Cyclic-ratio data

[From Bruce Abbott (950802.1130 EST)]

Bill Powers (950801.1130 MDT) --
    Bruce Abbott (950801.1220 EST)

    It may be more accurate to state that it's the rate at which food
    deliveries _are being_ obtained, rather than the maximum rate at
    which they _can be_ obtained.

No, the so-called reference level turns out to be 1/c, which is the
maximum rate at which food could be obtained with an infinite rate of
pressing. The actual rate of obtaining food is always less than 1/c.
This isn't a matter of the apparatus; it's the effect of collection
time, same as you computed. The finding that the "reference level" is
1/c when the pressing rate is assumed constant was a complete surprise
to me.

The way I'm looking at collection time, it is just the time required to
complete another set of actions once the pellet has been delivered. To make
this clear, imagine that the experiment were changed so that, on completion
of the ratio, the rat had to run down a long alleyway to reach the food cup.
Collection time would depend on the length of the alleyway and on the rat's
running speed. Now, imagine that the rate of lever-pressing and the rate of
running are both influenced by the level of error in the nutrient-control
system: larger error yields faster lever-pressing and faster running, up to
the limit of the animal's ability to increase these rates. So long as the
system is not "up against the stops," both the rate of lever-pressing and
the rate of running will vary with the error level (e.g., deprivation
level). A change in running rate is a change in collection time. In this
analysis, both the response rate and the collection time change with the
deprivation level.

This view is supported by Susan Motheral's data shown in Figure 7.18 of
Staddon's (1983) book, _Adaptive Behavior and Learning_, which shows the
"response function" (as Staddon calls it) for ratio schedules at 80% versus
95% ad libitum body weight. Staddon draws a straight line through what he
terms the "regulatory limb" (right side) of the two functions. The two
lines are nearly parallel, implying that the number of seconds per
lever-press and the number of seconds of collection time changed by the same
proportionate amount with the change in deprivation level. In fact,
extending Staddon's line to the y-axis and measuring from the figure, we get:

   Weight Food Rate Lever-Press Rate
(% ad lib) (dippers/hr) (presses/hr)
     80% 410.4 10,332.4
     95% 209.0 5,681.6


  % 80% Rate 0.51 0.55

   Weight Collection Lever-Press
(% ad lib) Time (s) Time (s)
     80% 8.8 0.35
     95% 17.2 0.63
  % 80% Time 1.96 1.82

Reducing the level of deprivation from 80% to 95% reduced both the food and
lever-press rates by just over 50% or, to put it another way, increased both
the collection and lever-press times by just under a factor of 2. At both
levels of deprivation the collection time is about 25 times the lever-press
time. In other words, in terms of time-consumption, collecting the food is
equivalent to about 25 additional lever-presses.

I should note that these data are based on averaging across the data of four
rats, but given the linear nature of the individual functions, the average
function (an average of four linear functions) would also be linear, so the
averages should yield the same general relationship.

The upper limit needn't be physical; it could simply be that the
reference level for rate of pressing (which is also, presumably, a
controlled perceptual variable) is set to some value as a result of
other considerations, such as degree of fatigue, cost-benefit ratio, or
what have you. Actually, that's more or less what you said. But since we
apparently have a constant value of rate of pressing, it's tempting to
think that some signal has reached a limit.

But that would not explain why the rate is still constant at the lower
deprivation level (95%), although the rate is clearly well below the maximum
possible. So in this case the "limit" isn't physical; it's just the rate
given by the reference level for rate of pressing, which is influenced by
those other considerations you mention, including deprivation level.

. . . It's just that the experiment is set up so the rat
is unable to maintain itself in a proper nutritional state -- and at the
same time meet all its other internal requirements -- under the
conditions of this experiment. It's like setting a small room air
conditioner to a temperature of 60 degrees when the outside air
temperature is 120 degrees. It tries, but it can't do it. it just pumps
heat at the maximum rate it can, given the line voltage, internal
friction, obstacles in the air path, and so forth.

But this assumes that the output is "doing everything it can." In my view
it's just performing at a level determined by the error signals for stomach
loading, effort, and so on; in these experiments the output rate is less
than the maximum of which the rat is capable under more extreme deviations
from set point.

     In the typical operant study, by holding error constant, at best
    we are able to measure only the gain of the output function at the
    particular level of error we have induced in the nutrient control

At best. The problem is that with protracted error, we can expect
reorganization to have an effect, which means that the system we're
trying to measure is changing while we're measuring it.

The data indicate that behavior on these schedules stabilizes rather
quickly, which suggests that changes after initial adaptation to the
schedule may be minimal. The animal is making the best of the situation,
given the constraints involved, so further reorganization will not be
supported by any consistant reduction in overall error.

I think that "allocation of time" is not an actual control process. It's
a side-effect of the actual processes. If you have an animal casting
about at random looking for a food source, the "selection" effect of
reinforcement (i.e., reorganization) will gradually increase the dwell-
time on behaviors that produce the most food, leading to a bias in favor
of those activities that produce the most food. It would take a more
advanced cognitive system to deliberately allocate time on the basis of
a sampling of experience with consequences of different behaviors. At
least that's the approach I would take to this problem when working with
rats or birds, rather than trying to design a system that controls the
fraction of time spent on each of several tasks.

Yes, that's my view, too. I'm looking forward to seeing how a proper
control-system model of the rat or pigeon in these situations reaches the
equilibrium values found in "behavioral allocation" studies.

I hope we're not done with the Staddon-Ettinger experiment. Our results
are well worth a paper and could have far-reaching effects.

In this post and my previous one I've taken a fresh look at some of the
findings concerning manipulations of lever force requirement and deprivation
level, and found the results to be exactly as expected given our new
understanding of what is going on in these experiments. There's more along
these lines to do, so we're clearly not done with the Staddon-Ettinger
studies. Before we move to publication, however, I want to take a careful
look at other results from studies in which ratio schedule parameters were
manipulated to confirm that the analysis is not limited to one type of
schedule manipulation (e.g., cyclic-ratio) or the particular geometry of one
operant chamber. And I would like to further develop our understanding of
what is going on in these experiments, as we still seem to have a number of
questions for which our answers are still speculative. In the end, I want a
generative model that does what the real rat does.