178
in the absence of a stimulus (Zeddies and Fay 2005 ), or as a probability of response
that results in a repeatable non-zero probability of response (Bhandiwad et al. 2013 ).
Auditory threshold criteria used with the method of limits are more well defi ned
than threshold criteria for the method of constant stimuli. Because the method of
limits uses multiple stimulus presentation trials to sequentially reduce stimulus
parameters, each trial ends at threshold estimation. By defi nition, the threshold is
described as the point at which the animal changes its pattern of response to the
delivered stimulus. The estimated threshold for the subject population is determined
by averaging the thresholds of multiple stimulus presentation sequences. The only
free parameter between experimenters is whether the ascending method of limits
(each stimulus step increases the intensity level until the animal responds once) or
the descending method (each stimulus step decreases intensity level until the animal
ceases to respond) is used. Although we assume thresholds obtained using these
methods should be identical, there is no a priori reason that establishes equivalency
between these two methods.
Auditory threshold criteria used with the staircase method are more well defi ned
than the stimulus presentation parameters discussed above. The adaptive quality of
stimulus presentation procedure allows for a greater sampling at or near threshold,
which can be mathematically determined. Earlier procedures defi ned threshold
similar to the method of limits, where the threshold was estimated from the averaged samples taken at the “reversal,” i.e., the sound level where the increasing or
decreasing stimulus level was reversed to estimate threshold (Jesteadt 1980 ).
However, this procedure is no longer used as the best measure for threshold determination (Garcı́ a-Pérez 1998 ). The total number of reversals, however, is still used
as a stopping condition. Threshold for an “ N -down, one up” protocol is defi ned as
the probability of getting N trials correct by chance. For example, in a protocol
where two “correct” answers result in the stimulus parameter becoming more diffi cult; threshold is defi ned as the point at which the probability of getting two correct answers in a row is 0.5. Threshold is therefore the square root of 0.5, or 0.71
(71 % correct). In the case of a three down, one up protocol, threshold is defi ned
as the cube root of 0.5, or 79 % correct. In the mathematical limit (i.e. as the number of presentations approach infi nity), threshold can be conceptualized as the
point at which the adaptive procedure is equally likely to increase or decrease after
each trial.
5 Conclusion and Future directions
Behavioral measures of hearing remain the best methods to investigate the perceptual hearing ability of an organism (Ladich and Fay 2013 ). Conditioning methods in
particular are powerful tools and should continue to be used in studies of fi sh hearing. However, we suggest that more studies should utilize innate behavioral
responses where appropriate, particularly the use of PPI assays to determine auditory sensitivity. Although this method has been used for larval fi sh, it can easily be
A.A. Bhandiwad and J.A. Sisneros
in the absence of a stimulus (Zeddies and Fay 2005 ), or as a probability of response
that results in a repeatable non-zero probability of response (Bhandiwad et al. 2013 ).
Auditory threshold criteria used with the method of limits are more well defi ned
than threshold criteria for the method of constant stimuli. Because the method of
limits uses multiple stimulus presentation trials to sequentially reduce stimulus
parameters, each trial ends at threshold estimation. By defi nition, the threshold is
described as the point at which the animal changes its pattern of response to the
delivered stimulus. The estimated threshold for the subject population is determined
by averaging the thresholds of multiple stimulus presentation sequences. The only
free parameter between experimenters is whether the ascending method of limits
(each stimulus step increases the intensity level until the animal responds once) or
the descending method (each stimulus step decreases intensity level until the animal
ceases to respond) is used. Although we assume thresholds obtained using these
methods should be identical, there is no a priori reason that establishes equivalency
between these two methods.
Auditory threshold criteria used with the staircase method are more well defi ned
than the stimulus presentation parameters discussed above. The adaptive quality of
stimulus presentation procedure allows for a greater sampling at or near threshold,
which can be mathematically determined. Earlier procedures defi ned threshold
similar to the method of limits, where the threshold was estimated from the averaged samples taken at the “reversal,” i.e., the sound level where the increasing or
decreasing stimulus level was reversed to estimate threshold (Jesteadt 1980 ).
However, this procedure is no longer used as the best measure for threshold determination (Garcı́ a-Pérez 1998 ). The total number of reversals, however, is still used
as a stopping condition. Threshold for an “ N -down, one up” protocol is defi ned as
the probability of getting N trials correct by chance. For example, in a protocol
where two “correct” answers result in the stimulus parameter becoming more diffi cult; threshold is defi ned as the point at which the probability of getting two correct answers in a row is 0.5. Threshold is therefore the square root of 0.5, or 0.71
(71 % correct). In the case of a three down, one up protocol, threshold is defi ned
as the cube root of 0.5, or 79 % correct. In the mathematical limit (i.e. as the number of presentations approach infi nity), threshold can be conceptualized as the
point at which the adaptive procedure is equally likely to increase or decrease after
each trial.
5 Conclusion and Future directions
Behavioral measures of hearing remain the best methods to investigate the perceptual hearing ability of an organism (Ladich and Fay 2013 ). Conditioning methods in
particular are powerful tools and should continue to be used in studies of fi sh hearing. However, we suggest that more studies should utilize innate behavioral
responses where appropriate, particularly the use of PPI assays to determine auditory sensitivity. Although this method has been used for larval fi sh, it can easily be
A.A. Bhandiwad and J.A. Sisneros