Fiddler crabs accurately measure two-dimensional distance over three-dimensional terrain

Some animals that are central-place foragers return home after foraging or revisit a food source primarily through a spatial navigation process called path integration (PI) (Mittelstaedt and Mittelstaedt, 1980). In this navigational process motion vectors– the directions and distances of locomotory movements – are measured and continually summed to form a single `home vector' linking the current location with the point of origin. A striking example of central-place foraging occurs in the fiddler crabs (genus Uca), which accurately and continuously monitor their burrow location, and align their bodies with its direction, even when they cannot see it (Hemmi and Zeil, 2003; Land and Layne, 1995; Layne et al., 2003a; Zeil, 1998). It is now well established that they do this using PI(Altevogt and von Hagen, 1964; Cannicci et al., 1999; von Hagen, 1967; Layne et al., 2003b; Walls and Layne, 2009; Zeil, 1998).

The specific mechanism by which fiddler crabs measure the direction of their movements is not yet known, but it has recently been shown that, like the well-studied desert ants of the genus Cataglyphis(Wittlinger et al., 2006; Wittlinger et al., 2007),fiddler crabs can measure distance using so-called `stride integration'(Walls and Layne, 2009). Indeed, they measure the distance to their burrows to within less than one-half body length, when tested on flat ground. In the present study we tested the hypothesis that fiddler crabs (Uca pugilator Bosc 1802),like desert ants, can successfully return home over terrain that is not flat,but has a significant vertical component that is dramatically different from that encountered on the outward journey(Wohlgemuth et al., 2001; Wohlgemuth et al., 2002).

Fiddler crabs do not forage over such amazing distances as desert ants, nor are they likely to encounter as much vertical relief during their journey. Nevertheless their sand flat and mudflat habitats abound with topographic features that are large on the scale of a 1–2 cm animal. Can they climb over such features and still accurately measure the horizontal distance they must travel to reach home, or do such obstacles so disrupt homing by PI that crabs must detour around them?

To answer this question, we buried an inflatable bladder amongst several burrows inhabited by fiddler crabs. We passively moved foraging crabs to a place such that their home vector laid across the deflated bladder, ending at a spot of empty sand, the `fictive burrow' [similar to Walls and Layne(Walls and Layne, 2009)]. This is the spot to which the crabs attempt to return as though it is their burrow. When the bladder was inflated, the crab and its burrow were separated by a hill that increased the walking distance required to reach the fictive burrow. As a result, the fiddler crabs not only had to travel farther to reach their destination but also had to do so over a substantial vertical detour. If they account for the vertical component, then they would travel the full horizontal distance of their home vector and reach the fictive burrow successfully,similar to control crabs that ran on flat ground. If they do not, then their travel distance would be foreshortened by a predictable amount. These two scenarios produced specific predictions for crabs' running distance, based on home vector length, size of the hill, and the path taken over the hill. The model that best predicted the observed distance traveled was assumed to represent the fiddler crabs' true path integrator.

Field experiments were carried out on fiddler crabs (Uca pugilatorBosc 1802) inhabiting intertidal sand flats located in Beaufort, NC, USA. Lab experiments were conducted on U. pugilator collected there and housed in the lab in Cincinnati, OH, USA.

Fiddler crabs were kept in a circular 1.2 m diameter arena filled with a sand–mud mixture also collected from Beaufort. In this arena crabs excavated and defended burrows, foraged across the terrain, and engaged in homing behavior similar to what is observed under natural conditions. A water pump, set on a 6 h cycle, moved brackish water, 20–30 p.p.t. Instant Ocean, in and out of the arena on a pseudo-tidal rhythm. Experiments were performed during pseudo-low tide.

All experiments were videotaped from above with a Sony HDR-HC1 camcorder. The procedure is shown in Fig. 1. A square (7 cm) of overhead projector acetate was covered with a thin layer of sand–mud substrate, and attached to fishing line on four corners, allowing an observer to move the patch anywhere within a 0.9 m² area. When a foraging crab walked onto the patch, an observer translated the crab so that its home vector passed over a bladder buried under the substrate, and ended at an open spot on the ground, the `fictive burrow',to which the crab invariably attempted to return. An observer inflated the bladder, creating a hill that increased the walking distance between the crab and the fictive burrow. When frightened by a wave of the observer's hand,crabs ran over the newly formed hill and abruptly stopped running and began a stereotypical crisscross search for their burrow. Controls were carried out the same way, but without inflating the bladder. All crabs tested were male.

The bladder consisted of a wooden board covered with a latex sheet, sealed to the board around the edges. Between the board and latex was an air balloon connected to the outside by a hose. The bladder was 24 cm in diameter, and 4.6–8.0 cm high when inflated, and so could be modeled as spheres of different radii intersecting the ground plane. Hence, walking distance traveled was calculated by assuming each crab's path over the hill was over a sphere that transected the ground. The size of the hill was standardized using the number of pumps of the hand-operated bicycle pump used to inflate the bladder. For each compression of the pump, the height of the hill at the center of the bladder was measured. From these, and using spherical trigonometry, the walking distance was calculated for any path across the hill. In the experiments walking distance to the fictive burrow was extended by 0.2–6.5 cm, or up to more than four times crab mean body width (1.6 cm).

All videos were digitized with Ulead 8.0 video capture software (Corel,Ottawa, Canada) and the digitized frames were analyzed with custom software written in MATLAB R2006a (The Mathworks, Natick, MA, USA). The following data were obtained for each trial (see Fig. 1): (1) the crab's position relative to its burrow immediately before being translated on the patch; (2) the crab's position after translation; (3) the location at which the crab stopped running and began searching.

The `observed distance' is the ground distance between points 2 and 3 and corresponds to the point at which the stored home vector is cancelled. This was compared with two distances predicted from alternative PI models. The first model, W (for `walking' distance), predicted the horizontal distance the crab would travel if the vertical dimension of the hill was not taken into account. As such, this prediction was the original home vector foreshortened by the walking distance added by the hill. The second model, G (for `ground'distance), assumed that the crabs accounted for the vertical dimension of the hill, and its prediction was equal to the original home vector, ending at the fictive burrow (Fig. 1).

The two PI models were evaluated by comparing the observed distance with those predicted by the two models. The difference between the observed and predicted distance is the prediction error, and this error reflects the accuracy of each model. Regression analysis of the controls found no effect of distance from the burrow on the crabs' homing accuracy so distance was excluded as a covariate (N=29, F=0.30, P=0.59). The prediction errors were compared among the two models and the controls with an analysis of variance (ANOVA). A Tukey's multiple comparison test was applied for significant results from the ANOVA. A one sample t-test was used to compare the actual distance to the predicted distance for each model and for the controls. Lab and field experiments did not differ significantly(P=0.78, Wilcoxon signed-rank) so they were pooled. All statistical analyses were performed with JMP IN 5.1(www.jmp.com).

Controls accurately ran out their home vectors, reaching the fictive burrow without significant error (P=0.18, t=1.4, d.f.=29, Student's t-test). For trials in which the bladder was inflated, a comparison of observed distance with the W prediction showed a significant prediction error wherein the experimental crabs ran farther than predicted(P<0.0001, t=5.7, d.f.=58, Student's t-test; Fig. 2). On the other hand, a comparison of the observed distance with the G prediction revealed no significant prediction error (t=–1.6, d.f.=58, P=0.10,Student's t-test). An ANOVA comparing the prediction errors among the two PI models and the controls found that the prediction errors were significantly different among the three groups (F=18.9, d.f.=147, P<0.0001; Table 1). According to a post hoc Student's t-test the W model underestimated the observed distance significantly more than both the controls(P<0.0001, t=3.5, d.f.=145) and the G model(P<0.0001, t=6.0, d.f.=145). In contrast, the same test revealed no significant difference between the G prediction and the controls(P=0.16, t=1.4, d.f.=145, Student's t-test).

The varied paths over the hill led to a range of model predictions. When a crab ran across the edge of the hill, rather than over its apex, this introduced only a slight increase in walking distance between the starting point and the fictive burrow. In this case the G and W models predicted almost the same distance and were difficult to distinguish from the observed distance. Of course, the difference between the two predictions increased substantially if crabs crossed near the center of the hill, so that the walking distance to the fictive burrow was significantly increased. Thus,depending on the paths across the hill, a range of increased walking distances led to a range of differences between model predictions. The results show that the larger this difference, the more the observed distance diverged from the W prediction (slope=1.13, P<0.0001, F=48.6, d.f.=58, ANOVA; Fig. 3), while remaining consistent with the G prediction (slope=0.13, P=0.41, F=0.68, d.f.=58, ANOVA). Thus, regardless of the amount of walking distance added by the hill, the crabs' ability to compute and travel the horizontal component of its path remained constant.

Three qualitative results shed light on the sophistication of the crabs'ability to measure distance over rough terrain. First, the bladder used in this experiment approximated a section of a sphere when inflated. If crabs maintained the same gait used to walk a straight path on flat ground as they traversed the hill, they would have followed longitudinal lines over the bladder. In practice the running paths showed brief stretches of this, but just as often they crossed longitudes to approximate a linear path, more like latitudes (Fig. 4). Thus,rather than taking the shortest route, they took a route that, when projected to the horizontal plane, was straighter. The change in gait here is an altered ratio of step sizes of the anterior and posterior legs, and the path integrator functions properly across these different gaits. A few times neither the longitudinal nor the latitudinal routes applied, namely when crabs declined to run across the face of a steep incline, opting instead to run more or less down the incline and recover the original path after reaching the base of the hill (see dotted paths in Fig. 4).

Second, inflating the bladder produced cracks in the expanding sand substrate, and when the sand overlying the bladder was thick these were quite wide and deep (∼2 cm). Crabs nevertheless negotiated these cracks, and despite apparently dramatic adjustments to their gait – switching to a climbing behavior in some cases – they maintained relatively straight paths and traveled the correct ground distance.

Third, crabs were sometimes translated so their home vector ended on the hill itself, often on a steep slope (see dashed paths in Fig. 4). In such cases, even though the fictive burrow location was so dramatically unlike the flat ground in which they had excavated their real burrows, crabs searched over their hillside fictive burrow in the same crisscross pattern used on flat ground,sometimes at steep inclines (40–50 deg.!). Even though the topography was deftly monitored by the crabs for PI, it was irrelevant after the home vector was run out, and irrelevant to the crabs' perception of the burrow location.

Fiddler crabs ran to the fictive burrow predicted under the assumption that they have access to the horizontal ground distance despite the hilly terrain(the G model). They did this by increasing the distance they traveled by up to nearly five body widths beyond the distance traveled by controls. This indicates crabs most likely perform one of two types of integration, both of which require them to acquire information about all three dimensions of their course over a hill. One possibility is that they perform three-dimensional PI,i.e. their home vector has a vertical component, as in Salticid spiders(Hill, 1979) and house mice(Bardunias and Jander, 2000). Alternatively, they measure and discard the vertical component, and continuously monitor their body's inclination to the horizontal, integrating its cosine to obtain ground distance, so their home vector is confined to the horizontal plane. The former system is not used by desert ants(Grah et al., 2005), but for fiddler crabs these two alternatives cannot yet be distinguished.

The vestibular organ of crustaceans, the statocyst, is strongly analogous to that of vertebrates, consisting of orthogonal toroid canals and a statolith that responds to gravity (Dijkgraaf,1956; Sandeman,1975). Given this similarity, and the fact that the vestibular system plays a central role in vertebrate navigation (for a review, see Angelaki and Cullen, 2008), it is natural to predict the same might occur in crabs. Indeed, Fraser(Fraser, 2006) reviews the properties of several crab vestibular interneurons that would suit a vestibular integrator. To date, however, the only behavioral studies on PI in fiddler crabs that might address this possibility show that inertial/acceleration cues are not necessary for distance estimation on flat terrain (Walls and Layne,2009), nor do they facilitate the integration of imposed body rotations (Layne et al.,2003b).

In crabs, several different proprioceptive organs respond to muscle strain and cuticular stress (Bush and Laverack,1982). Both types might provide a gravity sense if their collective activity reflected changes in the distribution of body mass, and so continuously indicated body tilt. Current evidence points to this as the way desert ants gauge topography. Insects lack internal gravity sensors like those in crabs, and instead use inter-segmental hair plates(Lindauer and Nedel, 1959). Abolishing or preventing the normal function of these, however, does not impede the desert ant's three-dimensional navigation(Wittlinger et al., 2007). Given the primacy of their motor system in measuring distance(Thiélin-Bescond and Beugnon,2005; Wohlgemuth et al.,2001; Wohlgemuth et al.,2002), leg proprioceptors would therefore appear to be the key to desert ant PI on both flat and hilly terrain.

Finally, there is another, less obvious possibility for the source of body tilt information in crabs. Unlike many invertebrates, decapod crustaceans move their eyes in relation to their body so that their eyes remain stable in space, including maintaining a vertical eyestalk posture when the body tilts(Milne and Milne, 1965). This vertical stability is especially pronounced in the semi-terrestrial crabs(Nalbach et al., 1989a), where it functions primarily to align the eyes properly with their visual world(Land and Layne, 1995; Layne, 1998; Layne et al., 1997; Zeil, 1990; Zeil and Al-Mutairi, 1996; Zeil et al., 1986). We suggest that this vertical stabilizing system may have an additional role in monitoring body tilt. Vertical eyestalk posture is initially acquired using gravity and a fixation response to the contrast at the horizon(Nalbach et al., 1989a), and thereafter the eye stalks are robustly stabilized by visual velocity-driven negative feedback control, and vestibular and proprioceptive feedforward control (Dijkgraaf, 1956; Nalbach, 1990; Nalbach et al., 1989a; Nalbach et al., 1989b; Varjú and Sandeman,1982). This multisensory control system could provide a continuous readout of eyestalk/body angle in both pitch and roll which, if stability is achieved and the eyes are properly (vertically) oriented, is equal to the body inclination. In this scenario, visual, vestibular and proprioceptive senses are integral parts of the system, but eyestalk/body angle (and thus body tilt)is not obtained directly from any of them. Rather, it is obtained by integrating their common signal to the eyestalk muscles and body tilt information is sent to the path integrator only if it also generates compensatory eyestalk tilt. Note that in our theory it is efference to the eyestalk muscles, and not afference from them, that provides the signal,because attempts to find evidence that proprioceptors in the eye stalks signal the eye/body angle found none (Horridge and Burrows, 1968). While this may be a non-intuitive source of spatial information, we believe it is likely to be a very accurate one, given the system's redundancy.

For simplicity we have presented our theory as the use of body tilt,indicated by the state of the eye pitch/roll control system, to acquire the horizontal component of the walking path, but it is crucial to note that fiddler crabs do not always orient the dorso-ventral axes of their eyes vertically. Rather, they orient them perpendicularly to the mean local substrate plane which, as dramatically illustrated by Zeil and Al-Mutairi(Zeil and Al-Mutairi, 1996)(see also Nalbach et al.,1989b; Zeil,1990), may deviate significantly from the horizontal plane,meaning the eye stalks deviate significantly from vertical. Fiddler crabs living on such flat, non-horizontal, planes navigate via PI just as well as those living on horizontal surfaces. Indeed, all of the experiments performed in the field in this and our other studies (roughly half) were done on sloped substrates, and the crabs navigate accurately. The important point here is that, if they are to successfully walk home over debris and small-scale topographical features, crabs should not acquire the horizontal component of the path, but instead that component which is in the plane of the local (sloped) substrate, because only this plane is relevant for navigating by PI.

How could the angle between the body and the sloped substrate be determined? By precisely the mechanism proposed above, i.e. the state of the eyes' pitch/roll control system – provided the crab, while orienting its eye stalk to the sloped substrate, also confers upon it the status of primary reference plane for behavior, or `behavioral plane'. This does not refer to the surface inflated bladder in our experiments, but to the substrate in which the bladder rests. We have reviewed some of the sensory mechanisms by which fiddler crabs orient their eye stalks perpendicularly to the substrate, but it is not known how different sensory modes are weighted when they are in conflict with one another, as is the case on sloped substrates. Perhaps it is by Bayesian integration, as is the case for multisensory integration across many contexts by other animals, including humans(Cheng et al., 2007; Deneve and Pouget, 2004).

Whatever the mechanism, the crabs' `decision'(Körding, 2007) to confer such status upon a given plane sets the spatial parameters of their sensory and behavioral world. It appears to determine the component of a walking path to be integrated, and thus influences the animals' sense of location relative to at least one feature in the environment (home). It also influences the animals' sense of object location relative to itself, i.e. what is where. Fiddler crabs in nature escape from any novel, moving stimulus occurring in their dorsal hemifield (Land and Layne,1995), a behavior that presumably evolved because virtually all danger approaches the tiny crabs from above. However, when visual cues are altered so as to induce crabs to tilt their eye stalks away from vertical,they attempted to escape from all stimuli occurring above the new, tilted plane bisecting their visual world, even when these were below the crabs' body(Layne, 1998). This result was interpreted at the time as indicating that the escape response was hard-wired into the dorsal part of the retina, but a new interpretation may be preferable; namely, that the pitch and roll of the eye stalks reflects a decision taken by the crab to establish a new orientation for its `behavioral plane'. Experiments in which homing is performed while body tilt is dissociated from eye stalk orientation will test the pitch/roll control system theory against a more direct readout of body tilt from the statocysts or proprioceptors. It may additionally test the tantalizing theory that multisensory integration establishes a plane for all of the crabs' spatial perception and behavior.