Medea selfish genetic elements as tools for altering traits of wild populations: a theoretical analysis

One strategy for controlling transmission of insect-borne disease involves replacing the native insect population with transgenic animals unable to transmit disease. Population replacement requires a drive mechanism to ensure the rapid spread of linked transgenes, the presence of which may result in a fitness cost to carriers. Medea selfish genetic elements have the feature that when present in a female, only offspring that inherit the element survive, a behavior that can lead to spread. Here, we derive equations that describe the conditions under which Medea elements with a fitness cost will spread, and the equilibrium allele frequencies are achieved. Of particular importance, we show that whenever Medea spreads, the non-Medea genotype is driven out of the population, and we estimate the number of generations required to achieve this goal for Medea elements with different fitness costs and male-only introduction frequencies. Finally, we characterize two contexts in which Medea elements with fitness costs drive the non-Medea allele from the population: an autosomal element in which not all Medea-bearing progeny of a Medea-bearing mother survive, and an X-linked element in species in which X/Y individuals are male. Our results suggest that Medea elements can drive population replacement under a wide range of conditions.