experimentally simulated shortcutting behav-
ior by translocation experiments. Unlike trans-
locations to far-off unfamiliar areas—aimed
to examine map-and-compass navigation—we
translocated bats to the periphery of the focal
population’s foraging area (Fig. 3B), yet
within detection range of their familiar area
as required for testing cognitive map–based
navigation ( 5 , 18 ). As predicted, all 22 trans-
located bats returned to their regular forag-
ing area immediately after release, in tracks that
did not differ significantly in straightness and
in turning angle and heading distributions
from all other tracks, including the subsequent
ones made by the same bats (Fig. 3C). Return
flights very likely represent novel shortcuts be-
cause these release sites were rarely or never
visited by any of the tracked bats of the focal
population over the 4 years of our study.
We further investigated the bats’naviga-
tional process by applying time-lag embed-
ding ( 19 ), a well-established method in dynamic
systems theory for characterizing mechanical,
physical, and mathematical systems [e.g., ( 20 )]
but also biological ones ( 21 ) using only the
recorded time series and requiring no a priori
knowledge of the underlying system ( 15 ). We
determined both the correlation dimension
( 19 , 22 ), a measure of the system’s number of
degrees of freedom, and the largest Lyapunov
exponent ( 23 ), measuring the system’s degree
of determinism or predictability. In animal
navigation, degrees of freedom indicate the
number of independent sensory modalities
involved in the navigational process ( 24 ), much
like the number of sensors or inputs necessary
for a robot to navigate ( 20 ). The correlation di-
mension thus indicates the type of navigation
strategy applied: Point-like information used in
beaconing or piloting offers only one degree of
freedom, hence is expected to result in a cor-
relation dimension of 1. By contrast, map-based
navigation requires multiple cues and therefore
higher dimensionality; hence, we predicted
a larger correlation dimension for the tracks
made by the bats ( 15 ).
The mean correlation dimension estimated
for the 1-Hz tracks ranged from 4.91 to 5.02
(Fig. 4A), suggesting a high-dimensional navi-
gation process involving at least five indepen-
dent navigational factors. The mean largest
Lyapunov exponent ranged from 0.028 to 0.034
(Fig. 4B), suggesting that the same chaotic-
deterministic process is in control throughout
the entire track. This is similar to the process
observed in homing pigeons, although here it
appears to have one additional degree of free-
dom ( 24 ). Repeating these analyses for lower-
resolution (0.5 to 0.125 Hz) tracks revealed very
similar results (tables S4 and S5).
Taken together, the very high correlation di-
mension and very low largest Lyapunov expo-
nent, along with shortcutting and characteristic
goal-directed movements, are strongly consist-
ent with cognitive map–based navigation; yet,
we took additional approaches to examine the
explanatory power of simpler point-like navi-
gational processes ( 1 , 15 , 18 ). If bats were pi-
loting, we expect strict movements consistent
with following a set of local landmarks. Thus,
when revisiting a target from multiple origins
located in different directions, piloting should
result in approach paths converging along a
certain line of landmarks leading to the target,
hence high directionality of arrival headings
( 25 ). By contrast, the same scenario under cog-
nitive map navigation is predicted to allow for
flexible approach paths, as was the case here:
Approach paths from multiple uniformly dis-
tributed origins were flexible, with 91% of arrival
headings having uniform rather than direc-
tional circular distribution ( 15 ) (Fig. 2E and
fig. S1). Furthermore, despite their strong pref-
erence to return to the same cave that they
emerged from (87% of nights), the bats did not
follow the reverse sequence of trees going
back to the cave in 91% of the nights in which
≥2 trees were visited. Such high flexibilities in
goal-oriented movement do not fit predictions
for piloting (or other models denoted as route-
based navigation or topological map).
Beaconing to a specific goal-emanating cue
was also unlikely, given the distribution of all
fruit trees in the study area ( 15 ) (probability of
a specific tree serving as beacon: 0.008; fig. S2)
and—for olfactory beaconing—the local wind
characteristics (fig. S3). An olfactory-based map
navigation, similar to that suggested for pi-
geons and other birds ( 2 , 26 ), is also unlikely for
the foraging fruit bats. The currently accepted
paradigm for pigeon olfaction navigation ne-
cessitates remembering ratios of atmospheric
trace compounds at the location of one goal—
their home—and how these ratios change with
wind direction and distance from that goal
( 2 , 26 ). Although each bat generally exhibited
high fidelity to a small number of specific
trees, they do track seasonal changes in fruit-ing and visit many other trees for much shorter
durations (some for just a few minutes) (fig.
S4). Under this model, foraging fruit bats must
therefore remember the specific ratios of nu-
merous goals, on the order of hundreds (fig.
S4), which seems an unlikely memory load.
Nevertheless, although olfactory-based navi-
gation is unlikely, experiments manipulating
the olfactory sense ( 26 ) are required to assess its
role in routine foraging navigation of fruit bats.
Path integration, the only mechanism other
than a cognitive map that allows for short-
cuts, was also ruled out by several lines of
evidence. First, observed trajectories failed to
meet theoretical and empirical predictions ( 15 ),
as return track straightness correlated neither
with outbound straightness (Spearman’s rho =
−0.04,P= 0.31) nor with total excursion length
(Spearman’s rho = 0.10,P= 0.49). Second, in
13% of all nights, a bat returned to a different
cave than the one it emerged from, 6.9 ± 5.5 km
away from its cave of origin. In many of these
cases, the bat returned to its previous cave only
after several nights. Such a feat cannot be ac-
complished using only path integration.
This study reports research results based on
data from the new wildlife tracking ATLAS sys-
tem ( 13 , 14 ). The system’s distinctive features—
real-time high-resolution movement tracking
of many small animals simultaneously for
relatively long durations at low costs—revealed
pervasive empirical evidence for cognitive
map–based navigation in wild Egyptian fruit
bats. ATLAS’main shortcomings—relatively
high installation costs and limited spatial cov-
erage compared to GPS—are less important
once a fully operational ATLAS system is estab-
lished (usually within several months), and in
cases where most of the range relevant for the
study population (here ~35 km by 25 km) can
be covered by the system. Notably, by having
smaller tags, ATLAS expands the range of track-
able mammals and birds from 30 to 35% for
the smallest currently commercially available192 10 JULY 2020•VOL 369 ISSUE 6500 sciencemag.org SCIENCE
Probability18%
16%
14%
12%
10%
8%
6%
4%
2%
0%
Correlation dimensionProbability18%
16%
14%
12%
10%
8%
6%
4%
2%
0%
Largest Lyapunov exponent246 8 0.02 0.04 0.06 0.08 0.1Unvalidated
Validated
Overlapping barsUnvalidated
Validated
Overlapping barsA BFig.4. Time-lag embedding analyses.Probability histograms for 1-Hz data before (light blue) and
after (orange) a validation procedure to compensate for undersampling ( 15 ). Dark blue areas are estimates
overlapping among the two categories. (A) Correlation dimension estimates. (B) Largest Lyapunov
exponent estimates.RESEARCH | REPORTS