ABSTRACT

Mantis shrimp of the species Neogonodactylus oerstedii occupy small burrows in shallow waters throughout the Caribbean. These animals use path integration, a vector-based navigation strategy, to return to their homes while foraging. Here, we report that path integration in N. oerstedii is prone to error accumulated during outward foraging paths and we describe the search behavior that N. oerstedii employs after it fails to locate its home following the route provided by its path integrator. This search behavior forms continuously expanding, non-oriented loops that are centered near the point of search initiation. The radius of this search is scaled to the animal's positional uncertainty during path integration, improving the effectiveness of the search. The search behaviors exhibited by N. oerstedii bear a striking resemblance to search behaviors in other animals, offering potential avenues for the comparative examination of search behaviors and how they are optimized in disparate taxa.

INTRODUCTION

Path integration is an efficient navigational strategy that many animals use to return to a specific location. During path integration, an animal monitors its body orientation and the distance it travels from a reference point using a biological compass and odometer. From this information, a home vector (the most direct path back to the reference point) is continuously updated, allowing the animal to return to its original location (Seyfarth et al., 1982; Müller and Wehner, 1988; Seguinot et al., 1993). Path integration is especially useful for central place foragers, animals which return to a home location between foraging bouts.

Because of small errors made in angular and odometric measurements during path integration, the home vector is prone to error accumulated over the course of an animal's outward path (the path from the animal's start location to the site of home vector initiation). Therefore, with a longer outward path, an increased error of the home vector is expected (Müller and Wehner, 1988; Cheung et al., 2007; Heinze et al., 2018). To account for this error, some path-integrating animals initiate a stereotyped search behavior if they fail to reach their goal after traveling the distance indicated by their path integrator (Wehner and Srinivasan, 1981; Hoffmann, 1983; Zeil, 1998; Durier and Rivault, 1999).

Many stomatopod crustaceans, more commonly known as mantis shrimp, are central place foragers that inhabit benthic marine environments. These animals occupy burrows in marine substrates, where they reside between foraging bouts (Dominguez and Reaka, 1988; Basch and Engle, 1989; Caldwell et al., 1989). Mantis shrimp of the species Neogonodactylus oerstedii employ path integration to efficiently navigate back to their burrows while foraging. During path integration, N. oerstedii exhibit homeward paths that are well oriented and are approximately equal in length to the direct distance from the point where they initiate their return trip to the burrow (Patel and Cronin, 2020). However, the return paths guided by their home vectors often do not lead them directly to their burrows. When this happens, N. oerstedii initiate searches to find their homes (Patel and Cronin, 2020). Here, we investigated the source of the home vector error in N. oerstedii and evaluated the means by which N. oerstedii copes with this error – the strategies that shape its search pattern.

MATERIALS AND METHODS

All data in this study were collected from experiments reported in Patel and Cronin (2020). Specifically, foraging behaviors from the ‘not manipulated’ and ‘animal displaced’ groups of trials enacted in the greenhouse on the University of Maryland Baltimore County (UMBC) campus in Patel and Cronin (2020) were used in the current study.

Animal care

Individual Neogonodactylus oerstedii (Hansen 1895) collected in the Florida Keys, USA, were shipped to UMBC. Animals were housed individually in 30 ppt sea water at room temperature under a 12 h:12 h light:dark cycle. Animals were fed whiteleg shrimp, Litopenaeus vannamei, once per week. Data were collected from 13 individuals (5 male and 8 female). All individuals were between 30 and 50 mm long from the rostrum to the tip of the telson.

Experimental apparatus

Four relatively featureless, circular navigation arenas were constructed from 1.5 m diameter plastic wading pools that were filled with pool filter sand and artificial seawater (30 ppt; Fig. 1A). Arenas were placed in a glass-roofed greenhouse on the UMBC campus. The spectral transmittance of light through the greenhouse glass was nearly constant for all wavelengths, excluding the deep-UV wavelength range (280–350 nm; Fig. S2A). Celestial polarization information was transmitted through the glass roof of the greenhouse (Fig. S2B–D). Vertical burrows created from 2 cm outer-diameter PVC pipes were buried in the sand 30 cm from the periphery of the arena so that they were hidden from view when experimental animals were foraging. Trials were recorded from above using C1 Security Cameras (Foscam Digital Technologies LLC) mounted to tripods placed above the arenas. During animal displacement experiments, a thin 11×82 cm acrylic track with a movable platform was placed 30 cm from the wall of the arena at its closest edge.

Fig. 1.

Error accumulated during outward foraging paths leads to error in the home vector. (A) Navigation arenas, 150 cm in diameter, contained a burrow (empty circle) buried in the base of the arena, 30 cm from the arena's periphery. During trials when animals were not manipulated, food was placed at one of two positions 50 cm from the periphery of the arena (filled circles). Trials were video recorded from above. (B) Example of a foraging path of Neogonodactylus oerstedii. The distance from the point where search behaviors were initiated to the burrow location is the error of the animal's path integrator. (C) Correlation between outward path lengths (log axis) and the path integration error during trials in which the animals were not manipulated (P=0.017, R=0.67, n=12).

Fig. 1.

Error accumulated during outward foraging paths leads to error in the home vector. (A) Navigation arenas, 150 cm in diameter, contained a burrow (empty circle) buried in the base of the arena, 30 cm from the arena's periphery. During trials when animals were not manipulated, food was placed at one of two positions 50 cm from the periphery of the arena (filled circles). Trials were video recorded from above. (B) Example of a foraging path of Neogonodactylus oerstedii. The distance from the point where search behaviors were initiated to the burrow location is the error of the animal's path integrator. (C) Correlation between outward path lengths (log axis) and the path integration error during trials in which the animals were not manipulated (P=0.017, R=0.67, n=12).

Experimental procedures

Individual N. oerstedii were placed in each arena and were allowed to familiarize themselves with the arena for 24 h. During familiarization, a vertical 2 cm diameter PVC column with alternating 1 cm thick black and white horizontal stripes was placed adjacent to the burrow, marking it during the animal’s initial explorations of the arena.

After familiarization, the column marking the burrow was removed from the arena. Empty Margarites sp. snail shells stuffed with pieces of food (whiteleg shrimp) were placed at fixed locations in the arena. During experiments when animals were not manipulated, food was placed at one of two locations, 50 cm from the periphery of the burrow. During experiments in which animals were displaced, food was placed on the movable platform on which animals were translocated. Each animal was allowed three successful foraging excursions (i.e. food placed in the arena was found) before foraging paths were used for analyses. If an individual did not successfully locate food within 1 week in the arena, it was replaced with a new individual.

During experiments when animals were not manipulated, food was placed in the arena between 2 and 3 h after sunrise and removed from the arena following sunset. Animal displacement experiments were run from sunrise to 4 h following sunrise and from 4 h preceding sunset to sunset. During animal displacement experiments, food was removed from the arena during the middle of the day.

During animal displacement experiments, once animals found food placed on the movable platform, they were carefully displaced along the track to a new location in the arena by pulling a thin fishing line tethered to the platform.

Data and statistical analyses

Foraging paths from the burrow to find food and from food locations back to the burrow were video recorded from above. In order to differentiate homeward paths from continued arena exploration, paths from the food locations were considered to be homeward paths when they did not deviate more than 90 deg from their initial trajectories for at least one-third of the beeline distance (the length of the straightest path) from the food location to the burrow. From these homeward paths, search behaviors were determined to be initiated when an animal turned more than 90 deg from its initial trajectory.

Paths were traced at a sampling interval of 0.2 s using the MTrackJ plugin (Meijering et al., 2012) in ImageJ v1.49 (Broken Symmetry Software), from which the output is given in Cartesian coordinates. From these data, the lengths of outbound, homebound and search paths were calculated. The distance of the point of search behavior initiation to the burrow (the path integration error) was also measured using the MTrackJ plugin.

Search behaviors lasting over 10 s with at least one completed loop were analyzed from all trials when animals were not manipulated (n=4) and/or were displaced to a new location in the arena (n=7, n=11 total). We defined a loop in the search as a path that increased in distance from the point of search initiation before the animal turned and moved back toward the search initiation point. The loop was determined to be completed when an animal moved closest to the point of search initiation before once again moving away from the search initiation point or when an animal turned more than 90 deg from its trajectory back towards the search initiation point after returning halfway back to it, whichever occurred first.

The radii of search behaviors were measured as the farthest distance of a search from the original point of search initiation (i.e. the end point of the home vector) using ImageJ. The radii of all searches were measured over three time ranges after search initiation: 0–20 s, 21–60 s and 61–180 s. The radii of individual searches lasting at least 60 s were also measured from the beginning to the end of the search, every 10% of the total search time until the search was completed (up to 10 min). As individuals traveled at different speeds during their searches, search time (in seconds) was multiplied by the individual's mean velocity during the search relative to the search with the highest mean velocity. In order to observe the general expansion pattern of the searches, the radii of searches were normalized by the initial search size (measured at 17 s into the search, the time at which the radius of the most extended search was first measured) and were fitted with a power function. Additionally, orientations of search loops when loops were at the farthest distance from the search initiation point were recorded using ImageJ. For these measurements, searches were oriented so the axis of each home vector preceding the searches was at 0 deg.

All statistical analyses were run on R (v3.3.1, R Core Development Team 2016) with the ‘CircStats’, ‘circular’, ‘plotrix’, ‘Hmisc’ and ‘boot’ plugins. As reported in Patel and Cronin (2020), no significant difference was observed between homeward orientations of males and females during experiments when animals were not manipulated (P>0.5; Fig. S3), so data from the two sexes were pooled for all experiments.

Rayleigh tests of uniformity were used to determine whether all loops within individual searches had a directional bias (Batschelet, 1981). All reported mean values for orientation data are circular means. All circular 95% confidence intervals were calculated by bootstrapping with replacement over 1000 iterations.

An analysis of variance test (ANOVA) was used to determine whether the radii of searches differed between the time intervals measured. A Tukey honest significant difference post hoc analysis was used to determine significant differences between groups.

Pearson's correlation tests were used for all correlative analyses.

RESULTS

Path integration in mantis shrimp is prone to accumulated error

In order to investigate the source of home vector error in N. oerstedii, individuals were placed in relatively featureless circular arenas with a sandy bottom filled with sea water. Vertical pipe burrows were buried in the sand so that they were hidden from view when experimental animals were away. Snail shells stuffed with small pieces of shrimp were placed at one of two fixed locations in the arena. Foraging paths to and from the location of the food were observed.

During these trials, animals would make tortuous paths away from the burrow until they located the food placed in the arena (the outward path). After animals located the food, they often executed a fairly direct homeward path (the home vector) before initiating a search behavior if their home vector did not lead them to the hidden burrow (Fig. 1B). We defined the distance from the point of search behavior initiation to the location of the burrow as the path integration error. We found that this path integration error correlated with outward path length during these trials (P=0.017, r=0.67, n=12; Fig. 1C), suggesting that the error of path integration is an outcome of error accumulated over the course of the mantis shrimps’ outward paths.

Search behaviors in N. oerstedii are stereotyped and flexible depending on error accumulated during path integration

Mantis shrimp execute stereotyped search behaviors when they have traveled the distances indicated by their path integrators without finding their burrows (Fig. 2; Fig. S1 and Movie 1). These search behaviors are composed of loops that start and end near the location where the search is initiated (Fig. 2). We defined a loop in the search as a path that increased in distance from the point of search initiation before the animal turned and moved back toward the search initiation point (Fig. 2D).

Fig. 2.

Search behaviors consist of a series of consecutive loopsof increasing size which start near and return to a central location. (A–C) Examples of search behaviors during trials when animals were displaced before they initiated a home vector (A,B) and when an animal was not displaced (C). Open circles represent the location of the burrow. Filled squares represent the location of search behavior initiation. Asterisks mark the location of the nearest edge of the arena. Lines are colored according to time, as indicated in the key in the bottom left corner. (A) During this trial, the individual carried a food-filled shell during its homeward path and dropped it once it initiated its search behavior (marked by the filled square). This offered an opportunity to observe the strategy behind the search behavior, where consecutive continually increasing concentric loops are made from the location of the initiation of the search behavior until the goal has been found. (B) This animal did not find its burrow until after 8 min of searching so the location of the burrow is not marked in the figure. The full search can be seen in Fig. S1. (D) The same search as in A with search loops color-coded by successive loops according to the key. (E) A heat map of search behaviors complied from all trials in which animals were displaced in the arena (n=7). Shades of gray indicate counts of video frames in which animals moving more than one body-length per second were present at that location. Darker areas represent areas in the arenas where animals spent more time searching. The red circle marks the location of search behavior initiation and the asterisk marks the average nearest edge of the arena. Search behaviors are centered near the point of initiation. The observed deviation of the highest trafficked areas from the exact point of search behavior initiation might have been due to the initiation point's proximity to the border of the arena (marked by an asterisk *). (F) The radii of search behaviors measured at 0–20 s, 21–60 s and 61–180 s after search initiation. Search behaviors widen over time (ANOVA, P=0.0015, F=8.41; 0–20 s, n=11; 21–60 s, n=10; 61–180 s, n=8). Bars represent medians, boxes indicate lower and upper quartiles, and whiskers show sample minima and maxima. Asterisks indicate a significant difference in search radii between groups (**P=0.001).

Fig. 2.

Search behaviors consist of a series of consecutive loopsof increasing size which start near and return to a central location. (A–C) Examples of search behaviors during trials when animals were displaced before they initiated a home vector (A,B) and when an animal was not displaced (C). Open circles represent the location of the burrow. Filled squares represent the location of search behavior initiation. Asterisks mark the location of the nearest edge of the arena. Lines are colored according to time, as indicated in the key in the bottom left corner. (A) During this trial, the individual carried a food-filled shell during its homeward path and dropped it once it initiated its search behavior (marked by the filled square). This offered an opportunity to observe the strategy behind the search behavior, where consecutive continually increasing concentric loops are made from the location of the initiation of the search behavior until the goal has been found. (B) This animal did not find its burrow until after 8 min of searching so the location of the burrow is not marked in the figure. The full search can be seen in Fig. S1. (D) The same search as in A with search loops color-coded by successive loops according to the key. (E) A heat map of search behaviors complied from all trials in which animals were displaced in the arena (n=7). Shades of gray indicate counts of video frames in which animals moving more than one body-length per second were present at that location. Darker areas represent areas in the arenas where animals spent more time searching. The red circle marks the location of search behavior initiation and the asterisk marks the average nearest edge of the arena. Search behaviors are centered near the point of initiation. The observed deviation of the highest trafficked areas from the exact point of search behavior initiation might have been due to the initiation point's proximity to the border of the arena (marked by an asterisk *). (F) The radii of search behaviors measured at 0–20 s, 21–60 s and 61–180 s after search initiation. Search behaviors widen over time (ANOVA, P=0.0015, F=8.41; 0–20 s, n=11; 21–60 s, n=10; 61–180 s, n=8). Bars represent medians, boxes indicate lower and upper quartiles, and whiskers show sample minima and maxima. Asterisks indicate a significant difference in search radii between groups (**P=0.001).

Loops within single searches were not oriented in a mean direction in most individuals (Fig. 3); however, searches in some individuals were biased away from the edge of the arena nearest to the location where the search was initiated (loops were only significantly oriented in 2 of 11 individuals: P=0.03 and P=0.025; Fig. 3; Table S1). These exceptions suggest that N. oerstedii can estimate the position of a goal using local structures (here, the walls of the arena) and use these estimates to alter its searches in some cases.

Fig. 3.

Search loop orientations per individual. Asterisks mark the direction of the nearest edge of the arena. The home vectors preceding the searches are oriented to the top of the plot (towards 0 deg). Arrows in plots represent mean vectors, where arrow angles represent vector angles and arrow lengths represent the strength of orientation (R̄). Dashed lines represent 95% confidence intervals. Means and 95% confidence intervals were only included in plots with significant orientations (AD F2: P=0.03, R̄=0.689; and AD M1: P=0.025, R̄=0.704). Loops appear to be biased away from nearest edge of the arena in these individuals.

Fig. 3.

Search loop orientations per individual. Asterisks mark the direction of the nearest edge of the arena. The home vectors preceding the searches are oriented to the top of the plot (towards 0 deg). Arrows in plots represent mean vectors, where arrow angles represent vector angles and arrow lengths represent the strength of orientation (R̄). Dashed lines represent 95% confidence intervals. Means and 95% confidence intervals were only included in plots with significant orientations (AD F2: P=0.03, R̄=0.689; and AD M1: P=0.025, R̄=0.704). Loops appear to be biased away from nearest edge of the arena in these individuals.

We also measured the radii of searches (the farthest distance of a search from the point of search initiation) within three time ranges (0–20 s, 21–60 s and 61–180 s) and found that searches tend to increase in size over time (ANOVA, P=0.0015, F=8.41; Fig. 2F). As search patterns accumulate error along the course of the search, optimal search theory predicts that the search radius should increase as the square root of the search time, radiusmax=time0.5 (Heinze et al., 2018). Data from desert ant searches (Wehner and Srinivasan, 1981) fitted to power functions match this prediction, where the maximum search radius is proportional to time0.48 (Heinze et al., 2018). We found that mantis shrimp search expansions agree with this prediction, where the exponential factor of time from a fitted power function of the searches we measured that lasted at least 60 s resulted in a maximum radius proportional to time0.43, indicating that mantis shrimp searches expand in a close to optimal manner (Fig. 4A,B).

Fig. 4.

Search behaviors expand similarly to those predicted by optimal search theory and are adjusted in size by positional uncertainty during path integration. (A) The radii of searches that lasted at least 1 min plotted every 10% of the total search time until the search was completed (n=8). As individuals were traveling at different speeds during their searches, search time (in seconds) was multiplied by the individual's mean velocity during the search relative to the search with the highest mean velocity. Colors represent individual searches. Each search was fitted with a power function (lines of corresponding colors). (B) The radii of searches in A normalized by the initial search size (measured at 17 s into the search, the time at which the radius of the most extended search was first measured). The black line is the power function of best fit for all data, resulting in the search expansion pattern, radiusmax=time0.43. Optimal search theory predicts that searches should expand by radiusmax=time0.5. (C) Correlation of the initial radii of search behaviors and positional error during path integration. The sizes of search behaviors were larger when the error in path integration was greater (P=0.018, R=0.79, n=8).

Fig. 4.

Search behaviors expand similarly to those predicted by optimal search theory and are adjusted in size by positional uncertainty during path integration. (A) The radii of searches that lasted at least 1 min plotted every 10% of the total search time until the search was completed (n=8). As individuals were traveling at different speeds during their searches, search time (in seconds) was multiplied by the individual's mean velocity during the search relative to the search with the highest mean velocity. Colors represent individual searches. Each search was fitted with a power function (lines of corresponding colors). (B) The radii of searches in A normalized by the initial search size (measured at 17 s into the search, the time at which the radius of the most extended search was first measured). The black line is the power function of best fit for all data, resulting in the search expansion pattern, radiusmax=time0.43. Optimal search theory predicts that searches should expand by radiusmax=time0.5. (C) Correlation of the initial radii of search behaviors and positional error during path integration. The sizes of search behaviors were larger when the error in path integration was greater (P=0.018, R=0.79, n=8).

We found that the radii of searches were variable at similar time points among searches, with some searches being over three times as wide as other searches (Fig. 2F, 4A; Fig. S1). We hypothesized that searches were wider when the error in a mantis shrimp's path integrator was higher (i.e. the animal's confidence in its home vector accuracy was lower). In order to test this hypothesis, we compared the radii of search behaviors lasting at least 60 s with the positional error in the home vector (path integration error) during those same trials. We found search radii were correlated with error in the path integrator (Pearson's correlation, P=0.018, R=0.79, n=8; Fig. 4C). This result suggests that the sizes of search behaviors are modulated by the reliability of the path integrator.

DISCUSSION

Path integration in N. oerstedii is inherently prone to error, which accumulates over the course of an animal's outward path. Error due to distance estimates is expected to increase linearly with increasing outward path length. However, the magnitude of angular errors differs depending on the manner in which angular measurements are taken. If directional information is measured in relation to a stable compass heading or environmental feature, angular errors would be expected to increase in a linear manner, similar to error accumulated from distance measurements; however, if angular information is measured from a previous rotational estimate, angular errors should compound, increasing at a rate greater than a linear relationship over the course of an animal's journey (Cheung, 2014; Heinze et al., 2018). Some models of error accumulation during path integration suggest that as a result of this large accumulated rotational error, path integration over extended distances (such as those exhibited by bees and ants) would require the use of a stable compass reference during navigation (Cheung et al., 2007; Cheung and Vickerstaff, 2010; Cheung, 2014; Heinze et al., 2018). This may be true for mantis shrimp as well, given the path integration error in our experiments accumulated at a rate less than that of a linear relationship over the length of outbound foraging paths (Fig. 1C); however, previous work suggests that mantis shrimp do rely on idiothetic orientation during path integration when celestial cues are obscured (Patel and Cronin, 2020). If mantis shrimp are indeed using idiothetic path integration when celestial information is unavailable, they would be relying on cumulative rotational estimates to measure their angular displacements under these conditions. Perhaps the typical limited foraging distances that N. oerstedii exhibit in nature (usually not greater than a couple of meters; Dominguez and Reaka, 1988; Patel and Cronin, 2020) allow them to home using idiothetic path integration with reasonable accuracy.

To cope with the error in the home vector, N. oerstedii executes stereotyped search behaviors composed of a series of non-oriented loops (unless local features are detected), which increase in size over the course of the search in a manner similar to that predicted by optimal search theory. Even though these searches are stereotyped, their sizes are scaled: they become larger with increased error in the path integrator. This flexible strategy improves the efficacy of the search.

In this study, some mantis shrimp searches were biased away from the edge of the arena nearest to where they initiated the search (Figs 2 and 3; Fig. S1). This result suggests that mantis shrimp can estimate the position of a goal from nearby structures, which may act as landmarks. Similar search biases to local features have been observed in other animals. Desert ants alter the geometry of their searches for their nests depending on the apparent image size of the local landmark array on their retinas (Akesson and Wehner, 1997). Trained honeybees also have been demonstrated to use the apparent sizes of landmarks in their environment to focus their searches for a hidden food source (Cartwright and Collet, 1983). Landmark navigation is a reliable way for animals to correct for error accumulated during path integration and is often used by other animals in tandem with path integration to lead them to their targets (Etienne, 1992; Collett, 1996; Wehner, 2003; Heinze et al., 2018). Mantis shrimps, many of which occupy structurally complex environments, may also use landmarks to assist their navigation.

The search behaviors of N. oerstedii closely resemble those executed by other animals, such as catagylphid desert ants (Wehner and Srinivasan, 1981), cockroaches (Durier and Rivault, 1999) and desert isopods (Hoffmann, 1983). The searches of these animals are similarly composed of ever-expanding loops centered near the animal's estimate of its shelter position and strikingly resemble the searches of mantis shrimp reported in this study. As in mantis shrimp, the size of desert ant searches is also flexible (Merkle et al., 2006; Schultheiss and Cheng, 2011). In cataglyphid ants, the search radii were found to be scaled to the length of the home vector (Merkle et al., 2006), not to the length of the outward foraging path (Merkle and Wehner, 2010) as we found in N. oerstedii, because error accumulated during outward foraging paths contributes to positional error in path integration (Fig. 1). However, Heinze et al. (2018) argue that after extensive search travel, optimal search theory predicts the small differences in search radii of groups with differing outward path lengths measured in Merkle and Wehner (2010) (who measured search paths at least 50 m long). Merkle and Wehner (2010) may have noticed greater differences in search sizes between their experimental groups if the radii of shorter searches or of earlier stages in the searches were used for their analyses. Regardless, given the similarities of searches in insects and malacostracan crustaceans, the neural programs of these search behaviors and the path integration circuits they are likely established from may either be ancient homologs or remarkable convergences between these disparate groups of animals. Even if the underlying mechanisms of the searches these groups exhibit are homologous, differences in how these searches are manifested and elaborated are likely to be present.

Acknowledgements

We thank N. S. Roberts and J. Park for research assistance and S. Heinze for helpful discussions.

Footnotes

Author contributions

Conceptualization: R.N.P.; Methodology: R.N.P.; Formal analysis: R.N.P.; Investigation: R.N.P.; Resources: T.W.C.; Data curation: R.N.P.; Writing - original draft: R.N.P.; Writing - review & editing: R.N.P.; Visualization: R.N.P.; Supervision: T.W.C.; Project administration: R.N.P.; Funding acquisition: T.W.C.

Funding

This work was supported by grants from the Air Force Office of Scientific Research under grant number FA9550-18-1-0278 and the University of Maryland, Baltimore County.

Data availability

The data from this paper are available from Mendeley: http://dx.doi.org/10.17632/whrcjjf7jx.1

References

Akesson
,
S.
and
Wehner
,
R.
(
1997
).
Visual snapshot memory of desert ants, Cataglyphis fortis
.
Proc. Göttingen Neurobiol. Conf.
25
,
482
.
Basch
,
L. V.
and
Engle
,
J. M.
(
1989
).
Aspects of the ecology and behavior of the stomatopod Hemisquilla ensigera californiensis (Gonodactyloidea: Hemisquillidae)
. In
Biology of Stomatopods
(ed.
E.A.
Ferrero
, coed.
R. B.
Manning
,
M. L.
Reaka
and
W.
Wales
), pp.
199
-
212
.
Modena
,
Italy
:
Mucchi Editore
.
Batschelet
,
E.
(
1981
).
Circular statistics in biology
.
London, UK
:
Academic Press
.
Caldwell
,
R. L.
,
Roderick
,
G. K.
and
Shuster
,
S. M.
(
1989
).
Studies of predation by Gonodactylus bredini
. In
Biology of Stomatopods
(ed.
E.A.
Ferrero
, coed.
R. B.
Manning
,
M. L.
Reaka
and
W.
Wales
), pp.
117
-
131
.
Modena
,
Italy
:
Mucchi Editore
.
Cartwright
,
B. A.
and
Collet
,
T. S.
(
1983
).
Landmark learning in bees: experiments and models
.
J. Comp. Physiol.
151
,
521
-
543
.
Cheung
,
A.
(
2014
).
Animal path integration: A model of positional uncertainty along tortuous paths
.
J. Theor. Biol.
341
,
17
-
33
.
Cheung
,
A.
and
Vickerstaff
,
R.
(
2010
).
Finding the way with a noisy brain
.
PLoS Comput. Biol.
6
,
e1000992
.
Cheung
,
A.
,
Zhang
,
S.
,
Stricker
,
C.
and
Srinivasan
,
M. V.
(
2007
).
Animal navigation: the difficulty of moving in a straight line
.
Biol. Cybern.
97
,
47
-
61
.
Collett
,
T.
(
1996
).
Insect navigation en route to the goal: multiple strategies for the use of landmarks
.
J. Exp. Biol.
199
,
227
-
235
.
Dominguez
,
J. H.
and
Reaka
,
M.
(
1988
).
Temporal activity patterns in reef- dwelling stomatopods: a test of alternative hypotheses
.
J. Exp. Mar. Biol. Ecol.
117
,
47
-
69
.
Durier
,
V.
and
Rivault
,
C.
(
1999
).
Path integration in cockroach larvae, Blattella germanica (L.) (Insect: Dictyoptera): direction and distance estimation
.
Learn. Behav.
27
,
108
-
118
.
Etienne
,
A. S.
(
1992
).
Navigation of a small mammal by dead reckoning and local cues
.
Curr. Dir. Psychol. Sci.
1
,
48
-
52
.
Heinze
,
S.
,
Narendra
,
A.
and
Cheung
,
A.
(
2018
).
Principles of insect path integration
.
Curr. Biol.
28
,
R1043
-
R1058
.
Hoffmann
,
G.
(
1983
).
The search behavior of the desert isopod Hemilepistus reaumuri as compared with a systematic search
.
Behav. Ecol. Sociobiol.
13
,
93
-
106
.
Meijering
,
E.
,
Dzyubachyk
,
O.
and
Smal
,
I.
(
2012
).
Methods for cell and particle tracking. Imaging and spectroscopic analysis of living cells
.
Methods Enzymol.
504
,
183
-
200
.
Merkle
,
T.
and
Wehner
,
R.
(
2010
).
Desert ants use foraging distance to adapt the nest search to the uncertainty of the path integrator
.
Behav. Ecol.
21
,
349
-
355
.
Merkle
,
T.
,
Knaden
,
M.
and
Wehner
,
R.
(
2006
).
Uncertainty about nest position influences systematic search strategies in desert ants
.
J. Exp. Biol.
209
,
3545
-
3549
.
Müller
,
M.
and
Wehner
,
R.
(
1988
).
Path integration in desert ants, Cataglyphis fortis
.
Proc. Natl. Acad. Sci. USA
85
,
5287
-
5290
.
Patel
,
R. N.
and
Cronin
,
T. W.
(
2020
).
Mantis shrimp navigate home using celestial and idiothetic path integration
.
Curr. Biol.
30
,
1981
-
1987.e3
.
Schultheiss
,
P.
and
Cheng
,
K.
(
2011
).
Finding the nest: inbound searching behaviour in the Australian desert ant, Melophorus bagoti
.
Anim. Behav.
81
,
1031
-
1038
.
Séguinot
,
V.
,
Maurer
,
R.
and
Etienne
,
A. S.
(
1993
).
Dead reckoning in a small mammal: the evaluation of distance
.
J. Comp. Physiol. A
173
,
103
-
113
.
Seyfarth
,
E.
,
Hergenröder
,
R.
,
Ebbes
,
H.
and
Friedrich
,
G.
(
1982
).
Idiothetic orientation of a wandering spider: compensation of detours and estimates of goal distance
.
Behav. Ecol. Sociobiol.
11
,
139
-
148
.
Wehner
,
R.
(
2003
).
Desert ant navigation: how miniature brains solve complex tasks. Karl von Frisch Lecture
.
J. Comp. Physiol. A
189
,
579
-
588
.
Wehner
,
R.
and
Srinivasan
,
M. V.
(
1981
).
Searching behaviour of desert ants, genus Cataglyphis (Formicidae, Hymenoptera)
.
J. Comp. Physiol.
142
,
315
-
338
.
Zeil
,
J.
(
1998
).
Homing in fiddler crabs (Uca lactea annulipes and Uca vomeris: Ocypodidae)
.
J. Comp. Physiol. A, 183, 367-377
.

Competing interests

The authors declare no competing or financial interests.

Supplementary information