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Keywords:

  • Age structure;
  • Bartonian waves;
  • population manipulation;
  • unstable equilibria;
  • Wolbachia

Many insects and other arthropods harbor maternally inherited bacteria inducing “cytoplasmic incompatibility” (CI), reduced egg hatch when infected males mate with uninfected females. CI-causing infections produce a frequency-dependent reproductive advantage for infected females. However, many such infections impose fitness costs that lead to unstable equilibrium frequencies below which the infections tend to be eliminated. To understand the unstable equilibria produced by reduced lifespan or lengthened development, overlapping-generation analyses are needed. An idealized model of overlapping generations with age-independent parameters produces a simple expression showing how the unstable point depends on the population growth rate, the intensity of CI, and the infection's effects on development time, longevity, and fecundity. The interpretation of this equilibrium is complicated by age structure. Nevertheless, the unstable equilibrium provides insight into the CI-causing infections found in nature, and it can guide potential manipulations of natural populations, including those that transmit diseases, through the introduction of infections that alter life-table parameters.