Yet another approach is illustrated by the use of structurally based categories to describe behavior, as in a study by Ray, Upson, and Henderson (1977). These authors analyzed eight successive hours of videotaped behavioral data of a captive killer whale (Orcinus orca) and described each and every form of behavioral variation observed based upon criteria of anatomical references, such as head turning, body rolling, etc. This approach, where relatively exhaustive descriptions of the behavioral repertoire of a given species is generated, is common in ethology and is typically referred to as the development of ethograms (cf., Fentress, 1976). In the Ray et al. study, 80 different categories were defined. In subsequent analyses of the statistical patterning of behavioral organization involving these various categories (an analytic strategy we will shortly review, known as kinematic analysis), Ray et al. reduced this number significantly by ignoring categories with singular frequencies of occurrence. In some cases this may not be justified because infrequent behaviors may be very important behaviors to the organism and/or its environment. Reproduction, which is only an annual event for many species, is but one of many examples that could be cited here. In humans, murdering another human being may also be such a case. In both the sex and murder examples, there is not only the standard of low frequency of occurrence, but also some obvious outcome to the behavior exists which supercedes the behavior's structural form. As such, it is useful further to consider such criteria as defining behavior in yet another way: that of the behavior's functional end point or accomplishment (cf., Hinde, 1970).

Functional Analysis

The aim of functional analysis is to describe the consequential impacts (sometimes referred to as the meaning, goal, purpose, or setting implications) of a system or its components. Functional analysis interfaces with structural analysis in that the former identifies alternative structural variations that have convergent functional implications (i.e., bring about common outcomes). Where structural analysis of bar presses specified the spatial-anatomical references of that event, a functional analysis of a bar press would specify the behavioral/relational implications of attendant stimuli, the actual closure of the microswitch as the measure that a bar had been pressed, and the contingently sequenced outcomes of food/reinforcement. Stimuli may be functionally classified, for example, as to discriminative, stator, manipulative, reinforcing, or informing/comparatory (in the homeostatic control sense) functions. Likewise, behaviors may be functionally classified as observing, pressing, and consumptive responses, regardless of their structural form.

Functional classifications are clearly not confined to highly artificial, laboratory-controlled behaviors such as the lever press. Many functional behaviors make up the daily stream of human events, and setting-generalized variations in structure often are misguidedly cited as evidence of intraorganismic states, such as "creativity," "cognitional problem solving," or "originality." Recognition that constituent structural elements of functional events can vary widely, yet bring about a common functional consequence, such as closing a door, allows quite a different descriptive strategy to the use of hypothetical internal states.

As hinted at by the suggestion of combined functional/structural strategies, close inspection of their interrelationships are quite instructive. Because many structural variations may accomplish a given functional outcome, functionally defined constituent elements are comprised of probabilistically organized structural micro- units. As with the acts of taking a bath, dressing, or eating, which involve many redundant micro components but singular end accomplishments, a description of structural composition and organization within the functional units of behavioral systems emphasizes the inherent hierarchical nature of a system's organization. For example, in psycholinguistic domains, the most elemental structural units of sound (phonemic micro units) combine sequentially to form low- level functional (i.e., simple meaning) macro units known as morphemes. Likewise, these low-level macro units combine to generate more meaningful macro units called words. Words combine to generate uniquely functional (i.e., coherent) phrases, and phrases combine into sentences, etc. (e.g., Bennett, 1977). Thus, structural micro-units become probabilistically chained to make up larger functional macro-units, which are themselves the constituent elements of even more macroscopically organized events defining the hierarchical organization of a given system (cf. Upson & Ray, 1984).

We believe that micro-to-macro hierarchical nesting applies to behavioral systems in a fundamental way. Indeed, the evolution or development of complex behavioral systems seems in large part a matter of the successive evolution of hierarchically organized structural/functional systems, where multiple, and lower-level (i.e., micro), functional units organize sequentially to accomplish more broadly defined (i.e., macro) functions (Fentress, 1983). Furthermore, it is the micro-to-macro hierarchical nesting of behavioral systems that makes many analyses at once both structural and functional (i.e., interactive between structure and function in focus - see Upson & Ray, 1984).

Thus the previously cited Ray et al. (1977) study of structural behavioral/environmental (i.e., activities above/below water surface) elements in killer whales (Orcinus orca) also focused on hierarchically defined functional elements. The probabilistic concentration (i.e., the coherence) of selective structural elements into specific and recurrent chains of events (i.e., into networks, as determined by the yet-to-be-discussed technique of kinematic analysis) served to define macro-level functional behaviors of Free-swim Activity, Head-Bob Breathing, Surfaced Float-Breathing, Submerged Floating, and Trained Show Performances (see illustrations in Figure 3). Ray et al.'s analyses of these functional components actually demonstrate that, whether structural or functional elements are the foci, the analytic strategy is virtually the same. Thus we may think of such analyses as structural/functional and turn to their further elaboration.

FIG. 3. Illustration of four macro-behavioral elements used by Ray, Upson and Henderson (1976) to describe activities of a killer whale (Orcinus orca).

Structural/Functional Analysis: Component Strategies

Domains refer to analyst-defined macro-categories that function to organize the more specific descriptions of the analysis. At a minimum, one domain will refer to a focal organism and another will refer to environmental components of relatively short (i.e., stimuli) and/or long (i.e., setting events) durations. In research involving interorganism interactions (e.g., mother-infant or other social interactions), responses of others often serve as environmental components.

After the domains and their constituent elements have been specified, analysis proceeds to the third phase. The investigator quantifies nontemporal characteristics of the elements as well as their sequential (i.e., kinematic) and concurrent (i.e., coupled) organizational patterning within and between domains. We have found it useful to identify the following six subclasses of structural/functional analysis strategies (i.e., different system characteristics to be analyzed): (a) systemic complexity; (b) element probability; (c) syntactic kinematics; (d) syntactic variability; (e) systemic coherence; and (f) concurrency analyses. The first five analyses reveal organization within domains and the sixth describes organization between domains.

Systemic complexity. A system's complexity refers to the number of all-inclusive categories within a domain necessary to describe the potential states of a system at a given level of resolution and under a given investigational condition. Ideally, complexity would yield an index of a systemic characteristic alone. Of course, in practice this measure also is an important index of the investigator's activities, and is thus confounded by the experimenter's own selectivity. Thus in two selected studies of baboon behavior, one study found eight behavioral categories suited to their problem (Bramblett & Coelho, 1985) while another used 200 categories (Coelho & Bramblett, 1981).

Both systemic complexity and element probabilities may be illustrated by Ray's (1977) investigation of behavioral and environmental element variations when dogs received reinforcers for selected stimulus interactions in a large room where they were free to roam. Specifically, dogs were trained to come to, and remain on, an object placed on the floor (i.e., to stand, sit, or otherwise stay on a floor mat) to await one of two possible discriminative signals. One of these signals (S+) indicated that if the dog ran to a specific part of the room (i.e., a selected food box which was elevated on a table) he would receive food reinforcement. The other signal (S-) indicated that no food reinforcement would be available. Figure 4 illustrates the proportional contributions (i.e., probabilities) of each type of behavioral/environmental element pairing preceding the one and only type of reinforced behavior, i.e., RUNNING to the food box.

Fig 4. Proportion (or probability) of antecedent contribution for each of five behavioral elements and eleven environmental elements preceding food-reinforced RUNs to a FOODTRAY in an indoor free-ranging dog learning experiment. The figure is from Ray (1977) depicting the conduct of research by Soviet experimenters using the Kupalov "situational reflex" paradigm.

STAND-on-MAT behavior is the experimenter-targeted behavior for subsequent presentations of the S+ (M120), and it progressively becomes the primary event of origin for RUN-to-FOODBOX sequences. This complex change in antecedent behavioral-environmental interactions is being generated from a history of EXPLORE/RUN-across- MAT behaviors which are secondarily reinforced (i.e., are temporally associated with TRAY OPERATION, which occasions the remote delivery of FOOD). Here, then, is a relatively rare example of multiple -response contingent presentations of a discriminative stimulus. That is, a variety of structural behaviors (e.g., RUN-, EXPLORE-, STAND-, SIT-on-MAT) initiated by the subject serve the singular prerequisite function of "stationing" the subject on the MAT long enough to receive the M120 S+ which is followed by reinforced Runs to the FOODBOX. Eventual introduction of yet another stimulus, in the form of a metronome beating at 60 beats per minute (M60, S- ), in Session 13, was used subsequently to occasion the animal's remaining on the MAT during M60 presentations. This function was intended by the experimenters, since they never paired M60 with the sound of the food tray and thereby never reinforced subsequent Runs that occurred earlier in training. As such, the animal initiated its own discriminative settings, both positive and negative, via the same set of multiple contingent behaviors (see Ray, 1977).

It is not our present purpose further to detail such operant discrimination functions, but merely to illustrate the use of behavioral-environmental interaction elements and their probability structures in research. Thus it will suffice for us to point out that similar analyses were accomplished for each separate behavioral category and were subsequently pieced together to depict the full chain of events occurring across each session. Unique paradigmatics for conditioning were implied in that several behaviors were reinforced, as long as contact with the mat was maintained by them. This suggests that complex learning may be more a process of probabilistic relations between some structural classes of behavior and not others, rather than a simple one-class contingency. Likewise, the function of these classes may themselves be probabilistic, where sometimes they function to bring about S-, sometimes S+, and, if reinforcement scheduling is involved, sometimes S+ implies reinforcement, and sometimes not. This is clearly not a perfectly deterministic circumstance, and behavior-environmental elements may become quite complexly organized within such conditions, as was illustrated by Ray's two subjects eventually acquiring individually differing response-stimulus pattern adaptations to these conditions (Ray, 1977).

Syntactic kinematics analysis. The analysis of sequential patterning in elemental transitions is an intradomain measure that yields the fundamental data describing the kinematics of a system. Frequency measures of specific transitions (specific element-to-element sequences) serve to establish estimates of the conditional probabilities for each type of kinematic sequence. The majority of kinematic analyses to date are thus based on a two-level analysis, where the probability of one element is conditionally determined by the occurrence of each type of immediately preceding element. Higher-level analyses are possible, where probabilities of specific three-element sequences, or even more, may be determined (cf., Altmann, 1965; Bennett, 1977; Ray et al., 1977). However, where several kinds of elements have been identified (i.e., in complex systems), multidimensional transition matrices become difficult to calculate, even with rather large computers. Thus the two-dimensional array is typically used as a statistical estimation/summary device and is most often represented via a kinematic flow chart demonstrating the probabilistic organizational implications of element sequencing.

FIG. 5. Kinematic organization charts from Ray and Brown (1975) depicting the conditional probability of behavioral sequences of rats under two different experimental settings. In the S+ setting rats were reinforced with water for each bar press, while in S- no bar presses were reinforced.

Figure 5 illustrates kinematic flow in two settings (S+/S-) of a discriminative barpress experiment (Ray & Brown, 1975). Rats received water for each bar press occurring in the presence of house light "on" setting conditions (S+). No reinforcement occurred in light "off' (S-) conditions. These kinematic flow charts represent a statistical summary of the conditional probabilities associated with each element-to-element transition considered for only two elements at a time. The charts include arrows depicting element transitions by having each arrow's width proportional to the probability of each specific sequence. All arrows following a given element collapsed represent a probability of 1.0. The graph is a summary based on three subjects combined, but it is highly representative of each individual subject. Note that behavior is quite different in kinematic organization under these two setting conditions. The pattern of behavioral sequencing during S- was determined to be essentially that which the animals demonstrated prior to barpress training.

This experiment demonstrates yet another important characteristic of organization. As noted, kinematic syntax describes the sequential organization within a given systemic domain. Usually, as is evident in all the flow charts in Figure 5, not all possible element sequences occur with the same frequencies, and some do not occur at all. This is another way of saying the organization of kinematic transitions is not a random process, but one with systematic, although probabilistic, organization to it. Thus, in addition to a simple hierarchy in elements' unconditional probabilities (cf., Catania's 1984 "behavioral hierarchy"), there is also a hierarchical status to the conditional probabilities governing element-to-element transitions. This is the hierarchy illustrated implicitly by the descendent rankings of terms depicted in the row arrangements within each column of kinematic flow charts (see Figure 5).

Systemic coherence. Somewhat related to the notion of syntactic variability is the concept of systemic coherence. The coherence of a system is a measure of concentration toward singular, or regular, paths of transition among those varieties of potential elements. For example, think of three alternative routes of transition between element "A" and element "B" (e.g., A-C-B, A-D-B, A-E-B). Now consider the possibility that one of these routes is almost always the one which occurs. Alternatively, all three transition routes could occur with equal frequencies, thus reducing the predictability of which will actually occur in any given instance. This is somewhat analogous to the foundational conceptions of Chi-squared testing, where concentrations of observations into specific pairings of events are disproportional to those expected by random distributional occurrences (cf, Ray (manuscript in preparation) for elaborations and mathematical measurement of coherence and associated concepts).

The concept of coherence gives us pause to reflect further on how hierarchical nestings of elements at one level of resolution serve to define higher-levels of elemental events, as discussed earlier. Many networks of localized transitional coherence may exist where specific multi-element transition result in a high probability path which then loops back to repeat the same set of kinematic transitions. In such reverberative loops, or networks, there are usually only a very few, and relatively infrequent, route by which the system transits from one net work to another. However, when these infrequent transitions do occur, a new and different network of recurrent patterns is usually maintained for a number of repetitions. This networking phenomenon allows us to discern higher-order macro-elements which emerge from inductive studies of structural-functional relations, because most changes from network to network typically occur when some function is finally accomplished, as with completing a bath, a meal, or any other task. There are actually many levels of definitional resolution possible, depending upon one's interest and problem, but each shift from one level of resolution to another changes the potential "noise" (i.e., the occurrence of low-frequency transitional kinematics which represent minor variations on the more dominant, and thus coherent, network's structure) in the analysis. It is thus most often useful to first approach a relatively unknown system at fairly micro levels of description, since descriptions of macro networks may inductively appear from micro level descriptions, but not vice versa.

Concurrency analysis. It is often the case that relations between elements of different domains are of interest in the structural/ functional analysis of a system. Concurrency analysis is a strategy for describing such interdomain organizations. It reveals "what occurs with what" across domains (i.e., concurrent organizations). A pilot study illustrates the concept at two levels simultaneously (Upson & Ray, 1984). In this experiment differentially proficient golfers, including beginners, average players, and a professional were filmed with high-speed cameras for a Cartesian-coordinate kinesiological (i.e., structural element) study. But these researchers also: (a) described categorically what part of the swing was being singled out for Cartesian analysis (a separate, and higher-order, category-based definitional domain for structural elements), including "ball address,"backswing," "downswing," and "follow-through"; and (b) recorded EKGs during the filmed swings. Thus they could compare precisely in time the moment-by-moment characteristics across each of the three domains (i.e., spatial-coordinates, categorical , somatic-structural, and cardiac). Upson and Ray (1984) summarize the most salient Observations for present purposes:

The timing for the back swing, down swing, and follow-through was consistent on successive swings for the pro, less consistent for the average player, and least consistent for the beginner, with the back swing varying as much as 0.2 seconds for the beginner. Heart rate occurring 4 seconds before the swing to 4 seconds after the swing in the professional was low, ranging from 52 BPM and increasing slightly to 58 BPM. Heart rate for the average player was higher and more variable, changing from 87 BPM to 97 BPM with a decrease in rate at the beginning of the swing and an increase at the end of the swing. The beginner showed variability similar to the intermediate. Although the stability and consistency of an autonomic response throughout the swing was of considerable interest, the more intriguing finding was the precise time of the R wave with reference to the arm position during the swing. In the professional the initiation of the swing was consistently related to the last heartbeat with an average latency of 0.74 seconds and a range of 0.72 to 0.80 seconds. After the swings were initiated, heartbeats occurred at virtually the same Cartesian coordinates, that is, position in the swing. (p. 509)

This study also serves to illustrate the somewhat complicated matter of classifying strategies based upon static (i.e., within a time-frame) versus dynamic (i.e., across succession of time, or time-series) characteristics in behavioral systems analysis. With the exclusion of only a small number of measurement strategies (e.g., spatial coordinates), all elements in a behavioral system also absorb time (i.e., are not punctate events). Thus time is embedded in both the concepts of element and of kinematic organization. That is why we have always referenced "within a given time window." The golf study is a clear illustration that concurrency analysis, even within so narrow a time window as that required to swing a golf club, is actually also parsing out the temporal pacing and synchrony between events, whether within a domain (as with the "timing of movement through the backswing"), or across different domains (as with the heartbeat and swing-initiation timing). Such issues are the foundation of yet another, and somewhat separated, strategy among the various behavioral systems analysis strategies: the analysis of dynamic operating characteristics, or operational analysis.

Operational Analysis

As just noted, structural and functional analyses require continuous tracking of constituent elements across time; therefore, they are sensitive to the continuity of organism-environment interactions. However, time itself only is of implicit interest in structural and functional analyses; elemental and organizational changes compared against real time are not a critical issue. In contrast, the operation of systems across time requires special techniques which, collectively, we identify as incorporating operational analysis strategies (see Ellson, 1949, for variations on present definitions and strategies).

Operational analysis as here defined thus overcomes a serious limitation of classical systems analysis as it relates to structural/ functional analysis. Specifically, classical analysis tends to treat structure and/or function as static. Operational analysis recognizes the dynamic nature of systemic elements and organization and describes systemic temporal operating characteristics in terms of structural/functional changes across time. As such, operational analysis focuses on temporal patterns, or organizational rules, which describe how a system (a) achieves and/or maintains its structural/functional characteristics, or (b) fluctuates systematically in those characteristics. Operational analysis is thus the study of the dynamic changes attendant to recurring process states assumed by systems and/or their component subsystems.

Elemental time-series operations. Analyses of elemental time-series operations for any given systemic domain provide descriptions of temporal variations in elements themselves. For example, rate of elemental onset, or initiation rate, typically varies across time in a very systematic fashion, as evidenced in the frequency plots in Figure 6. This figure presents data on the averaged hourly frequency of functional behavioral elements of a killer whale as described earlier (Ray et al., 1977; also see Figure 3). The data in Figure 6 represent an "average day" (i.e., the data for each plot are averages for each respective hourly period of the day across five days of actual observation), but are graphed as replicas across two hypothetically continuous days better to represent the periodic nature of the data. Lowest frequency occurrences for surface-float breathing and free swimming are between midnight and dawn, whereas submerged floating and head-bob breathing are least frequent during mid-morning just before noon. Highest frequencies are late afternoon for all behavioral elements. This diurnal variation is quite systematic and reliable for this subject.

FIG. 6. Illustration from Ray, Upson, and Henderson (1976) depicting smoothed-curve data from an "average day" of behavioral activity based on the four macro -behavioral categories for killer whales (Orcinus orca) illustrated in Figure 3. Circadian rhythms in behavioral frequency of initiations, averaged durations, and total minutes engaged for each behavioral element illustrate cycle and phase relations.

As noted, elemental initiation rates, stabilities, and budgets are measures which reference each specific element class within a given domain individually. This, of course, ignores ascribed interdependencies among elements. Assessments of interdependent organizational properties among elements within a domain require composite, as well as isolate, descriptions of elemental parameters. Such composite descriptions thus focus on the domain as a subsystem of the total behavioral system.

Both domains and systems which incorporate a greater preponderance of longer duration elements are more stable than those with a preponderance of shorter-duration elements. Static, synchronic methodological practices have heretofore made it virtually impossible to quantify such phenomena. But the general pace of event/ state changes within a subsystemic domain or a system is really quite simply measured, once conceptualized as a rate of change in multiples of measures (i.e., in the time-series) of subsystemic or systemic states. Consider, for example, the phenomenon which might be referred to as the pace of behavior.

One of Ray and Brown's reported findings, reproduced in Figure 7, illustrates the measure's sensitivity to various ambient setting conditions attending a relatively standard operant discrimination lever-pressing task. Rats were trained on constant reinforcement schedules to discriminatively press only during S+ conditions. General behavioral flow rates during S+ and S- were then used as baseline measures for comparing similar flow rates when ambient room temperatures were raised (heat condition) or lowered (cold condition) via changes in the room thermostat (maximum heat/cool). These ambient conditions were described as environmental settings. Other setting conditions (organismic) included various dosages of sodium pentobarbitol or water (reinforcement) satiety.

As Figure 7 illustrates, all setting manipulations lowered the rate of general behavioral flow compared to baseline (i.e., normal setting maintenance) conditions for both S+ and S- discriminative conditions, with the possible exception of lo-dosage drug injection impacts on S+ flow rates. Hi-dosage drug injections, pre-session satiation to the reinforcer, and heated ambient temperatures were the most influential setting conditions. All of these settings were associated with depressed behavioral flow rates in both bar pressing (S+) and in non pressing (S-) stimulus discrimination conditions.

FIG. 7. Average behavioral flow rate, or kinematic velocity, for a group of three rats engaged in a light-discrimination bar pressing experiment reported by Ray and Brown (1975). S+ represents lighting associated with water-reinforced bar pressing and S- represents light associated with non-reinforced pressing. Maintenance conditions are those using original training conditions. Organismic setting manipulations included various level injections of sodium pentobarbital or pre-experimental satiation of the reinforcer (water). Environmental setting manipulations involve maximum (heat) and minimum (cold) room thermostat settings.

To emphasize the point that the rate of change from one element-state to another (i.e., rate, or velocity, of element transitions) can be applied to any systemic domain, the measure introduced by Ray and Brown is now known more generally as a sub-system's kinematic velocity (Upson & Ray, 1984). To calculate kinematic velocity of a domain, the number of element transitions over a given time interval is determined. Successions of such intervals then generate a time-series measure which easily reflects changes in velocity (i.e., accelerations, decelerations, oscillations), assuming appropriate measurement interval usages. As such, kinematic velocity is a measure of average velocity, because data are obtained over successive time intervals (which results in an averaging process). It is the multiple of these intervals which establishes the time series. However, instantaneous velocity can be approached, just as in physical kinetics, by using narrower and narrower time intervals for measurement.

It should be clear from the kinematic velocity illustration that simple elemental and more integrative subsystemic operating characteristics include both differences and similarities. In the subsystemic case, we assess temporal organization within the domains of the system itself, rather than the individual operating characteristics of singular constituent elements/states. In addition to kinematic velocity, there are several other measures which focus on subsystemic operational properties and their time-series. Among these are the time-series in subsystemic complexity, kinematic organization and its coherence, and syntactic variability.

FIG. 8. Kinematic organization charts depicting circadian variations in conditional probabilities of behavioral sequencing in a killer whale (Orcinus orca) via twelve successive two-hour windows. The graph (from Ray, Upson, and Henderson, 1976) depicts changes in element complexity, syntactic variability, and coherence across the day/night cycle.

Both the number of different kinds of elements within a domain (subsystemic complexity), their probabilistic sequential structuring (kinematic organization) and their concentrations into specific higher/ lower-than-expected- probability sequences (coherence) are frequently far from static when considered across multiples of time intervals (i.e., as a time-series). Thus Ray et al's (1977) data from a captive killer whale (Orcinus orca) depicted in Figure 8 show systematic variations in all these measures across the diurnal period. For example, between 4:00 and 6:00 a.m. there are four different macro-behavioral elements engaged by the subject (submerged float, surface float, head-bob breath, and free swim). Between 10:00 a.m. and 12:00 noon a fifth category (show performance) appears by trainer intervention. Organizationally, an even more significant variation is occurring. The 4:00 to 6:00 a.m. period kinematic flow chart illustrates eight different kinds of sequences from element to element (the measure of kinematic variability, as determined by the number of arrows in the flow chart) compared to 13 different kinds during the 10:00 a.m. to 12:00 noon period. Likewise, the appearance of several low-probability sequences (as depicted in the figure by narrow arrows) in the 10:00 to 12:00 period disperses the concentration of high-probability sequences (number of wide arrows) for similar origin sequences occurring in the earlier time window. Thus free swims in the later period sequence into one of four different possibilities of subsequent behavior, compared to only two in the earlier period. Likewise, head-bob breathing has more variations in sequential states during the period just before noon. Submerged floating has almost equal probability distributions between free swim, head-bob breathing, and surfaced floating during the 10:00 to 12:00 period, compared to a highly concentrated probability of sequencing into head-bob breathing during the 4:00 to 6:00 a.m. period. This reflects a higher degree of coherence during the midday period.

When such comparisons are made as a consecutive time series, it becomes obvious that, like the individual elements themselves, subsystemic operations vary systematically across the diurnal cycle, thus reflecting a circadian (one cycle approximately every 24 hours) oscillation in their parametrics. For example, Figure 9 presents both the syntactic variability time series and the kinematic velocity time-series for this orca across successive two-hour blocks for the average 24-hour observation period. Syntactic variability is low in the morning and increases just prior to noon, reaching a maximum by late afternoon, after which it decreases. Kinematic velocity is synchronized with syntactic variability in phase and period; it shows the same circadian rhythm.

FIG. 9. Circadian variations in syntactic variability (variations) and kinematic velocity (changes) in a single killer whale's behaviors across twelve successive two-hour windows of an average day (from Ray, Upson, and Henderson, 1976).

Such periodic phenomena reveal important temporal qualities in the organization of behavioral systems that are not adequately addressed by conventional methodologies. Workers convinced of the value of a science of behavior should find it telling that traditional, static, synchronic methodologies make it virtually impossible to contact what is perhaps the most general phenomenon exhibited in the natural world. Specifically, physical science from the time of ancient civilization has focused on the great cyclicities of nature, ranging from the periodicities in the behavior of astronomical bodies to energetic wave phenomena. Because behavioral systems methodology involves the diachronic strategy of tracking systemic operations in time, it opens the possibility for the investigation of behavioral cyclicities, or regularly recurring successive elemental and/or systemic states, by applying, for example, spectral analytic techniques (Gottman, 1981). Spectral analysis begins with the assumption that time series can be described by the sum of a set of sinusoidal or periodic functions that have specific frequencies and amplitudes. The total variability in the time series is partitioned across a set of frequency bandwidths. Dominant cycles are revealed when the series is represented as a power spectrum, which is merely a family of plots representing the power (variance) across each of the various frequency bandwidths. We shall thus offer some further considerations of periodic operating characteristics in behavioral systems by reviewing relationships between domains.

System (interdomain) time-series operations. Because systems are comprised of multiple domains, complete descriptions of how behavioral systems operate require that we specify the joint (i.e., interdomain, or systemic) operating characteristics (e.g., coupling dynamics) between domains. Systemic time-series operational analysis involves identification of temporal patterning across different systemic domains. This type of analysis is extremely important for describing the temporal rules attendant to the operation of pairs, or other multiples, or domains such as organismic actions and environmental actions (chronobiology's entrainments--Sheving, Halbert & Pauly, 1974; Wever, 1979), physiological and overt motoric (as with Upson & Ray's 1984 heart rate and golf swing integration), multiple physiological domains (e.g., Sayers' 1975 analysis of informational, respiratory, and pressure "regulation" signatures in the spectral patterns of cardiovascular variability and also Upson and Ray's 1984 multiple brain hemispheric EEG synchronizations), or social interaction (Gottman, 1981; Ray, Carlson, Carlson, Carlson, & Upson, 1986).

Since cross-amplitude measures also may vary periodically, one could conceivably accomplish a power spectral analysis of the specific frequency power levels across a time series, but no research of this type appears to yet exist. Nevertheless, some reports clearly suggest the need for such applications. To cite but one instance, Figure 10 from Ray et al. (1986) illustrates that two captive killer whales of different sex often engaged in exactly the same behavior. The figure also shows that this social coupling between changes in behavioral states varied across the diurnal cycle.

FIG. 10. Proportion of behavioral changes which were socially initiated and which culminated in the same behaviors being engaged in by two killer whales (i.e., social synchrony). Data are successive three hour plots across a continuous 96-hour period (figure from Ray, Carlson, Carlson, Carlson, and Upson, 1987).

Where the operating characteristics of two or more domains are apparently coupled, the coupling may not be perfectly synchronized, thus indicating a shared periodic, but also implying a lead/lag phase difference in the periodics. Thus in the Ray et al. (1986) study on social coupling just cited, they found that the female tended to initiate the behavioral state changes from one coupled elemental state to another. However, this was mostly true at night, when the pair was maximally coupled. During the day, the two were most likely to initiate independent changes in behavior, and lead/lag analyses demonstrated no clear dominance of one over the other when coupled changes in behavior did occur.

Power spectral techniques also allow for an assessment strategy in such cases of lead/lag relations, in that phase relations may be measured by the phase angles. However, this strategy is infrequently applied to social and other behavioral systems. Nevertheless, this area promises some of the most unique and fruitful contributions of behavioral systems methodology. In addition to the female/male lead/lag data already reviewed, a second example of inter-domain couplings was found between the kinesiological and cardiovascular domains during golf swings (Upson & Ray, 1984). Professional golfers exhibited a consistent coupled relationship between cardiac activity and swing logistics, with a consistent cardiovascular lead time preceding swing executions. It is noteworthy that these domains were not coupled for less proficient golfers.

A similar strategy focusing on general interdomain time-series coupling dynamics was, this time focusing on pathological stereotypes, was discussed by Brusca (1985). Severely mentally retarded and autistic persons frequently display stereotypes such as body-rocking, head-banging, and armflapping. Brusca (1985) noted the cyclic nature of stereotypes and called for studies involving: (a) extended time windows of observation, (b) as near to continuous observations and recording as possible, and (c) time-series analyses that are sensitive to the detection of cycles. In brief, Brusca urged a behavioral systems methodological approach such as advocated here and applied to stereotypes by Lewis, MacLean, Bryson-Brockman, Arendt, Beck, Fidler, and Baumeister (1984), who examined interdomain operating characteristics for retarded persons' stereotyped body-rocking and cardiac activity.

Lewis et al. (1984) concurrently recorded cardiac activity and body-rocking. Consistent with the need for bivariate analyses, such as time-series techniques that track elements in time, a conventional correlational analysis (Pearson product-moment) between rocking rate and heart rate yielded a coefficient that was not significantly different from zero. However, cross-spectral analyses for all individuals tested showed a single peak frequency of power spectra, indicating that the motoric and cardiac domains shared a single common cyclic component. The data for each subject showed that the frequency bandwidth common to both domains was identical to the bodyrocking frequency. These findings suggest that stereotyped rocking and cardiac activity are coupled oscillatory domains, or subsystems.

Operational Perturbation: Recovery,
Resets, Resonance, and Reorganization

As illustrated by many electronic and/or mechanical control systems, oscillatory operating characteristics in a system typically imply incorporation of goal-state/actual-state comparisons which subsequently alter processing to maintain a homeostatic balance around some pre-specified goal states. Oscillations in such systems are produced by delay in the feedback loops to the comparators. Homeostatic balance is the "controlled quantity" in such control systems. Any dramatic change in the integrity of the systemic, or subsystemic, structure is usually accompanied by a dramatic shift in the otherwise dynamically stable operating characteristics (i.e., the precise states are dynamically changing within stable ranges of amplitude and/or periodicity). Such change-induced disturbances are referred to as perturbations, as when an opened window lets in cold outside air into a thermostatically controlled room heating system. In the fact of such a perturbation, most control systems have one of several response characteristics which may be observed. If the perturbation can be successfully accommodated within the capacity of the system's operating characteristics, the system or subsystem will recover normal functioning--as with a high-capacity heating system being able to cope with the relatively small cold air flow from a single window. In this practical illustration, only the periodics of the system will reflect this change having occurred, because the system will obviously have a longer on cycle to bring up the room temperature and a shorter off cycle to bring it down (assuming, of course, cold air is being injected into the room). In many control systems, recovery may even be tracked as a specific function in and of itself and may demonstrate damping characteristics related to rates of recovery. Systems may then be compared on any of a variety of operating parameters, including periodics, amplitude, and damping constants (e.g., Ray et al., 1977).

Mechanical engineers are also accustomed to working with stress phenomena created by resonance conditions. In such conditions, perturbing influences are actually sympathetic with the systemic operations in that they share harmonic periodics and phases. Under such conditions, normal oscillations are amplified in their amplitudes, which may carry the system quite beyond its capacity to maintain its own structural integrity and the results are systemic fatigue, deterioration, destruction, or operational failure (Sandor, 1972). Applications of these concepts to behavioral systems remain unexplored, but are certainly suggested by conceptualizations of contact between independent driving functions in environments and in individual organisms. Under such conditions, nearly equivalent periodics may merely synchronize via a process of entrainment, as in the 24-hour day/night cycle entraining the typically longer 23- 27-hour biological rhythms of most animals (as evident when such organisms are kept in constant light or darkness). In other cases, highly disruptive, but potentially sympathetic (i.e., harmonic) periodics between the environmental and biological systems may be demonstrated, as in the often cited case of "jet lag" induced by frequent transoceanic jet flights.

Where behavioral systems are concerned, select setting circumstances, events, and/ or elements may be more significant in their systemic reorganizational implications than are others. While not by any means being catastrophic, many functional events in psychological systemics carry implications for minor systemic reorganizations. For example, the stimulus events often referred to as informational, reinforcing, and/or discriminative often serve as pivotal events when contingently organized with select behavioral element occurrences. Thus traditional learning processes are really processes of behavioral, memorial, and even neural reorganization and development (Kandel & Schwartz, 1982; Ray, 1977).

Behavioral velocity and environmental velocity. Alvin Toffier in Future Shock (1971) argues that the rate of change in modern environmental setting conditions is a potentially dramatic source of psychological stress, and thus of stress-associated disease. Toffler's notion, along with Ray and Brown's (1975, 1976) findings, cited earlier, showing that behavioral flow rate (i.e., velocity) was much more sensitive to physical changes in ambient setting conditions than were such measures as lever-pressing rates, combined as an impetus for Ray and his colleagues to investigate further whether temporal changes in ambient setting conditions could be detected in behavioral velocity.

Three rats maintained on a water-restricted regimen were trained to bar press for access to water on a continuous reinforcement schedule. Rats received water following each bar press only in the presence of a bright house light (S+); water was never delivered when the house light was dim (S-). Critical testing occurred over four sets of eight sessions each. The first and fourth set of sessions were labeled the "rapid pace" condition, and involved an 18.5-s mean duration for alternating S+ and S- settings. In the second set of eight sessions, the "medium pace" condition, mean durations of each S+ and S- (37 s) were twice as long on the average as those of the rapid pace condition. During the third set of sessions, called the "slow pace" condition, mean durations of S+ and S- (74 s) were four times longer than those of the rapid pace condition. Thus the conditions as conducted were: Rapid, Medium, Slow, and a final return to Rapid setting schedule pacing. The behavioral domain was broken down into eight structural elements of behavior plus a ninth functional category of bar pressing which was electromechanically recorded via its environmental impact. The other eight elements are formally defined in Ray and Brown (1975).

Results from this study reveal that, as environmental pace slows, the velocity of behavior change gradually declines also. But more important, the data suggest the possibility of a systemic property familiar to almost all adaptive control systems theorists: intrinsic oscillatory driving function. These functions are shown in Figure 11; they appear in the velocity of behavior and (a) are only evident during S- (thus suggesting systemic driving functions are susceptible to environmental reinforcement-related driving conditions); (b) are different parametrically under differing environmental velocities; and (c) are sensitive to S- onset-induced perturbational effects, which include damped recovery functions in the behavioral velocity operating characteristics. A post hoc mathematical model of these characteristics was tested on comparable data from setting-influenced behavioral velocity changes in killer whales (see Figure 12). Although results were too variable to be fully conclusive, they were heuristically impressive in that the same mathematical functions fit the data when only the parametric constants were adjusted for species differences. Table 1 illustrates these comparisons with both the general model and equations. In addition it cites the implications of each parametric difference. For example, the rat's driving function oscillates much faster and has a lower amplitude than the whale, is more highly damped than the whale, etc.

FIG. 12. Average number of behavioral changes occurring across successive 30-s blocks of time following the onset of all free swim activities subsequent to behavioral engagements of show performance vs submerged floating by a killer whale (Orcinus orca). The figure is from Ray, Upson, and Henderson (1977).

Table 1. Model of Driving and Damping Functions in Rats and Killer Whales.

Environmental velocity and human activities. Yet another example extending Ray et al's (1977) interest in behavioral and environmental velocity relations, in this case with human subjects, was reported by Upson, Carlson, and Ray (1981). College students maintained self-report logs of categorized activities within several domains, including their physical setting (place), persons with whom they were currently engaged, behavioral activity, valence of attraction/repulsion, perceived locus of event control, magnitude of control exertion, time orientation (past, present, future), phenomenological pacing of events, and experiential states. Entries into this log were made every five minutes during all waking hours. After periods of initial accommodation to recording procedures, students were instructed to live under a succession of three different organizations of setting conditions. Condition I involved seven days of "normal" environmental settings, but under the scheduling specification of the experimenter. Condition II consisted of six days of "normal" environmental settings under each subject's own selective and temporal control. In Condition III subjects experienced highly limited choices of environmental setting varieties, but these were under their own control of selection and pacing. The conditions were accomplished within the context of a course on the Psychology of Leisure, and Conditions I and II involved students living on a college campus. In Condition III, students were taken to an out-island Bahamian community which was very isolated and devoid of usual stimuli to which students were accustomed, including absence of electricity, running water, various forms of entertainment, etc.

FIG. 13. Average number of different settings engaged and the velocity of setting change per hour initiated by human subjects under three different experimental conditions of setting complexity and external/internal control manipulation. Condition I included other-induced/complex setting changes, Condition 11 self-induced/ complex settings available, and Condition III self-induced/simple settings available (from Upson, Carlson, and Ray, 1981).

The primary purpose of this study was to assess the velocity and complexity of environmental change experienced/chosen by students under the various organizations of setting and execution-of-control conditions. When allowed their own control over settings, subjects chose a lower setting-change velocity than that imposed by the experimenter. Further, subjects decreased the variety of different settings experienced when under their own control. As Figure 13 illustrates, the simpler environment of the Bahamas (Condition III) allowed even fewer varieties of settings than those either imposed by the experimenter (Condition I) or those self-selected on campus (Condition II). Nevertheless, even with fewer varieties of environmental settings, subjects maintained consistent velocities across both campus and Bahamian environments when those were self-controlled. This means that the Bahamian settings, while offering less variety, also involved less stability (i.e., were engaged for shorter periods of time per contact) in order to accomplish equivalent total velocities of setting change between campus and Bahamian environments. Students were thus frequently changing back and forth between the same few settings in the Bahamas, thus experiencing their normal "variable setting environment" velocities.

Although too complex to summarize here, this study also utilized power spectral analyses of the time series involved in the changing setting variabilities and velocities to demonstrate very specific ultradian rhythms (i.e., periods shorter than 24 hours, including four-, six-, eight-, and 12 hour periodics) and circadian rhythms (i.e., approximately 24 hours per cycle) in both measures.

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