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Female preference functions for different sexual traits can differ significantly, from 'unimodal' to 'open ended'. Through the study of acoustic communication in anurans, several studies have reported an association between static (stereotyped) traits versus dynamic (variable) traits and preference function shape (unimodal versus open ended, respectively). Observing a similar pattern in a phylogenetically independent group would suggest that deterministic forces have caused a relationship between signal variability and preference function shape in acoustic signalling systems. We examined this phenomenon in crickets, another animal characterized by intersexual acoustic communication. We measured the within-male variability for three acoustic features of the male calling song in Laupala cerasina and the corresponding shape of the female preference function for each of these features. We offer support for the generalization that open-ended preference functions correspond to relatively dynamic courtship traits and unimodal preference functions correspond to relatively static courtship traits. We discuss the evolutionary significance of these findings in the context of the natural history of the Laupala species radiation.