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The mathematical model is constructed which describes the impacts of chaotically changing environment on the frequencies and productivity of partners in the legume-rhizobia symbiosis. The most sensitive for external impacts are the adaptively prospective bacteria strains which are specific with respect to hosts and are capable for the intensive evolution towards an improved symbiotic efficiency. An increased stability of these strains in symbiotic system may be an important factor of its evolution for the improved efficiency of partners’ interaction.

Simulation of evolution in the legume-rhizobial symbiosis allowed us to suggest the mathematical criterion (index) for the functional integrity of symbiosis (FIS). Calculation of FIS index is based on analysis of the covariance matrix of partners’ frequencies influenced by fluctuations of the systemic parameters. The positive correlations of FIS with ecological efficiency of symbiosis (its impact on the seed productivity of plants) and a negative correlation with the partners’ diversity indices were demonstrated. The revealed dependences allow us to explain the increasing of structural-functional integrity in mutualistic symbiosis byoperation of the natural selection in favor of an improved ecological efficiency of partners’ interactions.

Inactivation of genes involved in the dicarbyxylic acid transport in alfalfa rhizobia, Sinorhizobium meliloti (structural gene of succinate permease dctA and its transcriptional regulators dctBD, nifA, ntrA) resulted in the full or partial loss of Nsub2/sub-fixing activity while amplifications of these genes - in its improvement. It lead to the marked increases of N and C accumulation in alfalfa while its shoot mass was increased by a much lesser degree due to the incomplete N translocation from the roots. Factorial analysis suggested that dctABD amplification was important for improving the symbiotic efficiency in all trials while the effects of dctA, nifA and ntrA amplifications depend on the plant genotypes and growth conditions.

The model is suggested for evolution of Nsub2/sub-fixing legume-rhizobia symbiosis implemented under the conditions of multi-strain bacteria competition for inoculation of symbiotic habitats (rhizosphere, nodules). Competitiveness of each strain is characterized by the power coefficients which reflect the operation of frequency-dependent selection in the rhizobia population. When polymorphic bacteria populations are interacting with the dimorphic plant population, the selective pressures in favor of hostspecific symbionts (forming Nsub2/sub-fixing nodules only with one of the available plant genotypes) are higher than the pressures in favor of non-host-specific symbionts (forming these nodules with both plant genotypes). The highest mutualism efficiency is reached under an intermediate level of plant population diversity.

The mathematical model for evolution of legume-rhizobia mutualism based on the partners' positive feedbacks resulted from their metabolic (C-N) exchange is presented. Negative FDS in rhizobia population, combined with the partners' positive feedbacks ensure anchoring or even domination of the mutants which either acquired the mutualistic traits or changed the specificity in their expression with different host genotypes. The created model allows us to consider the mutualistic symbiosis as of a finely balanced population system in which the equilibrium may be shifted in favor of beneficial microbial genotypes due to natural selection for an improved symbiotic efficiency implemented in plant population. Research is supported by RFBR grant 06-04-48800a.

The method for mathematical simulation is suggested to analyze the balanced polymorphism in rhizobia population generated due to the interplay of Darwinian and frequency-dependent selection. Analysis of the model suggested that this polymorphism is determined not only by the selection pressures but also by the capacities of ecological niches occupied by bacteria in the «plant-soil» system. The model may be used for analyzing the selective processes in various symbiotic systems and for predicting the consequences of releasing of genetically modified plant symbionts into environment.

Formation of the cultured flora resulted in a decrease of plant symbiotic potential based on interactions with beneficial microorganisms. This decrease leads to transformation of plant micro-symbionts into the non-adaptive forms caused by: а) blocking the selection in favor of mutualistic strains; б) horizontal gene transfer in the microbial communities resulted in formation of virulent “symbiotic cheaters”. Mathematical simulation suggests that these tendencies may be overcome by formation of the optimal population structures in symbiotic system which should possess a high integrity and specificity of partners’ interactions as well as by a tolerance to the invasions of non-active aboriginal strains from the local soil populations.