Relationships between spawning fish (S) and surviving offspring (recruits, R) are typically assumed to be continuous and nonlinear. However, R may change abruptly with small changes in S if population-, community-, or ecosystem-scale processes trigger low adult reproduction and cause populations to shift abruptly to regimes of low recruitment. We simulated R with low mean and variation below a known S threshold and high mean and variation of R above it. We compared simulations with published S–R relationships. For all data, we fit a conventional Ricker-type S–R model, a logistic depensatory model, and also searched for an S breakpoint with a nonparametric test. The Ricker and logistic models often fit discontinuous simulated data. The nonparametric test found the S threshold in simulated data, although its accuracy depended on underlying distributions. The Ricker and logistic models and the nonparametric test identified apparent relationships within published data, sharing common results in <50% of the data sets. Although population models often assume continuous relationships, discontinuous threshold changes in R with small changes in S may occur. Identification of the conditions that reproductive state changes abruptly in fish populations may be necessary to develop risk-averse regulatory policies.