Variation in Herrnstein's r(o) as a function of alternative reinforcement rate.

The team tested pigeons on a VI key-peck schedule while changing water deprivation.

They tracked how Herrnstein’s r(o) parameter moved when thirst level changed.

Birds worked for water under two deprivation conditions inside a standard operant chamber.

r(o) rose when the birds were more water-deprived, just as the equation predicts.

Yet the overall fit was weak; the line explained only a small slice of the data.

Drinking rate also jumped around across schedules, muddying the picture.

Webb et al. (1999) ran almost the same thirst setup but looked at the k parameter instead.

They saw k drop when deprivation eased, a clear falsification of fixed-asymptote matching.

Together the two papers show both r(o) and k drift with motivation, not just reinforcement rate.

Hassin-Herman et al. (1992) later took the same hyperbola to human eye contact and got tight fits, hinting that social reinforcers may behave more neatly than water.

If you use matching equations to analyze client data, treat k and r(o) as moving targets.

Motivation, not just schedule values, can shift these numbers session-to-session.

Check for state changes like hunger, thirst, or fatigue before you lock parameters in your model.