The effects of functional response and host abundance fluctuations on genetic rescue in parasitoids with single-locus sex determination.

Many parasitoids have single-locus complementary sex determination (sl-CSD), which produces sterile or inviable males when homozygous at the sex determining locus. A previous study theoretically showed that small populations have elevated risks of extinction due to the positive feedback between inbreeding and small population size, referred to as the diploid male vortex. A few modeling studies have suggested that the diploid male vortex may not be as common because balancing selection at sex determining loci tends to maintain high allelic diversity in spatially structured populations. However, the generality of the conclusion is yet uncertain, as they were drawn either from models developed for particular systems or from a general-purpose competition model. To attest the conclusion, we study several well-studied host-parasitoid models that incorporate functional response specifying the number of attacked hosts given a host density and derive the conditions for a diploid male vortex in a single population. Then, we develop spatially structured individual-based versions of the models to include female behavior, diploid male fertility, and temporal fluctuations. The results show that producing a handful of successful offspring per female parasitoid could enable parasitoid persistence when a typical number of CSD alleles are present. The effect of functional response depends on the levels of fluctuations in host abundance, and inviable or partially fertile diploid males and a small increase in dispersal can alleviate the risk of a diploid male vortex. Our work supports the generality of effective genetic rescue in spatially connected parasitoid populations with sl-CSD. However, under more variable climate, the efficacy of the CSD mechanism may substantially decline.