• Evolutionarily stable strategies;
  • learning;
  • model;
  • sexual selection;
  • speciation

Sexual imprinting occurs when juveniles learn mate preferences by observing the phenotypes of other members of their populations, and it is ubiquitous in nature. Imprinting strategies, that is which individuals and phenotypes are observed and how strong preferences become, vary among species. Imprinting can affect trait evolution and the probability of speciation, and different imprinting strategies are expected to have different effects. However, little is known about how and why different imprinting strategies evolve, or which strategies we should expect to see in nature. We used a mathematical model to study how the evolution of sexual imprinting depends on (1) imprinting costs and (2) the sex-specific fitness effects of the phenotype on which individuals imprint. We found that even small fixed costs prevent the evolution of sexual imprinting, but small relative costs do not. When imprinting does evolve, we identified the conditions under which females should evolve to imprint on their fathers, their mothers, or on other members of their populations. Our results provide testable hypotheses for empirical work and help to explain the conditions under which sexual imprinting might evolve to promote speciation.