Frequency-dependent selection and fluctuations around an equilibrium for alternative reproductive tactics in a swordtail

Negative frequency-dependent selection (NFDS) should have an important role at maintaining equal fitness among different alternative reproductive tactics (ARTs) at an evolutionarily stable state (i.e. equilibrium). Empirical evidence to support both NFDS and equal fitness in the same system is limited. Using the swordtail fish Xiphophorus multilineatus we examined the hypotheses that NFDS may play an important role in maintaining the genetically influenced ARTs in this species at equal fitness. With a mesocosm study we found that sneaker males had a significantly lower reproductive success when they were more common, as expected. Field estimates of relative reproductive success also supported NFDS: the reproductive success of each tactic decreased when they were more common. We then used the field estimates of relative reproductive success and age to sexual maturity in a modified version of the Euler equation to determine whether the relative fitness of the two ARTs was equal in two different periods. Our analysis incorporated both the zero class of males and the invisible fraction, which are often missing from studies of the maintenance of polymorphisms. We found that the population was not at equilibrium during one sample (sneaker frequency 86%) but was at equilibrium during another (sneaker frequency 38%). We discuss factors that may be driving the fluctuations around the equilibrium, including variation in female preferences for courter males, while NFDS may be producing a stable limit cycle around it.