An experimental and modelling exploration of the host-sanction hypothesis in legume-rhizobia mutualism

1 An experimental and modelling exploration of the host-sanction hypothesis in legume-rhizobia mutualism Diana E. Marco 1, 6 , Juan P. Carbajal 2 , Sergio Cannas 3,6 , Rebeca Pérez-Arnedo 4 , Ángeles Hidalgo-Perea 5 , José Olivares 4 , José E. Ruiz-Sainz 5 and Juan Sanjuán 4 1Laboratorio de Ecología Matemática, Area de Producción Orgánica, Facultad de Ciencias Agropecuarias, Universidad Nacional de Córdoba, Ciudad Universitaria, CC 509, 5000 Córdoba, Argentina 2 Artificial Intelligence Laboratory, Dept. of Informatics, University of Zurich Andreasstr. 15, CH-8050 Zurich, Switzerland. 3 Instituto de Física de la Facultad de Matemática, Astronomía y Física (IFFMAMAFCONICET), Universidad Nacional de Córdoba,Ciudad Universitaria, 5000 Córdoba, Argentina. 4 Dept. Microbiología del Suelo y Sistemas Simbióticos, Estación Experimental del Zaidín, CSIC. Prof. Albareda 1, 18008 Granada, Spain. 5 Dept. Microbiología, Facultad de Biología, Universidad de Sevilla, Avda. Reina Mercedes, 41012 Sevilla, Spain. 6 Members of the National Research Council (CONICET), Argentina. Abstract Despite the importance of mutualism as a key ecological process, its persistence in nature is difficult to explain since the existence of exploitative, 'cheating' partners that could erode the interaction is common. By analogy with the proposed policing strategy N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 2 stabilizing intraspecific cooperation, host sanctions against non N 2 fixing, cheating symbionts have been proposed as a force stabilizing mutualism in legume-Rhizobium symbiosis. Following this proposal, penalizations would include decreased nodular rhizobial viability and/or early nodule senescence in nodules occupied by cheating rhizobia. In this work, we analyze the stability of Rhizobium-legume symbiosis when "cheating" strains are present, using an experimental and modelling approach. We used split-root experiments with soybean plants inoculated with two rhizobial strains, a cooperative, normal N 2 fixing strain and an isogenic non-fixing, “perfect” cheating mutant derivative that lacks nitrogenase activity but has the same nodulation abilities inoculated to split-root plants. We found no experimental evidence of functioning plant host sanctions to cheater rhizobia based on nodular rhizobia viability and nodule senescence and maturity molecular markers. Based on these experiments, we developed a population dynamic model with and without the inclusion of plant host sanctions. We show that plant populations persist in spite of the presence of cheating rhizobia without the need of incorporating any sanction against the cheater populations in the model, under the realistic assumption that plants can at least get some amount of fixed N 2 from the effectively mutualistic rhizobia occupying some nodules. Inclusion of plant sanctions merely reduces the time needed for reaching plant population equilibrium and leads to the unrealistic effect of ultimate extinction of cheater strains in soil. Our simulation results are in agreement with increasing experimental evidence and theoretical work showing that mutualisms can persist or even improve in presence of cheating partners. N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 3 Keywords: mutualism, cheating, legume-rhizobia symbiosis, host sanctions, experimentally-based modelling. 1. Introduction The origin and persistence of mutualism are difficult to explain since the existence of exploitative, ‘cheating’ partners taking benefits but not reciprocating is common (Bronstein, 2001). In the mutualism established between legumes and soil bacteria known as rhizobia, bacteria reproduce and differentiate inside root nodules into bacteroids able to fix atmospheric N 2 for plant nutrition, receiving carbohydrates in exchange. After nodule senescence, surviving rhizobia are released into the soil where, depending on their viability, can maintain resident populations (Hirsch, 1996). The occurrence of low N 2 -fixing and ineffective rhizobia cheating strains in the same plant is common (Singleton and Tavares, 1986; Bronstein, 2001), and accumulation of resources by some non-fixing rhizobia in bacteroid stage has been proposed as cheating advantage at plant´s expenses (Denison, 2000). However, this accumulation is a general metabolic consequence of reduced carbon demand from the plant (Lodwig, 2003) and not necessarily implies rhizobia further survival advantages (Streeter et al., 1995). Decreased nodular rhizobial viability and/or early nodule senescence have been proposed as plant host sanctions against non N 2 fixing, cheating rhizobia (Denison, 2000; Kiers et al., 2003, 2006). A decrease in rhizobial viability was reported when N 2 - fixing rhizobia were ‘forced’ to cheat soybean plants by replacing normal, N 2 containing atmosphere by an Ar:O 2 mixture (Kiers et al., 2003, 2006). However, this approach does not really test a sanction from the plant to a true cheating rhizobium N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 4 sharing the same plant with an effective strain. Besides, exposure to an Ar:O 2 atmosphere per se reduces nodule O 2 concentration in soybean nodules due to decrease in O 2 nodule permeability through a not yet entirely elucidated mechanism (King and Layzell, 1991; Diaz del Castillo and Layzell, 1995; Wei et al., 2006). Therefore we reexamined the plant host sanctions hypothesis using an experimental method avoiding potentially confounding effects. We tested the host plant sanction hypothesis using split-root soybean plants of Osumi cultivars, inoculated with two strains of Bradyrhizobium japonicum, a highly efficient nitrogen fixing wild-type strain USDA110, and its non-fixing, nifH mutant derivative H1 (Hahn et al., 1984). H1 represents the “perfect” rhizobium cheater since it lacks nitrogenase (the N 2 fixing enzyme) activity but shows similar infection and nodule formation levels respect to the wild-type (Hahn et al., 1984). We tested experimentally the two proposed sanctions, that the plant would reduce viability of cheating rhizobia inside nodules, performing viable rhizobia counts from nodules, and that the plant would cause early senescence of nodules occupied by the cheating strain, by measuring the relative expression of gene markers for nodule senescence and maturity (Alessandrini et al., 2003). We show that soybean plants do not punish defective, nonfixing rhizobia inside the nodules. The plant-level experiment we performed allows us to unequivocally test the plant-host sanction hypothesis. However, the relevant level for studying the long-term behaviour of the system is population level. Since at this level it is not straightforward to perform experiments similar to those we conducted on plants, we studied the longterm dynamics using a population modelling approach. Few modelling attempts on N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 5 legume-rhizobia mutualism have been made, and the available examples deal with spatial structure of rhizobia and evolution of nitrogen fixation (Bever and Simms, 2000), population genetics of rhizobia (Provorov and Vorobyov, 2000) and the stability of symbiosis mediated by kin selection and plant sanctions against cheating rhizobia (West et al., 2002 a,b). Here, based on our experimental approach and results, we analysed the ecological stability of Rhizobium-legume symbiosis when “cheating” strains are present, using a population dynamics model with and without the inclusion of plant host sanctions. We show that plant populations persist in spite of the presence of cheating rhizobia without the need of incorporating any sanction against the cheater populations in the model, under the realistic assumption that plants can at least get some amount of fixed N 2 from the effectively mutualistic rhizobia occupying some nodules. Inclusion of plant sanctions merely reduces the time needed for reaching plant population equilibrium and leads to the unrealistic effect of ultimate extinction of cheater strains in soil. 2. Experimental test of plant sanction hypothesis 2.1. Plant split-root experimental setting Seeds of soybean (Glycine max) cultivar Osumi were surface sterilized and germinated. Tip root was removed to generate regrowth of two equally sized half-roots, each placed in a glass tube containing sterilized N 2 free liquid Fahraeus nutrient solution (Vincent, 1970). Each tube was inoculated and sealed to prevent cross-contamination, with the appropriate strain of Bradyrhizobium japonicum, either the wild type, normally N 2 fixing USDA 110 or the Nod+ Fix-, nifH:: Tn5 mutant H1 derived from the wild N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 6 type (Hahn et al. 1984) in the following treatments: half roots of the same plant (USDA110-1/H1-1), or in both roots of the same plant (USDA110-2 or H1-2) (Fig. 1). Each tube was carefully filled with nutrient solution as needed, while maintaining the other tube sealed. Plants were placed in a growth chamber with 16 h and 600 µEm-2 s-1 photosynthetically active radiation at 25 EC, and 8 h darkness at 18 EC. Control uninoculated plants showed no nodulation. Nodule numbers were counted in each half root every three days until nodule production reached a plateau. Three, four and five weeks after inoculation nodules of each half root of five plants/treatment were collected. Two nodules per half root were independently weighted and used immediately for rhizobia viable counts. Groups of the remaining nodules were weighted and immediately storaged at -80 EC for further determination of nodule gene marker expression. 2.2. Viable rhizobial counts Two individual nodules from each half-root from five to three plants per treatment for each date were surface sterilized using Cl 2 Hg (2.5%), manually crushed, homogeneized and resuspended in a buffer containing 0.05M Tris-HCL and 0.25 manitol. Appropriate serial dilutions were plated (two replicates per dilution) in yeast extract-mannitol (YEM, (Vincent, 1970)) supplemented with selective antibiotics depending on the strain (Spc for USDA 110 and Spc + Kan for H1). Plates were incubated at 28 EC for a week or until no further growth was detected, and colonyforming units (c.f.u.) were counted. c.f.u. numbers were compared using paired t-test analysis on untransformed data (n between 10 to 6). 2.3. Nodule gene expression N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 7 cDNA markers differentially expressed in mature (DD10) and senescent (DD15) soybean nodules (Alessandrini et al., 2003) were used to assess the developmental stage of nodules and to detect any early senescence in the different treatments. DD10 expression increases with nodule development reaching a peak with nodule maturity and then decreases slowly with nodule age, while DD15 expresses only in senescent nodules. Total RNA was extracted and treated with DNAse I (RNeasy Kit, Qiagen) from two nodule groups from each half-root of two plants of each treatment for weeks 3, 4 and 5, previously weighted and frozen (individual nodules did not yield enough RNA). Expression of the nodule markers of senescence DD15 and maturity DD1022 was assessed using quantitative real-time PCR (RT-qPCR), with the soybean 18S ribosomal subunit as internal control, using three dilutions and appropriate controls. 20- mer primers were designed with a G/C content of 50-60 %, and a Tm of about 60 EC. Length of PCR products ranged between 152-180 bp. Primer design software (Primer3) was used to select primer sequences. Secondary structures and dimer formation were checked (Oligo Analyzer 3.0 software). Designed DD15 primers 5´- TGGTTTTCTCCTCCTGCTGATT-3´ and 5-GGCAGCATACTCACTTTCACTT-3´, DD10 primers 5´-AGAAGAAGCTGGTGGTATTGGT-3´and 5´- GGAGTTGCTGAGATTGGATTGA-3´, and 18S primers 5´- TACAACGCGCAAAACCTTACCA-3´and 5´-GTTTCGCTCGTTATAGGACTTG-3´ were purchased from Roche. RT-qPCR was performed with a iCycler iQ real-time PCR detection system from Bio-Rad. Primer efficiencies were between 85 an 100%. RT- qPCR was performed with a iCycler iQ real-time PCR detection system from Bio-Rad, using Reverse Transcriptase SuperScript II and Platinum Taq DNA polymerase (Invitrogen). The cycling program was 1 cycle: 5 min at 94 EC, 30 cycles: 1 min at 94 N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 8 EC, 1 min at 60 EC and 30 s at 72 EC, and 1 cycle: 10 min at 72 EC. Transcript expression levels of DD15 and DD10 were related to the expression levels of the soybean 18S gene that served as an internal standard. We therefore expressed the standardized transcript expression ct levels as DD15/18S and DD10/18S ratios. ct ratio values were compared using paired t-test analysis (n= 12). 2. 4. Experimental results The cheater rhizobial strain showed similar infection and nodule formation levels and temporal patterns respect to the wild-type (Fig. 2). Addressing the first sanction mechanism proposed in the experimental test, results from the rhizobial viability experiments show that the plant is able of tolerating cheating by non-fixing rhizobia when it can get some amount of fixed N 2 from at least half of total plant nodules. Obviously, plants with all nodules occupied by cheating rhizobia are not able of maintaining good vegetative conditions and high rhizobia populations as plants partially or exclusively associated with fixing rhizobia (Fig. S1a, b), and ultimately they die due to N starvation about 6 weeks after inoculation (Fig. S1c). Viability of the cheating, non-fixing strain per nodule mass was not significantly lower comparing half roots of the same plant separately inoculated with each strain for the two soybean varieties (Fig. 3). Comparing treatments where both half roots of each plant were inoculated with the same strain, cheating rhizobia viability was significantly lower (Fig. 3). In addition, we found no evidence of early nodule senescence in nodules occupied by cheating rhizobia when compared with half roots inoculated with the N 2 -fixing strain in the same plant (Fig. 4a). In an apparently puzzling way, plants with both roots inoculated with the cheating strain showed decreased expression of the senescence marker compared with plants inoculated only with the N 2 -fixing strain (Fig. 4a). However, this correlates with N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 9 the expression of the molecular marker for nodule maturity, showing increased expression in plants with both half roots inoculated with the cheating strain (Fig. 4b). 3. Model development and biological background The model is built up on the grounds of an experimental approach allowing to directly and unambiguously testing a potential sanction from the plant to a true cheating rhizobium sharing the same plant with an effective strain. To evaluate the effect of the sanctions, and in agreement with the experimental design, we avoided factors like strain competition.We based the model formulation on several biological features of the mutualistic system and the following assumptions, either checked or supported by the experimental test: * Fixing and non-fixing bacterial strains only differ in their N 2 fixing ability, and they have the same ecological abilities (competition in soil and nodule initiation). * Nodules are initiated and occupied by a single bacterium of either fixing or non-fixing strain. * Nodules are occupied to their carrying capacity, are functionally equivalent and metabolically independent of each other. * At the end of each annual cycle nodules undergo senescence and release surviving bacteria into the soil. * Fixing and non-fixing nodules can develop and coexist in the same plant. We discuss next the biological background of the assumptions. Cheating rhizobia can vary in their N 2 fixation ability, from no fixation to low fixation levels compared with highly effective strains. To simplify the system, we deal here with N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 16 only through α and this number remains constant in time (therefore g is also independent of time), the plant population always decreases, even when the fixing bacteria population increases. Once the plants went extinguished, the bacterial populations in the rhizosphere follow a logistic dynamics until they become stationary. On the other hand, when α > α c the plant population always reaches a non-zero stationary value. Again, the closer the value of α to α c the slower the convergence to the stationary situation. More details on how the critical value of α can be obtained analytically are given in Appendix B. For the set of parameters values used in this work we have α c = 0.169. When p m ≠ 0, α changes with time when p m > 0 and the overall behaviour depends on the initial values of both types of bacterial populations, instead of depending only on its ratio α (0). The behaviour of the final plant population is more complex now, since it depends on whether α (t) overcomes the critical value α c (see Appendix B) during the dynamics of the coupled system. However, we found that again both bacterial and plant populations always reach a stationary value for long times. If the initial populations of both type of bacteria are below the threshold p m , their dynamics is completely decoupled from the plant system and they develop logistically, while the plants go extinguished after the first iteration. If the initial populations of both type of bacteria are above the threshold p m , the dynamics is exactly the same as in the p m = 0 case, so again plants survive when α (0) >α c . The main difference with the p m = 0 case is that the plant population goes always extinguished when p + (0) < p m , no matter the value of α (0). Fig. 6 a shows the typical behaviour of p + , p - and p p , for σ = 0, α = 1.5 α c and p m > 0. N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 17 With intermediate sanction (σ = 0.5), i.e., half of the nodules prevented from releasing bacteria into the soil, the plant population survives equally well, but, as expected, a substantial reduction in p - numbers can be seen (Fig. 6b). With extreme sanction (σ = 1), the plants halt all the non-fixing bacteria inside the nodules coming into the soil. In this situation the only way the non-fixing bacteria may persist in the system is due to their reproduction in the soil (Fig. 6c). The fixing bacterial populations grow faster due to the reinsertion of the bacteria coming from the senescent nodules. It is clear that α, the number of fixing bacteria, will increase with time and eventually go to 1. This means that, in the long term when the plant population persists by applying sanctions, only fixing rhizobia will be present in the system. We calculated numerically the dynamics of the system for p m = 10 3 g -1 . When α < α c and/or p + (0) < p m the plant population is extinguished after a few iterations (not shown), as in the case with no sanction. When α > α c and p + > p m the population of non-fixing bacteria slowly decreases while the fixing bacteria and plant populations increase until they reach their carrying capacities. The main difference with the case without sanction is that when p + > p m the plant population can persist even when the initial number of fixing bacteria is smaller than α c , depending of the value of p + (0). For values of α smaller but close to α c the plant population can show a nonmonotonous behaviour. In this case the number of seeds and the plant population decrease in the first iterations but the remaining plants are enough to increase the population of fixing bacteria so that α(t) exceeds the critical value. This can be observed in more detail in Fig. 7. Hence, the main effect of the sanction is to reduce the required initial value of α for the plants to survive. The minimum value of α for which this effect N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 18 can be observed is approximately α ≈ 0.9 α c . However, this reduction operates at unrealistically low values of α. Another effect of the presence of sanction is to reduce slightly the time needed for populations to reach a stationary state, as shown also in Fig. 6c. 4. Discussion Using a combined experimental and population model approach we showed that ecological persistence of legumerhizobia mutualism under field comparable conditions is not compromised by the presence of non-fixing, cheating rhizobia in the symbiotic system. Under a restrictive scenario, that the only source of nitrogen is from symbiosis, experimental plants survive in good conditions and simulated plants are able of maintaining viable populations despite being cheated by non-fixing rhizobia when they can at least get some amount of fixed N 2 from the effectively mutualistic rhizobia occupying some nodules, which is a common situation in field (Amarger, 1981; Singleton and Tavares, 1986; Simms et al., 2006). Taken together, the experimental results and the simulation outcomes provide evidence against functioning plant host sanctions. Addressing the first sanction mechanism proposed in the experimental test, results from the rhizobial viability experiments show that the plant is able of tolerating cheating by non-fixing rhizobia when it can get some amount of fixed N 2 from at least half of total plant nodules. Plants partially or exclusively associated with fixing rhizobia are able of maintaining good vegetative conditions and high rhizobial populations. Plants with all nodules occupied by cheating rhizobia are not able of surviving and N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 19 ultimately they die due to N starvation about 6 weeks after inoculation, as expected since rhizobial symbiosis was the only nitrogen source. Testing the second sanction mechanism, data of expression of nodule maturity and senescence markers provide complementary results to the first mechanism and interesting explanations to the lack of evidence for the sanction hypothesis we found. The finding of no greater senescence in nodules occupied by cheating rhizobia in plants associated with both strains is in agreement with the rhizobial viability results and reinforces the evidence against functioning plant host sanctions. Besides, higher nodule maturation and lower senescence in the extreme case of entirely cheated plants may suggest that cheating rhizobia are exerting some control over the plant to accelerate nodule development and counteract nodule senescence to get ready early viable populations in face of premature host death by starvation, acting in a true parasitic way (Ferriere et al., 2002). It is known that some rhizobia can overcome the plant controlled nodule initiation (Ma et al., 2002). However, to our knowledge this is the first work providing evidence on a possible control of nodule maturation and senescence by normally nodulating but non-fixing rhizobial strains. This proposed control and possible mechanisms operating behind it deserve to be further tested. Our results also show that a simple population model can explain the coexistence of fixing and cheating rhizobia strains commonly found in real conditions. Our model predicts a critical number (α c ) of total soil rhizobia population size represented by fixing rhizobia needed to provide a minimum N 2 amount for plant population persistence. In our knowledge, this critical number has not been experimentally determined yet. Plants with all nodules occupied by cheating rhizobia are not able of maintaining good vegetative conditions and ultimately die due to N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 20 nitrogen starvation, as showed in the plant experiment, but still a viable population of non-fixing, cheater rhizobia would persist in the soil, as we showed in the simulations. The assumption of no different competitive abilities between strains either in soil or for nodulation ensures a source of cheating strains for nodulation in the next plant population cycles. Relaxing the assumption of no ecological differences and assuming for example competitive advantage of cheating strains, the critical number (α) could be even more difficult to meet. This is a common and problematic situation in crops, where a few years after inoculation with highly efficient rhizobia strains nodulation becomes produced by less efficient or even non-fixing strains residing in soil (Amarger, 1981; Singleton and Tavares, 1986; Dowling and Broughton, 1986). Similarly, relaxing the assumption on the restriction of nitrogen source and allowing for plants taking also nitrogen from soil would set conditions even more favorable for cheating rhizobia persistence. Surprisingly, no experimental work assessing the performance of nonfixing and fixing rhizobial strains in soil in legume systems under external nitrogen fertilization is available in the literature. However, we can hypothesize that the critical α would become even smaller as part of the required nitrogen could be obtained from soil, and a greater number of non-fixing rhizobia could be thus allowed to compose the total rhizobial soil population. We incorporated the plant sanction in the model as a reduction of non-fixing rhizobial survival from nodules to soil, in the same way proposed by authors advocating the need of sanctions for legume-rhizobia mutualism (West et al., 2002 a,b). However, in contrast with the modelling approaches followed by these authors, we did not include any genetic relatedness between rhizobia involving kin selection nor any hypothesized trade-off involving energetic expenditure on nodules by the plant and nitrogen gain. By N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 21 simply introducing a minimum number of fixing nodules to guarantee plant survival in absence of other nitrogen source (supported by field information and our own experiments), we showed that sanctions are not needed to explain the legume-rhizobia mutualistic system persistence. When we included plant sanctions in the model, we found that results did not change significantly. The main effects consisted in reducing the time needed for plants to reach population equilibrium and to lower the critical α. Since the sanction is lowering or halting the return of cheating rhizobia to soil, it is expected that after few growing cycles mainly fixing rhizobia will be available in the soil for nodulation thus allowing more plants to produce enough viable seeds to reach population equilibrium earlier and with a smaller α. In any case, a minimum bacteria population is needed to trigger nodulation. Another expected result from applying plant sanction is that populations of cheating rhizobia will go extinguished from soil with time. As previously noted, this is not a realistic situation since persistent cheating strains may chronically hamper crop productivity (Amarger, 1981). Using a simple population model we were able of explaining the commonly found coexistence of fixing and cheating rhizobial strains in field conditions. However, further complications providing even more realism could be easily added to our model, for example, co-occupation of the same nodule by strains with different fixation abilities. About 20 % of total nodules can be co-occupied by different rhizobial strains in artificial inoculations (Rolfe and Gresshoff, 1980). Another potential complication is the horizontal transmission of symbiotic plasmids, turning non-nodulating strains into nodulating rhizobia, that is frequent between different strains of rhizobia (Sullivan et al., 1995). This genetic exchange can also be easily added to our model. However, none N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 22 of these further complications is expected to pave the way for the plant sanction hypothesis. The two main assumptions behind the sanction hypothesis in mutualisms, that it is costly for the host to be associated with the exploiter, and that mutualism would break unless cheaters are punished, seem not to hold for the majority of mutualistic associations known (Bronstein, 2001). Moreover, for the rhizobia-legume mutualism, costs of being cheated may not be as high as assumed if the host is still able of obtaining benefits from other mutualistic partners, for example in co-infected plants which is a common situation in field (Singleton and Tavares, 1986; Dowling and Broughton, 1986). Punishment evidence in addition to that already obtained under Ar:O 2 treatment (Kiers et al., 2003, 2006) is needed to hold the sanction assumption. Another proposed evidence of plant host sanctions, an inverse relationship between nodule size and strain fixation effectiveness in a field experiment using Lupinus arboreus plants and associated Bradyrhizobium spp. was reported (Simms et al., 2006). However, nodule rhizobial population sizes were measured and related only to nodule size and not to strain efficiency in independently field collected nodules (Simms et al., 2006), thus not really testing the main host sanction assumption. On more general theoretical grounds, our results support the point of view that cheating does not necessarily menace rhizobia-legume mutualism. There is increasing empirical evidence that punishment is not always applied to defective mutualistic partners (Ferriere et al., 2002). For example, in a palm-pollinator mutualistic association, female plants inhibit the development of a weevil pollinator eggs and larvae, benefiting from pollination services but not reciprocating, thus cheating their N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 23 partner (Dufay and Anstett, 2004). It was expected that the weevils would suspend pollination visits to female plants. However, no evidence of sanctions against female plants was found, and apparently the mutualism persistence is not compromised (Dufay and Anstett, 2004). Coexistence of cheaters and true mutualistic partners is also theoretically possible (Ferriere et al., 2002; Foster and Kokko, 2006). Acknowledgements We thank S. Muñoz, H. Blanca and S. Moussaid for lab assistance, N. Ferroll for primer design assistance, and the staff of the Dept. Microbiología (EEZ-CSIC), for general help. We thank H-M Fischer (ETH, Zürich) for B. japonicum USDA 110 and H1 strains. This work was partially supported by grants from the Spanish Ministry of Education and Science and the Education Council of Junta de Andalucía to J. S. and J. E R., Secyt – Universidad Nacional de Córdoba, Agencia Córdoba Ciencia and CONICET (Argentina). D.E.M. was supported by a Sabbatical Visit of the Ministry of Education of Spain. D.E.M. and S. A. C. are members of the National Scientific Council (CONICET) of Argentina. References Alesandrini, F., Frendo, P., Puppo, A., Hérouart, D. 2003. Isolation of a molecular marker of soybean nodule senescente. Plant Physiol. Biochem. 41, 727-732. Amarger, N. 1981. Competition for nodule formation between effective and ineffective strains of Rhizobium meliloti. Soil Biol. Biochem. 13, 475-480. N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 24 Amarger, N., Lobreau, J. P. 1982. Quantitative Study of Nodulation Competitiveness in Rhizobium Strains. Appl. Environ. Microbiol. 44, 583-588. Bever, J. D., Simms, E L 2000. Evolution of nitrogen fixation in spatially structured populations of Rhizobium, Heredity 85, 366-372. Bronstein, J. L. 2001. The exploitation of mutualisms. Ecol. Lett. 4, 277-287. Cannas, S. A., Marco, D. E., Paez, S. A. 2003. Modelling biological invasions: species traits, species interactions and habitat heterogeneity. Math. Biosci. 183, 93-110. Denison, R. F. 2000. Legume sanctions and the evolution of symbiotic cooperation by Rhizobia. Am. Nat. 156, 567-576. Diaz del Castillo, L., and Layzell, D. B. 1995. Drought stress, permeability to O 2 , diffusion, and the respiratory kinetics of soybean root nodules. Plant Physiol. 107, 1187-1194. Dowling, D. N., Broughton, W. J. 1986. Competition for nodulation of legumes, Annu. Rev. Microbiol. 40,131-157. Dufay, M., Anstett, M. C. 2004. Cheating is not always punished: killer female plants and pollination by deceit in the dwarf palm Chamaerops humilis, J. Evol. Biol. 7, 862–868. Ferriere, R, Bronstein, J.L., Rinaldi, S., Law, R., Gauduchon, M. 2002. Cheating and the evolutionary stability of mutualisms. Proc. R. Soc. Lond. B 269, 773-780. Foster, K. R., Kokko, H. 2006. Cheating can stabilize cooperation in mutualisms, Proc. R. Soc. B 273, 2233–2239. N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 25 Gage, D. J., Bobo, T., Long , S. R. 1996. Use of green fluorescent protein to visualize the early events of symbiosis between Rhizobium meliloti and Alfalfa (Medicago sativa). J. Bacteriol. 178, 7159–7166. Goldenfeld, N. 1992. Lectures on Phase Transitions and the Renormalization Group, Frontiers in Physics 85. Addison-Wesley Publishing Co., Illinois. Hahn, M., Meyer L., Studer D., Regensburger, B., and Hennecke, H. 1984. Insertion and deletion mutations within the nif region of Rhizobium japonicum. Plant Mol. Biol. 3,159-168. Hirsch, P. 1996. Population dynamics of indigenous and genetically modified rhizobia in the field, New Phytol. 133, 159-171. Kiers, E.T., Rosseau, R.A., West, S.A., Denison, R.F. 2003. Host sanctions and the legume-rhizobium mutualism. Nature 425, 78-81. Kiers, T. E., Rousseau, R. A., Denison, R. F. 2006. Measured sanctions: legume hosts detect quantitative variation in rhizobium cooperation and punish accordingly. Evol. Ecol. Res. 8, 1077–1086. King, B. J., and Layzell, D. B. 1991. Effect of increases in oxygen concentration during the argon-induced decline in nitrogenase activity in root nodules of soybean. Plant. Physiol. 96, 376-381. Lodwig, E. M., Hosie, A. H. F., Bourde, A., Findlay, K., Allaway, D. A., Karunakaran, R., Downie, J. A., Poole, P. S. 2003. Amino-acid cycling drives nitrogen fixation in the legume–Rhizobium simbiosis. Nature 422, 722-726. Ma, W., Penrose, D. M., Glick, B. R. 2002. Strategies used by rhizobia to lower plant ethylene levels and increase nodulation. Can J Microbiol. 48:947-54. N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 32 Figure 3. Rhizobia viability per nodule mass in the soybean plant split-root experiments. R h i z ob i a i n s i de nodu l e s i nfe c ted b y the N - f i x i ng U S D A 110 s t r a i n 2 N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 33 o r the non - f i x i ng, c heat i ng s t r a i n H 1, e i the r i n ha l f r oot s of the s a m e p l ant ( U S D A 110 - 1/ H 1 - 1 ) , o r i n both r oot s of the s a m e p l ant ( U S D A 110 - 2 o r H 1 - 2 ) w e r e c ounted a s c o l on y fo r m i ng un i t s ( c .f.u. ) th r ee, fou r and f i v e w ee ks afte r i no c u l at i on. * P < 0.05, ** P < 0.01 s i gn i f i c ant d i ffe r en c e s b y pa ir ed t - te s t s pe r fo r m ed on unt r an s fo r m ed data. B a r s a r e m ean s " 1 s .d. N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 34 Figure 4. Relative expressions of gene markers DD15 of nodule senescence (a) and DD10 of nodule maturity (b) in nodules from the N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 35 soybean plant split-root experiments. * P < 0.05 s i gn i f i c ant d i ffe r en c e s b y pa ir ed t - te s t s . B a r s a r e m ean s " 1 s .d. T r eat m ent s a s i n F i g. 1. N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 36 Figure 5. Schematic structure of the model dynamics in a single iteration. In i t i a l v a l ue s of p l ant and ba c te ri a popu l at i on s ( p p fo r p l ant s ; p + and p - fo r ba c te ri a ) s et the v a l ue s of ba c te ri a i n nodu l e s ( p N + and p N - ) ; K s r ep r e s ent s the nu m be r of nodu l e s a v a il ab l e fo r c o l on i s at i on and K N the nu m be r of c o l on i s ed nodu l e s . T he ba c te ri a i n nodu l e s p r o v i de N 2 to the p l ant s and the ne w popu l at i on s a r e c a l c u l ated ba s ed on the p r odu c ed s eed s ( g ) and the r e l ea s ed ba c te ri a ( ∆ p + and ∆ p - ) . N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 37 Figure 6. Temporal behaviour of the variables p p (triangles), p + (filled circles) and p − (empty circles) for α = 1.5 α c , p p (0) = 0.1 δ p , and different N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 38 values of σ. ( a ) σ = 0 ( no s an c t i on ) , ( b ) σ = 0.5 ( m ode r ate s an c t i on ) , and ( c ) σ = 1 ( tota l s an c t i on ) . T i m e i s m ea s u r ed i n nu m be r of i te r at i on s . Figure 7. The effect of sanction on final plant population (fraction of carrying capacity δ p ). p p / δ p ( f ill ed c ir c l e s ) , α ( e m pt y c ir c l e s ) . α c i s the dotted ho ri z onta l li ne. W hen α e xc eed s the c ri t i c a l v a l ue the p l ant popu l at i on s ta r t s i n c r ea s i ng. T he i n i t i a l v a l ue of α i s 0.9 αc . N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 39 Parameter Value Description r s 10 −4 g −1 Intrinsic rate of growth of bacteria in the rhizosphere (per g of soil) δ s 10 6 g −1 Rhizosphere´s carrying capacity (per g of soil) δ n 10 6 Nodule´s carrying capacity δ p 2 × 10 5 Ha −1 Plants´ field carrying capacity m s 1.5 × 10 5 g ・ Ha −1 Soil mass per hectare associated to plant population n 45 Typical number of nodules per plant K 0 0.15 × n Minimum number of fixing nodules per plant needed for seed production G 55 Maximum number of viable seeds produced per plant N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 40 P g 0.69 Probability of a viable seed reaching the adult stage σ 0-1 Sanction intensity 0 = No sanction, 1 = maximum sanction p m 0 − 10 3 g −1 Minimum bacteria population per g of soil needed to trigger the nodulation process Table 1. Parameter values used in the simulations. N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008 41 Appendix A. Invariance of α for p m = 0 and σ = 0 In the following appendix it is shown that the magnitude α is a constant for these particular values of the parameters p m and σ. The definition of α given in 6 applied for t + 1 produces )()()( )()()( )1()1( )1( )1( tpnftptp ttpnftp tptp tp t pn pn δ αδ α ++ + = = −++ + =+ −+ + −+ + (A.1) the second term of the equality comes from (16) and (17) where the second factor was canceled. Should be noted that for p m = 0 and σ = 0 corresponds Θ (p i − p m ) = 1 and f + = f − = f. Replacing f δ n n p p (t) = Β (t) and equating to zero produces, α (t + 1) [p + (t) + p − (t) + B(t)] − p + (t) − B(t) α (t) = 0 (A.2) p + (t) [α (t + 1) − 1] + α (t + 1) p − (t) + B(t) [α (t + 1) −α (t)] = 0 (A.3) Noting that, )1()1( )1( 1)1( +++ + −=−+ −+ − tptp tp t α ( A .4 ) It can be written, 0)()( )1()1( )()1( )1()1( )1()( =ΔΒ+ −++ + + +++ + − −+ −+ −+ −+ tt tptp tptp tptp tptp α (A.5) 0)()( )1()1( )1()()()1( =ΔΒ+ +++ +−+ −+ −+−+ tt tptp tptptptp α (A.6) Analising the first term in A.6 it is noted that p + (t + 1)p − (t) − p + (t)p − (t + 1) = = [p + (t) + B(t) α(t)] p − (t) − p + (t) [p − (t) + B(t)(1 − α(t))] = N atu r e P r e c ed i ng s : hd l :10101/np r e.2008.1964.1 : P o s ted 10 J un 2008