[From Bruce Abbott (950721.1100 EST)]

Ettinger and Staddon (1983) reported the results of an investigation of

"operant regulation of feeding" using a new procedure they described as a

"cyclic-ratio" schedule, which I described in my last post (950718.2055

EST). Within each session, rats were exposed to an ascending and then

descending series of ratio values: 2, 4, 8, 16, 32, and 64

responses/reinforcement. Because each ratio is evaluated twice each session

in counterbalanced order, order effects such as satiation or fatigue are

minimized. Because all ratios are evaluated in a session, long-term changes

which might occur over sessions are also controlled.

Ettinger and Staddon reported data for the same four subjects (C1, C2, C3,

and C4) in three experiments. Experiment 1 simply compared the performances

of these subjects on the cyclic-ratio schedule to those of four other

subjects on the standard (single-ratio) schedule (in which ratio was

manipulated over sessions). Experiment 2 manipulated pellet taste (quinine

was added) and deprivation level (80% ad lib weight versus 95% ad lib

weight). Experiment 3 manipulated amphetamine dosage. Experiment 2

included a replication of the Experiment 1 cyclic-ratio conditions (80% ad

lib weight); experiment 3 included two such replications (one non-drug

control for each of two amphetamine levels); together this provides four

cyclic-ratio assessments of the same animals under the same conditions.

Examination of the four curves for each subject under this condition

revealed some variability from replication to replication but were generally

similar; on the other hand there were reliable differences between subjects

in the slopes of these curves. To provide more stable estimates of the

relationships I averaged the data for each subject across replications. The

resulting subject averages are given below.

Responses/Hour

Ratio C1 C2 C3 C4

2 1007 1050 1088 1125

4 1767 1825 1887 2022

8 2711 3026 3120 3522

16 3660 4146 4723 5243

32 4255 4820 5821 6486

64 4711 5893 6575 7481

Dividing each row by the ratio gives the reinforcers/hour:

Reinforcers/Hour

Ratio C1 C2 C3 C4

2 503.5 525.0 544.0 562.5

4 441.8 456.3 471.8 505.5

8 338.9 378.3 390.0 440.3

16 228.8 259.1 295.2 327.7

32 133.0 150.6 181.9 202.7

63 76.6 92.6 102.7 116.9

Plotting responses/hour as a function of reinforcements per hour as in the

Motheral data produces four curves, one for each subject, in which rate of

responding increases as rate for reinforcement decreases (i.e., typical

right limb of Motheral-type curve). The slope of the curve is lowest for

subject C1 and increases in order of subject number, so that the steepest is

for C4. Projecting the intercepts of these curves with the X axis gives

estimated reference levels for reinforcement rate in the 580-610 rft/hr

range, in order for subject number from lowest to highest. That is,

subjects whose curves have the lowest slopes also have curves with the

lowest intercepts.

These data appear consistent with a control model for reinforcement rate and

as I described in the previous post were interpreted essentially that way by

Ettinger and Staddon.

However. Converting reinforcements/hour to seconds/reinforcement (by

dividing the former numbers into 3600) gives the following data:

Seconds/Reinforcement

Ratio C1 C2 C3 C4

2 7.15 6.86 6.62 6.40

4 8.15 7.89 7.63 7.12

8 10.62 9.52 9.23 8.18

16 15.73 13.89 12.20 10.99

32 27.07 23.90 19.79 17.76

64 48.91 39.09 35.05 30.80

If you plot Seconds/Rft as a function of the ratio requirement a strange and

wonderful thing happens. Within a small amount of error you can fit four

straight lines to these data, all having the same Y-intercept at 5.5 seconds

for 0 responses. I interpret this as the time required to move from the

lever, collect the reinforcer, and return to the lever. It would appear

that under 80% ad lib weight and using 45 mg noyes pellets as reinforcers,

all four animals required the same amount of time to perform this collection

of actions. The four lines have different slopes, which represent the

average time required to complete a lever press (including any pauses).

Parameters of the four lines are:

Subject Intercept Slope

C1 5.5 s 0.68 s/rsp

C2 5.5 s 0.52 s/rsp

C3 5.5 s 0.46 s/rsp

C4 5.5 s 0.39 s/rsp

Basically, these functions indicate that the time required to collect a

reinforcer is equal to the 5.5 seconds "collection" time plus the time

required to complete the ratio requirement. For example, at a ratio of 64,

subject C1 would be estimated to require 5.5 + 64*0.68 = 49.0 s on average

per reinforcement. The rate of reinforcement sustained would be estimated

to be 73.4 rft/hr. The actual rate was 73.6 rft/hr.

Reinforcers/Hour: Predicted Vs. Observed

----C1---- ----C2---- ----C3---- ----C4----

Ratio Pred. Obs. Pred. Obs. Pred. Obs. Pred. Obs.

2 525 504 550 525 561 544 573 563

4 438 442 475 456 490 472 510 506

8 329 339 373 378 392 390 418 440

16 220 229 260 259 280 295 307 328

32 132 133 163 151 178 182 200 203

64 73 74 93 92 103 103 118 117

You will note that the predictions at ratio 2 are consistently too high;

this is no doubt because the 5.5 s intercept estimate (by eyeball from the

chart) is just slightly too low. Even so, I think you'll agree that the

fits are impressive.

So what does it mean? The simplest interpretation is that reinforcement

rate is not being controlled. As the response requirement increases, the

time required to collect a reinforcer increases in direct proportion. Thus

there appears to be no opposition to the "disturbance" to reinforcer rate

produced by changing the ratio requirement.

What does stay the same across all ratio requirements are (a) the time

required to collect the reinforcer and return to the lever (about the same

for all subjects) and (b) the average rate of responding (which differs

across subjects). At a given level of deprivation, and for a given reward,

the rat maintains a given rate of responding. The decline in rate of

reinforcement with increasing ratio requirement is exactly that which would

be expected given the longer time required to complete a ratio while

maintaining the same rate of responding.

Back to the drawing board?

Regards,

Bruce