Quantifying the buildup in extent and complexity of free exploration in mice

Abstract

To obtain a perspective on an animal's own functional world, we study its behavior in situations that allow the animal to regulate the growth rate of its behavior and provide us with the opportunity to quantify its moment-by-moment developmental dynamics. Thus, we are able to show that mouse exploratory behavior consists of sequences of repeated motion: iterative processes that increase in extent and complexity, whose presumed function is a systematic active management of input acquired during the exploration of a novel environment. We use this study to demonstrate our approach to quantifying behavior: targeting aspects of behavior that are shown to be actively managed by the animal, and using measures that are discriminative across strains and treatments and replicable across laboratories.

One of the challenges faced by researchers of animal behavior is how to interpret the behavior emitted by an animal from the perspective of the animal's own functional world. In our studies, we meet this challenge by capturing the momentary developmental dynamics of exploratory behavior. The apparent dynamics disclose the presumed function of this behavior: a systematic active management of perceptual input acquired during the exploration of a novel environment and of the arousal associated with the acquisition of that novel input.

Other students of behavior have treated this and other behaviors differently. For example, in the context of the open field test (1), in which a mouse is forced to explore a novel empty arena, the measures that are mostly used by behavior geneticists and pharmacologists to quantify the behavior are Cumulative Distance Traveled and Percent Time spent in the Center by the animal. The first estimates the animal's level of activity and the second is presumed to estimate its level of anxiety. The use of these measures reflects the assumption that moment-by-moment open field behavior is largely stochastic (Fig. 1) and that these measures are informative only when aggregated over the entire session. Neither measure provides insight into the generative process that shapes the behavior as it is being emitted.

Fig. 1.

Path plot of a selected 30-min mouse session of forced exploration.

A quantifiable representation that captures the generative process is preferable, because it is likely to correspond to neurophysiologic mechanisms that mediate the behavior, and, as we will show, is likely to expose functional aspects of the behavior. To expose this generative process, we use a setup that consists of a home cage from which a mouse is allowed to explore a large circular arena for an extended period at a rate regulated by itself (Dimensionality Emergence Assay; Materials and Methods). This setup allows a gradual, stretched-out growth, exposing the elementary building blocks of behavior as they are progressively added to the animal's repertoire, indicating kinematic quantities that appear to be actively managed by the animal (2).

Having access to technology that allows us to track and record a time series of locations occupied by a mouse during free exploration, and having developed analytical methods for quantifying continuous kinematic variables (https://www.tau.ac.il/~ilan99/see/help/), we segment the path, based on intrinsic statistical and geometrical properties, into processes involving approach and avoidance: repetitive peep and hide motions from the home cage into the arena, repetitive cross and retreat motions performed across the doorway, repetitive outbound–inbound movement along the wall, and repetitive incursions from the wall toward the center of the arena and back to the wall. All these are examples of sequences of repeated motion. These motions are performed in relation to specific reference values from which motion commences and to which it returns. We further identify growth of behavior that is manifested through a build up in the extent of each of these motion types separately and an increase in complexity through the recruitment of additional sequences of repeated motion that are superimposed on previously emerged sequences of repeated motion.

As a new sequence of repeated motion appears, the previous sequences do not necessarily disappear but continue to be embedded in the ongoing behavior, contributing to its richness and complexity. For example, increasingly longer roundtrips are performed in a mixture with short roundtrips. Our analytical method allows us to trace the growth in the extent of the “envelope” of the time series, traced by the longer roundtrips, without letting older ongoing sequences of short roundtrips obscure the growth, and without obscuring these previously identified “older” sequences.

In this report we review previous work (notably refs. 2, 3), and present results demonstrating that free mouse exploration is a sequence of sequences of repeated motion with quantifiable buildup in extent and complexity. These results are presented both for their own sake and to illustrate our approach to the quantification of behavior. Our methodology has wider implications for measuring behavior, regarding what could be quantified, how it may be quantified, and the inextricable relationship between the how and the what.

Background

Evidence for a Buildup in Extent in Inherited Motor Patterns.

Studies of behavior growth processes on a moment-by-moment time scale were already performed in the early days of ethology, as its founders studied the morphogenesis of inherited motor coordinations [also termed “instincts” or “innate behavior” (4, 5)].

The classical ethologists referred to behavior dynamics at a moment-by-moment time scale as actual genesis to distinguish it from ontogeny and phylogeny time scales. They noted that the actual genesis of these patterns involved a progressive buildup in extent and in complexity. An undisturbed hawk, for example, “takes off spontaneously by first performing aiming movements with its head and neck, then treading alternately on one foot and then the other, then crouching in preparation for jumping off and even half opening its wings, and only then (combining all components by) taking flight” (5). Similarly, in cichlid fish, agonistic behavior starts with barely noticeable “intention movements,” proceeds to several motor patterns that are performed in precisely the same order, and culminates with full-intensity fighting. In the vast majority of cases, “the higher stage of intensity is reliably predicted by the preceding step… Intention movements forecasting the next higher intensity patterns are performed in a mixture with lower-intensity patterns” (6, 7). This and other sequences of inherited patterns thus share (i) an “almost absolute predictability” (5) of the order in which late components are added on top of earlier ones and (ii) a progressive increase in amplitude and a gradual buildup to full-blown behavior.

The early ethologists had no access to instruments capable of measuring high-speed time-series phenomena, let alone being capable of analyzing the huge amount of data generated by such techniques. As a consequence, they were confined to counting and sequencing ad hoc “fixed action patterns”—monolithic units—such as “pointing with head and neck,” “treading with feet,” and “crouching” as their basic behavior units.

The use of predetermined behavior patterns that were established on the basis of a claim for expertise was a mixed blessing: On the one hand, they provided a first approximation description of many behaviors by experts in the field, allowing comparative scoring of frequencies of loosely defined patterns across closely related species (8). On the other hand, in the vast majority of cases, specific performances of such behavior patterns were shown to be “modal” rather than fixed, involving a variable number of parts of the body that moved in relation to each other with variable speeds and variable phase relations (9). That is, the opinion of the experts was subjective, which may be viewed as an advantage and a disadvantage, depending on one's scientific “agenda.” In addition, as locomotor movements are performed in specific spatial directions, they disclose critical information with regard to the animal's momentary emotional state, its direction of attention and its intention; this information was lost irrevocably in the ad hoc classification process, yielding representations that were relatively uninformative and idiosyncratic to particular species, situations, and observers, and preventing quantifiable comparisons across wider systematic groups or diverse pharmacological treatments (3). Neither interobserver reliability nor a computational follow-up of this classification process by a neural network trained by a skilled human observer (e.g., ref. 10), can compensate for the associated loss of information.

The paucity of low-level descriptions of free whole-animal behavior led to the dwindling of the study of the actual genesis of behavior over the years, except in the study of bird song, in which it flourishes to this day as a result of the availability of low-level descriptors such as frequencies, amplitude, and pitch (Tchernichovski and Lipkind, ref. 11).

Evidence for Buildup and Shut Down in Mobility in Mammals.

A more recent round of descriptions reporting a buildup in extent and complexity has been presented in a series of studies on vertebrate behavior at the level of interlimb coordination (12, 13). These studies, involving a representation of movements of the parts of the body within a polar coordinate system of reference (14, 15), described a mobility gradient involving a progressive addition of degrees of freedom to the animal's movement in autocentric space and a gradual increase in amplitude within each degree of freedom during the transition from immobility to mobility. Within it, the animal first exercises a single spatial dimension by side-to-side movements and pivoting in place, then it adds a second spatial dimension by moving forward, and finally it adds to its repertoire a vertical dimension by head-raising and rearing. The parts of the body are recruited cephalocaudally along each of these dimensions separately, thereby increasing the complexity and extent of the behavior. Under the influence of psychoactive drugs, the progressive motor expansion that unfolds during exploratory behavior (i.e., warmup) reverts into progressive motor constriction in terms of both extent and complexity [i.e., shutdown (16)].

A gradual increase in extent and complexity is a fundamental property of many developmental histories of so-called instincts. Although in the present study we measure quantitatively these growth processes in mouse exploration, our methodology and results pertain to a wide class of behaviors that have a strong innate component and substantial heritability.

Evidence for Sequences of Repeated Motion Away from and Back to Specific Reference Values.

Another fundamental property of behavior addressed in the present study is that motion is often performed in relation to specific reference values from which motion commences and to which it returns. It has been demonstrated that, in many species including man, exploratory behavior consists of roundtrips performed from a reference location termed home base (17–19). Early in the exploration, motion away from the home base is slow and intermittent and motion back is continuous and fast (20), and in rats the probability of returning home increases after each stop (21, 22), revealing that the home base acts both as a reference location and an attractor. At the daily time scale of visits to the same environment, new home bases are progressively formed at larger distances from the original home base, and visits in later days involve a transition across the sequentially positioned reference places in the order in which they were formed (23).

The arena wall, like the home base, acts as a reference and attractor during forays into the center of the arena: in several mouse strains, motion away from the wall is slower than motion toward it (24). Whereas sighted mice move faster toward the wall than away from it, blind mice use similar speeds in both directions (25).

Repeated motion away from and back to a reference location is not limited to exploratory behavior. In drawing parallels between rodent exploration and a human newborn's spontaneous hand and leg movements in supine position, it was pointed out that several preferred static configurations of the limbs are used as reference positions for spontaneous reaching and kicking behavior (26, 27). In addition, the formation of transient temporally associated and sequentially positioned reference positions is common to both the exploratory process and the spontaneous limb movements of the newborn (23, 26). The parallels suggest a general principle of the organization of movement.

Results

Mouse Exploratory Behavior Is Composed of Sequences of Repeated Motion.

To obtain a perspective on the developmental dynamics of open field behavior, we designed a setup in which behavior unfolds gradually: a doorway opens from the mouse's home cage into a large circular arena, allowing the mouse to explore it deliberately for an extended period (Materials and Methods). The gradual exploration process allows us to identify natural growth processes we call “sequences of repeated motion,” which we characterize and quantify algorithmically by using three low-level elements: (i) the reference value(s) from which motions depart and to which they return, (ii) the motions' buildup in extent, and (iii) the motions' buildup in complexity. Here we demonstrate how we identify and define some of the motions’ reference values, how we identify repeated motions, and how nonmonotone growth can be quantified. Along the way we compare the behavior of the neophobic BALB/c strain (28) to that of the commonly used C57BL/6 strain and discuss the role of such comparisons. Finally, we put quantification in a wider perspective by returning to the meaning of what it is that we quantify.

Defining Motions: The Peep and Hide Motion.

A session of free exploration commences with peeping into the arena in both BALB/c and C57BL/6 mice, in which the mouse crosses the doorway into the arena, always leaving part of its body behind the doorway, and retreats back (Movie S1). We use this as a simple example of the parsing of a location time series of recorded behavior into a sequence of repeated peep and hide motions, and of measuring their extent. The shaded part of Fig. 2 displays the time series of the proportion of the body of the mouse that extends into the arena as measured in each frame. The point just behind the doorway (where the mouse is invisible) serves as the reference for this motion, and the mouse's presence is easily detected in the time series by a body area outside value of zero followed by a nonzero value a frame later. The time series of the proportion of body area is thus parsed by runs of zeroes into the separate peep and hide motions (vertical lines). Each such motion has many measurable attributes, such as duration and speed of exit. The maximal proportion of body area in the arena throughout the motion (full circles) serves as a measure of the extent, resulting in a sequence of peep and hide motions and their measured extent. By considering the motions one after the other, in their order of performance, time is essentially rescaled by activity.

Fig. 2.

The proportion of mouse body area extending into the arena as a function of time. The vertical lines that follow runs of zeroes, where the mouse is entirely out of the arena, parse the time series into separate peep and hide motions. The maximal proportion of body extending into the arena throughout a motion is recorded as the extent of the peep and hide motion.

Even from this short example, recorded at the beginning of exploration, it is evident that the extent of the motion grows. It is important to note that, although such motions appear frequently in the beginning, they may be performed throughout the session.

Buildup in Extent in Sequences of Borderline Roundtrips.

In both strains, the peep and hide sequence is followed by other sequences of motion that define an origin of axes for subsequent movement in the arena. BALB/c mice perform cross and retreat, circle in place, and entry head on, and rarely, extended garden roundtrip, before commencing with the borderline roundtrip motion sequence. C57BL/6 mice tend to skip the cross and retreat sequence and add the extended garden roundtrip (2). At this stage, both strains commence with borderline roundtrips, but whereas BALB/c mice tend to move strictly near and along the wall until the exhaustion of the borderline dimension, C57BL/6 mice start with movement along and near the wall and then, being less “wall huggers” than the BALB/c mice, include a radial component in the roundtrip that nevertheless tends to proceed along the wall (2). In both strains, the mouse proceeds from a reference area near the doorway that we term the garden, first away and then back into the garden (Movies S2 and S3). Although defining algorithmically the reference point for the peep and hide motion was quite obvious, its definition was more complicated for other repeated motions. We demonstrate one such case subsequently with the definition of the reference for Borderline Roundtrips.

Identifying the reference values: the garden and its boundary.

As the session progresses, the mouse may skip entering the cage, stopping by the doorway before commencing with a new borderline roundtrip. A contour plot of the density of cumulative dwell time defines algorithmically a garden in the proximity of the doorway. This garden in turn serves as the reference location from which borderline roundtrips commence and where they often end (Fig. S1).

Quantifying the buildup in extent in sequences of borderline roundtrips.

When the reference location has been defined and sequences of borderline roundtrips identified, the extent of each roundtrip is measured by the maximal circular arc covered by the mouse in that roundtrip. In the beginning, this arc tends to increase across roundtrips, first when performed in one direction and then in the other. Fig. 3 shows examples for one C57BL/6 and one BALB/c mouse.

Fig. 3.

Two selected examples of sequences of repeated borderline roundtrips leading to the occupancy of the entire circumference of the arena. Upper: The first 27 roundtrips of a selected C57BL/6 mouse session. Lower: The first 57 roundtrips of a selected BALB/c mouse session. Doorway is located at 6 o'clock. Yellow to red indicates roundtrip's direction, gray represents path history, blue represents arena wall.

The quantification of the buildup in maximal amplitude of borderline roundtrips is not a simple task, as the growth is not monotone. It is achieved by first estimating a smoothed high percentile (e.g., 90%) of the percent of the circle covered for each roundtrip of the mouse, and then calculating the ordinal number of roundtrips it took (i.e., “time”) to reach some threshold (e.g., 20% of the circle perimeter) and the rate of growth at that threshold. The process is explained and demonstrated in Fig. 4.

Fig. 4.

Quantifying the buildup in angular amplitude during successive borderline roundtrips in the main direction of the mouse's exploration. A 10-roundtrip-long window is being moved along the roundtrip ordinal number, with an 80% window overlap, and the 90th percentile in each window is estimated (full green circles). A threshold is chosen (20%, horizontal line), and the point where the LOESS-smoothed percentile function (smooth line in red) reaches the prescribed threshold is calculated, determining both the time to reach the threshold (in terms of number of borderline roundtrips; vertical line) and the rate estimated by the slope of the smoothed percentile function there (in terms of percent of full circle per roundtrip; blue line).

Comparing buildup in borderline roundtrips between strains.

Fig. 5 presents a quantitative comparison of buildup in maximal angular amplitude reached during successive borderline roundtrips in the two strains. Their times to reach the threshold and their growth rates there are compared between the strains. The differences are both large and highly statistically significant (the two groups are almost entirely separated), showing that the growth rates were higher for C57BL/6 than for BALB/c (P = 0.00046), and the time to threshold was longer for BALB/c (P = 0.049).

Fig. 5.

Quantitative comparison of the rate of growth of the maximal angular amplitude reached during successive borderline roundtrips in the two strains. Left: Smoothed percentile functions for all mice (pink for C57BL/6, blue for BALB/c) and the 20% threshold used (horizontal line). Upper Right: Box plots comparing the growth rates of the mice in the two groups (rates are measured as additional percent of circle covered per roundtrip). Lower Right: Box plots comparing the time to reach the threshold of the mice in the two groups (time is measured in terms of roundtrips performed). P values are for the significance of the difference in magnitude between the two strains by using Wilcoxon test.

Other thresholds could be used, such as 30% and 40%, which are reported in Figs. S2 and S3. The choice of 20% yields the best discrimination of the three, and this is an important aspect directing the choice. It is here that a second aspect—the replicability across laboratories—should enter the decision, and this should be finalized only after the experiment is repeated in other laboratories (Discussion).

Comparing the Growth in the Primary and Secondary Directions.

A similar analysis was conducted on the secondary direction of borderline roundtrips (Fig. S4). Again, time to threshold was longer for BALB/c, but there was no difference in rate (P = 0.015 and P = 0.8, respectively). The explanation is that, for both strains, time to threshold increased (BALB/c, P = 0.0005; C57BL/6, P = 0.012), although for the BALB/c mice, the rate increased from the main to the secondary direction (P = 0.00098) whereas for the C57BL/6 mice it hardly changed (P = 0.49).

The results indicate that the C57BL/6 mice explore both directions in a similar way, not being committed to a main one first, whereas the BALB/c mice first explore slowly one main direction, then turn to the second direction, exploring it faster.

Buildup in Extent and Complexity in Sequences of Incursions.

The behavior along the border is essentially one-dimensional (24). Incursions are forays into the center that start and end near the wall, and their addition to the mouse's repertoire transforms linear into planar movement. In both strains, the mouse proceeds from a reference area near the wall that we term the wall-ring, first away from the wall-ring and then back to it (Movie S4).

Identifying the reference values: The wall-ring and its boundary.

A density plot of the cumulative dwell time, studied as a function of the distance from the wall (Fig. 6 and Fig. S5), highlights a Gaussian component in the proximity of the wall. The Gaussian component (Fig. S5B) represents a cross section of a wall-ring extending along the arena circumference. Its boundary defines the thickness of the wall-ring, whose width is mouse-specific, exhibiting strain differences.

Fig. 6.

Quantitative comparison of the rate of growth of the maximal distance from the wall reached during successive incursions between strains. Left: Smoothed percentile functions for all mice (pink for C57BL/6, blue for BALB/c) and the 20% threshold used (horizontal line). Upper Right: Box plots comparing the rates of growth of the mice in the two groups (measured as additional percent of radius covered per roundtrip). Lower Right: Box plots comparing the time to reach the threshold of the mice in the two groups (measured in incursions). P values are for the significance of the difference in magnitude between the two strains by using Wilcoxon test.

Quantifying the buildup in extent in sequences of incursions.

During a sequence of incursions, the maximal distance from the wall and the arc of the circle lying between the start and the end of each incursion tend to increase across performances (Movie S4). Fig. 6 presents a quantitative comparison of buildup in the maximal distance from the wall reached during successive incursions in the two strains. Both their times to reach the threshold (20%) and their growth rates there are compared between the strains. The differences are both large and highly statistically significant, even more so than for the borderline roundtrips, showing that the growth rates are higher for C57BL/6 than for BALB/c mice (P = 0.00021), and the time to threshold is longer for BALB/c mice (P = 0.00001). For other thresholds, see Figs. S6 and S7.

Quantifying the buildup in complexity in sequences of incursions.

In both strains, all early incursions consist of a single center-bound segment and a single wall-bound segment. With repeated performance, the wall-bound segment is interrupted by a reversal in direction, as the mouse turns around and again moves in a center-bound direction, which is again followed by a second wall-bound direction. We call the first wall-bound segment together with the second center-bound segment a wall-related shuttle. The time to the first wall-related shuttle (in incursions) is 87.3 (68.1) incursions for BALB/c and 41.4 (19.6) for C57BL (P = 0.017).

Mouse Exploratory Behavior Is Composed of a Sequence of Sequences of Repeated Motion.

The selected sequences of repeated motion that are quantified in this report belong to a list of 13 types of sequences of repeated motion exposed so far in mouse free exploration (2). Starting with a sequence of peep and hide, new sequences are progressively added on top of each other, generating increasingly richer and more complex behavior (Fig. 7).

Fig. 7.

Four successive intervals of free exploratory behavior in a novel arena of a selected BALB/c mouse. A sequence of motion types, each represented by a distinct color within the top horizontal line, is composed of sequences of repeated motion, each represented within an especially dedicated horizontal line. As shown, the sequences emerge successively in a prescribed order. The sequence of sequences is represented in the bottom horizontal line by the first performance of each of the landmark motion types.

The original, “raw” sequence of motions of a selected BALB/c mouse is presented in the top horizontal line in Fig. 7. This raw sequence is algorithmically screened for the different types of motion, yielding multiple sequences of repeated motion, each sequence presented within a horizontal line in Fig. 7, in the order in which its motions emerged. In the first four sequences, the mouse maps its zero-dimensional location of entry into the arena, in the next four it maps the one-dimensional border of the arena, in the next three it maps the (entire) 2D arena, and in the last sequence of repeated motion it attends to the third dimension (this particular BALB/c mouse performed only 12 sequences of repeated motion).

The first occurrence of a new type of motion heralds its repeated performance in the immediate period that follows. The first performance of a new type of motion is identified by us as a landmark. The bottom line in Fig. 7 represents the sequence of landmarks in the proper order and time of their occurrence.

Discussion

Sequences of Repeated Motion.

The formalization of a mouse's exploratory behavior as a sequence of sequences of repeated motion with quantifiable reference values, quantifiable growth rates in extent, and quantifiable growth rates in complexity appears to apply to a large number of developmental histories of so-called instincts—complex inherited motor patterns that were discovered during the early days of ethology (5). The iterative cycle of approach and withdrawal, the tendency for an incremental growth from one cycle to the next, the gradual addition of new reference locations that are positioned progressively closer to the interface with the yet-unexplored terrain, all the while reiterating motions in relation to the older reference places, all point to a general principle of organization of behavior, a principle that is orthogonal to a strategy involving the performance of a straight path or direct action toward a final goal lacking the component of repetitive action (29).

Iterative performance associated with buildup is a basic attribute in learning processes, and in the manifestation of inherited behavior (30–32) including inherited tool-using skills, in which early iterations involve the manipulation of objects in ways that anticipate future functional movements before the animals are skilled enough to reap any objective rewards from this behavior (5, 33). In being common to maturational and learning processes, iterative performance with buildup does not distinguish in and of itself between neural maturation and learning (5). However, the differential growth rates of specific types of motion within sequences and the different number of iterations preceding the attainment of a criterion could perhaps reflect differential learning and information processing capacities of different strains, treatments, and preparations, setting the ground for a study of the allometry of behavior (2).

Dimensionality of Growth Process.

In all sequences of repeated motion studied so far, the growth is faster and steeper in C57BL/6 mice than in BALB/c mice. Following the estimation of growth rate for all types of sequences, it would be interesting to study the correlation structure between them within individuals and across strains.

In a study along such lines of forced open-field behavior that used 25 different measures in eight inbred strains of mice across three laboratories, and involving standardized housing and experimental conditions (34), it was found that the two traditional measures discussed above, distance traveled and center time, accounted for only 7% of the variance (3). Can the measures of buildup of the different processes be captured by a few parameters, indicating thereby that the growth of arena occupancy is controlled by very few mediating mechanisms, or are the measures of growth controlled by multiple mediating mechanisms? For example, is a strain that is neophobic along borders also neophobic with regard to center occupancy?

Need for Experimental Validation of Hypothetical Motivational and Cognitive Underlying Mechanisms.

As this and a previous study (2) focus on observables, it would be useful to examine experimentally at least two hypotheses that stem from the observed behavior and concern motivational and cognitive mechanisms underlying it.

First, the periodic return to the home cage is suggestive of a perceptual input cutoff mechanism (35), whereby after being exposed to a given amount of novel environmental input, the mouse appears to rush back home to cut off the novel input. Hence, the incremental growth between two successive roundtrips reflects the amount of input the mouse can take in before having to cut it off by returning home. It follows that a mouse having a low capacity for novel input, or, for that matter, lower information processing capacity, would cover smaller stretches of new terrain than a mouse with a higher capacity. It is therefore expected that low input capacity mice (e.g., mice who are highly aroused) would have gentler growth curve slopes than mice with high input capacity (e.g., mice that are experiencing low arousal).

Second, faced with the challenge of mapping a novel environment, periodic return to the home cage may reflect the need to parse environmental input into manageable chunks collected during a roundtrip. An animal with a lower information processing capacity would correspondingly be expected to parse the novel input into smaller chunks (such as BALB/c mice) than an animal with a higher information processing capacity (such as, perhaps, C57BL/6 mice).

Taken together, these two hypotheses expose two presumed functions indicated by our analysis of free mouse exploration: (i) active management of the arousal associated with the acquisition of the novel input and (ii) active management of dimension-specific perceptual input acquired during the exploration of a novel environment. Regardless of the validity of these two hypotheses, our results beg for experimental manipulations that would modify the magnitude of the incremental input managed by the animal.

Inextricable Relationship Between the What and the How.

The problem of what to quantify in a behavior and its inextricable relationship to how it is quantified can be illustrated in the quantification of incursions: incursions are forays performed by the animal from the proximity of the wall into the arena and back to the wall.

Quantification reveals that incursions are a sequence of repeated motion, performed relative to a functionally defined reference value (the wall ring): they are (i) actively managed by the animal and (ii) show discriminability across strains (Quantifying the buildup in extent in sequences of incursions).

The fact that exploring the second dimension of the arena is accomplished via sequences of repeated incursions that commence after a buildup in the exploration of the borderline dimension (Movie S5) and before the emergence of vertical movement (i.e., jumps), and that incursions’ maximal distance from the wall increases with regularity along time (scaled by activity), support the active management hypothesis.

Discriminability across strains is supported by the facts that incursions’ timing to reach a threshold, rate of growth, and emergence of first wall-related shuttle all discriminate between strains (Quantifying the buildup in extent in sequences of incursions and Quantifying the buildup in complexity in sequences of incursions).

We previously added yet another demand for a good quantitative description (3, 34): that of replicability across laboratories. This is an expectation that the measure will remain discriminative when the behavior is measured in different laboratories.

Our current study of free exploration is a single laboratory experiment, so we turn to explain this point by using interstrain differences in the number of incursions per session as analyzed in forced exploration (24), wherein experiments were performed simultaneously in three laboratories according to a standardized experimental and housing protocol (Materials and Methods and SI Materials and Methods). The demand for replicability of the strain difference in the number of incursions per session across laboratories (captured by the mixed-model analysis in ref. 34) revealed that the strain difference was no longer significant (P > 0.08; upper left in Fig. S8), which deemed this measure of little value.

A second round of analysis revealed, however, that the aggregate of all incursions is a mixture consisting of three relatively distinct incursion types (Fig. 8). Ignoring the “near wall” incursion type, for which the strain differences were found to be nonreplicable across laboratories (P = 0.28), leaves us with two distinct incursion types. Measuring their number per session, both strain differences were replicable indeed: P = 0.03 for intermediate incursions and P = 0.01 for arena-cross ones (Fig. S8).

Fig. 8.

(A) Black: Density plot of the distribution of the maximal distances from wall of center segments (log-transformed) in a single C57BL/6J session. Red: Three Gaussian functions fitted to the distribution by the EM algorithm. The intersection points between the Gaussians serve as cutoff values for dividing all incursions performed in this session into three types. (B) Path plots of the incursions belonging to each type. (Used with permission from ref. 24).

This type of analysis thus illustrates our approach to the design of improved measures for the quantification of behavior. An aspect of behavior is worth quantifying if its quantification supports the hypothesis that it is actively managed by the animal, indicating functionality in the animal's own umwelt (36). A specific quantification is useful if it has discriminative power (e.g., across strains and treatments) and it is replicable across laboratories. The use of these criteria jointly may require a search through many candidate measures, but it can guide the design of better ways to describe and quantify behavior.

Materials and Methods

Animals, Experimental Setup, and Testing Protocol and Analysis.

Keeping one animal per cage in the BALB/c experiment and three in the C57BL/6 experiment reflects their respective phenotypes: whereas keeping the BALB/c mice in a group implied aggression-induced stress because of their high aggression, isolating the C57BL/6 mice implied separation-induced stress. Confronting this dilemma, we decided to reduce stress before the experiment by housing each of the strains in conditions optimal for it. Animals of both strains were, however, kept singly in the home cage attached to the arena in the 24 h preceding the opening of the door to the arena. The two strains were tested at different times. Details on this and other aspects are provided in SI Materials and Methods.

In the forced exploration experiment reported in Inextricable Relationship Between the What and the How, we used BALB/cByJ mice, known for their diminished aggression in comparison with the BALB/c mice (37), and housing and experimental conditions were accordingly standardized (SI Materials and Methods).

Statistical Methods.

The growth in the extent of a measure of motion is estimated by a modification of the algorithm in Sakov et al. (38), where a high percentile (quantile) is estimated within the window, and the window is moving along and its dependence on (transformed) time is estimated by using the robust smoothing algorithm of Cleveland known as LOESS (with the “symmetric” option) or LOWESS (locally weighted scatterplot smoothing), in different applications of the R program (39). The differences from that algorithm are that the windows are overlapping, and the window value is identified with the last point of the window. The starting values were padded with six zeroes.

Significance of strain differences in a single laboratory are assessed by using the Wilcoxon rank-sum or signed-rank test as appropriate. Significance of strain differences involving multiple laboratories are assessed by using a mixed-model ANOVA with laboratory as a random factor after an appropriate transformation to approximate Gaussianity.