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vol. 178, no. 1 the american naturalist july 2011

Negotiation, Sanctions, and Context Dependency in the

Legume-Rhizobium Mutualism

Erol Akcay1,* and Ellen L. Simms2

1. National Institute for Mathematical and Biological Synthesis, University of Tennessee, Knoxville, Tennessee 37996; 2. Department ofIntegrative Biology, University of California, Berkeley, California 94720

Submitted June 4, 2010; Accepted February 28, 2011; Electronically published June 2, 2011

Online enhancements: appendix, Mathematica file.

abstract: Two important questions about mutualisms are how thefitness costs and benefits to the mutualist partners are determinedand how these mechanisms affect the evolutionary dynamics of themutualism. We tackle these questions with a model of the legume-rhizobium symbiosis that regards the mutualism outcome as a resultof biochemical negotiations between the plant and its nodules. Weexplore the fitness consequences of this mechanism to the plant andrhizobia and obtain four main results. First, negotiations permit theplant to differentially reward more-cooperative rhizobia—a phenom-enon termed “plant sanctions”—but only when more-cooperativerhizobia also provide the plant with good outside options duringnegotiations with other nodules. Second, negotiations may result inseemingly paradoxical cases where the plant is worse off when it hasa “choice” between two strains of rhizobia than when infected byeither strain alone. Third, even when sanctions are effective, they areby themselves not sufficient to maintain cooperative rhizobia in apopulation: less cooperative strains always have an advantage at thepopulation level. Finally, partner fidelity feedback, together with ge-netic correlations between a rhizobium strain’s cooperativeness andthe outside options it provides, can maintain cooperative rhizobia.Our results show how joint control over the outcome of a mutualismthrough the proximate mechanism of negotiation can affect the evo-lutionary dynamics of interspecific cooperation.

Keywords: sanctions, partner choice, partner fidelity feedback, bio-logical markets, partner control, context dependency.

Introduction

Evolutionary biologists have long wondered how it is thatcostly traits that benefit the fitness of unrelated individualscan be adaptive (Darwin 1859; Herre et al. 1999; Bronsteinet al. 2003; Sachs et al. 2004). The puzzle is especially acutefor mutualisms in which individuals encounter and in-teract with multiple partners from the environment, astheir fitness interests often conflict (Bull and Rice 1991;Noe and Hammerstein 1995; West et al. 2002b, 2002c;

* Corresponding author; e-mail: [email protected].

Am. Nat. 2011. Vol. 178, pp. 1–14. ! 2011 by The University of Chicago.0003-0147/2011/17801-52213$15.00. All rights reserved.DOI: 10.1086/659997

Sachs and Wilcox 2006). In such mutualisms, selectionwill favor any individual with a mutation that increasesits own fitness by increasing fitness benefits received frompartners and/or reducing the fitness cost of benefits pro-vided to partners. In the absence of counterselection, thisevolutionary trajectory destabilizes the mutualism.

One proposed counterselection mechanism follows themetaphor of a “biological market” (Noe and Hammerstein1994, 1995; Hammerstein 2001; Noe 2001; Simms andTaylor 2002). In this extended metaphor, controlling in-dividuals choose “trading partners” from a market of po-tential “traders” (Noe and Hammerstein 1994). Partnersare chosen according to their relative quality, quantifiedas the fitness benefits they provide minus the costs theyimpose. For such choice to maintain cooperation andhence mutualism, controlling individuals must accuratelytarget fitness benefits to high-quality partners (Bshary andGrutter 2002; Simms and Taylor 2002; Foster and Kokko2006). However, biological market theory does not con-sider how such targeting may be achieved, implicitly as-suming that the controlling individuals have completecontrol over “payments” in their market transactions. Inreality, the allocation of rewards is likely to be determinedby a biological process that gives both parties some degreeof control. In this article, we ask how such an allocationmechanism affects the predictions from biological markettheory, using a mathematical model of the symbiosis be-tween legumes and rhizobia.

Rhizobia are soil-dwelling alpha- and beta-proteobac-teria that form nitrogen-fixation symbioses with many le-gumes (Sprent 2007; Masson-Boivin et al. 2009). Rhizobiainfect legume roots, stimulate hosts to produce nodules,and differentiate into specialized endosymbiotic cells calledbacteroids, which reduce atmospheric dinitrogen in ex-change for plant photosynthates (Trainer and Charles2006; Prell et al. 2009). Several aspects of the symbiosisdecouple plant and rhizobial fitness. Rhizobia are trans-mitted horizontally among hosts and not vertically

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2 The American Naturalist

through seeds (Sprent et al. 1987), and symbiotic rhizobialikely derive fitness benefits through release into the soilfrom senescing nodules (Kiers et al. 2003; Denison andKiers 2004; Simms et al. 2006; Heath and Tiffin 2009).Further, individual plants usually host multiple rhizobialgenotypes (Dowling and Broughton 1986; Hagen andHamrick 1996; Burdon et al. 1999; Thrall et al. 2000; Sachset al. 2009), making them vulnerable to free riders, whichare endosymbiotic rhizobia that hoard plant resourcesrather than investing in the energy-intensive nitrogen-fixation reaction (Denison 2000; Trainer and Charles 2006;Ratcliff et al. 2008). In response, host legumes might selectagainst less-mutualistic rhizobia by targeting resources tomore-mutualistic partners (Denison 2000; Simms and Tay-lor 2002). Several empirical studies (Singleton and Stock-inger 1983; Singleton and van Kessel 1987; Kiers et al.2003, 2006; Simms et al. 2006) have supported key com-ponents of this hypothesis, which has been termed “plantsanctions” (Denison 2000; West et al. 2002c) and “partnerchoice” (Simms and Taylor 2002).

The existing conception of plant sanctions implicitlyassumes that legume hosts completely control resourceallocation. However, selection will favor any rhizobia thatcan “manipulate” plant resource allocation, which makesit likely that the allocation of resources is ultimately underjoint control. It is not clear whether plants lacking absolutecontrol over rhizobial fitness can exert selection in favorof more cooperative rhizobia. Furthermore, although sev-eral reports have found support for plant sanctions, othershave not (Marco et al. 2009; Gubry-Rangin et al. 2010).This suggests that the mechanisms determining fitnesscosts and benefits might produce sanctions under someconditions but not under others, which leads to the ques-tion of when each case is expected. Finally, plant sanctionshave often been conceptualized as all-or-none, where apartner is either cut off or not (Denison 2000; West et al.2002c), whereas plants are likely to adjust rewards to anodule much more continuously, for example, by adjust-ing the carbon allocation to each nodule. Using eithernaturally occurring strains (Simms et al. 2006) or exper-imental manipulation of atmospheric N availability tonodules (Kiers et al. 2006), studies have found that nodulegrowth exhibits continuous variation that correlates withstrain performance (or N concentration in the air), sug-gesting that plant allocation of resources also varies con-tinuously. When sanctions are not binary and partnersvary in quality, questions arise regarding how much theplant should reward each partner and how this value isdetermined.

A recent model by Akcay and Roughgarden (2007) isuseful for answering these questions. In keeping with thetrade metaphor, this model considers cooperation as theoutcome of biochemical “negotiations” between the plant

and the rhizobia. In contrast to the purely plant-controlledsanctions model, the negotiation model affords both part-ners some degree of control over the outcome and predictsa stable division of benefits to each party. Akcay andRoughgarden (2007) proposed that this kind of negotia-tion process might underlie differential rewarding of nod-ules. However, they did not venture beyond the simplestcase of a single nodule on one plant and did not modelvariation in rhizobium traits that would make rhizobiamore or less mutualistic. Here, we address these issues byextending their negotiation model to the case of two nod-ules on a single plant. Our results challenge importantaspects of the prevailing theories of partner choice andplant sanctions.

Our negotiation model is meant to represent an un-derlying biological process during which both partners ina mutualism can exert control over the outcome of aninteraction. In “Mechanisms for Control of the Mutual-ism” in the online edition of the American Naturalist, wereview the current knowledge of possible mechanisms ofcontrol by each party in the legume-rhizobium symbiosis.The plant has a number of possible mechanisms for reg-ulating the allocation of resources to the nodule, includingadjusting the oxygen flux into the nodule’s cortex(Denison 2000) and regulating the active transport of C4

dicarboxylic acids (Benedito et al. 2010). There is muchless known about the mechanisms by which rhizobia cancontrol the outcome, but this situation is due partly tomethodological difficulties and partly to a tacit assumptionthat the plant is in complete control. One potential path-way of rhizobium control might involve regulating thecycling of amino acids, which has been implicated in thesymbiosis between pea plants and Rhizobium legumino-sarum (Lodwig and Poole 2003; Prell et al. 2009), but thishypothesis has yet to be tested. Nonetheless, as we showbelow, several empirical observations regarding legume-rhizobium mutualisms can be better explained under anassumption of joint control via a negotiation-like mech-anism than under the assumption of pure plant control.We therefore hope that our results will spark empiricalresearch into mechanisms by which rhizobia can exertcontrol over resource allocation decisions; to that end, wepoint out potentially fruitful avenues for empirical re-search in “Discussion.”

The Negotiation Model with Two Nodules

We model the negotiation process between a legume hostand two nodules, each occupied by a single rhizobial ge-notype, on the basis of the dynamics introduced by Akcayand Roughgarden (2007). We label the nodules N1 andN2. The carbon flux into and nitrogen flux out of N1 andN2 are denoted (IC1, IA1) and (IC2, IA2), respectively (C is

Negotiation and Plant Sanctions 3

for carbon and A for ammonium or amino acid). Thesefluxes give rise to growth rates rp, rN1, and rN2 for the plant,nodule 1, and nodule 2, respectively. Akcay and Rough-garden (2007) use simple metabolic models to derive thegrowth of the plant and the nodule as functions of thecarbon and nitrogen fluxes; we use slightly modified ver-sions of their growth rates (see “Different Growth Func-tions” in the online edition of the American Naturalist).Our results are qualitatively unchanged when differentgrowth functions are used, as long as these functions ex-hibit diminishing benefits from the resource received (i.e.,nitrogen for the plant and carbon for the nodules) andaccelerating costs for the resource given up (carbon forthe plant, nitrogen for the nodules). Plant growth rate isa function of the total nitrogen flux received from thenodules and the carbon flux allocated to them, that is,rp(IAt, ICt), where and , whileI p I ! I I p I ! IAt A1 A2 Ct C1 C2

the growth rate of each nodule depends only on the carbonflux it receives and the nitrogen it exports.

Like Akcay and Roughgarden (2007), we assume thatat each negotiation step there are small, stochastic fluc-tuations in the carbon flowing into and the nitrogen flow-ing out of one of the nodules, say N1, which brings thegrowth rates of the plant and the nodules to , , and! !r rp N1

. This creates three possible cases: (1) and! !r r 1 rN2 p p

; (2) and ; or (3) one growth rate! ! !r 1 r r ! r r ! rN1 N1 p p N1 N1

is higher, and the other is lower. In the first two cases,there is no conflict between the nodule and the plant. Incase 1, the new rates are accepted, and in case 2, the ratesrevert back to the previous values. In the third case, how-ever, one player’s growth rate is lowered. This player re-sponds by shutting down the fluxes completely, which rep-resents an effort on this player’s part to regain the moreadvantageous previous fluxes. This move triggers a phaseduring which both players stop exchanging nutrients andtherefore forgo the growth resulting from this exchange.We call this phase the “war-of-attrition game,” because ofits similarity to models of animal conflicts where individ-uals engage in costly behavior (by displaying, fighting, orsimply waiting) to wear down their opponent and obtaina resource (Bishop and Cannings 1978).

The duration over which each party stays in the war-of-attrition game is determined by its potential gain fromwinning this stage of the game and its opportunity costof staying in the war of attrition. Akcay and Roughgarden(2007) proposed that each party stays in the war of attri-tion until its potential gain equals its loss. Suppose that

but . If the fraction of the period the plant! !r 1 r r ! rp p N1 N1

stays in is given by p, we have!p(r " r ) p (1 " p)(r " r ), (1)p p, 2 p p

where rp, 2 denotes the growth rate that the plant canachieve with its other nodule (N2) alone. We assume that

a nodule cannot grow when not receiving carbon fluxesfrom the plant, so we have, for the fraction of time q thatnodule N1 stays in the game,

! !qr p (1 " q)(r " r ). (2)N1 N1 N1

If , the plant wins, and the new growth rates of thep 1 qplant and N1 are and . (N2 is unaffected by the! !r rp N1

negotiation between the plant and N1.) In the one-nodulecase, where , these negotiation dynamics lead tor p 0p, 2

the maximum of the product of rp and rN1, which in bar-gaining theory is called the “Nash bargaining solution”(Nash 1950, 1953) and has been proposed by Roughgardenet al. (2006) as an alternative to the Nash equilibrium asan outcome of behavioral dynamics between animals. Inthe two-nodule case, we are interested in whether and howthe plant can use the negotiation process to distinguishbetween rhizobia of differing mutualistic quality and re-ward them accordingly, a phenomenon that has variouslybeen termed “plant sanctions” (Denison 2000; West et al.2002c) and “partner choice” (Simms and Taylor 2002).

Variation in Partner Quality and Negotiation

To model variation in partner quality, we introduce a rhi-zobium trait that modulates the negotiation behavior ofa nodule. Suppose that a rhizobium strain occupying N1,instead of staying in the war-of-attrition game for a frac-tion q of the time, as given by equation (2), stays for atime bN1q, with . Thus, strains with higher b willb 1 0N1

stay in the war-of-attrition stage longer, making them lesslikely to accept losses in their growth rate and more likelyto impose losses on the plant’s growth rate. In anthro-pomorphic terms, these strains are more “stubborn” dur-ing negotiations. In a single-nodule setup, the outcome ofnegotiation with such strains would be skewed towardbenefitting the nodule to the detriment of the plant. Thus,strains with high b would appear as low-quality partners(fig. 1).

At the long-term equilibrium of the negotiation dy-namics, all new rates will be rejected and the followingconditions hold for a focal nodule N1: (1) no alternativepair of rates R ! exists that is simultaneously more beneficialto both the nodule and the plant; (2) for and!r 1 rp p

, ; and (3) for and , .! ! !r ! r bq 1 p r ! r r 1 r p 1 bqN1 N1 p p N1 N1

For small fluctuations around the equilibrium, these threeconditions can be summarized into a first-order condition:

!r1 1 !rp N1! b p 0, (3)N1" "r " r !I r !Ip p, 2 A1 N1 A1

!r1 1 !rp N1! b p 0, (4)N1" "r " r !I r !Ip p, 2 C1 N1 C1


Figure 1: Change in the growth rates of the plant and the nodule in a single-nodule case, where the equilibrium is given by equations (3)and (4), with . The solid line represents the plant’s growth rate, , and the dashed line represents the nodule’s, rN1.

"r p 0 rp, 2 p

where and are the equilibrium growth rates of the" "r rp N1

plant and N1, respectively, and rp, 2 is the growth rate thatthe plant can achieve by relying only on N2 while thecarbon and nitrogen fluxes with N1 remain shut down.

Similarly, the outcome of the negotiation with N2 ischaracterized by the following conditions:

!r1 1 !rp N2! b p 0, (5)N2" "r " r !I r !Ip p, 1 A2 N2 A2

!r1 1 !rp N2! b p 0, (6)N2" "r " r !I r !Ip p, 1 C2 N2 C2

where rp, 1 is the growth rate the plant can achieve byrelying only on N1. The quantities rp, 1 and rp, 2 representthe “outside options” available to the plant and determinehow long the plant can “hold out” during the war-of-attrition stage. Intuitively, the equilibrium outcome bal-ances the gains of the plant and each nodule, given by thepartial derivatives of rp, rN1 and rN2, relative to their op-portunity costs of holding out during negotiations, givenby the denominators in each term. The relative gains ofthe rhizobia are weighted by their b traits. The opportunitycost for the plant depends on its outside options whennegotiating with a given nodule, which in general will bea function of the external environment and all partners’traits.

Outside Options and Plant Sanctions

The Outside Option Equals the Current Rates

The war-of-attrition phase with a focal nodule is the crucialdeterminant of the long-term negotiation outcome. Itsoutcome depends on the growth rate the plant can achievewith the other nodule only, that is, the plant’s outsideoption. This outside option determines how much “bar-gaining power” the plant holds vis-a-vis the negotiatingnodule. We first consider the case where, when negotiatingwith N1, the plant simply maintains the current nitrogenand carbon fluxes with N2. Thus, the plant’s growth rateduring the war-of-attrition phase with N1 is given by

r p r (I , I ). (7)p, 2 p A2 C2

Similarly, the outside option when negotiating with N2 isgiven by . Hence, at equilibrium, ther p r (I , I )p, 1 p A1 C1

plant’s outside options will be and" "r p r (I , I )p, 1 p A1 C1

. Substituting these terms into equations" "r p r (I , I )p, 2 p A2 C2

(3)–(6), we can find the equilibrium nitrogen fixation andcarbon allocation rates for particular pairs of strains withbN1 and bN2. Furthermore, by the implicit-function the-orem, we can express the equilibrium fluxes of carbon toand nitrogen from the nodules as functions of bN1 andbN2. To find how the equilibrium fluxes change with chang-ing bs, we take the total derivative of each of the fourequations with respect to bN1 and bN2 and solve the re-sulting eight equations for the eight partial derivatives


Figure 2: Comparison of growth rates of nodules with different btraits. The black region denotes pairs of bN1 and bN2 for which N2has a higher growth rate than N1, ; the white region denotesr 1 rN2 N1

pairs for which N1 has a greater growth rate than N2, . Ther 1 rN1 N2

region above the diagonal is black, which means that the nodulewith the higher b always has a higher growth rate than the nodulewith the lower b. Thus, under the assumption that the outside optionequals current rates, negotiations cannot produce effective sanctions.

, , , and so on, as a function of" " "!I /!b !I /!b !I /!bA1 N1 C1 N1 A1 N2

the first and second derivatives of the growth rate functionsat the equilibrium. We found analytical expressions forthese partial derivatives, but they are too cumbersome toreproduce here. Instead, we compared the growth rates oftwo nodules with different bs by evaluating the equilib-rium conditions numerically (fig. 2). The nodule with thehigher b always has a higher growth rate. Thus, a nego-tiation process in which the current rates represent theplant’s outside option will not lead to effective sanctionsby the plant, since it fails to withhold rewards from theless beneficial strain.

This result can be understood intuitively by consideringthe plant’s negotiation with one of the nodules, say N1.With constant outside options, a nodule with higher balways receives a higher growth rate because it is less likelyto accept losses during negotiation. In turn, paying ahigher price for nitrogen from a tougher negotiator in N1diminishes the plant’s outside option when negotiatingwith N2. This shift gives the plant a poorer equilibriumbargain with N2, which further depresses the plant’s out-side option against N1 (i.e., rp, 2).

Temporary Redirecting of Fluxes

In the previous subsection, we assumed that the plant doesnot use the carbon withheld during the attrition phase toimprove its outside option. We now suppose that, whenlocked in a war of attrition with N1, the plant redirects afraction r of the carbon flux IC1 (that would have gone toN1) to N2 and in return receives an added nitrogen fluxat rate kN2rIC1, with . Here, k stands for a strain-k # 0specific rhizobium trait that quantifies how much thestrain (temporarily) ramps up nitrogen fixation when sup-plied with additional carbohydrates: a strain with high ksupplies the plant with more extra nitrogen than does astrain with lower k. We assume that the added nitrogenfixation and exchange of fluxes operate at a very shorttimescale and hence are not themselves subject to nego-tiation. When the plant redirects its carbon flux, its growthrate while in the war of attrition becomes

r p r (I ! rk I , I ! rI ), (8)p, 2 p A2 N2 C1 C2 C1

and similarly for rp, 1,

r p r (I ! rk I , I ! rI ). (9)p, 1 p A1 N1 C2 C1 C2

When all else is equal, increasing a strain’s k has littleinfluence on the equilibrium growth rate of its own nodulebut decreases the equilibrium growth rate of the othernodule (see Mathematica code, available through the on-line edition of the American Naturalist). When a planthosts two strains of rhizobia, one with low and the otherwith high b, the low-b strain can have a higher equilibrium

growth rate than a strain with higher b, provided that itsk is sufficiently larger than the high-b strain’s k (fig. 3).Thus, for the plant to effectively impose sanctions againsthigh-b rhizobia, there must be a negative correlation be-tween the b and k traits of the strains.

The intuition underlying this result is simple: the plantbenefits by relying on a strain with high k for temporarynitrogen needs in a way that is similar to a firm managerwho hires substitute workers when the union goes onstrike. A strain with higher k improves the outside optionfor the plant, allowing it to drive a tougher bargain withthe other nodule. Thus, a low-b strain with high k canoffset the bargaining advantage of a high-b, low-k nodule,drive down the latter’s growth rate, and make plant sanc-tions appear effective.

Soil Nitrogen

Another outside option for the plant is to take up mineralnitrogen from the soil. However, increasing nitrogen up-take from the soil requires growing new roots, which isunlikely to happen fast enough to affect nitrogen uptakeduring the brief war-of-attrition stage. We therefore in-clude the effect of a constant nitrogen uptake from thesoil by adding it to the plant’s total nitrogen supply. Aswe show in “Mineral Nitrogen Uptake from the Soil” inthe online edition of the American Naturalist, allowing for


Figure 3: Comparison of the growth rates of nodules with different (b, k) pairs. As in figure 2, the black regions indicate when N2 has ahigher growth rate than N1, and vice versa for white regions. We assume that ; the X-axis in each panel shows the difference inb 1 bN2 N1

the b traits. Therefore, black regions correspond to cases where negotiations lead to ineffective sanctions (higher growth rate of less cooperative,higher-b nodules), while the white regions correspond to effective sanctions. The figure shows that effective sanctions are possible whenkN1 is sufficiently greater than kN2, with the threshold difference being an increasing function of . Here, .b " b r p 0.5N2 N1

mineral nitrogen uptake does not affect the growth raterelationship between two nodules with different b and ktraits. In other words, the conditions under which plantsanctions appear to be effective are qualitatively unchan-ged. However, higher mineral uptake rates move the ne-gotiation equilibria in the plant’s favor for a given valueof rhizobium b and, at the same time, increase the selectionpressure for higher b, all else being equal. This happensbecause increasing the availability of nonnegotiated nitro-gen improves the plant’s bargaining position, which de-creases rhizobium growth rate. As the nodule’s growth asa function of b is concave (as can be seen in fig. 1), thisincreases the marginal benefit of increasing b. In otherwords, as the nodule’s bargaining position deteriorates,the advantage of being a tougher negotiator (i.e., havinga higher b) increases. Empirical research on mycorrhizaesupports this prediction (Johnson 1993): when big blue-

stem plants were fertilized, less beneficial fungal speciestook over their roots. Kiers et al. (2002) note that noconclusive data exist for the evolutionary response of rhi-zobia to nitrogen fertilization and go on to argue that theeffect of increased nitrogen fertilization on the evolutionof rhizobium effectiveness is ambiguous, as plant sanctionsmight counteract the effect of reduced plant dependenceon nodules. Our model suggests otherwise.

Effect of Negotiations on Plant’s Growth Rate

Here, we compare the plant’s growth rate when it hostsdifferent strains in the two nodules (i.e., has an oppor-tunity to exert choice) with that when it hosts the samestrain in both nodules. Figure 4 shows that in most cases,the plant’s growth rate with choice is intermediate betweenits growth rates with each strain alone. However, for some


Figure 4: Effect of choice on plant’s growth rate. This figure compares the plant’s growth rate when it has a choice between two strainswith negotiation traits (bN1, kN1) and (bN2, kN2) with its growth rate when it is infected with either of the strains alone. Here, ,b p 1N1

, and . The gray points correspond to a plant that has an intermediate growth rate when it has a choice, relative to a plantk p 0 r p 0.5N1

that hosts either of the strains alone. The black points correspond to a plant that has a lower growth rate when it has a choice, relative toa plant that hosts either of the strains alone. This happens when the higher-b strain also has a higher k.

combinations of b and k, the plant’s growth rate is lowerwhen it has a choice than when it is infected with onlythe worse strain. This happens when a high-b, high-k strainis paired with a lower-b, lower-k one, which is roughlythe opposite of the conditions that make plant sanctionseffective.

To understand this rather counterintuitive result, con-sider first what happens when a plant hosts high-b, high-k strains in both nodules. Both nodules drive a hard bar-gain, yet during the negotiation phase, each also gives theplant temporarily increased nitrogen fluxes that improvethe plant’s bargaining position. These two effects coun-teract each other, giving the plant an intermediate growthrate. Conversely, a low-b, low-k strain will accept lossesreadily yet will not grant the plant good outside optionswhen it is negotiating with a competing nodule, againresulting in an intermediate growth rate for the plant.When these two strains are paired on the same plant,however, the high-b strain can take advantage of the plant’sweak bargaining position, created by the low k of the otherstrain, while at the same time being very unwilling toaccept losses during the negotiation. This situation reducesthe plant’s growth rate below that reached with eitherstrain alone. Furthermore, the plant cannot exercise ef-fective sanctions under these conditions and ends up re-warding the high-b nodule disproportionately.

Negotiation and the Evolution of Cooperative Rhizobia

To ask how the negotiated outcomes affect the evolution-ary dynamics of the rhizobium traits b and k, we assumethat the fitness of the rhizobium strain occupying a nodule

is reflected in the growth rate of the nodule. We conductan invasion fitness analysis in a monomorphic populationwith resident values br and kr by considering the growthrate of a mutant strain when it coinfects a plant with theresident strain. By implicit differentiation of the first-orderconditions (eqq. [3]–[6]) and using the expressions (8)and (9) for the outside options, we calculate the partialderivatives of the growth rate of a mutant nodule rm withrespect to its negotiation traits, bm and km, and evaluatethese derivatives at and . Under the as-b p b k p km r m r

sumptions of adaptive dynamics, these derivatives give thedirection of evolutionary change of the population aver-ages of b and k in the absence of a covariance betweenthese traits (Dieckmann and Law 1996; Brown et al. 2007).The vector field depicting the gradient of the invasionfitness for a range of resident b and k values (fig. 5a)shows that selection will uniformly act to increase b. Theselection gradient acting on k is mostly flat, except whenthe resident has a high b, in which case there is weakselection for intermediate values of kr. Selection on k ismostly flat because a nodule’s k trait affects its own growthrate only indirectly, through its effect on the other nodule’snegotiation equilibrium. Therefore, the effect of k on astrain’s own fitness can be thought of as a second-ordereffect.

To check whether these results carry over to a morerealistic population with many rhizobial strains, we con-ducted simulations of diverse rhizobium populations withdifferent correlations between b and k. These simulations(see Mathematica code for details) confirm that, regardlessof the correlation between the two traits, the highest-bstrains almost always win out in the long term.


Figure 5: Vector field depicting the selection gradients on the ne-gotiation traits, b and k. Panel a is for the case without partnerfidelity feedback (PFF; in eq. [10]), and b is for the case withs p 0PFF ( ). In a, there is selection to increase b throughout itss p 1range, while selection to increase k is weak when b is small butbecomes stronger as b grows. Selection gets weaker on each trait asit increases in magnitude. In b, there is still selection to increase b,but the magnitude of this selection is weaker than that in a. Incontrast, there is strong selection to increase k because k helps theplant’s growth rate, which yields a payoff to the rhizobia throughPFF while imposing no direct cost.

These results show that plant sanctions through nego-tiation, even when effective at the level of a single plant,are still unable to maintain beneficial rhizobia in the pop-ulation. The fundamental reason for this result is that thenegotiation process allows a nodule with a high b to “ma-nipulate” the plant into providing it with more carbon.To resist this manipulation, the plant must rely on strainswith higher k. But even if these strains fare better whenthey cohabit a plant with a high-b, low-k strain, they domuch worse when they are the sole occupant, since theplant can then play two high-k nodules against each other.Thus, high-b strains are able to invade a population oflow-b strains, regardless of their k values.

Partner Fidelity Feedback

What constrains b from increasing indefinitely? One pos-sibility is that a higher b imposes costs on the rhizobium:

during the transient negotiation dynamics, strains withhigher b spend less time growing because they spend moretime in the war-of-attrition phase than do strains withlower b. This cost is not accounted for in our analysesabove, which consider only the equilibrium of the nego-tiation dynamics. Akcay and Roughgarden (2007) foundin their simulations that the war-of-attrition stage im-posed, on average, a roughly 7% cost, relative to the samenitrogen fixation and carbon fluxes reached by a cost-freeprocess. This cost will be higher for high-b strains, becausethey will stay in the war-of-attrition stage longer, and itmight eventually grow so large as to negate the advantageof increasing b.

Partner fidelity feedback (PFF), that is, benefits thatrhizobia obtain from increased plant growth rate, mightalso constrain b. Intuitively, PFF must play some role inthe legume-rhizobium symbiosis, since plants that growmore also photosynthesize more and have more resourcesavailable for dividing among themselves and their sym-bionts. To model the effect of PFF, suppose that the lifetimefitness of nodule N1 is given by

sw p r r , (10)N1 N1 p

where is a parameter denoting the strength of PFF.s # 0When , there is no automatic fitness benefit to thes p 0nodule from the plant’s growth; implies some benefit,s 1 0which becomes stronger as s increases. Although this ben-efit could be derived from a model that accounts forgrowth and reproduction of both the nodule and the plant,s provides a simple way to account for PFF. Note that thebehavior of the parties during the negotiation is still basedon the growth rates of the plant (rp) and the nodule (rN1),as opposed to being determined by the fitness functionwN1. To assume otherwise would require that the partnersexchange information about their growth rates and antic-ipate future returns, both capabilities that we are reluctantto ascribe to plants and bacteria.

To find how PFF affects the selection gradients for band k, we again calculate the derivatives of rhizobial fitnessgiven by equation (10) with respect to these traits (fig. 5).Adding PFF (e.g., when ) favors higher k and doess p 1so more strongly as b increases. This is because hostingstrains with high k increases the growth rate of the plant,which then yields a return on the rhizobium fitnessthrough PFF. Positive selection to increase b is diminishedbut has not vanished. Nonetheless, the strong selection forincreased k arising from PFF, together with a negative co-variance between k and b, can maintain low-b strains inthe population. To illustrate this, we computed the evo-lutionarily stable (ES) (b, k) pairs as a function of the PFFexponent s, assuming a negative, linear relationship be-tween b and k (fig. 6). The evolutionarily stable b decreaseswith the PFF exponent s, meaning that the ES rhizobia


Figure 6: Evolutionarily stable strategy (ESS) values of b (a) and k (b) as a function of the partner fidelity feedback (PFF) exponent s.Here, we assume a negative, linear relationship between b and k, with two different values for the slope. For the solid curve, we assume

, while the dashed curve is drawn under the assumption . In each case, the maximum value of b is assumedk p 0.6 " 0.3b k p 1.2 " 0.6bto be 2 (making k nonnegative). While the particular value of this upper limit is arbitrarily chosen for our numerical calculations, itsempirical value can be interpreted as corresponding to the least cooperative strain in the population. As can be seen, this least cooperativestrain will be evolutionarily stable up to a threshold PFF coefficient s, and only for higher s will more-cooperative strains be able to persistin the population. This threshold s is lower when the relationship between b and k is more negative.

become more cooperative with stronger PFF. Further, fora given value of the PFF coefficient s, a more negativerelationship between b and k will decrease the ES valueof b and increase the ES value of k.

Discussion

Negotiation Can Undermine Partner Choice/Sanctionsand Creates Context Dependency

Our model yields four main results. First, the correlationbetween the rhizobium negotiation traits b and k affectsthe plant’s ability to reward more-cooperative strains.When b and k are negatively correlated, strains that de-mand less carbon per nitrogen fixed also provide the plantwith better outside options; moreover, negotiation pro-vides higher rewards for the more cooperative rhizobiumstrain. This combination enables plant sanctions. However,negotiation disables plant sanctions when these traits arenot negatively correlated. These results partially supportthe conjecture by Akcay and Roughgarden (2007) that thenegotiation process might underlie plant sanctions, yetthey also illuminate a more complex picture where effec-tive sanctions depend on the combination of strains co-infecting the host plant. These findings also provide a pos-sible explanation for the empirical results that showeffective plant sanctions in some cases (Kiers et al. 2003,2006; Simms et al. 2006) but not in all (Marco et al. 2009;Gubry-Rangin et al. 2010).

Our second result is that negotiation creates context-dependent variation in the plant’s fitness costs and ben-efits. Context dependency here refers to the fact that thenegotiation outcome and its effect on the plant’s overallgrowth depend on the combination of strains with which

the plant is interacting. In particular, with certain com-binations of strains (low-b, low-k strains paired with high-b, high-k strains), a plant might be worse off when it hasa “choice” between two strains than when it is infected byeither strain alone. This prediction might explain the re-sults of an inoculation experiment by Heath and Tiffin(2007), in which Medicago truncatula plants were some-times less fit when they had a choice (i.e., inoculated withtwo Sinorhizobium medicae strains that offered differentlevels of benefit) than when inoculated with either strainalone. This result is paradoxical from a naive market-theory perspective but arises naturally from an underlyingnegotiation model where exerting choice is predicated onhaving good outside options.

Maintenance of Mutualism Requires BothPartner Fidelity Feedback and Sanctions

Our third result is that, regardless of the correlation be-tween k and b, selection always favors higher b, even whenplants can successfully reward lower-b nodules. This resultunderscores a general point about sanction models thatseems to have been overlooked so far. Consider two sym-biont strains that interact with a single host species. Sup-pose that strain 1 is the more cooperative strain; that is,the host grows better when singly inoculated by strain 1.Denote by wij the fitness of strain i when it coinfects thehost with strain j. Effective host sanctions should result in

; that is, when both strains infect a single host,w 1 w12 21

strain 1 has a higher fitness than does strain 2. On theother hand, the evolutionary stability of strain 1 requires

, and conversely, the evolutionarily stability ofw 1 w11 21

strain 2 requires . In general, effective host sanc-w 1 w22 12

tions do not guarantee or preclude either condition. For


example, our model without PFF generates the followingpattern: . Thus, even effective hostw 1 w 1 w 1 w22 12 21 11

sanctions cannot maintain strain 1 in the population.Our final result is that both sanctions and partner fi-

delity feedback (PFF; Bull and Rice 1991; Sachs et al. 2004;Foster and Wenseleers 2006) might be necessary to main-tain mutualism. West et al. (2002c) showed that PFF aloneis not sufficient to maintain cooperative rhizobia, becausethe feedback benefits that a cooperative strain producesby helping the host are diluted across all nodules, regard-less of strain, giving rise to a “tragedy of the commons.”This effect is present in our model as well: even with PFF,selection favors higher b, albeit with diminished strength.On the other hand, our second negotiation trait, k, doesnot suffer from the commons tragedy, because while higherk in a focal nodule improves the plant’s position againstthe other nodule, it does not directly affect the negotiationoutcome between the focal nodule and the plant. Hence,a focal nodule’s k value affects its own growth rate onlyindirectly, by changing the plant’s baseline growth rate(this effect is small but positive). On the other hand, withPFF, a higher-k strain receives feedback benefits from im-proving the plant’s growth, which means that PFF stronglyfavors higher k. Nonetheless, favoring high k does not byitself maintain low-b strains. For this to occur, k and bmust be negatively correlated, which brings us back to thecondition for effective plant sanctions. Note, however, thatsanctions here play a rather incidental role; their existenceis a side consequence of adequate negative correlation be-tween the negotiation traits.

Control and Outside Options in Biological Markets

The main thrust of our article is that whenever rhizobiahave some control over the outcome, the plant must relyon other rhizobia to sanction less cooperative ones, at leastin the short term. This basic fact creates evolutionary andecological patterns that are more complex than those frompure host-control models (e.g., West et al. 2002c). Ourmodel provides possible explanations for empirically ob-served patterns that had not been anticipated by previoussanctions models, a fact that offers indirect support forour model and for rhizobium control in general. Moregenerally, the issue of joint control of the mutualistic out-come and its effects on evolutionary and ecological dy-namics presents a fertile ground for future theoretical andempirical work.

The partner-choice model of Kummel and Salant (2006)in a mycorrhizal mutualism offers an interesting compar-ison in this regard. Kummel and Salant characterize eachfungal strain by an exchange function that describes howmuch resource the strain yields in exchange for a givenamount of carbon. The plant then allocates carbon in a

way that equalizes the marginal costs of obtaining re-sources from the strains that it chooses. Even though Kum-mel and Salant did not consider fungal fitness in theirpaper, their model can also yield cases with ineffectivesanctions, that is, where the less beneficial strain is evo-lutionarily stable despite optimal partner choice by theplant (E. Akcay, unpublished analysis). One possible in-terpretation is that this outcome arises because plantchoices are constrained by the set of available supplycurves, which is determined by the fungal population’scomposition. Hence, plants in this model lack completecontrol over the allocation of rewards and can exercisechoice only when interacting with the right combinationof fungal strains.

Another set of models, by Johnstone and Bshary (2002,2008), explores how control over the interaction influencesthe exchange of services in the cleaner-fish mutualism,where there is conflict over the duration of the interactionbetween an “exploiter” (cleaner fish) and a “victim” (clientfish). Johnstone and Bshary (2002) find that as exploitercontrol increases, so too does the evolutionarily stable levelof exploitation, while the duration of each interaction de-creases. Johnstone and Bshary (2008) add a market contextto this model, where interaction duration influences part-ner availability for both types of partners, and find thatthe market cannot prevent the cooperation breakdown thatis caused by increased exploiter control. In one sense, thecontrol variable in Johnstone and Bshary (2002, 2008)fulfills a role similar to that of b: it shifts the stable outcomein the exploiter’s favor. A major difference between thesemodels and ours is that the clients in Johnstone and Bshary(2008) have no way of retaliating against the cleaner’smanipulation of interaction duration, either during theinteraction itself (e.g., by manipulating the exploitationlevel) or by exercising outside options, such as visiting lessmanipulative cleaners (e.g., chosen by reliable indicatorsof their tendency to manipulate). Furthermore, theirmodel does not consider evolution of the control trait inthe cleaner population. Selection in their model wouldalways favor higher control by the exploiters (since thereis no immediate cost to higher control) and therefore leadto the breakdown of cooperation, just as selection in ourmodel favors increased b.

We suggest that the next stage of biological market the-ory should include more-explicit models of the mecha-nisms determining the exchange rates for services and re-sources and the effect of outside options within thesemechanisms. Such models would require more detailedknowledge of the proximate mechanisms of resource ex-change (Bshary and Bronstein 2004), which often is notimmediately available. Nonetheless, models such as oursunderscore the importance of these mechanisms and pro-vide a theoretical motivation for empirical inquiry into


them. For example, from current knowledge that we reviewin “Mechanisms for Control of the Mutualism,” we mightinfer that plants have the upper hand in the legume-rhizobium interaction. However, this view might just aswell reflect our relative ignorance about mechanisms ofrhizobial control. Methodological difficulties have ham-pered inquiry into how endosymbiotic bacteroids mightexert control during the nitrogen-fixation stage of the in-teraction. Further, most studies of bacteroid physiologyare purely mechanistic and focus on single nodules, rarelyif ever considering how bacteroid traits expressed in onenodule might influence the trait expression and perfor-mance of strains in other nodules. In contrast, empiricalresearch on the regulation of nitrogen fixation adopts theplant’s perspective and assumes plant control (e.g., Schulze2004). We suggest that our approach can usefully mergethese two perspectives by integrating evolutionary theorywith a mechanistic approach to control and regulation ofthe symbiosis. Such a synthesis produces many new em-pirical questions, some of which we consider below.

Rhizobium Traits and Empirical Questions

Our model predicts that the effect of a rhizobium strainon the plant’s growth will depend on which other strainsoccupy the other nodules of the plant. This kind of contextdependency poses a problem for defining and measuringcooperativeness of rhizobium strains. In principle, a quan-tity such as the ratio of nitrogen fixation to carbon allo-cation, , might denote how beneficial a nodule is toI /IA C

the plant, but these rates will vary, depending on the otherstrains being hosted by the same plant. Therefore, a strain’scooperativeness must be defined and measured within aspecified context, which challenges the use of terms suchas “cooperators” and “cheaters” to denote genotype-specific properties of rhizobia. Nonetheless, it is possibleto define a standard context in which to evaluate strains,such as single inoculation, as is done in most empiricalstudies (e.g., Simms et al. 2006; Heath and Tiffin 2009;Heath 2010). In that case, our model posits that there ismore than one way to be cooperative: a strain can eitherhave a low b and thereby “demand” less during the ne-gotiation process or have a high k and thereby help theplant drive a harder bargain with another nodule. In asingle-strain inoculation, the strain’s b is evaluated in thecontext of its k and its k is evaluated in the context of itsb, and the joint action of the two traits determines thestrain’s nitrogen-fixation level. Thus, to predict a strain’scooperativeness in other contexts (e.g., in mixed inocu-lations or in soil), we must understand what biologicalmechanisms underlie such traits and determine how bestto measure them.

One can identify the rhizobium traits important to the

interaction outcome by investigating in detail the physi-ological mechanisms by which legumes and rhizobia in-teract. For example, a recent study by Ratcliff and Denison(2009) showed that an ethylene inhibitor produced byrhizobia shifts the symbiotic outcome in favor of the rhi-zobia. More research into the mechanistic basis for sucheffects is needed. An evolutionary perspective suggests thatit might be especially profitable to find and study mech-anisms underlying natural polymorphisms in functionallyrelevant genes. Functional genetic studies of nitrogen fix-ation (Masson-Boivin et al. 2009) and cellular interactionsbetween plant and rhizobium cells (Lodwig et al. 2003;Prell et al. 2009) should be conducted with an eye towarduncovering such variability in rhizobial populations. Oncecontrol traits have been identified, our model makes anumber of specific predictions about the outcome of themutualism as a function of different combinations of traits.These predictions should be tested, as they have importantimplications for the evolutionary dynamics of thisinteraction.

Another way to test whether bacteroids exercise anycontrol in the interaction is to detect variation in theseunidentified traits by observing the fitness associations thatthey create between mutualism partners. For example, bis predicted to generate antagonistic covariation betweenplant and rhizobium fitnesses. So variation in b can bedetected as a negative correlation between the fitnesses ofrhizobium and host plant across genetically identical hostplants that have been singly inoculated with different rhi-zobium genotypes. In turn, k is predicted to generate an-tagonistic variation between the fitnesses of strains thatcoinfect a plant. Hence, variation in k can be detected bymeasuring individual fitnesses of pairs of rhizobium ge-notypes inoculated onto different individual host plants,with the pairs representing “cells” in a factorial array ofrhizobium combinations. One caveat is that a negativegenetic correlation between b and k might mask somefitness covariances. Nonetheless, examining fitness co-variances among plant genotypes and rhizobial strains anddetermining whether such covariation maps onto specificgenetic loci in rhizobia is an area ripe for study. Few studieshave measured genetic variation and covariation betweenthe fitnesses of plants and rhizobia in either natural ormanaged systems.

Future Directions for Theory

Our extension of the negotiation framework of Akcay andRoughgarden (2007) to interactions with two nodules gen-erates interesting insights about the evolution of the sym-biosis but does not yet capture all important aspects ofthe interaction. We briefly discuss some of these aspects,


both to delineate limitations of our model and to sketchout questions that we intend to tackle in future work.

First, we assume that the plant does not simply cut offa nodule with high b. In the short term, such a movewould not be optimal for the plant, as the remaining nod-ule would have a much better bargaining position andtherefore be able to shift the outcome in its own favor. Inthe longer term, however, the plant can replace the cutoffnodule with one or more new nodules. More generally,the number of nodules on a single plant is highly plastic,and plants continue to “search” for more rhizobia andinitiate nodules while negotiating with existing nodules.This means that the plant is not constrained by its currentoutside options but instead might expand its outside op-tions and gain advantage when dealing with existing nod-ules. The optimal nodulation strategy of the plant thereforeremains an important question to be answered by futurework.

Second, we assume that only nodule growth determinesrhizobial fitness. Nodule growth might be the appropriatequantity for studying sanctions after nodule formation,but the overall evolutionary dynamics of the rhizobia willalso depend on the number of nodules each strain initiates(Heath and Tiffin 2009). Plants that host effective nodulesinitiate fewer nodules (Gao et al. 2010; Gubry-Rangin etal. 2010), which will have additional selective effects onthe soil population of rhizobia. Furthermore, strains differin their competitiveness for nodulation (e.g., Amarger1981; Dowling and Broughton 1986), with potential trade-offs between nitrogen fixation and nodulation effective-ness. Future theory, therefore, must address the nodulationdynamics of the interaction.

A related issue is the evolutionary consequence of thespatial population genetic structure of rhizobia (Bever andSimms 2000). In a structured population, a rhizobiumstrain might co-occur on a plant with others of its owngenotype more frequently than with a strain randomlyselected from the population. This situation would createindirect fitness effects on the rhizobium traits, which willbe largely neutral for b (as b has little effect on the othernodule), but negative for k (because higher k harms theother nodule). An indirect cost of high k could counteractsome of the positive selection pressure on this trait. Onthe other hand, spatial structure also makes it more likelyfor rhizobia to compete with kin (West et al. 2002a), whichmight negate some of the indirect costs and benefits ofrhizobium traits (depending also on population elasticity;Platt and Bever 2009). Predicting which of these effectswill be stronger requires a model that more explicitly spec-ifies the life cycle of rhizobia, including dispersal. Anotherpotential effect of spatial structure is to increase the chancethat the same plant and rhizobium genotypes interact re-peatedly over generations, adding intergenerational part-

ner fidelity feedback to the “developmental” PFF that wemodeled here, with largely similar effects.

Finally, we have yet to consider variation in plant ne-gotiation traits. Here, we have concentrated on the evo-lution of rhizobium traits. There is some justification tothis simplification, as rhizobia might be expected to evolvefaster than would plants. However, to fully understandthis mutualism, we must also consider plant traits andtheir evolution. In particular, plants might also evolve tobe more or less “stubborn” during negotiations. Variationin plant traits will likely influence the distribution of ben-efits and generate genotype-by-genotype interactions innatural populations (Heath 2010). This question and thequestion of coevolution of plant and rhizobial negotiationtraits we leave for future study.

Acknowledgments

The National Institute for Mathematical and BiologicalSynthesis (NIMBioS), where E.A. is a postdoctoral fellow,is sponsored by the National Science Foundation, the U.S.Department of Homeland Security, and the U.S. Depart-ment of Agriculture through National Science Foundation(NSF) award EF-0832858, with additional support fromthe University of Tennessee, Knoxville. This work was par-tially conducted when E.L.S. was a short-term visitor atNIMBioS; she has also been supported by NSF award DEB-0645791. We thank the editors and three anonymous re-viewers for helpful comments that improved thismanuscript.

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Simms, E. L., D. L. Taylor, J. Povich, R. P. Shefferson, J. L. Sachs,M. Urbina, and Y. Tausczik. 2006. An empirical test of partnerchoice mechanisms in a wild legume–rhizobium interaction. Pro-ceedings of the Royal Society B: Biological Sciences 273:77–81.

Singleton, P. W., and K. R. Stockinger. 1983. Compensation againstineffective nodulation in soybean. Crop Science 23:69–72.

Singleton, P. W., and C. van Kessel. 1987. Effect of localized nitrogenavailability to soybean half-root systems on photosynthate parti-tioning to roots and nodules. Plant Physiology 83:552–556.

Sprent, J. 2007. Evolving ideas of legume evolution and diversity: ataxonomic perspective on the occurrence of nodulation. New Phy-tologist 174:11–25.

Sprent, J. I., J. M. Sutherland, and S. M. de Faria. 1987. Some aspectsof the biology of nitrogen-fixing organisms. Philosophical Trans-actions of the Royal Society B: Biological Sciences 317:111–129.

Thrall, P. H., J. J. Burdon, and M. J. Woods. 2000. Variation in theeffectiveness of symbiotic associations between native rhizobia andtemperate Australian legumes: interactions within and betweengenera. Journal of Applied Ecology 37:52–65.

Trainer, M. A., and T. C. Charles. 2006. The role of PHB metabolismin the symbiosis of rhizobia with legumes. Applied Microbiologyand Biotechnology 71:377–386.

West, S. A., I. Pen, and A. Griffin. 2002a. Cooperation and com-petition between relatives. Science 296:72–75.

West, S. A., E. T. Kiers, I. Pen, and R. F. Denison. 2002b. Sanctionsand mutualism stability: when should less beneficial mutualists betolerated? Journal of Evolutionary Biology 15:830–837.

West, S. A., E. T. Kiers, E. L. Simms, and R. F. Denison. 2002c.Sanctions and mutualism stability: why do rhizobia fix nitrogen?Proceedings of the Royal Society B: Biological Sciences 269:685–694.

Associate Editor: Christopher A. KlausmeierEditor: Judith L. Bronstein

Tessellated darter Boleosoma nigrum olmstedi (Storer). From “Records of Pennsylvania Fishes” by Henry W. Fowler (American Naturalist,1907, 41:5–21).

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! 2011 by The University of Chicago. All rights reserved. DOI: 10.1086/659997

Appendix from E. Akcay and E. L. Simms, “Negotiation, Sanctions,and Context Dependency in the Legume-Rhizobium Mutualism”(Am. Nat., vol. 178, no. 1, p. 1)

Mechanisms for Control and Extensions of the ModelMechanisms for Control of the Mutualism

Several physiological aspects of the legume-rhizobium symbiosis suggest that both partners have some controlover the distribution of benefits from the interaction. We provide biological context for the negotiation model bybriefly reviewing current knowledge about the cellular processes that operate during the symbiosis, beginningwith mechanisms that afford the plant control over the division of benefits.Nodule cells take up rhizobia via endocytosis, enclosing them within a structure called the symbiosome, which

is surrounded by a plant-derived membrane called the symbiosome membrane. The nature of this membrane andthe biochemistry of the nitrogen-fixation reaction provide the legume host with several control points (Schulze2004). First, because the nitrogenase enzyme is oxygen sensitive yet catalyzes a reaction needing abundantenergy and reductant (Hauser et al. 2007), the nodule must provide the proper chemical environment in whichbacteroids can fix nitrogen. Plant respiration and leghemoglobin, a family of oxygen-binding heme proteinsfunctionally similar to myoglobin (Ott et al. 2005), provide high oxygen flux for bacteroid metabolism whilemaintaining a very low concentration of free oxygen (Hauser et al. 2007). Thus, legumes might use oxygen tosanction poorly performing nodules, by either starving them of oxygen or reversibly inhibiting their nitrogenasewith too much oxygen (Denison 2000).Second, the plant has many ways to control carbon allocation to bacteroids. Phloem delivers sucrose to nodule

cells, where it is converted to C4 dicarboxylic acids, such as malate, which appear to be actively moved acrossthe symbiosome membrane by a dicarboxylate transporter (Benedito et al. 2010). Nodule-specific transporters ofmany other substances (Benedito et al. 2010) might provide additional opportunities for plant control. On theother hand, Bradyrhizobium japonicum bacteroids also express dicarboxylate transporters (Delmotte et al. 2010),which suggests that they might be capable of refusing proffered carbon.Finally, ammonium has been thought to diffuse passively from the bacteroid cytoplasm to the plant cytoplasm

along a strong concentration gradient generated by rapid fixation in bacteroids and prompt assimilation by thehost cell (Lodwig and Poole 2003), suggesting joint control. However, recent genetic work has shown that in atleast some hosts, mutualistic symbiosis might depend on the active transport and, potentially, the cyclingbetween host and bacteroid of amino acids (Lodwig et al. 2003; Prell et al. 2009). In particular, Prell et al.(2009) showed that Rhizobium leguminosarum bacteroids in pea plants depend on branched-chain amino acidsimported from the plant while downregulating their own synthesis of these amino acids. Furthermore, plant cellshosting bacteroids might become dependent on aspartate exported from the symbiosome (Lodwig et al. 2003).Such cycling and possible mutual interdependence suggest that both partners exert some control over theoutcome of the mutualism. However, this hypothesis has yet to be tested thoroughly; further, the mechanismmight not be general to all rhizobia, as expression-array analyses have found that most genes in these transportsystems were not similarly upregulated in B. japonicum and Sinorhizobium meliloti symbioses (MacLean et al.2007).There is currently less understanding of how bacteroids might exercise control, in part because it has been

difficult to determine when during the symbiotic process the phenotype of a metabolic mutation is expressed andin part because host plants exercise control over bacteroid development in ways that determine how bacteroidsmight obtain fitness benefits (Denison 2000; Simms and Taylor 2002; Ferguson et al. 2010; Oono et al. 2010). Insome host species, individual bacteroids survive nodule senescence and therefore directly benefit from traits thatenhance their own survival and reproduction. On another host species, however, the same rhizobial strain might

Appendix from E. Akcay and E. L. Simms, Negotiation and Plant Sanctions

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produce terminally differentiated bacteroids that have no individual fitness. In the latter hosts, bacteroid traits canevolve in response to selection only if they affect the fitness of undifferentiated rhizobia that carry the same trait.Bacteroids that are not terminally differentiated, such as B. japonicum in soybean nodules, might divert carbon

from ammonium-producing nitrogen fixation to their own benefit. For example, it has been suggested that theability to accumulate and then degrade intracellular storage polymers, such as glycogen or poly-b-hydroxybutyrate (PHB), could be advantageous to free-living rhizobia, potentially allowing them to fuel celldivision and resist starvation (Klucas 1974; Cevallos et al. 1996; Trainer and Charles 2006; Ratcliff et al. 2008).Recent data from Bradyrhizobium elkanii grown on Siratro plants (Macroptilium atropurpureum cv. Siratro)suggest that an ethylene inhibitor produced by rhizobia (rhizobitoxine) might facilitate PHB accumulation whilenegatively affecting host plant growth (Ratcliff and Denison 2009). This finding suggests that rhizobia may havesome control over resource exchange and PHB accumulation rates.On the other hand, terminally differentiated bacteroids, such as S. meliloti in alfalfa nodules, would not

directly benefit from internal accumulation of carbon polymers. Indeed, PHB has not been detected indifferentiated bacteroids from alfalfa nodules (Aneja and Charles 1999), and proteomic analysis of S. melilotibacteroids from Medicago truncatula and Melilotus alba nodules revealed no evidence of PHB production(Djordjevic 2004). Such bacteroids might instead gain inclusive fitness benefits by reducing their own metabolicactivity, which might divert plant carbon resources to nonfixing and still reproductive kin in the nodule (Anejaand Charles 1999; Djordjevic 2004; Oono et al. 2009). Differentiated bacteroids might also produce “private”nutrients that could be utilized by reproductive kin in the nodule or adjacent rhizosphere. It was hypothesizedthat one class of compounds, termed “rhizopines,” might fulfill this function (Murphy et al. 1995). However,subsequent studies suggest that the ability to make optimal use of rhizopines and other unusual carbon sources ismore likely to be important in competition for nodulation (Jiang et al. 2001) or in colonization of nodule tissue(Fry et al. 2001; Prell and Poole 2006), processes that occur before nitrogen fixation.Our conclusion from this brief review is that both partners in the symbiosis might plausibly exert some control

over the outcome but that the mechanisms of rhizobium control are less well understood and in particular needof further work. Our negotiation model depends on joint control and could help motivate empirical research onthe mechanisms of rhizobium control (see “Discussion”).

Extensions of the ModelDifferent Growth Functions

Akcay and Roughgarden (2007) derived the growth functions for the nodule and the plant from simple metabolicmodels of how nitrogen and carbon are utilized for growth and symbiotic exchange. Their model for the noduleyields a growth rate that is equal to the difference between carbon influx and nitrogen export by the nodule.With two nodules, this growth function creates a degeneracy in the negotiation equilibrium, since the derivatives

, , and so on, become constants. This outcome, however, is not structurally stable, as small,!r /!I !r /!IN1 A1 N1 C1

nonlinear additions to the growth-rate terms make these derivatives nonconstants and therefore allow uniquesolutions to the negotiation equilibrium. In particular, the adjustments that we use make the nodule’s growth rateconcave in IC1 and convex in IA1, corresponding to assumptions of diminishing returns from increased carbongain and accelerating costs of increased nitrogen fixation. The specific functional forms used for the calculationsdepicted in the manuscript are

1 2 2!r p L ! I " I ! k k " I ! 2I (I " L ! k k )! (L " I ! k k ) , (A1)[ ]p p At Ct 1 2 At At Ct p 1 2 p Ct 1 222!r p I ! 0.01 I " I " 0.01I . (A2)N1 C1 C1 A1 A1

Here, we briefly demonstrate that different growth functions do not qualitatively alter our results, as long as theyhave the diminishing marginal benefits and accelerating costs. To do that, we carried out the calculations for thefollowing functions for the plant’s and the rhizobium’s growth, respectively:

1 2!r p I " I , (A3)p At Ct22!r p I " I . (A4)N1 C1 A1


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Figures A1–A4 depict that our main results remain unchanged for these alternative functional forms.

Figure A1: Change in the growth rates of the plant and the nodule in a single-nodule case with the alternative growth ratefunctions given by equations (A3) and (A4). This figure corresponds to figure 1. The solid line represents the plant’s growthrate, , and the dashed line represents the nodule’s, rN1. Note that while the absolute value of the growth rate is different from*rpthat in figure 1, the pattern of change in the growth rate is the same.

Figure A2: Comparison of the growth rates of two nodules with different b traits under the assumption that the outside optionsequal the current rates, corresponding to figure 2. The black region denotes pairs of bN1 and bN2 for which N2 has a highergrowth rate than N1, ; the white region denotes pairs for which N1 has a greater growth rate than N2, . As inr 1 r r 1 rN2 N1 N1 N2

figure 2, the nodule with the higher b always has a higher growth rate than the nodule with the lower b.


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Figure A3: Comparing the growth rates of two nodules with different sets of (b, k) pairs, where , corresponding tor p 0.5figure 3. As in figure 3, the black regions indicate when N2 has a higher growth rate than N1, and vice versa for the whiteregions. We assume that ; the X-axis in each panel shows the difference in the b traits. Therefore, black regionsb 1 bN2 N1

correspond to cases where negotiations lead to ineffective sanctions (higher growth rate of less cooperative, higher-b nodules),while the white regions correspond to effective sanctions. The figure shows that effective sanctions are possible when kN1 issufficiently greater than kN2. The threshold difference is a somewhat steeper function than that in figure 3, but the pattern remainsqualitatively unchanged.


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Figure A4: Relative standing of the plant’s growth rate when it has a choice between two strains with negotiation traits (bN1,kN1) and (bN2, kN2), as compared to when the plant is infected with either of the strains alone. This figure corresponds to figure4, with , , and . The gray points indicate a plant that, when it has a choice, has an intermediate growthb p 1 k p 0 r p 0.5N1 N1

rate, relative to a plant that hosts either of the strains alone. The black points correspond to a plant that, when it has a choice,has a lower growth rate relative to a plant that hosts either of the strains alone. This happens when the higher-b strain also hasa higher k. Again, note the general similarity between this graph and figure 4.

Mineral Nitrogen Uptake from the Soil

Here, we include the results when the plant can take up nitrogen from the soil. As explained in “Soil Nitrogen,”we assume that nitrogen uptake is constant during the negotiation process, since increasing nitrogen uptakerequires that the plant grow more roots, which would take place over longer timescales than does the adjustmentof fluxes with a given nodule. Therefore, we add a constant nitrogen supply to the plant’s growth functionduring both the normal and war-of-attrition phases. In our notation, we have

I p I ! I ! I (A5)At A1 A2 A0

for the total nitrogen supply to the plant, where IA0 denotes the mineral nitrogen uptake from the soil. Likewise,the plant’s growth rate when negotiating with nodule N1 is given by

r p r (I ! rk I ! I , I ! rI ), (A6)p, 2 p A2 2 C1 A0 C2 C1

and similarly, rp, 1, the plant’s growth rate when negotiating with N2, is

r p r (I ! rk I ! I , I ! rI ). (A7)p, 1 p A1 1 C2 A0 C1 C2

With these outside options, we can evaluate the equilibrium conditions given by equations (3)–(6) and apply allof the same analyses. Here, we show only the results for the end point of evolution for rhizobium traits as afunction of the PFF exponent s and the mineral nitrogen uptake IA0. Figure A5 depicts the evolutionarily stable band k values when the traits are negatively related to each other. It shows that the qualitative pattern found withno mineral nitrogen uptake persists when we allow the plant to have a constant source of nitrogen. Interestingly,increasing the plant’s outside source of nitrogen selects for higher b (and therefore lower k). The intuition behindthis result is that as the plant has more nitrogen, its marginal valuation of carbon increases. Hence, rhizobia mustbe more “stubborn” during negotiations to extract a given increase in carbon, which increases selective pressureon b.


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Figure A5: Evolutionarily stable (ESS) (b, k) pairs as a function of the partner fidelity feedback exponent s, with mineralnitrogen uptake from the soil, IA0, equal to 0 (solid curve), 0.05 (dashed curve), and 0.1 (dotted curve). There is a linear, negativerelationship between rhizobium traits; specifically, . As can be seen, the basic pattern of decreasing ESS b withk p 1.2! 0.6bincreasing s continues to hold. In addition, increasing mineral nitrogen uptake from the soil increases selection for higher b, allelse being equal.

Incomplete Shutoff of Fluxes during the War-of-Attrition Phase

The final extension to our basic model concerns a case that was suggested to us by a reviewer, who observedthat when plants sanction nodules, they appear to decrease the oxygen supply to the nodule, which might reducecarbon uptake but is unlikely to shut it down completely. One caveat to this argument is that the sanctioning thathas been observed in laboratory experiments (e.g., Kiers et al. 2003) corresponds to the negotiation equilibrium(or lack thereof) better than to the war-of-attrition phase in our model. Nonetheless, it is plausible that thebiochemistry of the interaction might not allow complete shutdown of fluxes during the fast-timescale war-of-attrition phases, and therefore it is of interest to check the robustness of our results against modifications of thisassumption.Therefore, we consider the case where, during the war of attrition, the carbon flux to a given nodule is

decreased by a fraction d while the nitrogen flux out of the nodule decreases by a fraction g (the special case ofcorresponds to our base model). For this case, we must amend the growth rate of a plant negotiatingd p g p 1

with nodule N1 to

r p r (I " rk dI " (1! g)I , I " rdI " (1! d)I ). (A8)p, 2 p A2 N2 C1 A1 C2 C1 C1

At the same time, the rhizobium is now growing at some nonzero rate during the war-of-attrition phase, andtherefore its willingness to concede will depend on the difference between this reduced growth rate and its“normal” growth rate. The first-order equilibrium conditions must be changed to reflect this fact:

!r1 1 !rp N1" b p 0, (A9)N1* * * *r ! r !I r ! r ((1! g)I , (1! d)I ) !Ip p, 2 A1 N1 N1 A1 C1 A1

!r1 1 !rp N1" b p 0, (A10)N1* * * *r ! r !I r ! r ((1! g)I , (1! d)I ) !Ip p, 2 C1 N1 N1 A1 C1 C1

!r1 1 !rp N2" b p 0, (A11)N2* * * *r ! r !I r ! r ((1! g)I , (1! d)I ) !Ip p, 1 A2 N2 N2 A2 C2 A2

!r1 1 !rp N2" b p 0. (A12)N2* * * *r ! r !I r ! r ((1! g)I , (1! d)I ) !Ip p, 1 C2 N2 N2 A2 C2 C2

Note that we assume that the reduction in fluxes for both nodules is the same, the most parsimonious assumptionto make at the moment, as both the plant and the rhizobium would try to reduce the fluxes to each other to thelargest extent possible. Therefore, the incompleteness of the reduction would likely represent a physiologicalconstraint rather than a strategy on either party’s part.


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Figure A6 denotes the conditions for effective plant sanctions with and . It shows that ourd p 0.8 g p 0.6main result continues to hold with incomplete shutoff of fluxes: effective sanctions are possible when the lower-bstrain also has higher k, but not otherwise.One can also demonstrate that the patterns of selection on b and k remain qualitatively unaffected by

incomplete shutoff of fluxes. The Mathematica code depicts the selection gradients in the b-k space. Here, webriefly explore the end point of evolution, assuming a negative relationship between b and k, depicted in figureA7. The qualitative pattern of decreasing b with increasing partner fidelity feedback is again unchanged. Themain effect of increasing the “leakage,” that is, how much flux is still taking place, is that it shifts theevolutionarily stable b to higher values, although this effect is likely to be sensitive to the functional shape ofthe growth rates.

Figure A6: Analog of figure 3 with incomplete shutoff of fluxes during the war-of-attrition phase, depicting the conditionswhere the plant can exercise effective sanctions, that is, where the higher-b strain has a lower growth rate than the lower-b strainwhen they co-occupy a plant. Black depicts regions with ineffective sanctions and white regions with effective sanctions. Effectivesanctions are possible only when the high-b strain has a low k, and vice versa.


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Figure A7: Evolutionarily stable (ESS) values of b and k traits as a function of the partner fidelity feedback exponent s. As infigure A5, we assume that and consider three sets of values for the reduction in fluxes during the war-of-attritionk p 1.2! 0.6bphase: (solid curve), (dashed curve), and (dotted curve).d p g p 0.7 d p g p 0.5 d p g p 0.3

Literature Cited Only in the AppendixAneja, P., and T. C. Charles. 1999. Poly-3-hydroxybutyrate degradation in Rhizobium (Sinorhizobium) meliloti:isolation and characterization of a gene encoding 3-hydroxybutyrate dehydrogenase. Journal of Bacteriology181:849–857.

Cevallos, M. A., S. Encarnacion, A. Leija, Y. Mora, and J. Mora. 1996. Genetic and physiologicalcharacterization of a Rhizobium etli mutant strain unable to synthesize poly-beta-hydroxybutyrate. Journal ofBacteriology 178:1646–1654.

Delmotte, N., C. H. Ahrens, C. Knief, E. Qeli, M. Koch, H. M. Fischer, J. A. Vorholt, H. Hennecke, and G.Pessi. 2010. An integrated proteomics and transcriptomics reference dataset provides new insights into theBradyrhizobium japonicum bacteroid metabolism in soybean root nodules. Proteomics 10:1391–1400.

Djordjevic, M. 2004. Sinorhizobium meliloti metabolism in the root nodule: a proteomic perspective. Proteomics4:1859–1872.

Ferguson, B. J., A. Indrasumunar, S. Hayashi, M.-H. Lin, Y.-H. Lin, D. E. Reid, and P. M. Gresshoff. 2010.Molecular analysis of legume nodule development and autoregulation. Journal of Integrative Plant Biology 52:61–76.

Fry, J., M. Wood, and P. Poole. 2001. Investigation of myo-inositol catabolism in Rhizobium leguminosarum bv.viciae and its effect on nodulation competitiveness. Molecular Plant-Microbe Interactions 14:1016–1025.

Hauser, F., G. Pessi, M. Friberg, C. Weber, N. Rusca, A. Lindemann, H.-M. Fischer, and H. Hennecke. 2007.Dissection of the Bradyrhizobium japonicum NifA"s54 regulon, and identification of a ferredoxin gene (fdxN)for symbiotic nitrogen fixation. Molecular Genetics and Genomics 278:255–271.

Jiang, G., A. H. Krishnan, Y.-W. Kim, T. J. Wacek, and H. B. Krishnan. 2001. A functional myo-inositoldehydrogenase gene is required for efficient nitrogen fixation and competitiveness of Sinorhizobium frediiUSDA191 to nodulate soybean (Glycine max [L.] Merr.). Journal of Bacteriology 138:2595–2604.

Klucas, R. V. 1974. Studies on soybean nodule senescence. Plant Physiology 54:612–616.MacLean, A., T. Finan, and M. Sadowsky. 2007. Genomes of the symbiotic nitrogen-fixing bacteria of legumes.Plant Physiology 144:615–622.

Murphy, P., W. Wexler, W. Grzemski, J. Rao, and D. Gordon. 1995. Rhizopines: their role in symbiosis andcompetition. Soil Biology and Biochemistry 27:525–529.

Oono, R., R. F. Denison, and E. T. Kiers. 2009. Controlling the reproductive fate of rhizobia: how universal arelegume sanctions? New Phytologist 183:967–979.

Oono, R., I. Schmitt, J. I. Sprent, and R. F. Denison. 2010. Multiple evolutionary origins of legume traitsleading to extreme rhizobial differentiation. New Phytologist 187:508–520.

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Geigenberger, and M. K. Udvardi. 2005. Symbiotic leghemoglobins are crucial for nitrogen fixation in legumeroot nodules but not for general plant growth and development. Current Biology 15:531–535.

Prell, J., and P. Poole. 2006. Metabolic changes of rhizobia in legume nodules. Trends in Microbiology 14:161–168.

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