Case study of plant-microbial symbiosis model using evolutionary game theory

A. V. Abramova ; A. G. Topaj

Matematičeskaâ biologiâ i bioinformatika, Tome 13 (2018) no. 1, pp. 130-158.

Résumé

Nitrogen-fixing bacteria (rhizobia) have symbiotic relationships with legumes: they inhabit legume root nodules and convert atmospheric nitrogen to a plant available form in exchange for photosynthates. Generally, this symbiotic process called biological nitrogen fixation is mutually beneficial to both plants and bacteria. Using this mechanism symbionts acquire alternative sources of hard-to-reach individual growth resources (carbon for rhizobia and nitrogen for plants). However, not all rhizobia provide fixed nitrogen to the host plant honestly: some of them can behave as a kind of cheaters. Unlimited cheating rhizobia strains propagation may potentially disrupt the symbiotic relationships. This raises the question of plant–rhizobia mutualism evolutionary stability. This paper presents the results of the legume–rhizobia interactions investigation implemented as AnyLogic agent-based models. Three modifications of interaction model (“one plant – one strain of rhizobia”, “one plant – several strains of rhizobia”, “one plant with root nitrogen uptake – several strains of rhizobia”) in the form of evolutionary games in two populations (rhizobia and plants) are considered by the authors. Simulated natural selection is driven by populations heterogeneity: each agent has its own cooperation parameter which determines its strategy in evolutionary game. In the set of numerical experiments the following results were obtained. Simulated populations tend to become homogeneous with cooperation parameter value close to the theoretically optimal. Such degenerated structure of populations is evolutionarily stable and maximizes the total growth of the entire symbiotic system. Thus, the logic of symbionts co-development simulation itself prevents the emergence of parasitic strategies and automatically provides rational and mutually beneficial partnership sustainability. This remains true in the early stages of ontogenesis or under the assumption that life cycle duration is unlimited.  

Bibliographie

[1] Sprent J. I., Sutherland J. M., de Faria S. M., “Some aspects of the biology of nitrogenfixing organisms”, Philosophical Transactions of the Royal Society B: Biological Sciences, 317 (1987), 111–129 | DOI

[2] Ridli M., Proiskhozhdenie altruizma i dobrodeteli. Ot borby za vyzhivanie k sotrudnichestvu, Eksmo, M., 2016, 416 pp.

[3] Liu Y., Wu L., Baddeley J. A., Watson C. A., “Models of biological nitrogen fixation of legumes”, Agronomy for Sustainable Development, 31:1 (2011), 155 | DOI

[4] Khvorova L. A., Topazh A. G., Abramova A. V., Neupokoeva K. G., “Podkhody k opisaniyu simbioticheskoi azotfiksatsii. II. Analiz podkhodov k matematicheskomu modelirovaniyu protsessa”, Izvestiya AltGU, 1:85/1 (2015), 192–196 | DOI

[5] Abramova A. V., Topazh A. G., Khvorova L. A., “Agentnyi podkhod v modelirovanii simbioticheskoi azotfiksatsii: ot passivnykh ob'ektov k aktivnym sub'ektam vzaimodeistviya”, Agrofizika, 4:20 (2015), 49–62

[6] Denison R. F., “Legume Sanctions and the Evolution of Symbiotic Cooperation by Rhizobia”, The American Naturalist, 156 (2000), 567–576 | DOI

[7] Maynard Smith J., Evolution and the Theory of Games, Cambridge University Press, 1982, 234 pp. | Zbl

[8] Friesen M. L., “Widespread fitness alignment in the legume-rhizobium symbiosis”, New Phytologist, 194 (2012), 1096–1111 | DOI

[9] Akcay E., Roughgarden J., “Negotiation of mutualism: rhizobia and legumes”, Proceedings of the Royal Society B: Biological Sciences, 274:1606 (2007), 25–32 | DOI

[10] Simms E. L., Taylor D. L., “Partner choice in nitrogen-fixation mutualisms of legumes and rhizobia”, Integrative and Comparative Biology, 42 (2002), 369–380 | DOI

[11] Kiers E. T., Rousseau R. A., West S. A., Denison R. F., “Host sanctions and the legumerhizobium mutualism”, Nature, 425 (2003), 78–81 | DOI

[12] Bever J. D., Simms E. L., “Evolution of nitrogen fixation in spatially structured populations of Rhizobium”, Heredity, 85:4 (2000), 366–372 | DOI

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

[14] Fujita H., Aoki S., Kawaguchi M., “Evolutionary Dynamics of Nitrogen Fixation in the Legume-Rhizobia Symbiosis”, PLoS ONE, 9:4 (2014), e93670 | DOI

[15] Moyano G., Marco D., Knopoff D., Torres G., Turner C., “Explaining coexistence of nitrogen fixing and non-fixing rhizobia in legume-rhizobia mutualism using mathematical modeling”, Mathematical Biosciences, 292 (2017), 30–35 | DOI | MR | Zbl

[16] Topazh A. G., Abramova A. V., “Gibridnye modeli simbioticheskoi azotfiksatsii”, Imitatsionnoe modelirovanie. Teoriya i praktika, IMMOD-2015, Sbornik trudov Sedmoi vserossiiskoi nauchno-prakticheskoi konferentsii, ed. Yusupov R. M., 2015, 380–384

[17] Uchinomiya K., Iwasa Y., “Optimum resource allocation in the plant-fungus symbiosis for an exponentially growing system”, Evolutionary Ecology Research, 16 (2014), 363–372

[18] Adami C., Schossau J., Hintze A., “Evolutionary game theory using agent-based methods”, Physics of Life Reviews, 19 (2016), 1–26 | DOI

[19] Berezovskaya F. S., Kareva I. G., Karev G. P., Vozmozhno li predotvratit «tragediyu obschego resursa»?, Matematicheskaya biologiya i bioinformatika, 7:1 (2012), 30–44 | DOI | Zbl

[20] Gorban A. N., “Selection Theorem for Systems with Inheritance”, Mathematical Modelling of Natural Phenomena, 2 (2007), 1–45 | DOI | MR | Zbl