Why Control Theory is All Wrong

[From Bruce Abbott (960517.1445 EST)]

For the past couple of months I have been conducting a study in which
laboratory rats work for a portion of their daily meals during one-hour
sessions in an operant chamber. The rats must press a lever to receive 45
mg food pellets on what is termed a CRF (continuous reinforcement) schedule:
1 press per pellet. My students and I have been recording the number of
pellets earned in the chamber, the amount of the earned food actually
consumed, the amount of food subsequently consumed in the home cage, and the
rats' body weights, for each day since the study began. Our intention is to
develop a control-system model that will account for variations in food
consumption in the operant chamber as the amount of food available in the
home cage is systematically varied.

While conducting a review of the scientific literature on feeding and
weight-control, I have been surprised to discover that a control-systems
approach was quite in vogue during the late 1960s and early 1970s, and some
elegant models were constructed to account for the then-available data.
However, it seems that subsequent data did not appear to fit readily into a
control-systems framework, and before long a concensus seems to have
developed that the classical control system does not provide a useful or
compelling account of either feeding or the stability of body weight. No,
to develop an adequate account of these phenomena, one must turn to
external, environmental factors such as food availability, palatability, the
economics of supply and demand, competition among different activities, the
ecological niche occupied by the organism, things of that sort. Needless to
say, I found this conclusion rather discouraging. On what was it based?
Well, I looked for the answer to this question, and I found it. The main
problem turned out to be that pesky concept, the set point. Nobody could
find it.

The problem was highlighted by Wirtshafter and Davis in a 1977 paper
entitled "Set Points, Settling Points, and the Control of Body Weight."
Although there is more to this story than Wirtshafter and Davis's
contribution, I thought I'd focus on their paper as an example of the kind
of thinking that derailed control theory in the decade of the 70s.

Wirtshafter and Davis (1977) begin their paper by noting the growing
interest in applying control theory to the problem of body-weight stability.
They then briefly describe the basic control system:

  The defining characteristic of such a system is that it contains a
  reference point against which the current state of the organism is
  compared. Deviations from the set point generate an error signal
  which activates the system to correct the deviation. The effect of
  such a system is to maintain a relatively constant value of the
  controlled quantity in the face of disturbances imposed by the
  environment. It is natural, therefore, when investigating homeo-
  static systems which adjust to disturbances by making appropriate
  corrections, to assume that the adjustments are made in response to
  an error signal indicating the deviation from the desired state.

So far, so good. In fact, it's a rather nice description. But now comes
the caveat:

  In spite of the popularity of this notion there is a real question
  concerning its value in furthering our understanding of the control
  of body weight. Postulating the existence of a neural set point in
  order to account for the constancy of body weight does not explain
  much; it merely assigns to the central nervous system (CNS) just
  that property needed to account for body weight constancy.

Wirtshafter and Davis (1977) go on to note that such a concept has
difficulty explaining such facts as the increase in body weight that
precedes hibernation, or migration, or accompanies pregancy, or follows the
offering of a highly palatable diet, as observed in various species.

  To explain these phenomena within the context of a set point model, one
  would have to assume either that the set point is labile or that it
  becomes inoperative under certain conditions such as the availability of
  a high fat diet. Of course, either or both of these assumptions may be
  correct, but skepticism begins to develop as the hypothetical set point
  begins to acquire just that amount of variability which is necessary to
  explain observed variability in body weight.

After describing some of the evidence used to support a control-systems
analysis, Wirtshafter and Davis present an alternative model that nicely
accounts for these data and also for data which they believe pose
difficulties for the control-systems model:

  Let us now consider an alternative model for body weight control. Let
  us suppose that an animal's feeding mechanism is activated by sensory
  stimuli arising from available food, which we will represent by the
  letter S, and inhibited by a feedback signal which is proportional to
  body weight which we will represent by the letter W. A control system
  incorporating these assumptions is shown in Fig. 1.

···

+
            S----->[X]-------->[ G ]-------+------> W
                  - ^ |
                    > >
                    +----------[ H ]<------+

        Fig. 1. Diagram of a simple body weight control
                 model which contains no set point.

This model is intended to deal with data showing that the body weight rats
defend varies with the palatability of the food. When the food is bitter,
rats eat less and lose weight, but will defend against disturbances to the
new, lower weight. A similar thing happens when food of high palatability
is offered, with weight increasing to a new level but defended at that
level. To describe the operation of this system, the authors introduce a
new term: "settling point."

  The value which W assumes is the predicted steady state weight of an
  organism whose body weight is controlled by the system shown in Fig. 1.
  We call the value which W takes the settling point of the output of the
  system, since any changes in the values of S, G, or H will alter the
  value of W and cause it to settle to a new value. ... We prefer the
  term settling point since this term is neutral with respect to the way
  in which stability is achieved, which may or may not be by means of a
  neural set point.

The authors illustrate how this model can be used to account for several
pieces of evidence, including the effect of food palatability and of lesions
to the rat's lateral or vertromedial hypothalamus. They note that changes
in the "settling point" W of the system can be produced by changes in (a)
the sensory stimuli arising from the food, (b) the forward gain G, or (c)
the feedback gain H, and that therefore, changes in body weight (settling
point) following a manipulation do not necessarily reflect changes in a set
point for body weight. In this assessment they are correct. Moreover:

  This model suggests that the defense of body weight by animals may reflect
  not the existence of an internal standard, but rather a constant magnitude
  of stimuli which drive the intake mechanism.

This is also true of their model. Furthermore:

  If body weight is regulated by an internal set point mechanism one
  naturally wonders why it is singularly ineffective in maintaining a
  constant weight in the face of altered dietary palatability. Rejection
  of a set point concept of weight regulation would have the additional
  advantage of resolving the problem of an animal's willingness to ingest
  highly palatable substances in the absence of deprivation.

Wirtshafter and Davis admit that their model is far too simple to provide a
complete explanation, but they state that it does draw attention to several
points, among which is the following:

  ... the postulation of a neural set point is not necessary to account
  for weight control. The fact that a given quantity is, under some
  circumstances, maintained at a relatively constant value does not by
  itself imply the existence of an internal reference value.

So there you have it: the concept of set point is unnecessary; body weight
may be determined more by external (stimulus) factors than by internal set
points.

But wait. Does Wirtshafter and Davis's argument make sense? Take a look at
their Figure 1. What role is S playing in the diagram? The neural
representation of the sensory quality of the food enters the comparator, as
does the neural representation of body weight. As S varies, W follows. In
fact, the Wirtshafter and Davis "alternative" to "set point" control systems
is nothing less than a "set point" control system, with S playing the role
of the set point. This is a _very_ peculiar sort of control system,
however, in that the reference level (set point) for _body weight_ is
determined by the magnitude of the sensory input representing _food
palatability_. Imagine that: the environment determining the reference
level! The animal's body weight is entirely at the mercy of the sensory
qualities of its food, and it will starve to death if presented with
perfectly good food having no taste, or a bad taste. It seems doubtful that
such an important variable would be left at the mercy of the environment.
But this is not what is observed; rats given quinine adulterated food
suppress feeding, but only until their body weights decline sufficiently
that they are willing to tolerate the bad taste. This fact strongly
suggests that weight (or a close correlate) is being referenced to an
internal standard, with increasingly severe deviations below reference
bringing about a greater and greater tendency to overlook the bitter taste
and consume the food anyway. And rats given quinine adulterated (bitter)
food injected directly into the stomach (eliminating gustatory stimuli) turn
out to regulate their nutrient intake quite well and do not lose weight.
[This latter bit of evidence was not available to Wirtshafter and Davis at
the time of their article was published.]

So, what are we to conclude? After suggesting that the notion of an
organism governed by control systems with internal set points is too
seductive, Wertshafter and Davis propose an organism governed by control
systems with _external_ set points whose levels are dermined by
environmental caprice, thus demonstrating that the concept of set-point
control is unnecessary? To paraphrase the character Fagan in the musical
"Oliver," I think they better think it out again.

Regards,

Bruce

[Avery Andrews 960518]
(Bruce Abbot 1960517)

Very interesting. I can't resist the speculation that the inhibitory
effects of bitter-tasting food isn't the effect of a toxin-avoidance
control system. Modelling this system is a bit of a challenge, since
it shouldn't supress appetite in general, but inhibit eating
particular items or kinds of things that are discovered to be
unpalatable. I gather that rats are pretty clever at this, does
anyone know much about what kinds of cues they are actually
sensitive to?

Still, the low quality of the reasoning deployed against control systems
in the 70s really is astonishing, as I found in my foray into motor
control.

Avery.Andrews@anu.edu.au

[From Bruce Abbott (960518.1615 EST)]

Avery Andrews 960518 --

Very interesting. I can't resist the speculation that the inhibitory
effects of bitter-tasting food isn't the effect of a toxin-avoidance
control system. Modelling this system is a bit of a challenge, since
it shouldn't supress appetite in general, but inhibit eating
particular items or kinds of things that are discovered to be
unpalatable. I gather that rats are pretty clever at this, does
anyone know much about what kinds of cues they are actually
sensitive to?

I'm not by any means an expert on the rat's ability to use of taste cues,
but if I recall correctly, not only do rats display innate preferences for
or against certain tastes (e.g., for sweet, against bitter), but they can
develop strong aversions to unfamiliar tastes after a single pairing of the
new taste with illness. Together with a strong neophobia (distrust of
anything novel to them), this accounts for the legendary difficulty in
controlling rat populations via poisons. The rat will only sample a small
bit of the bait, and if illness follows, it won't take the bait a second time.

Still, the low quality of the reasoning deployed against control systems
in the 70s really is astonishing, as I found in my foray into motor
control.

Amen. Still, Wirtshafter and Davis (1977) did make some good points while
mudding the waters on others. I rather like their distinction between set
points and settling points (although not because the latter is
"theoretically neutral" whereas the former is not, as the authors would have
it, but because it calls attention to the fact that in the steady state the
system output is not equal to the reference level, and may be far from it),
and they were correct to emphasize the point that the value around which a
system stabilizes is not necessarily its reference level.

I did a check this afternoon to determine how often this paper has been
cited. According to Social Science Citations Index, only 14 papers
referenced the Wirtshafter and Davis (1977) article between 1977 and 1991,
the last year for which our library subscribed to the service. If this is
any reflection of its influence, it apparently had little.

By the way, I neglected to supply the reference for this article, so I'll
give it here:

  Wirtshafter, D., & Davis, J. D. (1977). Set points, settling points, and
      the control of body weight. _Physiology & Behavior_, _19_, 75-78.

Hey, they _did_ use "control" correctly!

Chris Kitzke (960517.1705 EST) --

Chris, Bill Powers did such a nice job explaining the relationship of data
to theory to data to theory that I think I'll just leave it at that.

Regards,

Bruce