Population genetics of rhizobia: construction and analysis of an "Infection and Release" model

A mathematical model is created to assess the inputs of sym gene transfer of in planta multiplication and of interstrain competition into dynamics of the rhizobia populations. Their microevolution is presented as a series of the "infection and release" cycles; each cycle includes transfer of sym genes from virulent initial symbionts to avirulent local bacteria yielding the virulent novel symbionts; competition between initial symbionts and novel symbionts for the host nodulation; multiplication of initial symbionts and novel symbionts in planta and their release into soil; competition between the released novel symbionts and resident local bacteria for ex planta survival. A recurrent equation is created to determine the number of novel symbionts at each cycle of evolution of the closed bacteria-plant system. Its analysis demonstrates that under certain, really allowable values of the introduced parameters two major effects may occur: (a) rapid multiplication of novel symbionts arisen from sym gene transfer; and (b) increase of frequency of rare local bacteria genotypes after acquisition of virulence. Multiplication of very rare strains (p<10(-19)) in the plant-associated bacteria population is possible at certain parameters of the system. Variation of the sizes of bacteria populations and of the parameters for interstrain competition may influence the evolutionary rate of the bacteria population. The "infection and release" model represents a selective mechanism which may be responsible for a high taxonomic diversity of rhizobia and for a panmictic structure of their populations.