Nitrogen is essential for all forms of life in that it is required to biosynthesize basic building blocks of plants, animals and other life forms. Atmospheric nitrogen is relatively inert; however, the fixation process can free up the nitrogen atoms from their diatomic form (N2) to compound form (NH3) so they could be used in many ways. Biological nitrogen fixation provides about 65% of the biosphere’s available nitrogen, and most of this is done by the cooperation between legume and rhizobia. In fact, symbiotic nitrogen fixation by rhizobia in legume root nodules injects approximately 40 million tonnes of nitrogen into agricultural systems each year.
The symbioses is achieved through a series of intricate interactions. And rhizobia are found as bacteroids in infected legume hosts’ root nodules, where they would perform nitrogen fixation and obtain sources of energy (like photosynthate) from the plant. Were there no oppurtunity cost in the fixation process, natural selection among rhizobia would favor those strains whose bacteroids fix the most nitrogen. However, nitrogen fixation is energy-intensive. In the case of multiple infection, it is mots likely that the “free-rider” scenario would take place. “Cheating” rhizobia would exploit plant resources for their own reproduction rather than nitrogen fixation, resulting in their outcompeting the fixing rhizobia and the symbioses’ falling apart. Thus, host monitoring of symbiont performance and the imposition of sanctions on “cheats” are crucial in preserving mutualistic relations and stablizing the system.
The model is built upon several features of the mutualistic system and the following assumptions ,
Limited resource: naturally, all three populations follow logistic growth; soil has carrying capacity Sp for legume, and St for rhizobia in total;
Homogeneity: fixing and cheating bacterial strains only differ...