Southern-Summer School on Mathematical Biology

Wolbachia are bacterias that infect a wide range of Arthoprods. This particular bacterial infection is maternally inherited and often result on bacterial manipulation on host reproduction dynamics. One of the main reproduction manipulations of Wolbachia are Citoplasmatic Incompatibility (CI) and Male-killing (MK).

CI occurs when males infected with Wolbachia mate with females that are not infected. Such a cross results in aborted fertilization. By contrast, infected females can mate successfully with both infected and uninfected males (Figure 1).

MK Wolbachia kill a large proportion of a female’s male offspring. This phenotype is advantageous to the bacteria as surviving (and infected) daughters benefit from the death of their brothers through some form of fitness compensation (e.g. resource reallocation). These mechanisms give females infected with Wolbachia the upper hand, assisting the spread of Wolbachia into wild host population.

It is expected that the interplay of infected and healthy males and females can lead to different scenarios. In one extreme, Wolbachia succeeds and can even fixate permanently in an infected asexually-reproducing all-female population. In other scenarios, Wolbachia might become its own executioner, leading to the collapse of the whole system. Nevertheless, other intermediate scenarios encompass males and females, infected or not, coexisting in the population.

Propose and analyze a mathematical model to investigate the effects of proportion of infected offspringson Wolbachia infections as well as the effects of male offspring mortality on invasiveness and dominance of Wolbachia infected host population.

• Investigate the the system response to varying degrees of maternal inheritance of Wolbachia infection. How can infected host population establish and dominate?

• It has been proposed that Wolbachia infections can lead to the extinction of the male population (and to the collapse of the whole system in some cases) [Merçot and Poinsot, 2009]. According to your model, in which situations does this collapse occur and in which is it avoided ?

• Considering a system composed only of infected males and females, can the healthy (susceptible) phenotype invade the population? Is there a possibility of lasting coexistence among infected and uninfected individuals on a population?

BONUS: consider a trade-off between maternal inheritance and offspring population size of infected hosts and explore parameter the regions in which Wolbachia can invade the population

• Merçot, Hervé, and Denis Poinsot. “Infection by Wolbachia: from passengers to residents.” Comptes rendus biologies 332, no. 2-3 (2009): 284-297.