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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.