Invasion, Coexistence, and Extinction Driven by Preemptive Competition and Sex Ratio*

We investigate competitive invasion in a simple population dynamics model, where females can differ genetically in the sex ratio of their offspring, and males can differ in mortality. Analyzing of the mean-field dynamics, we obtain conditions for ecological stability of a given sex-ratio allele for any mortality rate parameters. We also found that stable coexistence of the two alleles is possible, but only males can differ; one female phenotype is present. Our results show that the success of invasion is determined by the female birth sex ratio. A lower female ratio never excludes a larger female sex ratio; in case of coexistence, the surviving female phenotype always has the greater female sex ratio. Finally, we identified an interesting invasion-to-extinction scenario: successful invasion followed by extinction occurs when the invader initially propagates with the resident allele, but after excluding the resident, cannot survive on its own.