Collier et al. (1972) data

[From Bruce Abbott (950805.1900 EST)]

Collier, Hursh, & Hamlin (1972) report data from two experiments in which
the ratio requirement was manipulated as rats earned their entirely daily
ration via lever pressing. They lived in the apparatus 24 hr/day. In the
first experiment, completion of the ratio provided access to a food hopper,
which remained accessible until it had not been visited for 10 min. In the
second experiment, each ratio completion provided one 45 mg pellet, as in
most standard operant experiments. In both experiments, each ratio remained
in effect for 10 days.

In the first experiment, one hopper-raising constituted a "meal," which
could be of variable duration depending on the rat's behavior. The
following data are from Figure 1:

Ratio Rat 1 Rat 2 Rat 3
  FF 10.6 8.9 14.4
   1 8.9 9.1 11.4
   5 7.9 8.3 9.7
  10 6.8 7.0 9.3
  20 7.5 6.4 5.8
  40 5.2 5.4 6.0
  80 5.8 4.2 4.8
160 4.6 1.6 6.8
320 3.4 1.0 3.8
640 2.0 --- 2.2
1280 1.2 --- 2.2
2560 1.2 --- 1.4
5120 0.6 --- 1.1

"FF" indicates "free feeding" (free, continuous access to food).

The second rat was losing weight at ratios above 320 and so was not
continued on the higher values. The data indicate that the rats continued
to respond even at very high ratios; at the highest values they were
spending most of their time lever-pressing in order to gain access to one
meal or less per day.

I have not yet reduced the figures to numbers, but the data for meal
duration and grams consumed show that the rats compensated for the reduced
number of meals at higher ratios by increasing the size of the meal. Food
intake declined from about 22 g/day ad lib to about 10-12 g/day at 5120, but
body weight actually climbed up to around FR-80 and then showed only a small
decline at the higher ratios. Given the 50% decrease in intake, this
suggests that the rats were using the energy more efficiently at the higher
ratios, thus offsetting the loss in intake to a great extent.

In the second experiment the rats could not vary meal duration or size to
compensate for a declining rate of ratio completion. Here are the number of
pellets earned per day as a function of the schedule value:

Ratio Rat 1 Rat 2
   1 484.4 498.8
   5 460.4 503.6
  10 491.6 498.8
  20 503.6 531.2
  40 476.0 455.6
  60 459.2 436.5
  80 431.7 423.3
100 398.1 416.1
120 431.7 387.3
140 398.1 360.9
160 401.7 383.7
180 328.5 336.9
200 332.1 308.2
220 326.1 278.2
240 275.8 -----

The data are a bit "noisier" than one would like, but the general trend is
clear. By FR-160 and beyond, the rats were responding in excess of 60,000
rsp/day and spending nearly 14 hrs/day at the lever. Their daily food
intake had fallen from about 23 g/day to about 13 g/day. Both rats
continued to gain weight up to FR-80; after this point Rat 1's weight was
steady or slowly falling; Rat 2's weight begin a steep decline and was taken
off the high ratios prior to experiencing FR-240.

I have not yet had time to reduce the data for the other figures (e.g., food
consumed, body weights), nor to really think about the implications. In
both experiments the rate of responding did not increase sufficiently with
ratio to prevent a significant loss of food "income." In Experiment 1 there
was a compensatory increase in food intake per access (not possible in
Experiment 2), which would have minimized energy expendature per gram of
food consumed. It wil be interesting to compare the cost/benefit ratio for
responding in the two experiments: in Experiment 1 the number of ratio
completions per day equals the number of "meals."

Bill P.: can we get an estimate of calories expended per lever-press if we
know the force requirement and lever movement-distance? In this experiment
the lever force requirement was 25 g (0.25 N) and I would guess at a lever
travel-distance of perhaps 1 cm.

One thing to keep in mind when considering these data is that any computed
times would include everything the rat does during its day, including
sleeping. At the moment I don't know how long rats usually sleep per day;
if they were doing it for, say, 6 hrs, that would leave only 18 hrs for
earning food pellets. I fit the average interfood interval (based on 24
hrs) to the ratio requirement for Experiment 2, Rat 1 and obtained the

  Sec/pellet = 175.9 + 0.268*Ratio

Obviously the rat isn't going to require 175.9 seconds to collect a food
pellet. The observed FR-1 rate was 484.4 pellets/day, which gives an
interpellet interval of 178.4 seconds; this is probably close to a true
reference level. 175.9 sec/pellet implies a reference for this rat of 491.1
pellets/day, or about 20.5 per hour, on average. 491.1 * 45 mg/pellet gives
22.1 g/day. Given your _Joy of Cooking_ value of 4 large calories per gram,
this comes to 88 calories per day. At the highest ratio tested for each
rat, they were earning about 276 pellets/day or 12.4 grams/day, yielding
about 50 calories, and they were losing weight. By FR-160 it would appear
that Rat 2's output was up against the stops: about 61,000 responses per day
regardless of the actual ratio value.

You may have noticed that the consumption is about twice that reported in
the Teitelbaum experiment. Teitelbaum's rats were female (about 250 g);
these were male (about 350-400 g).

In Experiment 1, the rats were able to maintain their weights or even
increase them up to a ratio of 160. It seems likely that up to this value
they were able to compensate for decreasing number of meals by eating more
at each meal. Perhaps after FR-160 the rats simply did not have the storage
capacity to increase their meal sizes enough to continue compensating.