Evolutionary maintenance of selfish homing endonuclease genes in the absence of horizontal transfer

Homing endonuclease genes are "selfish" mobile genetic elements whose endonuclease promotes the spread of its own gene by creating a break at a specific target site and using the host machinery to repair the break by copying and inserting the gene at this site. Horizontal transfer across the boundary of a species or population within which mating takes place has been thought to be necessary for their evolutionary persistence. This is based on the assumption that they will become fixed in a host population, where opportunities of homing will disappear, and become susceptible to degeneration. To test this hypothesis, we modeled behavior of a homing endonuclease gene that moves during meiosis through double-strand break repair. We mathematically explored conditions for persistence of the homing endonuclease gene and elucidated their parameter dependence as phase diagrams. We found that, if the cost of the pseudogene is lower than that of the homing endonuclease gene, the 2 forms can persist in a population through autonomous periodic oscillation. If the cost of the pseudogene is higher, 2 types of dynamics appear that enable evolutionary persistence: bistability dependent on initial frequency or fixation irrespective of initial frequency. The prediction of long persistence in the absence of horizontal transfer was confirmed by stochastic simulations in finite populations. The average time to extinction of the endonuclease gene was found to be thousands of meiotic generations or more based on realistic parameter values. These results provide a solid theoretical basis for an understanding of these and other extremely selfish elements.