Evolution and invasion dynamics of multiple infections with Wolbachia investigated using matrix based models

Endosymbiotic bacteria are often transmitted vertically from one host generation to the next via oocytes cytoplasm. The generally small number of colonizing bacteria in the oocytes leads to a bottleneck at each generation, resulting in genetic homogenization of the symbiotic population. Nevertheless, in many of the species infected by Wolbachia (maternally transmitted bacteria), individuals do sometimes simultaneously harbor several bacterial strains, owing to the fact that Wolbachia induces cytoplasmic incompatibility (CI) that maintains multiple infections. CI occurs in crosses in which the male is infected by at least one Wolbachia strain that the female lacks, and consequently it favors individuals with the greatest symbiotic diversity. CI results in death of offspring in diploid species. In haplodiploid individuals, unfertilized eggs hatch normally into males and fertilized ones, which would lead to females, either die (female mortality type: FM) or develop into males (male development type: MD). Until now, only one theoretical study, restricted to diploid species, has investigated the associations where multiple CI-inducing Wolbachia co-exist, and explored the conditions under which multiple infections can spread. The consequences of double infections on Wolbachia maintenance in host populations, and the selective pressures to which it is subjected have not yet been analysed. Here, we have re-written a model previously developed for single infection in matrix form, which allows easy extension to multiple infections and introduction of mutant strains. We show that (i) the CI type has a strong influence on invasiveness and maintenance of multiple infections; (ii) double infection lowers the invasion threshold of less competitive strains that hitch-hike with their companion strain; (iii) when multiple infections occur, as in single infections, the strains selected are those which maximize the production of infected offspring; and (iv) for the MD CI type, invasion of mutant strains can carry the whole infection to extinction.