator, on theother hand, never gains another fixed point, and its only stablefixed point is at s = 1. I note, however, that the recursionfunction of the immune cooperator approaches asymptoticallyfrom above the identity function as N increases. This resultimplies that the convergence time to the fixed point becomes

Eldar www.pnas.org/cgi/content/short/1102923108 8 of 20

longer as N increases. In Fig. S4 E and F I show the numericalvalue of Fg as a function of N for the two cooperators for 50,100, and 200 cycles of selection. Clearly, the naive cooperatorconverges to a specific monotonously decreasing function,whereas the immune cooperator approaches Fg = 1, as thenumber of cycles increases. I note that the growth model isdeterministic and assumes an infinite number of demes. Ananalysis of a more realistic scenario may add other effects ofneutral drift.

b) The recursion function f(s) is stable at a fixed point sf iff′(sf) > 1. s = 1 is always a fixed point of the recursionfunction. I can calculate the derivative of this function ats = 1, by expanding it around this fixed point using thevariable y =1 − s:

I can therefore use the linear approximation to calculate thederivative of f:

df ðsÞdsjs¼1

¼ −df ðsÞdyjy¼0

¼ Nntotð1Þ

�ntot

�1−

1N

�− nc

�1−

1N

��

¼

�dncdx

−dntotdx

�

ntotþ o�1N

�¼

ntotdncdx

− ncdntotdx

n2totþ o�1N

�

¼d�ncntot

�

dxþ o�1N

�¼ dfc

dxþ o�1N

�< 1:

[S67]

I find that for large enough N the fixed point at s = 1 becomesunstable.6.3. Summary. I find that for both local and global selection, the twocooperators behave the same for a bottleneck of a single lineage(as they should, because the cooperators behave identically ontheir own). However, as bottleneck size increases, the naive co-operator frequency approaches zero, whereas the immune co-operator frequency remains constant (at least after a long periodof selection). This striking difference exemplifies the strong se-lective force for the fixation of the novel cheating immune co-operator.

7. Divergence Is Selected in Complex Models. The model presentedin this paper and discussed and analyzed in the previous sectionshas several simplifying assumptions compared with the realisticscenarios expected for many QS systems:

a) I assume full orthogonality of the different signalingpathways. It is more likely to assume, however, that fullorthogonality is the result of gradual evolution throughmutations that slowly reduce the crosstalk between path-ways.

b) The model does not take into account null alleles in thereceptor, the signal, or the public goods enzyme.

c) From a network perspective, the model assumes an open-loop structure, whereas many QS pathways have a positivefeedback from an active receptor on both receptor andsignal production.

d) The model assumes that the enzyme is a complete publicgood, but under various conditions the public good may ben-efit more the producing bacteria, resulting in a snowdrift typeof social interaction and not in a prisoner’s dilemma type.

In this section I show that divergence is still selected even if anyof these simplifications are removed.7.1. Nonorthogonality of alleles does not prevent their diversification. Iuse the same Eqs. S15–S18 to define the interaction betweenvarious strains, but now assume that each receptor is still acti-vated by the noncorresponding signal but with a lower affinity,

Kaccross ¼ ρKRS with ρ < 1. In the following, I show that all se-

lective steps assumed when signals are orthogonal (ρ = 0) arekept positive if 0 < ρ < 1:

Step 1: Selection of a strain with an alternative receptor asa cheater. In this case the new receptor has a lower affinity to

the signal. The interaction matrix is therefore KacΙ ¼

1 1ρ ρ

!

and the activation of each receptor is

Ractive1 ¼ ðs1 þ s2Þ

KRS þ ðs1 þ s2Þ [S68]

Ractive2 ¼ ðs1 þ s2Þ

KRS=ρ þ ðs1 þ s2Þ: [S69]

Therefore,

Ractive2 −Ractive

1 ¼ ðs1 þ s2ÞKRS=ρ þ ðs1 þ s2Þ−

ðs1 þ s2ÞKRS þ ðs1 þ s2Þ< 0 for 0< ρ< 1:

[S70]

By using Eq. S20, I find that

dsdt

¼ rPd

Pd þ 1�f�Ractive2

�− f�Ractive1

��s< 0: [S71]

Therefore, strain 2—having the evolved cheater receptor withreduced affinity—will unconditionally invade into strain 1, theoriginal cooperator. I note that the invading “partial” cheaterwill not lead to a full collapse of the population, as it continuesto produce public goods. If final levels of signal are saturating forpublic goods production, it will have a very similar steady state tothe one of the original strain. I note that the lower the reductionin affinity is in the mutant, the slower the invasion dynamics willbe, as it is proportional to the difference in public goods pro-duction (Eq. S20).

f ðyÞ ¼∑N

k¼0

�N

k

�nc

�kN

�ð1− yÞkyN − k

∑Nk¼0

�N

k

�ntot

�kN

�ð1− yÞkyN − k

¼ncð1Þð1−Nyþ oðyzÞÞ þ Nnc

�1−

1N

�ðyþ oðyzÞÞ þ y2∑N¼z

k¼0

�N

k

�nc

�kN

�ð1− yÞkyN − k− z

ntotð1Þð1−Nyþ oðyzÞÞ þ Nntot

�1−

1N

�ðyþ oðyzÞÞ þ y2∑N¼z

k¼0

�N

k

�ntot

�kN

�ð1− yÞkyN − k− z

¼ncð1Þ−Ny

�ncð1Þ− nc

�1−

1N

��þ oðyzÞ

ntotð1Þ−Ny�ntotð1Þ− ntot

�1−

1N

��þ oðyzÞ

¼ 1þ Ny�nc

�1−

1N

�− ntot

�1−

1N

��þ oðyzÞ: [S66]

Eldar www.pnas.org/cgi/content/short/1102923108 9 of 20

Step 2: Immunity of novel cooperator. In this case, a strain witha new signal (R1S1, strain 1) evolves from the intermediatecheater strain with the altered receptor (R2S1, strain 2). I assumethat the novel signal’s affinity to the novel receptor is increasedback to the original affinity. The interaction matrix now is

therefore KacII ¼

1 ρ1 ρ

!. Similarly to what is described in SI

Text, section 5, both strains have the same receptor and therefore

f�Ractive1

� ¼ f�Ractive2

� ¼ ðs1 þ s2ρÞKRS þ ðs1 þ s2ρÞ: [S72]

Using Eqs. S10–S15 I find that the frequency of the novel co-operator in the system will be maintained:

dntotdt

¼�

Pd

Pdþ1

�1− rf

�Ractive1

��− ntot − γn

�ntot [S73]

d�n2n1

�

dt∝ f�Ractive1

�− f�Ractive2

� ¼ 0⇒ n2ntot

¼ α [S74]

dS1dt

¼ βSðð1− αÞntot − S1Þ [S75]

dS2dt

¼ βSðαntot − S2Þ [S76]

dEdt

¼ f�Ractive1

�ntot − βEE [S77]

dPd

dt¼ VmaxE− βpd

pdpdþ1

ntot: [S78]

At steady state I easily find S1 = (1− α)ntot, S2 = αntot, and

f ðRactiveÞ ¼ ntotKRS=ðð1− αÞ þ ραÞ þ ntot

: This result is equivalent

to the steady state of a single strain with public goods produc-tion intermediate between those of the cheater strain and thenovel immune cooperator strain. As in the case of full orthog-onality, any level of population structure in global competitionwill always lead to the full selection of the novel cooperator.

Step 3: Competition between original and novel cooperators.Note that I did not have to assume anything until now aboutthe affinity of the novel signal to the original receptor. Thisasymmetry is discussed in SI Text, section 8. For the sake ofthis analysis I assume symmetry, implying that this affinity isalso ρKRS. I find that the interaction matrix is therefore

KacIII ¼

1 ρρ 1

!. Receptor occupation is therefore:

Ractive1 ¼ ðs1 þ s2ρÞ

KRS þ ðs1 þ s2ρÞ ¼ gðsþ ρÞ;

Ractive2 ¼ ðs2 þ s1ρÞ

KRS þ ðs2 þ s1ρÞ ¼ gð1þ sρÞ;[S79]

where

gðxÞ ¼ xKRS=n2 þ x

and s ¼ s1s2

≈n1n2: [S80]

g is an increasing function of x and therefore the difference inactivation of the two receptors will depend on the value of x. If

n1 > n2, (s > 1), I find that (1 + sρ) − (s+ ρ) = (ρ − 1)(s − 1) < 0and as both g(x) and f(R) are monotonous this result implies(using Eq. S20) that if n1 > n2,

dsdt

¼ rPd

Pd þ 1�f�Ractive2

�− f�Ractive1

��s

¼ rPd

Pd þ 1ðf ðgð1þ sρÞÞ− f ðgðsþ ρÞÞÞs< 0: [S81]

Therefore, the levels of the minority strain will always increaseand therefore the steady state at n1 = n2 is stable.7.2. Divergence in the presence of null mutants. Diversificationrequires certain types of mutations to the receptor and signalthat will occur in a certain order. Most likely this process isa rare event and the majority of signal or receptor mutationswill just lead to an effectively null mutant. An importantquestion is whether the presence of these null mutants affectsthe evolution of diversity. Several points are well worth notingin this context:

a) Although abundant, null mutants are obligate cheaters thatare bound to be eliminated by an extreme structured pop-ulation (such as the very small bottlenecks that often occurin bacterial ecology). The picture emerging from a struc-tured population is one where cooperators are repeatedlyinvaded by cheaters that are then eliminated and replacedby others. In such a framework two cheater mutants arenot required to compete, as they may arise sequentially.Therefore, the intermediate strain R2S1 may arise like anyother null mutant, on the background of a cooperator strainwith negligible interaction with other null mutants. Theuniqueness of the intermediate strain is that it can regaincooperation by a second mutation, which cannot be done bya null mutant.

b) Despite these remarks, I carried out a simulation of a struc-tured population three-way competition (SI Text, section 6)between the cooperators (either original or immune) andthe intermediate strain, in the background of three differenttypes of signaling null mutants: receptor null, signal null, ora double mutant. In addition to the model, I specificallyassume that a signaling null mutant is saving the cost ofsignal, which is defined to be 1/10th of the maximal costof quorum response. As can be seen in Fig. S5, I find thateven under these conditions, the intermediate can invadeinto the original cooperator strain, but be eliminated in thepresence of the immune cooperator. Some peculiarities ofthe three-way model include a positively selected interac-tion between the intermediate strain (which makes the sig-nal S1) and a signal null receptor (which does not make thesignal and therefore saves the cost of signaling) whose re-ceptor is induced by S1. These types of interactions areprobably unstable in a more realistic structured populationmodel.

7.3. Generalizing the model to include feedbacks on receptor and signal. Inow prove that a generalized system of equations that allow-feedback into the production of receptor and signaling mole-cule and more general cost and benefit terms will show the samebehavior of facultative cheating, as long as all generalizedfunctions are monotonously increasing functions and a fewother simple rules stand as well. The set of equations isas follows:

dnidt

¼ �f1ðPÞ�1− f2�½RS�i��− f3ðntotÞ

�ni [S82]

dsidt

¼ f4�½RS�i�ni − βsSi − n

�kþRiSi þ k− ½RS�i

�[S83]

Eldar www.pnas.org/cgi/content/short/1102923108 10 of 20

I find that time evolution of the ratio s ¼ n1n2

is a generalizationof Eq. S20:

dsdt

¼ f1ðPÞ�f2�½RS�2�− f2

�½RS�1��s: [S88]

I now show the following three characteristics of the above sys-tem:

i) Cheaters take over cooperators: For a mix of cheaters andcooperators, cheaters’ fractions always increase: When con-sidering a QS mutant (strain i = 1), I assume that it pays noenzyme production cost, and therefore its cost function iszero. Using Eq. S88 I find that

dðn1=n2Þdt

¼ n1n2

f1ðPÞ�f2�½RS�2�− f2ð0Þ

�> 0: [S89]

The inequality is true because f2 is monotonously increasing.ii) Divergent QS systems are facultative cheaters with n1 = n2

as a stable steady state. I want to show that if n1 < n2 thendðn1=n2Þ

dt> 0; and vice versa. To show this result I want to

show that

n1 < n2 ⇒ f2�½RS�2�> f2

�½RS�1�⇔½RS�2 > ½RS�1; [S90]

where the equivalence stems from the monotonous increasingproperty of f2. If I assume that the change in cell density is slowcompared with signaling molecule level, receptor–signaling mol-ecule binding, and receptor production, I can assume a quasi-steady state for Eqs. S82–S87 and find

d½RS�idt

¼ g�ni; ½RS�i

�¼ nif4ð½RS�iÞβsKRS

f5�½RS�i�− βR½RS�i: [S91]

The quasi-steady state solution of Eq. S91 is given by

Si ¼ KRSβR½RS�i

f5ð½RS�iÞ. The condition for [RS]i to be monotonous

with Si is {I define s([RS]i) = f4([RS]i)f5([RS]i)}

d½RS�idni

¼ 1dni=d½RS�i

¼ s�½RS�i�2

s�½RS�i�− ½RS�is′

�½RS�i�> 0 [S92]

or

s�½RS�i�> ½RS�i s′

�½RS�i�: [S93]

Eq. S77 is also the condition for the stability of the quasi–steady-state solution:

dgd½RS�i

jg¼0

< 0⇔ niKRS

s′�½RS�i�− βR< 0⇔ ½RS�is′

�½RS�i�< s�½RS�i�:[S94]

Therefore, every stable steady state of receptor level followsa monotonous increasing dependence on cell density, as requiredby Eq. S92.Note that I assume here that all reactions are faster than the

change in cell density for the quasi–steady-state approximationsto be valid. Nevertheless, the conditions in Eq. S92 will be trueunder more general parameters.iii) Cooperation is beneficial: A community of cooperators will

have a higher cell density than a community of cheaters.Using Eqs. S82–S87 I find that the density of pure coop-erators and cheaters is

ncoop f3�ncoop

� ¼ Vmax

βPd

f7ðEÞ�1− f2

�½RS�i�� [S95]

ncheat f3ðncheatÞ ¼ Vmax

βPd

f7ð0Þ: [S96]

Therefore, the condition for ncoop > ncheat (as f3 is monotonouslyincreasing) is

f7ðEÞ�1− f2

�½RS�i��> f7ð0Þ: [S97]

This condition basically reflects the condition that benefit ofcooperation will be larger than the cost of cooperation.7.4. Diversification of quorum sensing under snowdrift conditions. In thissection I demonstrate that QS systems can diversify also underconditions where the quorum response leads to a snowdrift type ofsocial interaction between the producing and nonproducing strains.The snowdrift game between two players occurs when the payoffmatrices imply that defection by one player will not lead to thedefection of the other player. In a multiplayer system (like thecase of bacteria), snowdrift conditions will lead to coexistence ofproducers (cooperators) and nonproducers (cheaters). Re-cently, Gore et al. demonstrated that sucrose metabolism byinvertase secretion in yeast leads to coexistence of producers andcheaters, interpreted as a snowdrift game (21). They demon-strated that partial localization of the enzyme to the yeast peri-plasm leads to internalization of a small fraction of the glucoseproduced by sucrose cleavage directly into the enzyme-producingcell. They showed that preferential growth at a low glucose leveland the preferential internalization of glucose by the producingcells can lead to the observed snowdrift game.Following Gore et al. (21), I model snowdrift conditions by

assuming that the enzyme is bound to the producing cell and thata fraction ε of the substrate is directly internalized by the pro-ducing cell. I also assume that the growth rate of each cell isproportional to the availability of nutrient to the power α. Itherefore need to write a new set of equations where each strainhas also an enzyme population, Ei, and a local nutrient pool, Pi.The set of equations defining the population dynamics now istherefore

dnidt

¼ �H�Pi þ Ppub; α��1− rf

�Ractivei

�− rs�− ntot − γn

�ni [S98]

dsidt

¼ βsðni − SiÞ [S99]

dRi

dt¼ fs

�½RS�i�− kþRiSi þ k− ½RS�i − βRRi [S84]

d½RS�idt

¼ kþRiSi − k− ½RS�i [S85]

dEdt

¼ PE∑if6�½RS�i�ni − βEE [S86]

dPd

dt¼ Vmax f7ðEÞ− βPd

f1ðPÞntot: [S87]

Eldar www.pnas.org/cgi/content/short/1102923108 11 of 20

dEi

dt¼ f�Ractivei

�ni − βEEi [S100]

dPi

dt¼ εVmaxEi − βPd

�Pi

Pi þ PpubH�Pi þ Ppub; α

��1− rf

�Ractivei

�− rs�

[S101]

dPpub

dt¼�JPd þ∑i

�ð1− εÞVmaxEi − βpd

Ppub

Pi þ PpubH�Pi þ Ppub; α

�

×�1− rf

�Ractive1

�− rs�ni

�ntot:

[S102]

Unlike in Eqs. S15–S18, I have defined the enzyme and nutrientpools here for a single bacterium, because of the private natureof some of the nutrients. Ractive

i is defined as in Eq. S14 for thedifferent pairs of strains. The function H is the Hill function:

Hðx; αÞ ¼ xα

1þ xα: [S103]

Note that when ε = 0 and α = 1, the above equations are es-sentially equivalent to Eqs. S15–S18.In Fig. S6 I show the results of competition between the dif-

ferent divergent strains under homogenous conditions (Fig. S6A–D) and in a structured population model identical to the onediscussed in SI Text, section 6 (Fig. S6 E–H). The only differencein the homogenous conditions is that the cheater strain R2S1invades into the original QS strain R1S1 only to coexistence of∼75% (the number depends on the exact parameters used). Asin the prisoner’s dilemma case, the fraction of the novel immunecooperator, R2S2, does not change with time in its competitionwith R2S1, so the immunity property remains the same. Thisresult is clear, as immunity is related to the nature of signalingand not to the nature of social competition. Finally, the com-petition between the strains R2S2 and R1S1 has the 50%:50%coexistence state, as an only stable state, whereas the cheater:cooperator coexistence frequencies are destabilized.Fig. S6 E–G demonstrates the fate of the three competitions

between the strains under a structured population with globalcompetition (as in Fig. 3 of the main text). As you can see, thenovel strain R2S2 is selected under these conditions. Becausesnowdrift conditions lead to coexistence of the cheater R2S1 andthe original cooperator R1S1, I considered also the three-waycompetition between R1S1, R2S1, and R2S2. As shown in Fig.S6H, the two cooperators reach coexistence under these con-ditions whereas the intermediate strain is eliminated.In summary, the snowdrift nature of the social interactions

does not prohibit the evolution of diversified quorum-sensingpathways.

8. The Evolution of Cross-Interactions. When considering the ob-served relations between various strains carrying divergent formsof the same QS system, one can find several types of cross-interactions; in more closely related QS systems (from a sequenceperspective), one often finds some level of cross-activation thatmay not be necessarily equal between different strains. In moredistantly related QS systems, one often finds cross-inhibitionbetween the two strains, again, not always to the same extent.Both cross-inhibition and cross-activation may be a direct effectof mechanistic inability to fully diverge or result from specificadaptations that select for those interactions. In this section Iconsider the second option, to understand the full richness ofsocial interactions arising during diversification.

8.1. Cross-inhibition is maintained in a complex population structure. Asexplained in themain text, cross-inhibition is a facultative cheatingstrategy of the inhibited strain in my model: It will produce publicgoods when alone and avoid producing themwhen in the presenceof the inhibiting strain. I claimed that this strategy cannot beeliminated well by a structured population as demonstrated bythe analysis of random bottlenecked populations.This argument can be understood by following the steady-state

levels of the three strains for the three-way competition and thethree two-way and three one-way competitions, as presented inFig. S7A. As can be seen, in the three-way competition cross-inhibition is strongly selected over orthogonality. In two-waycompetition cross-inhibition will be selected over orthogonality ifthe inhibited orange strain performs better than the orthogonalorange strain when in competition with the cyan strain—that is,if Δ1 > 0. Otherwise, a two-way competition will select for or-thogonality. Also, the two-way competitions leads to cooperationbetween the two orange strains (orthogonal and inhibited)against the cyan strain—if Δ1 > 0, then the only strain that losesin the two-way competition is the cyan strain. One-way growth isalways equivalent for all strains. Different structured populationswill assign different probabilities for the different types ofcompetitions. In the random bottleneck model with bottlenecksize N, the total number of initial conditions is 3N, of which only∼3 × 2N cases are of two-way or one-way type (where one ormore of the strains are absent from initial conditions). There-fore, over N ≅ 5 the three-way competition will dominate thespectrum of competitions and cross-inhibition will evolve. Forn < 6 I may find a parameter-specific solution to the problem.The evolution of one-sided cross-inhibition can lead to the

evolution of mutual cross-inhibition, as a cheating strategy of theother (cyan) strain.8.2. Unilateral cross-activation can be a direct outcome of divergence andbenefit the signaling strain. In the model presented in this paper Iassumed that one system with receptor R1 and signaling moleculeS1 will diverge into a novel QS system with receptor R2 andsignaling molecule S2. I assumed that R2 and S2 are specific anddo not interact with the original strains. A closer observation ofthe evolutionary dynamics exposes further complexity: The sec-ond signal, S2, is actually not selected against activation of R1.This asymmetry between S1 and S2 is formed because the mu-tations leading to the formation of S2 occur in the strain R2S1and are selected to activate R2. Because R1 is already absent atthis stage, there are no selective constraints on its interactionwith S2.What are the implications of such unilateral cross-activation: S2

activating R1, but S1 not activating R2? In Fig. S7B I demonstratethe striking difference between the case of a pair of non-interacting divergent strains and a pair with unilateral cross-ac-tivation. In the former case, analyzed above and in the main text,the two strains will coexist with equal densities. In the latter case,the signaling cell will become dominant once the strength ofcross-activation (the affinity of S2 to R1) becomes of the sameorder of magnitude as the self-affinity of the two systems. Thisresult occurs because now the signaling QS strain is inducing theoriginal QS strain to work also under conditions where it has notreached a quorum. Therefore, a possible scenario for selectionfor divergence is a nonsymmetric relation with the evolved straindominating over the previous strain.What are the possible adaptations the cross-activated QS strain

can undergo to counteract a cross-activation? There are severalpossible answers with different functional outcomes:

i) Receptor divergence: The receptor can further diverge tolose the cross-activation. This action will return the systemto the scenario described in the main text.

ii) Inhibition: The receptor can diverge to be inhibited by thesignal, as was discussed in the previous subsection. It is not

Eldar www.pnas.org/cgi/content/short/1102923108 12 of 20

clear a priori whether option i or ii is more accessible to thereceptor.

iii) Overactivation: In this case, the signal of the induced strainwill mutate to induce the receptor of the inducer strain.The cross-induction is described in SI Text, section 3. Iteffectively reduces the difference between the strains andin general reduces the chances of mutual invasion. It isunlikely that this type of mutation will be selected underthe inducing selective pressure, because it does not benefitthe mutant under these conditions (it will survive, but notincrease in frequency).

9. Comparison Between QS Divergence and Kin-Recognition Systems.In the last decade, kin discrimination has gained a considerableinterest from evolutionary biologists and sociobiologists andseveral models analyzing the social dynamics of kin-recognizingcooperators have been devised (22–26). All of these models shareseveral assumptions: First, they assume that kin discrimination ischaracterized by a single locus (tag locus) with multiple alleles(tag colors). Second, another locus (cooperation) has two alleles,cooperate or defect. Third, they assume kin-specific cooperation:Cooperators will cooperate only with organisms with the sametag color, whereas defectors will always defect. The underlyingquestion of all of the works is whether kin recognition can easethe evolution of cooperation by directing cooperative behavioronly toward kin with higher relatedness than the average (26)(Fig. S8 A and B). Note that unlike a greenbeard locus, kinrecognition is a multilocus system and is not supposed to beimmune from defection (or cheating)—an organism carryinga specific kin phenotype can still be a defector.The main findings of these works (as this author understands

them) are that kin recognition can evolve and benefit cooperationonly if population structure is complex enough (24, 26) or linkagedisequilibrium between the kin and cooperation loci is high (23)or if the kin locus mutation rate is very high compared with thedefection mutation rate (25). In the generic case (and specificallyin well-mixed environments with relatively low mutation rates),the population will consist of a single kin-recognition type,making the allele ineffective in promoting cooperation. This kin-recognition allele will occasionally mutate into a new allele; ifthis mutation happens in a cooperator and the general level ofcooperation of the previous kin type is low, then it will quicklyinvade to fixation (23, 24). The underlying reason for this be-

havior is the positive frequency selection that is imposed by kinrecognition: The majority kin is more likely to meet counterparts(which by lineage are likely first to be cooperators) and gainbenefits, compared with a minority kin that only rarely meet itsown kin.Themodel I present for the evolution of QS is different from all

of the above models in two critical aspects:

i) Two loci for kin type: All of the previous models assumedthe existence of a single locus for kin type. My model hasthe more realistic assumption that at least two loci areneeded for kin recognition: a locus for tag display anda locus for tag recognition (Fig. S8C). This problem wasmentioned briefly in one of the above works (23) and itwas suggested that neutral evolution can lead to a coordi-nated switch in both loci. My model, to the contrary,shows that coevolution of tag and recognition loci is pos-itively selected through cheating and immunity. Whereasmy model assumed a public signal and a public good, thisresult can be shown to be true also in a model of directcooperation between pairs, for exactly the same reasons(Fig. S8D).

ii) Negative frequency selection on alternative kin types: Incontrast to the previous models, my model results in co-existence of different kin types even in homogenous con-ditions. This fundamental difference between my modeland the rest of the models stems from the public goodsnature of cooperation: In my model, organisms decide tocooperate on the basis of the presence of kin, but oncecooperating, they will benefit all of the surrounding organ-isms, not just their kin. This non-selective cooperation sta-bilizes minority strains that invade through facultativecheating dynamics but comes with an obvious cost: Publicgoods cooperation through kin recognitions cannot in-crease the level of cooperation in a population (and maydecrease it). This cost is clearly so, as defectors (irrespec-tive of their kin type) will always exploit active cooperators.

iii) Whereas the kin recognition system described in my modeldoes not lead to an increase in the total level of sociality, itdoes serve to diversify the number of “colors” used in therecognition system. The focus of my work is to explain thispattern of diversity and not to suggest new mechanisms forstabilization of cooperation.

1. Hense BA, et al. (2007) Does efficiency sensing unify diffusion and quorum sensing?Nat Rev Microbiol 5:230–239.

2. Dubey GP, Ben-Yehuda S (2011) Intercellular nanotubes mediate bacterialcommunication. Cell 144:590–600.

3. Jelsbak L, Søgaard-Andersen L (2000) Pattern formation: Fruiting bodymorphogenesis in Myxococcus xanthus. Curr Opin Microbiol 3:637–642.

4. Aoki SK, et al. (2010) A widespread family of polymorphic contact-dependent toxindelivery systems in bacteria. Nature 468:439–442.

5. Pfeiffer T, Schuster S, Bonhoeffer S (2001) Cooperation and competition in theevolution of ATP-producing pathways. Science 292:504–507.

6. Kreft J-U (2004) Conflicts of interest in biofilms. Biofilms 1:265–276.7. Parkinson K, Buttery NJ, Wolf JB, Thompson CR (2011) A simple mechanism for

complex social behavior. PLoS Biol 9:e1001039.8. Visick KL, Foster J, Doino J, McFall-Ngai M, Ruby EG (2000) Vibrio fischeri lux genes

play an important role in colonization and development of the host light organ.J Bacteriol 182:4578–4586.

9. Lupp C, Urbanowski M, Greenberg EP, Ruby EG (2003) The Vibrio fischeri quorum-sensing systems ain and lux sequentially induce luminescence gene expression and areimportant for persistence in the squid host. Mol Microbiol 50:319–331.

10. Ruby EG (1996) Lessons from a cooperative, bacterial-animal association: The Vibriofischeri-Euprymna scolopes light organ symbiosis. Annu Rev Microbiol 50:591–624.

11. Cornes R, et al. (1996) The Theory of Externalities, Public Goods, and Club Goods(Cambridge Univ Press, Cambridge, UK).

12. Redfield RJ (2002) Is quorum sensing a side effect of diffusion sensing? TrendsMicrobiol 10:365–370.

13. Venturi V, Bertani I, Kerényi A, Netotea S, Pongor S (2010) Co-swarming and localcollapse: Quorum sensing conveys resilience to bacterial communities by localizingcheater mutants in Pseudomonas aeruginosa. PLoS ONE 5:e9998.

14. Xavier JB, Foster KR (2007) Cooperation and conflict in microbial biofilms. Proc NatlAcad Sci USA 104:876–881.

15. Kreft J-U (2004) Biofilms promote altruism. Microbiology 150:2751–2760.16. MaClean RC, Fuentes-Hernandez A, Greig D, Hurst LD, Gudelj I (2010) A mixture of

“cheats” and “co-operators” can enable maximal group benefit. PLoS Biol 8:e1000486.

17. Diggle SP, Griffin AS, Campbell GS, West SA (2007) Cooperation and conflict inquorum-sensing bacterial populations. Nature 450:411–414.

18. Chuang JS, Rivoire O, Leibler S (2009) Simpson’s paradox in a synthetic microbialsystem. Science 323:272–275.

19. Wilder CN, Diggle SP, Schuster M (2011) Cooperation and cheating in Pseudomonasaeruginosa: The roles of the las, rhl and pqs quorum-sensing systems. ISME J,10.1038/ismej.2011.13.

20. Griffin AS, West SA, Buckling A (2004) Cooperation and competition in pathogenicbacteria. Nature 430:1024–1027.

21. Gore J, Youk H, van Oudenaarden A (2009) Snowdrift game dynamics and facultativecheating in yeast. Nature 459:253–256.

22. Axelrod R, Hammond RA, Grafen A (2004) Altruism via kin-selection strategies thatrely on arbitrary tags with which they coevolve. Evolution 58:1833–1838.

23. Jansen VA, van Baalen M (2006) Altruism through beard chromodynamics. Nature440:663–666.

24. Rousset F, Roze D (2007) Constraints on the origin and maintenance of genetic kinrecognition. Evolution 61:2320–2330.

25. Antal T, Ohtsuki H, Wakeley J, Taylor PD, Nowak MA (2009) Evolution of cooperationby phenotypic similarity. Proc Natl Acad Sci USA 106:8597–8600.

26. Gardner A, West SA (2010) Greenbeards. Evolution 64:25–38.

Eldar www.pnas.org/cgi/content/short/1102923108 13 of 20

a b

c

‘Che

ater

’Fre

quen

cy

Tota

l Cel

l den

sity

Exo -

Enzy

me

leve

ls

Time

Time

Time

dPublic goods

R1S1 R0S0

Fig. S1. QS− is a cheater. (A) A QS− strain (R0S0, cheater) can invade a QS+ strain (R1S1, cooperator) by not paying the cost of public goods production (red

arrow), but gaining its benefits (green arrow). (B–D) Numerical results of an invasion of a QS− strain into a QS+ strain. I use Eqs. S15–S18 with Kacij ¼

0 00 1

!.

Initial QS− (strain 1) frequency is set to 1% of the producer frequency. Shown are the following: (B) Frequency of the QS− strain. This frequency increases withtime. (C) Total cell density. This density initially increases, but as the cheater strain invades the population, it decreases again. Total cell densities of a pure QS+

population (gray line) and QS− population (dashed gray line) are also shown. (D) Public goods (enzyme) levels. These levels follow a similar trend to that oftotal cell density. Gray lines show enzyme production in QS+ only and QS− only strains.

Log10( )

Log 10

(KRS

)

z

Fig. S2. The steady-state value of cooperator for different levels of ζ, KRS.

Cooperator mixed withQS mutant cheater

Cooperator mixed withQS inducer cheater

QS mutant cheater

QS inducer cheater

Time

Cell

dens

ity

Fig. S3. Properties of an inducer cheater. Shown are the cell densities as a function of time of a quorum-sensing strain (green) that is mixed with a cheater(red) who has a 100-fold smaller initial cell density. Two types of cheaters are compared: complete QS null cheater (solid lines) that lacks both receptor andsignal and an inducer cheater that is still producing the signal and therefore induces the cooperator strain’s quorum response. As can be seen, in my model, theinducer cheater levels are maintained higher for a longer time. Nevertheless, the qualitative behavior of the cheater is independent of induction.

Eldar www.pnas.org/cgi/content/short/1102923108 14 of 20

Immune cooperator

N=1

N=30

e f

F(i)F(i)F(

i+1)

F(i+

1)

F(i)F(i)

F(i+

1)

F(i+

1)

c d100% cooperators Co-existence

g Naïve cooperator

N c

ells

bo

�le

neck

a

N c

ells

bo

�le

neck

s

b

Fig. S4. Selection in a structured population based on bottlenecks. (A and B) The two selection processes. (A) Local competition. (B) Global competition. (C–G)Cooperator frequency in global competition can be calculated using iteration maps. (C and D) The frequency of cooperators after a cycle is a function of theirfrequency before the cycle. The limit of many cycles can be calculated from the iteration map as shown in (C) the 100% cooperator map and (D) coexistence ofcooperators and cheaters. (E and F) Iterations map for (E) naive cooperator and (F) immune cooperator for varying bottleneck size. Shown are the maps forbottleneck size N = 1, 2, 4, 8, 16, and 30. N = 1 and 30 are indicated in E and the colors are the same for both plots. As can be seen, the naive cooperator’s maphas a coexistence fixed point for n > 4. The immune cooperator always has only the pure cooperator as a fixed point, but as N increases the iteration mapconvergence to the identity function and convergence time to pure cooperators become longer. (G) Cooperator frequency as a function of bottleneck size forthe naive (blue) and immune (green) cooperators for 50 (solid line), 100 (dashed line), and 200 (dotted line) selection cycles. As can be seen, the naive co-operator’s dependence converges quickly to a limit, whereas the immune cooperator’s dependence converges slowly toward pure cooperators.

Eldar www.pnas.org/cgi/content/short/1102923108 15 of 20

0 10 200

0.5

1R1S1/ R2S1/ R1S0

Stra

in fr

eque

ncy

0 10 200

0.5

1R1S1/ R2S1/ R0S0

0 10 200

0.5

1R1S1/ R2S1/ R0S1

0 10 200

0.5

1R2S2/ R2S1/ R1S0

Stra

in fr

eque

ncy

Bottleneck size0 10 20

0

0.5

1R2S2/ R2S1/ R0S0

Bottleneck size0 10 20

0

0.5

1R2S2/ R2S1/ R0S1

Bottleneck size

b

a

Fig. S5. The effect of obligate cheaters on the diversification of QS systems. (A and B) Shown are the frequencies of the various competing strains asa function of bottleneck size in a structured population three-way competition. The competing strains are the cooperator [blue, either the naive (A) or theimmune (B)], the intermediate strain R2S1 (green), and one of three types of null mutants of the original naive cooperator R1S1 (red). These types are signal nullmutant (Left), signal and receptor null mutant (Center), and receptor null mutant (Right). I assume here that constitutive signaling has a constitutive cost that issaved by the signal null mutant. This cost is 10 times lower than the maximal quorum response cost. As can be seen, the intermediate mutant strain R2S1 alwaysinvades into the original cooperator R1S1 and is invaded by the immune cooperator R2S2. R2S1 is not eliminated by the immune cooperator when in thepresence of a signaling mutant of the original cooperator. This outcome is because the signal of R2S1 is inducing a quorum response from the null mutant. Inote here that the exact fate of the three strains will strongly depend on the length of growth and the assumptions about the structured population. A three-way Poisson distribution as I use here (SI Text, section 6) is probably unrealistic. A more likely scenario is that most demes carry only two of the three strains andthat three-way competition is rare. Parameters of the model are the same as defined in Materials and Methods in the main text. Signaling mutants are as-sumed to save a constitutive cost that amounts to rs ¼ r

10¼ 0:01 of the maximal growth rate. Interaction matrices are defined appropriately to reflect the

various types of strains.

Eldar www.pnas.org/cgi/content/short/1102923108 16 of 20

a b c dR1S1 R2S1 �R1S1 R2S2 �R2S1 R2S2 �R1S1

ε=0.1, α=0.2ε=0, α=1

e f

g h

R2S1 vs. R1S1

R2S2 vs R1S1

R2S1 vs. R2S2

R2S1 vs. R2S2 vs. R1S1

R 1S1

freq

uenc

yR 1S

1fr

eque

ncy

R 2S2

freq

uenc

yFr

eque

ncy

Bo�leneck size Bo�leneck size

Fig. S6. The selection of QS diversification in a snowdrift interaction model. (A–D) For each case I show the total population as a function of time (Upper) andthe frequency of the invading strain as a function of time (Lower). For each situation I show the result of a snowdrift type of interaction (solid line, ε = 0.1, α =0.2) and a prisoner’s dilemma type of interaction (dashed line, ε = 0, α = 1). The cases are (A) a single cooperator strain, R1S1 [no competition and hence noinvader (Lower)], (B) R2S1 invades into R1S1. Note that in the snowdrift case the cheater strain invades only to a frequency of ∼75%. (C) R2S2 invades into R2S1.The immune cooperator is neutral in invasion—frequency remains constant with time. (D) R2S2 invades into R1S1. The two strains coexist in equal frequency. (E–H) Competition in a snowdrift model under a structured population. (E–G) Shown are the results of global competition under a structured population asa function of bottleneck size. The competitors are shown at the top, and the y axis defines which strain’s frequency is shown (the other strain’s frequencycomplements to 1). The results are essentially the same as for a prisoner’s dilemma case: The intermediate strain invades for a large enough bottleneck size (E),whereas the immune cooperator fully invades the intermediate strain (F). The two competing quorum-sensing strains coexist except for the case of a bot-tleneck size of 2, where the system is bistable. (H) As the intermediate strain R2S1 coexists with the original quorum-sensing strain R1S1, I must consider also thetriple competition between R1S1 (blue), R2S1 (green), and R2S2 (red) to determine the fate of strain R2S2 after its formation. Shown are the frequencies of thethree strains as a function of bottleneck size. For all cases (except for a bottleneck of size 2), the two divergent strains coexist in a frequency of 50% whereasthe intermediate strain is eliminated.

Eldar www.pnas.org/cgi/content/short/1102923108 17 of 20

0 H/2+ 1 H/2- 2

HHH

Hx Hy

P(z=0)

H/2+ 1 H/2- 2

P(x=0)

H/2 H/2

P(y=0)

P(x,y=0)P(x,z=0)P(y,z=0)

3-way

2-way

1-way

KselfKcross

Kcross/Kself

Stra

in F

requ

ency

a

b

Fig. S7. The effects of cross-interaction between divergent strains. (A) Cross-inhibition is a cheating strategy of the receiving strain. Schemes show the in-teraction between the communication systems of three strains: two divergent ones (orange and cyan) and a mutant of the orange system in which the receptoris inhibited by the signal of the cyan strain. Shown are the interactions during a three-way competition as well as those for two-way and one-way populations.The expression below each term defines the approximate steady-state cell density of this strain in the specific competition. The expression on the top of eachcompetition box displays the probability of attaining this competition. x, y, and z are the initial frequencies of the orthogonal orange, inhibited orange, andcyan strains, respectively. However, three-way competition always leads to the elimination of the orange orthogonal strain (Fig. 3 B and C). The results of two-way competitions are parameter dependent. The three strains are equivalent during one-way growth. (B) Cross-activation is a cheating strategy of the sig-naling strain. If signal from one strain (cyan in this case, see scheme) cross-activates the receptor of the second strain, but not vice versa, the cross-activatingstrain will cheat on the activated strain, by inducing its public goods production at lower concentrations. This result is similar to the case of an inducer–cheaterdiscussed in SI Text, section 4. The graph shows the steady-state levels of the two strains for varying levels of the ratio between cross-activation affinity and self-activation affinity.

Eldar www.pnas.org/cgi/content/short/1102923108 18 of 20

Cooperator Cheater

-C B

a

b

c

d

Muta�on

Coopera�on

Iden�fica�on

e

M=2N=4

1

0

Freq

uenc

y

Time

1

0

Freq

uenc

y Other kin-recogni�on models

QS kin-recogni�on model

f

Fig. S8. Kin recognition and QS diversification model. (A) Typical models of cooperation include two types of strategies: cooperator (Inset, smiley face) andcheater (Inset, sad face). A cooperator will invest a cost C to give its partner (either a cooperator or a cheater) a benefit B. A green arrow directs from co-operator to beneficiary. (B) Kin-recognition models assume that each organism is characterized by a tag (orange or cyan beard in this case). A cooperator willinvest and benefit only an organism with the same tag. (C–E) The QS model differs in two substantial ways from previous kin recognition models. (C and D)Two-locus kin recognition. (C) The QS diversification model applies to a case where kin is represented by two loci: a recognition locus (eye color) and a tag locus(beard color). A cooperator will invest and benefit only when it recognizes a tag of the same color, i.e., the cooperator’s eyes should have the same color as thebeneficiary’s beard. (D) The social and genetic relations between the four types of cooperators for two alleles/two loci kin types. Black dashed arrows representmutations. Blue arrows represent social interaction. Social relations form a cycle of social helping between the four genotypes. Unicolored organisms helpthemselves whereas multicolored organisms help each other. Each of the organisms can also mutate into a cheater that can cheat its ancestor and the co-operator preceding it in the cycle. (E) Decoupling help and recognition. The QS model assumes that identification (red arrows) leads to cooperation (greenarrows), which equally benefits all neighbors of the cooperators (including nonkin). For the example above, the number of identified neighbors is M = 2,

leading to a cost of investment M × C for the cooperating cell and a benefitM×CN

for each neighbor (n = 4 in this case). (F) Frequency-dependent selection in

the two models. (Upper) In other kin recognition models, the selection is positive frequency dependent—the majority strain will be fixed in the population.(Lower) Decoupling between cooperation and identification cannot promote the level of cooperation but leads to negative frequency selection and co-existence of multiple kin types.

Eldar www.pnas.org/cgi/content/short/1102923108 19 of 20

Table S1. Examples of secreted QS-dependent molecules in various bacteria, including known species with a divergent quorum-sensingsystem

Organism Gram +/−

QSsignalinggene Signal type

QS-regulatedsecretedmolecule Function Ref. Notes

Bacillus subtilis + comX Modified peptide Surfactin (srf) Surfactant (1) Diverging signalStaphylococcusaureus

+ agr Modified peptide Alpha toxin (hla) Hemolysin Diverging signal,cross-inhibition

Streptococcuspneumoniae

+ comC Unmodified peptide iga IgA1 protease (2) Diverging signal

Bacillus cereus + papR Unmodified peptide Hemolysin Hemolysin (3) Diverging signalErwinia carotovora − expI AHL (3-oxo-C6-HSL/3-

oxo-C8-HSL)Cel Cellulase (4) Diverging signal

Chromobacteriumviolaceum

− cviI AHL (C6-HSL/3-oxo-C10-HSL)

Chitinase (5–7) Diversifying signals,cross-inhibition

Pseudomonasaeruginosa

− lasI AHL Elastase Protease (8)

P. aeruginosa − rhlI AHL Rhamnolipid Surfactant (8)Ralstoniasolanacearum

− solI AHL Egl Endoglucanase (9)

Serratiaproteamaculans

− sprI AHL lipB Secretionmachineryfor multipleexo-enzymes

(10)

Burkholderiacenocepacia

− cepI AHL zmpA Extracellular zincmetalloprotease

(11)

Lactococcus lactis + nisA Nisin Nisin Antibiotic (12) The antibiotic isalso the signal

Enterococcusfaecalis

+ fsrB Modified peptide Gelatinase Extracellular zincmetalloprotease

(12)

AHL, acyl homoserine lactone.

1. Nakano MM, et al. (1991) srfA is an operon required for surfactin production, competence development, and efficient sporulation in Bacillus subtilis. J Bacteriol 173:1770–1778.2. Rimini R, et al. (2000) Global analysis of transcription kinetics during competence development in Streptococcus pneumoniae using high density DNA arrays. Mol Microbiol 36:

1279–1292.3. Slamti L, Lereclus D (2002) A cell-cell signaling peptide activates the PlcR virulence regulon in bacteria of the Bacillus cereus group. EMBO J 21:4550–4559.4. Chatterjee A, Cui Y, Liu Y, Dumenyo CK, Chatterjee AK (1995) Inactivation of rsmA leads to overproduction of extracellular pectinases, cellulases, and proteases in Erwinia carotovora

subsp. carotovora in the absence of the starvation/cell density-sensing signal, N-(3-oxohexanoyl)-L-homoserine lactone. Appl Environ Microbiol 61:1959–1967.5. Chernin LS, et al. (1998) Chitinolytic activity in Chromobacterium violaceum: Substrate analysis and regulation by quorum sensing. J Bacteriol 180:4435–4441.6. Morohoshi T, Kato M, Fukamachi K, Kato N, Ikeda T (2008) N-acylhomoserine lactone regulates violacein production in Chromobacterium violaceum type strain ATCC 12472. FEMS

Microbiol Lett 279:124–130.7. McClean KH, et al. (1997) Quorum sensing and Chromobacterium violaceum: Exploitation of violacein production and inhibition for the detection of N-acylhomoserine lactones.

Microbiology 143:3703–3711.8. Pearson JP, Pesci EC, Iglewski BH (1997) Roles of Pseudomonas aeruginosa las and rhl quorum-sensing systems in control of elastase and rhamnolipid biosynthesis genes. J Bacteriol 179:

5756–5767.9. Flavier AB, Schell MA, Denny TP (1998) An RpoS (sigmaS) homologue regulates acylhomoserine lactone-dependent autoinduction in Ralstonia solanacearum.Mol Microbiol 28:475–486.10. Christensen AB, et al. (2003) Quorum-sensing-directed protein expression in Serratia proteamaculans B5a. Microbiology 149:471–483.11. Sokol PA, et al. (2003) The CepIR quorum-sensing system contributes to the virulence of Burkholderia cenocepacia respiratory infections. Microbiology 149:3649–3658.12. Kleerebezem M, Quadri LE, Kuipers OP, de Vos WM (1997) Quorum sensing by peptide pheromones and two-component signal-transduction systems in Gram-positive bacteria. Mol

Microbiol 24:895–904.

Eldar www.pnas.org/cgi/content/short/1102923108 20 of 20