Preference functions, which quantify preference strength relative to variat
ion in male traits or signals, are central to understanding mechanisms and
consequences of female choice. Female tree frogs (Hyla versicolor) choose m
ates on the basis of advertisement calls and prefer long calls to short cal
ls. Here we show, in two experimental designs, that preference strength inc
reased significantly as the difference in call duration was increased only
if the absolute durations of alternative stimuli were below average. Hence
preference strength was a non-linear function of duration, and females did
not base preferences solely on the percentage difference in duration. In ex
periments simulating costly choice (unequal playback levels), non-linear ef
fects were more pronounced than in the conventional design (equal playback
levels). Repeated estimates of preference strength using the unequal-playba
ck design revealed significant among-female variation. These patterns of pr
eference suggest that selection by female choice for males producing calls
of average duration over males producing very short calls is stronger than
selection for males producing very long calls over males producing calls of
average duration. Female preferences, especially in tests simulating a pot
entially costly choice, could reflect differences in the net benefits to fe
males of mating with males producing calls of different duration.