Quantifying the buildup in extent and complexity of
free exploration in mice
Yoav Benjaminia, Ehud Foniob, Tal Galilia, Gregor Z. Havkinc, and Ilan Golanid,1
a
Department of Statistics and Operations Research, Tel Aviv University, Tel Aviv 69978, Israel; bDepartment of Neurobiology, Weizmann Institute of Science,
Rehovot 76100, Israel; cPrinceton Biometrics, Princeton, NJ 08540; and dDepartment of Zoology, Tel Aviv University, Tel Aviv 69978, Israel
Edited by Donald W. Pfaff, The Rockefeller University, New York, NY, and approved January 3, 2011 (received for review October 4, 2010)
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.
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Dimensionality Emergence Assay dynamics of behavior open field test
phenotyping mouse behavior sequences of repeated motion
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ne 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.
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 stawww.pnas.org/cgi/doi/10.1073/pnas.1014837108
tistical 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
This paper results from the Arthur M. Sackler Colloquium of the National Academy of
Sciences, “Quantification of Behavior” held June 11–13, 2010, at the AAAS Building in
Washington, DC. The complete program and audio files of most presentations are available
on the NAS Web site at www.nasonline.org/quantification.
Author contributions: Y.B., E.F., and I.G. designed research; E.F., G.Z.H., and I.G. performed research; Y.B. and T.G. contributed new reagents/analytic tools; Y.B., E.F., T.G.,
and G.Z.H. analyzed data; and Y.B., E.F., T.G., G.Z.H., and I.G. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
1
To whom correspondence should be addressed. E-mail: [email protected].
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.
1073/pnas.1014837108/-/DCSupplemental.
PNAS Early Edition | 1 of 8
cological 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).
Fig. 1. Path plot of a selected 30-min mouse session of forced exploration.
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 fullblown 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
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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 be-
havior 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
Benjamini et al.
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.
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.
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.
Benjamini et al.
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.
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.
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
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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.
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).
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
Fig. 4. Quantifying the buildup in angular amplitude during successive
borderline roundtrips in the main direction of the mouse’s exploration. A 10roundtrip-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).
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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.
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 wallbound 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
Benjamini et al.
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.
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).
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 pre-
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.
Benjamini et al.
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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.
ceding 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?
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
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
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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).
Benjamini et al.
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 dimensionspecific 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
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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
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Statistical Methods. The growth in the extent of a measure of motion is
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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.
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