Sleep
11(5):488-496, Raven Press, Ltd., New York
© 1988 Association of Professional Sleep Societies
Theoretical Presentation
An Objective Behavioral Model of Sleep
Wilse B. Webb
Department of Psychology, University of Florida, Gainesville, Florida, U.S.A.
Summary: Theories and models are useful in organizing research data. This
paper reviews earlier models and a recent model that combines restorative and
adaptive models into a two-factor theory. A model emphasizing a three-factor
model with modulators is presented as an organizing schema. Key Words:
Theory-Sleep-Restorative model-Adaptive model.
I hope the title of this article has not daunted too many of you. For those of you
engaged in the creation of the empirical foundations of the area or others of you who are
coping with individuals struggling with disorders of sleep, the world "theory" may
raise problems. The term may call forth ideas about air-borne speculations by woolyheaded, ivory-towered types who could not distinguish an electrode from a shoe lace or
would be frightened into squeaks by a patient.
However, a scientific effort is comprised of three parts: data, application, and theorizing, i.e., the organization and coordination of the data by the use of principles and
constructs. A good theory helps us (and others) to better understand and use our data
more effectively. It is my purpose today to consider this aspect of sleep research and
hopefully to demonstrate the necessary and simplifying role of theorizing.
I am made optimistic about this effort by a significant development in sleep theories
that has resulted in the reconciliation of two major theoretical positions. I shall briefly
review the background of this development and outline its current form. I shall then
present my own variation on this model, which I think appropriately extends and
emphasizes aspects of that theory.
In an earlier review of the extant theoretical positions, I presented five formulations
of varying degrees of completeness, independence, and contradictions.
Restorative: Sleep is a necessary period of recovery from a state that has been
depleted or noxiously developed during waking. These theories emphasized internal
state changes.
Accepted for publication March 1988.
Address correspondence and reprint requests to Dr. Wilse B. Webb at Department of Psychology, University of Florida, Gainesville, FL 32611, U.S.A.
A version of this paper was presented at the 1987 Elliot Weitzman Memorial Lecture.
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MODEL OF SLEEP
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Protective: Sleep avoids continued exercise or excessive stimulation. As Claparede
put it, sleep does not occur because we are exhausted but to prevent exhaustion. This
was at the heart of Pavlov's theory of protective inhibition and sleep.
Energy conservation: This position emerged from the empirical relationship between
metabolic rates and total sleep time. Smaller animals with high metabolism tended to
have higher total sleep time. Thus, sleep was seen to be a form of enforced rest to
reduce metabolic requirements.
Instinctive: Sleep is viewed as an instinctive expression of innate behavior elicited by
"inducing" stimuli.
Adaptive theories: Sleep is considered to be an adaptive behavioral responses associated with predator/predatee and foraging requirements of species. These theories
focused on sleep amount, period length, and timing of sleep and emphasized environmental determinants.
These were not discrete positions and were implicitly and explicitly combined in
various ways. For example, Pavlov's protective theory contained a recovery component, and energy conservation theories could be viewed as a special form of a protective theory. Moruzzi's instinctive theory was combined with a restorative model. My
own earlier adaptive theorizing was combined with an instinctive position.
When examined closely, two major oppositional positions were apparentrestorative and adaptive models. A brief examination of these, however, reveals their
limitations.
Both positions fit parts of the empirical facts of sleep well. The restorative theories
accounted for many of the impelling facts of sleep deprivation and sensibly fit the
commonsensical truths of "sleep that knits the raveled sleeve of care." The adaptive
theories neatly accounted for the wide ranges of animal sleep in environmental terms.
However, both suffered empirical embarrassments. The most reasonable recovery
models of sleep would have sleepiness linearly increasing across time and recovery
time being some direct function of wake time. However, it was quite clear that sleepiness developed in a wave-like fashion. It was also apparent that recovery time within
and across species was not a simple relationship. Within species, the longer waking
individual recovered in the shorter time periods, and across species, many animals
recovered from 20 h of daily wakefulness in 4 h and others required 18 h to recover from
6 h of wakefulness. Most crucially, this model was hopeless in studies involving sleep
displacement. When sleep was shifted from night to daytime, the daytime sleep with
equal amounts of prior wakefulness was quite different.
The adaptive models, perhaps to distinguish themselves from the recovery models,
tended to eschew need/restorative notions and were faced with the intractable facts of
increasing sleepiness associated with sleep loss. Furthermore, as it was pointedly
noted, rest was certainly more adaptive than sleep, thus making sleep unnecessary.
Both suffered crucial theoretical problems with their hypothetical constructs. Simply, neither could empirically specify in a predictive (thus testable) fashion the ostensible "mechanism" underlying their theory. Thus, for the restorative theories, the
"substance" or "juice" being depleted could not be identified and its time course
specified. For the adaptive theories, the behavioral control mechanism needed to account for the variations in sleep amounts and placements could not be specified in a
predictive fashion.
Through the 1970s, the theoretical arguments, when of concern, were fitfully restated
with little clarification. Fortunately, empirical research proceeds in absence of overSleep, Vol. 11, No.5, 1988
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W.B. WEBB
arching theories. In the 1960s, generally independent of such considerations, a development began within the sleep domain that would markedly affect the general conception of sleep. The techniques, procedures, and findings of chronobiology or biological
rhythms began to slowly infuse sleep research. From studies in time-free environments
and displaced sleep designs, such as shift work studies, it became increasingly apparent
that sleep behavior was significantly determined by an endogenous timing system.
Simply, it became clear that sleep, at least partially, was time determined or a circadian
biological rhythm.
From my perspective within the adaptive theory position, it was increasingly clear
that this construct, a biological rhythm, could be appropriately considered the
"mechanism" underlying the "adaptive" timings of sleep in coordination with the
environment. Light/dark changes were associated with environmental survival advantages and disadvantages, such as predators, foraging, and territorial distributions, and
these "placed" sleep and waking activities.
Beginning in the 1970s, Alex Borbely and the group in Zurich began explorations of
a two-factor theory of sleep. Based on elegant experiments with both animals and
humans, they related sleep need, primarily indexed by slow wave sleep (SWS) indices,
to time of prior wakefulness and sleep time and conjoined this with the developing
research on circadian rhythms that were related to sidereal time. In 1984, Borbely
outlined the details of this formulation with his colleague Beersma and one of the
outstanding rhythm theorists, Serge Daan (1). The overall aspects of this theory are
presented in Fig. 1 from that paper.
As can be seen in this figure, there is a sleep need (S) process that arises during
wakefulness and diminishes during sleep. This interacts with a circadian system (C) that
oscillates on a circadian time scale. These tendencies combine in resultant sleep-wake
tendencies in relation to sleep (H) and wake (L) thresholds. In an "entrained" 24-h day,
the rise in sleep need (S) coincides with the circadian timing (C) at the sleep threshold
(H), and sleep tendencies are maximum. The reversal or decline of S and the rise of the
circadian function (C) occurs during sleep, and waking coincides with the waking
threshold (L).
An important aspect of this theory is seen at the upper right of this figure, "conscious
decisions." These are hypothesized as affecting the sleep and waking thresholds (H and
L, respectively). Thus, we may elevate the sleep threshold (H), and the sleep need will
continue to rise. However, there will be an oscillation ofthe sleep tendencies as a result
of the oscillation of the sleep tendencies as a function of the circadian (C) factor.
This model clearly fits the rise of sleep tendencies within an entrained circadian day
and the decline of sleep tendencies associated with sleeping. By the incorporation of a
circadian factor, it can account for the empirical oscillation of sleep tendencies as
wakefulness is extended as a result of the interaction of rising sleep demand with the
oscillating circadian factor. This incorporation of the circadian factor also provides an
effective model for displacement designs such as shift work schedules. If, by "conscious decisions," sleep onset is displaced so that sleep occurs during the low point of
the circadian oscillation, say 7:00 a.m. rather than 11:00 p.m., a conflict of C and S
tendencies will result in predictable sleep consequences.
The model that I am presenting is completely compatible with that proposed by
Borbely et al. I have labeled it an "objective behavioral model" of sleep, as this
describes its domain and gives due homage to the approach of Clark L. Hull that I was
taught in graduate school.
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MODEL OF SLEEP
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EXTERNAL CONDITIONS
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affects
synchronizes
PHYSiOlOGICAL. OSCILLATKJNS
masks
e.g., TEMPERATURE,
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FIG. 1. Daan/Beersma/Borbely
model. See text for explanation.
CIRCADIAN SLEEP WAKE CYCLE
b
The domain of concern is an attempt to provide a model for the prediction of sleep
as a behavioral event. The bases of these predictions are set in terms of objectively
measurable antecedents and concomitants.
The format of the model is the approach espoused by Clark L. Hull, which he
outlined in his book Principles of Behavior (2), where he proposed an "objective theory
of behavior." His aim was to elaborate "the basic molar laws underlying the 'social'
sciences." There is little doubt that Hull's aim far exceeded his grasp and that the
Hullian theory is a historical relic among the "grand" behavioral theories of the 1930s
and 1940s. However, Hull's failure does not necessarily invalidate his approach. It was,
after all, modeled on the highly successful Newtonian model of the physical sciences,
which was (and remains) a powerful model for comprehending and predicting the molar
aspects of the physical world.
The essence of the approach is straight-forward and explicit. It is a hypotheticodeductive model based on empirical observations, and "explanation" is defined by the
accuracy of predictions made on the basis of "laws" and "principles" underlying the
observations.
At a theoretical level, observations and their interrelationships are organized as
principles or theorems that presumably underlie these relations. These are tested and
rejected, modified or elaborated on the basis of their predictive strength.
To be emphasized is the procedure by which a construct is introduced. Although the
scientist may chose the level of observations (microscopic to macroscopic), the inferred
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W.B. WEBB
processes or constructs must be anchored in observable terms of both the antecedent
or consequence.
My variation of the Borbely, Beersma, and Daan model is presented in Table 1. As
can be seen in this table, the dependent variable is sleep behavior (R sleep), which is,
in part, indexed by sleep onset and termination. These variables, in turn, define the
presence or absence of sleep and such subsidiary variables as sleep latency, length of
sleep, amount, and placement of sleep in the 24-h period. The dependent variables also
include sleep structure, which is measured by sleep stages and continuity (awakenings
within sleep). In addition, the dependent variables include subjective sleep-related
responses subsequent to sleep (sleep evaluations) and within sleep (dream reports,
cognitions, and thresholds).
This complex of sleep-related measures are hypothesized to be a function of three
primary "intervening variables" or dispositional constructs: sleep demand, circadian
tendencies, and behavioral facilitators and inhibitors. Each of these variables, in turn,
is defined in observable (or potentially observable) terms.
Sleep demand is indexed by the time of wakefulness preceding sleep and is a positive
exponential function of time. It will be noted that this is simply a time variable and does
not include variations of activities in time. A second component of sleep demand is that
it is a negative exponential function of time asleep. I consider this last to be a provisional statement in the face of increasing evidence that this may have to be modified to
take into account the continuity of sleep.
Circadian tendencies are indexed by the timing of sleep within a 24-h matrix. The
specific "laws" underlying the tendencies are likely to be complex. For example, the
tendencies holding within an entrained 24-h environment we know must be modified
under "time-free" or "free-running" environments. Or, as we know, those circadian
tendencies present on the first night after a sleep displacement from the entrained sleep
time will be different from the predisplaced tendencies and will be modified under
continued entrainment in the displaced condition.
Behavioral facilitators and inhibitors are likely to be yet more complex. They refer to
individual behaviors that facilitate or inhibit the sleep response. In a simple illustration
in humans, sleep is facilitated by the prone position and inhibited by an erect position.
More complexly, as examples, sleep may be inhibited by behaviors reSUlting from
noises, or incompleted "day residues," or pain and may be facilitated by relaxation or
by monotonous nondemanding stimuli.
Two facts must be noted. These behaviors may be voluntarily or involuntarily determined, and they are under the control of a complex set of antecedent variables. They
mayor may not be "conscious decisions." One may lie down on the basis of habits,
urging, fatigue, or boredom. One may not lie down due to a complex variety of ante-
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TABLE 1. An objective behavioral model of sleep
R sleep = f Sleep demand x circadian tendencies ± behavioral facilitators and inhibitors
R sleep = Sleep onset, sleep termination, sleep structure (stages and continuity), and subjective
responses
Sleep demand = f(positive) wakefulness time and (negative) sleep time
Circadian tendencies = f circadian time of sleep
Behavioral facilitators and inhibitors = f Voluntary and involuntary, compatible and incompatible with
sleep responses
These primary variables are modulated by species differences, developmental status, organismic states,
and individual differences
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cedents and states: anxiety, work demands, stimulating needs, etc. In short, sleep
behavior may be delayed, interrupted or terminated, or facilitated by a vast range of
voluntary or involuntary, consciously or unconsciously determined responses. All,
however, are potentially measurable in their relationship to the facilitation or inhibition
of sleep.
The model then specifies that, with the measurement of these three variables and the
specification of the laws relating these variables to the sleep behaviors, accurate prediction could be made, for example, in the case of the young human adult. Or, if one
controls two of these variables, such as circadian time and behavioral factors, sleep
would be a direct function (predictable from), sleep demand.
To relieve us from the abstract and to illustrate that many of the laws underlying this
model are already present, Figs. 1 and 2 display applications of the model. Figure 1
presents the "prediction" of sleep latency as a function of sleep demand (indexed by
the amount of prior wakefulness) with "time to sleep" (circadian time) and behavioral
tendencies held constant by laboratory sleep conditions. Figure 2 illustrates the
"prediction" of sleep stages as a function of sleep demand (indexed by ongoing sleep
time) with similar controls.
In a more general situation, we may illustrate the functional aspects of these primary
determinants by considering the probability of a nap occurring. If there is a high sleep
demand level (up the night before), and it is mid afternoon (there is good evidence of a
circadian effect at this time), and the lecture is not eliciting high attending behavior
(behavioral facilitation), a nap is predicted. If on the other hand, there is a low sleep
demand (awakening at 8:00 a.m. after a good night's sleep), it is 10:00 a.m., and the
person is preparing a lecture, a nap is not predicted.
The preceding statements explicitly or implicitly are only referent to "human
adults." To make the model more comprehensive, additional variables are required.
The empirical data of our research makes clear that the three primary variables are
modulated by four additional variables: species differences, developmental stages, organismic states, and individual differences.
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W. B. WEBB
494
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FIG. 3. Sleep stages and time asleep (from reference 4).
Between species there is a wide range of sleep demand levels, circadian tendencies,
and behavioral repertoires. Very simply, elephants sleep like elephants, rats like rats,
and humans like humans. More specifically, sleep demands vary widely. For example,
grazing animals, in general, sleep between 2 and 4 h in brief bursts across the 24 h,
whereas smaller animals, such as rodents, sleep 12 h or more and primates tend to sleep
in intermediate amounts. Similarly, circadian tendencies show wide ranging patterns
that include nocturnal, diurnal, and acircadian distributions. There are also different
behavioral repetoires. For each species then, for each of the primary determinants,
different values must be determined and assigned for predictive purposes. The sleep of
the rat, for example, does not rise exponentially across 16 h and decline across 8 h.
Rather, it must be heavily weighted in the "light-time" hours and timed in intermittent
bursts. Sleep demand is approximated at 12 h, and the behavioral facilitator and inhibitors are heavily determined by natural environmental cues.
It is further apparent that the primary variables are responsive to developmental
stages. Again, very simply, babies sleep as babies, adults as adults, and older persons
as older persons. In humans, sleep demand varies from an average of some 16 hi24 in
infants to half that amount in adults. Circadian tendencies move from an acircadian,
polyphasic pattern at birth, through nap patterns, and back to nap patterns in the
elderly. And certainly the prone behavior of the infant is vastly different from the active
adult. These differences are modulators of the three primary variables.
All sleep variables are, of course, mediated by organismic states. In this formulation,
however, I am referring to those objectively identified induced or extant states that
have been shown to modulate one or more of the primary variables. These would
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MODEL OF SLEEP
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include pharmaceutically or biochemically induced states associated with, for example,
sleeping pills or central nervous system (eNS) activators, such as caffeine. These
would also include pathologic conditions as narcolepsy or sleep apnea.
Finally, for the crucial matter of individual predictions, individual differences must
be included. Within any species, developmental stage, or organismic state, the primary
variables show a range of individual differences. Again, as an illustration, relative sleep
demand averages about 7.5 h across human adults. However, the standard deviation is
about 1 h. In short, there are relatively stable individual levels of sleep demand ranging
from about 4.5 h to 10.5 h. Though less clearly defined, it is clear that systematic
individual variations are present in circadian tendencies and behavioral tendencies. In
the prediction of individual behaviors, the primary variables must be "modulated" to
reflect the individual tendencies of each individual.
From these considerations, it follows that the prediction of sleep behaviors is a
formidable but sensible process. To make such a prediction, one must specify the
primary variables: sleep demand, circadian tendencies, and behavioral facilitators and
inhibitors. We must, in addition, specify the species, developmental status, organismic
state, and individual tendencies. With what we know about these variables, particularly
in that well-studied species human kind, with such specifications we can make remarkably good predictions about a range of sleep behaviors. For example, regarding sleep
onset or sleep structure, specifying time awake (sleep demand), sidereal time (circadian
tendencies), and the behavioral conditions (facilitors and inhibitors) and referencing a
human who is 60 years old, normal, and drug-free and with a knowledge of his repetition tendencies, we can speak with some accuracy and confidence about how quickly
that person will go to sleep, what the structure of that sleep will be, and when the
person will awaken. Without such specifications and our body of research, we must
resort to necromancy or fraud.
What may be said about this particular model? First, as noted, it is compatible with
the Borbely, Beersma, and Daan model. As a consequence, it carries the major theoretical advantage of incorporating sleep demand and circadian tendencies. As such, like
their model, it reconciles the two major competing theoretical positions and yields both
their strengths in predicting sleep behaviors.
It is far less elegant, in its present form, in the interactive relations of these components relative to such constructs as thresholds. As a consequence, it is less capable of
being tested with precision. This, of course, gives to my model an unfair advantage.
There is an old adage in theory building that the less testable a model, the longer is its
probable lifespan.
I believe that the broadening and emphasizing of their construct of "conscious
decisions" to include the broader range of behavioral facilitators and inhibitors is not
only desirable, but also crucial. These processes are preeminent and necessary considerations in predicting the probability (and improbability) of sleep and can be better
operationally defined than "lurking" cognitive states. In short, I am espousing and
advocating a three-factor, rather than a two-factor, model.
The incorporation of the four modulators-species, age, organismic states, and individual differences-gives due emphasis to variables that have been experimentally
demonstrated to be crucial determinants of the sleep responses. However, the primary
purpose of this exercise has been to try to fulfill one of the heuristic roles of modeling
or theorizing-that of organizing our multitudinous facts into a relatively simple, coherent, understandable whole.
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W.B. WEBB
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Nearly 20 years ago, in a small book titled Sleep: An Experimental Approach (5), I
wrote:
it has been my experience that data gathering in absence of theory or concepts may result in a
mound of facts which often miss ultimate causes or effects or indeed may bury them ...
It seems, however, that the time is approaching when we shall be increasingly certain of our
facts, and our concepts and theories will become more sophisticated and clear. At this point, we
shall begin to see more clearly the multilevel causes of sleep ranging from genetic influences and
early training to immediate environmental influences as well as biochemical factors. In addition,
we shall be able to specify the resultant effects of sleep at levels ranging from neurobiological
and cellular to psychological and behavioral. (p. 56)
There is little doubt that our facts have continued to burgeon. The last publication of
Sleep Research (6) presents an annual yield of 651 abstracts presented at the annual
meeting and 1,882 bibliographic citations. The citations are over an incredible range of
topics from single nerve cell to jet lag, from cockroaches to apneas, from drugs to
dreams. However, I fear that this outpouring presents problems as well as opportunities. To quote another favorite author (7):
(In modern science) inductive data fall upon us from all sides like the lava from Vesuvius; we
suffocate with uncoordinated facts; our minds are overwhelmed with science breeding and
multiplying in specialist chaos for want of synthetic thought. (p. 91)
Hopefully, such a schema as I have presented, and more sophisticated ones that may
follow, will didactically aid us in seeing these data in a way that will let us view our
individual efforts in a more comprehensive framework and help us to communicate this
grand enterprise to our students, consumers, and the general public.
A final comment is in order. Relative to sleep research, the model presented can only
be viewed as chapter 1. It is a treatment of sleep as a dependent variable, i.e., the
prediction of sleep as a function of antecedent and concomitant variables. Chapter 2
must encompass sleep as an independent variable. This must systematically organize
the relationships between variations in sleep relative to the consequences. Hopefully,
here we can organize our multifarious finding relative to sleep loss (partial, total, and
selective), sleep continuity, sleep displacement, dreams, and sleep-induced neurophysiologic variations in terms of their relationship to our waking life.
REFERENCES
1. Daan S, Beersma DGM, Borbely AA. Timing of human sleep: recovery process gated by a circadian
pacemaker. Am J PhysioI1984;246:RI61-178.
2. Hull CL. Principles of behavior. New York: Appleton-Century, 1943.
3. Agnew HW, Webb WB. Sleep latencies in human subjects: age, prior wakefulness and reliability. Psychnom Sci 1971;24:253-254.
4. Webb WB, Agnew HW. Analyses of sleep stages in sleep wakefulness regimens of varied length. Psychophysiology 1974;14:445-450.
5. Webb WB. Sleep: an experimental variable. New York: Macmillan, 1968.
6. Chase M, McGinty D (eds) Sleep Research, 1987, Vol 16.
7. Durant W. The story of philosophy. New York: Washington Square Press, 1961.
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