Cyclic Ratio Data

[From Bruce Abbott (950718.2055 EST)]

While the conferees are conferring, I'll just post some of the information
I've been running across that relates to the operant schedules project Bill
P. and I are working on. Those who may be interested but are at the
conference can catch up later.

In the last episode, our hero was examining data on within-session variation
in responding on variable interval schedules and concluded that much of the
extant data on variation of response rate with schedule value may be
confounded by satiation effects, including the ratio data collected by Susan
Motheral and reported by John Staddon. Today I obtained an article by
Ettinger and Staddon (1983) reporting on results using what was then a new
procedure called a "cyclic ratio" schedule. This procedure appears to
circumvent the within-session satiation problem by programming each ratio to
be tested in both ascending and descending sequence within the same session.
Subjects are run on the procedure until responding on the cyclic ratio
schedule stabilizes. This procedure is in contrast to the usual one in
which the same ratio holds throughout each session and ratios are varied
between sessions.

Ettinger and Staddon used ratios of 2, 4, 8, 16, 32, and 64 in their cyclic
ratio schedule and compared their results to those produced using the more
usual single ratio procedure. The results were essentially the same for the
two procedures _except_ at the highest ratio value (64). On the cyclic
ratio schedule this ratio produced the highest levels of responding. On the
single ratio schedules the rate sustained at a ratio of 64 was either equal
to or less than that sustained at the ratio of 32. The authors noted this
difference but offered no explanation (nor, at the moment, do I have one).
However, it is encouraging that the functions are similar at the lowest
ratios as this suggests that satiation effects, if any, which would have
been expected to be greater under the single ratio schedules, had little or
no effect on the slope and position of the curve.

An interesting effect to emerge from the cyclic ratio schedule is that the
"post reinforcement pause," whose size tends to vary with the ratio
requirement in simple ratio schedules, actually was shown to vary with the
size of the _upcoming_ ratio rather than the just-completed ratio. These
animals were given plenty of experience with the cyclic ratio schedule and
thus had learned the sequence of ratio requirements. Also, lower "running
rates" during the completion of larger ratios were shown to be a product of
periodic interruptions of a steady rate of responding rather than a slowing
of the steady rate, as the peak interresponse time (time between responses)
remained unchanged across the ratio requirements. The steady rate was close
to the 0.2 sec/response rate I had suggested in an earlier post might be
typical for rats under reasonably high motivation.

The article reports on changes in response rate functions that accompany
changes in deprivation level, adulteration of the food pellets with quinine
and injection of amphetamine. These changes are evaluated in light of a
"static" regulatory model of the form

x = G(Ro - Rx) + K,

where x = overall response rate,
      G = system gain,
      Ro = reference level,
      Rx = overall reinforcement rate,
and K = a constant

K is essentially the incentive value of the food, e.g., its tastiness.

Ettinger and Staddon use this model to make predictions as to the effects of
the parameters manipulated, but they do not provide a computer model which
implements this system and interacts with an actual ratio schedule. The
model simply states that the output rate will be some multiple of the
difference between reference and actual reinforcement rates, plus a
constant. The model "fits" the "regulatory" limb of the bitonic function
(right side) but does not account for the downturn which forms the left side
of that function.

At any rate, the cyclic-ratio schedule performance shows that rats can
rapidly adjust to different ratio requirements within a single session if
given sufficient training. A question remains as to whether experience with
these different ratios in quick succession results in a contrast effect that
could alter the relationships as compared to those seen in single ratio
schedules.

Regards,

Bruce