Direct evidence for distance measurement via flexible stride integration in the fiddler crab

Landmark use by ghost crab (Ocypode quadrata) during wayfinding in a complex maze

Species of crab have been shown to spatially track and navigate to consequential locations through different processes, such as path integration and landmark orienting. Few investigations examine their ability to wayfind in complex environments, like mazes, with multiple intersections and how they may utilize specific features to benefit this process. Spatial learning potentially would lend a fitness advantage to animals living in complicated habitats, and ghost crab (Ocypode quadrata) is a semiterrestrial species that typically occupies extensive beach environments, which present many navigational challenges. Despite their potential, there are currently no studies that investigate forms of spatial cognition in these animals. To better diversify our knowledge of this trait, the current research exposed ghost crab to a maze with seven intersections. Animals were given multiple trials to learn the location of a reward destination to a specific criterion proficiency. In one condition several landmarks were distributed throughout the maze, and in another the environment was completely empty. Results showed that ghost crab in the landmark present group were able to learn the maze faster, they required significantly fewer trials to reach the learning criterion than those in the landmark absent group. However, only approximately half of the total sample met the learning criterion, indicating the maze was rather difficult. These findings are interpreted through theories of route learning that suggest animals may navigate by establishing landmark-turn associations. Such processes have implications for the cognitive ability of ghost crab, and spatial learning in this species may support the notion of convergent evolution for this trait.

Distance estimation in the goldfish (Carassius auratus)

Neurophysiological advances have given us exciting insights into the systems responsible for spatial mapping in mammals. However, we are still lacking information on the evolution of these systems and whether the underlying mechanisms identified are universal across phyla, or specific to the species studied. Here we address these questions by exploring whether a species that is evolutionarily distant from mammals can perform a task central to mammalian spatial mapping-distance estimation. We developed a behavioural paradigm allowing us to test whether goldfish (Carassius auratus) can estimate distance and explored the behavioural mechanisms that underpin this ability. Fish were trained to swim a set distance within a narrow tank covered with a striped pattern. After changing the background pattern, we found that goldfish use the spatial frequency of their visual environment to estimate distance, doubling the spatial frequency of the background pattern resulted in a large overestimation of the swimming distance. We present robust evidence that goldfish can accurately estimate distance and show that they use local optic flow to do so. These results provide a compelling basis to use goldfish as a model system to interrogate the evolution of the mechanisms that underpin spatial cognition, from brain to behaviour.

Visual odometry of Rhinecanthus aculeatus depends on the visual density of the environment

Distance travelled is a crucial metric that underpins an animal's ability to navigate in the short-range. While there is extensive research on how terrestrial animals measure travel distance, it is unknown how animals navigating in aquatic environments estimate this metric. A common method used by land animals is to measure optic flow, where the speed of self-induced visual motion is integrated over the course of a journey. Whether freely-swimming aquatic animals also measure distance relative to a visual frame of reference is unclear. Using the marine fish Rhinecanthus aculeatus, we show that teleost fish can use visual motion information to estimate distance travelled. However, the underlying mechanism differs fundamentally from previously studied terrestrial animals. Humans and terrestrial invertebrates measure the total angular motion of visual features for odometry, a mechanism which does not vary with visual density. In contrast, the visual odometer used by Rhinecanthus acuelatus is strongly dependent on the visual density of the environment. Odometry in fish may therefore be mediated by a movement detection mechanism akin to the system underlying the optomotor response, a separate motion-detection mechanism used by both vertebrates and invertebrates for course and gaze stabilisation.

Walking is like slithering: A unifying, data-driven view of locomotion

Legged movement is ubiquitous in nature and of increasing interest for robotics. Most legged animals routinely encounter foot slipping, yet detailed modeling of multiple contacts with slipping exceeds current simulation capacity. Here we present a principle that unifies multilegged walking (including that involving slipping) with slithering and Stokesian (low Reynolds number) swimming. We generated data-driven principally kinematic models of locomotion for walking in low-slip animals (Argentine ant, 4.7% slip ratio of slipping to total motion) and for high-slip robotic systems (BigANT hexapod, slip ratio 12 to 22%; Multipod robots ranging from 6 to 12 legs, slip ratio 40 to 100%). We found that principally kinematic models could explain much of the variability in body velocity and turning rate using body shape and could predict walking behaviors outside the training data. Most remarkably, walking was principally kinematic irrespective of leg number, foot slipping, and turning rate. We find that grounded walking, with or without slipping, is governed by principally kinematic equations of motion, functionally similar to frictional swimming and slithering. Geometric mechanics thus leads to a unified model for swimming, slithering, and walking. Such commonality may shed light on the evolutionary origins of animal locomotion control and offer new approaches for robotic locomotion and motion planning.

The evolution of quantitative sensitivity

The ability to represent approximate quantities appears to be phylogenetically widespread, but the selective pressures and proximate mechanisms favouring this ability remain unknown. We analysed quantity discrimination data from 672 subjects across 33 bird and mammal species, using a novel Bayesian model that combined phylogenetic regression with a model of number psychophysics and random effect components. This allowed us to combine data from 49 studies and calculate the Weber fraction (a measure of quantity representation precision) for each species. We then examined which cognitive, socioecological and biological factors were related to variance in Weber fraction. We found contributions of phylogeny to quantity discrimination performance across taxa. Of the neural, socioecological and general cognitive factors we tested, cortical neuron density and domain-general cognition were the strongest predictors of Weber fraction, controlling for phylogeny. Our study is a new demonstration of evolutionary constraints on cognition, as well as of a relation between species-specific neuron density and a particular cognitive ability.

This article is part of the theme issue ‘Systems neuroscience through the lens of evolutionary theory’.

The ecological significance of time sense in animals

Time is a fundamental dimension of all biological events and it is often assumed that animals have the capacity to track the duration of experienced events (known as interval timing). Animals can potentially use temporal information as a cue during foraging, communication, predator avoidance, or navigation. Interval timing has been traditionally investigated in controlled laboratory conditions but its ecological relevance in natural environments remains unclear. While animals may time events in artificial and highly controlled conditions, they may not necessarily use temporal information in natural environments where they have access to other cues that may have more relevance than temporal information. Herein we critically evaluate the ecological contexts where interval timing has been suggested to provide adaptive value for animals. We further discuss attributes of interval timing that are rarely considered in controlled laboratory studies. Finally, we encourage consideration of ecological relevance when designing future interval-timing studies and propose future directions for such experiments.

A re-evaluation of silk measurement by the cecropia caterpillar (Hyalophora cecropia) during cocoon construction reveals use of a silk odometer that is temporally regulated

The late 5th instar caterpillar of the cecropia silk moth (Hyalophora cecropia) spins a silken cocoon with a distinct, multilayered architecture. The cocoon construction program, first described by the seminal work of Van der Kloot and Williams, consists of a highly ordered sequence of events. We perform behavioral experiments to re-evaluate the original cecropia work, which hypothesized that the length of silk that passes through the spinneret controls the orderly execution of each of the discrete events of cocoon spinning. We confirm and extend by three-dimensional scanning and quantitative measurements of silk weights that if cocoon construction is interrupted, upon re-spinning, the caterpillar continues the cocoon program from where it left off. We also confirm and extend by quantitative measurements of silk weights that cecropia caterpillars will not bypass any of the sections of the cocoon during the construction process, even if presented with a pre-spun section of a cocoon spun by another caterpillar. Blocking silk output inhibits caterpillars from performing normal spinning behaviors used for cocoon construction. Surprisingly, unblocking silk output 24-hr later did not restart the cocoon construction program, suggesting the involvement of a temporally-defined interval timer. We confirm with surgical reductions of the silk glands that it is the length of silk itself that matters, rather than the total amount of silk extracted by individuals. We used scanning electron microscopy to directly show that either mono- or dual-filament silk (i.e., equal silk lengths but which vary in their total amount of silk extracted) can be used to construct equivalent cocoons of normal size and that contain the relevant layers. We propose that our findings, taken together with the results of prior studies, strongly support the hypothesis that the caterpillar uses a silk "odometer" to measure the length of silk extracted during cocoon construction but does so in a temporally regulated manner. We further postulate that our examination of the anatomy of the silk spinning apparatus and ablating spinneret sensory output provides evidence that silk length measurement occurs upstream of output from the spinneret.

Path integration in a three-dimensional world: the case of desert ants

Desert ants use path integration to return from foraging excursions on a shortcut way to their nests. Intriguingly, when walking over hills, the ants incorporate the ground distance, the paths’ projection to the horizontal plane, into their path integrator. This review discusses how Cataglyphis may solve this computational feat. To infer ground distance, ants must incorporate the inclination of path segments into the assessment of distance. Hair fields between various joints have been eliminated as likely sensors for slope measurement, without affecting slope detection; nor do postural adaptations or changes in gait provide the relevant information. Changes in the sky’s polarization pattern due to different head inclinations on slopes were ruled out as cues. Thus, the mechanisms by which ants may measure slopes still await clarification. Remarkably, the precision of slope measurement is roughly constant up to a 45° inclination, but breaks down at 60°. An encounter of sloped path segments during a foraging trip induces a general acceptance of slopes, however, slopes are not associated with specific values of the home vector. All current evidence suggests that Cataglyphis does not compute a vector in 3-D: path integration seems to operate exclusively in the horizontal plane.

Interaction between path integration and visual orientation during the homing run of fiddler crabs

Foraging fiddler crabs form a strict spatial relationship between their current positions and burrows, allowing them to run directly back to their burrows when startled even without visual contacts. Path integration (PI), the underlying mechanism, is a universal navigation strategy through which animals continuously integrate directions and distances of their movements. However, we report that fiddler crabs also use visual orientation during homing runs using burrow entrances as cues, with the prioritised mechanism (i.e. PI or visual) determined by the distance (which has a threshold value) between the goal, indicated by PI, and the visual cue. When we imposed homing errors using fake entrances (visual cue) and masking their true burrows (goal of PI), we found that frightened fiddler crabs initially ran towards the true burrow following PI, then altered their behaviour depending on the distance between the fake entrance and masked true burrow: if the distance was large, they kept running until they reached the true burrow, ignoring the visual cue; however, if the distance was small, they altered the homing path and ran until they reached the fake entrance. This suggests that PI and visual mechanism in fiddler crabs are mutually mediated to achieve their homing behaviour.

Visual motion processing subserving behavior in crabs

Motion vision originated during the Cambrian explosion more than 500 million years ago, likely triggered by the race for earliest detection between preys and predators. To successfully evade a predator's attack a prey must react quickly and reliably, which imposes a common constrain to the implementation of escape responses among different species. Thus, neural circuits subserving fast escape responses are usually straightforward and contain giant neurons. This review summarizes knowledge about a small group of motion-sensitive giant neurons thought to be central in guiding the escape performance of crabs to visual stimuli. The flexibility of the escape behavior contrasts with the stiffness of the optomotor response, indicating a task-dependent early segregation of visual pathways.

Comparative analyses of olfactory systems in terrestrial crabs (Brachyura): evidence for aerial olfaction?

Adaptations to a terrestrial lifestyle occurred convergently multiple times during the evolution of the arthropods. This holds also true for the "true crabs" (Brachyura), a taxon that includes several lineages that invaded land independently. During an evolutionary transition from sea to land, animals have to develop a variety of physiological and anatomical adaptations to a terrestrial life style related to respiration, reproduction, development, circulation, ion and water balance. In addition, sensory systems that function in air instead of in water are essential for an animal's life on land. Besides vision and mechanosensory systems, on land, the chemical senses have to be modified substantially in comparison to their function in water. Among arthropods, insects are the most successful ones to evolve aerial olfaction. Various aspects of terrestrial adaptation have also been analyzed in those crustacean lineages that evolved terrestrial representatives including the taxa Anomala, Brachyura, Amphipoda, and Isopoda. We are interested in how the chemical senses of terrestrial crustaceans are modified to function in air. Therefore, in this study, we analyzed the brains and more specifically the structure of the olfactory system of representatives of brachyuran crabs that display different degrees of terrestriality, from exclusively marine to mainly terrestrial. The methods we used included immunohistochemistry, detection of autofluorescence- and confocal microscopy, as well as three-dimensional reconstruction and morphometry. Our comparative approach shows that both the peripheral and central olfactory pathways are reduced in terrestrial members in comparison to their marine relatives, suggesting a limited function of their olfactory system on land. We conclude that for arthropod lineages that invaded land, evolving aerial olfaction is no trivial task.

Symmetry and order parameter dynamics of the human odometer

Bipedal gaits have been classified on the basis of the group symmetry of the minimal network of identical differential equations (alias cells) required to model them. Primary bipedal gaits (e.g., walk, run) are characterized by dihedral symmetry, whereas secondary bipedal gaits (e.g., gallop-walk, gallop- run) are characterized by a lower, cyclic symmetry. This fact has been used in tests of human odometry (e.g., Turvey et al. in P Roy Soc Lond B Biol 276:4309-4314, 2009, J Exp Psychol Hum Percept Perform 38:1014-1025, 2012). Results suggest that when distance is measured and reported by gaits from the same symmetry class, primary and secondary gaits are comparable. Switching symmetry classes at report compresses (primary to secondary) or inflates (secondary to primary) measured distance, with the compression and inflation equal in magnitude. The present research (a) extends these findings from overground locomotion to treadmill locomotion and (b) assesses a dynamics of sequentially coupled measure and report phases, with relative velocity as an order parameter, or equilibrium state, and difference in symmetry class as an imperfection parameter, or detuning, of those dynamics. The results suggest that the symmetries and dynamics of distance measurement by the human odometer are the same whether the odometer is in motion relative to a stationary ground or stationary relative to a moving ground.

Flexible kinesthetic distance perception: when do your arms tell you how far you have walked?

Given the flexible organization of locomotion evidenced in the many ways the limbs can be coordinated, the authors explored the potentially correspondingly flexible organization of nonvisual (kinesthetic) distance perception. As kinesthetic distance perception is known to be affected by how the limbs are coordinated, the authors probed the potential perceptual contribution of the arms during locomotion by manipulating arm-leg coordination patterns in blind-walked distance-matching tasks. Whereas manipulation of arm-leg coordination for walking with free-swinging arms had no observable perceptual consequences, comparable manipulation for walking with hiking poles did affect distance matching. These results suggest that under conditions in which the arms act to propel the body (e.g., crawling or stair-climbing) a person's nonvisual sense of movement is conveyed in the coordinated actions of all four limbs.

Homing distance in desert ants, Cataglyphis fortis, remains unaffected by disturbance of walking behaviour and visual input

Desert ants gauge walking distance by means of a stride integrator and, to a minor extent, by optic flow integration. With the present experiments we attempt to interfere with both, stride integration and optic flow input in order to reveal possible interactions of the two modes of odometry and further functional details of the stride integrator. We tried to impair stride integration by amputating two of the six walking legs. Amputation of left middle and right hind legs had especially severe effects since it left only the right front leg in one of the support tripods that are alternately used in walking. We tried to impair optic flow input - which is used for distance estimation to a minor extent - by covering both ventral eye halves. These two sets of manipulations were carried out in combination to study possible compensatory effects, for instance, of optic flow input in the case of an impaired stride integrator. Unexpectedly, none of the manipulations we carried out had significant effects on homing performance. This was true with regard to homing distance estimation (as determined by the centres of the ants' nest searches) and homing certainty (as determined by the search spreads). These results corroborate the surprising robustness of odometry by stride integration, and they indicate that leg proprioceptive feedback is used for stride integration. The question of a possible interaction of optic flow input and stride integration remains open.

Equivalence of human odometry by walk and run is indifferent to self-selected speed

Humans and other animals can measure distances nonvisually by legged locomotion. Experiments typically employ an outbound measure (M) and an inbound report (R) phase. Previous research has found distance reproduction to be maximally accurate, when gait symmetry and speed of M and R are of like kind: Successful human odometry manifests at the level of the M-R system. In the present work, M was an experimenter-set distance produced by a blindfolded participant using a primary gait (walk, run). R was always by walk. Fast and slow versions of walk and run were adopted by participants, such that when M was fast R was slow, and vice versa. Distance was underestimated when M was slower than R and overestimated when M was faster than R. However, the pattern of participant-adopted velocities indicated that it was the instructions, not the speed as such, that yielded the pattern of results. The results are interpretable through a dynamical perspective and indicate speed is an imperfection parameter acting on the attractors of the M-R system.

Neuronal processing of translational optic flow in the visual system of the shore crab Carcinus maenas

This paper describes a search for neurones sensitive to optic flow in the visual system of the shore crab Carcinus maenas using a procedure developed from that of Krapp and Hengstenberg. This involved determining local motion sensitivity and its directional selectivity at many points within the neurone's receptive field and plotting the results on a map. Our results showed that local preferred directions of motion are independent of velocity, stimulus shape and type of motion (circular or linear). Global response maps thus clearly represent real properties of the neurones' receptive fields. Using this method, we have discovered two families of interneurones sensitive to translational optic flow. The first family has its terminal arborisations in the lobula of the optic lobe, the second family in the medulla. The response maps of the lobula neurones (which appear to be monostratified lobular giant neurones) show a clear focus of expansion centred on or just above the horizon, but at significantly different azimuth angles. Response maps such as these, consisting of patterns of movement vectors radiating from a pole, would be expected of neurones responding to self-motion in a particular direction. They would be stimulated when the crab moves towards the pole of the neurone's receptive field. The response maps of the medulla neurones show a focus of contraction, approximately centred on the horizon, but at significantly different azimuth angles. Such neurones would be stimulated when the crab walked away from the pole of the neurone's receptive field. We hypothesise that both the lobula and the medulla interneurones are representatives of arrays of cells, each of which would be optimally activated by self-motion in a different direction. The lobula neurones would be stimulated by the approaching scene and the medulla neurones by the receding scene. Neurones tuned to translational optic flow provide information on the three-dimensional layout of the environment and are thought to play a role in the judgment of heading.

Odometry and insect navigation

Animals have needed to find their way about almost since a free-living life style evolved. Particularly, if an animal has a home – shelter or nesting site – true navigation becomes necessary to shuttle between this home and areas of other activities, such as feeding. As old as navigation is in the animal kingdom, as diverse are its mechanisms and implementations, depending on an organism's ecology and its endowment with sensors and actuators. The use of landmarks for piloting or the use of trail pheromones for route following have been examined in great detail and in a variety of animal species. The same is true for senses of direction – the compasses for navigation – and the construction of vectors for navigation from compass and distance cues. The measurement of distance itself – odometry – has received much less attention. The present review addresses some recent progress in the understanding of odometers in invertebrates, after outlining general principles of navigation to put odometry in its proper context. Finally, a number of refinements that increase navigation accuracy and safety are addressed.

Human odometer is gait-symmetry specific

In 1709, Berkeley hypothesized of the human that distance is measurable by 'the motion of his body, which is perceivable by touch'. To be sufficiently general and reliable, Berkeley's hypothesis must imply that distance measured by legged locomotion approximates actual distance, with the measure invariant to gait, speed and number of steps. We studied blindfolded human participants in a task in which they travelled by legged locomotion from a fixed starting point A to a variable terminus B, and then reproduced, by legged locomotion from B, the A-B distance. The outbound ('measure') and return ('report') gait could be the same or different, with similar or dissimilar step sizes and step frequencies. In five experiments we manipulated bipedal gait according to the primary versus secondary distinction revealed in symmetry group analyses of locomotion patterns. Berkeley's hypothesis held only when the measure and report gaits were of the same symmetry class, indicating that idiothetic distance measurement is gait-symmetry specific. Results suggest that human odometry (and perhaps animal odometry more generally) entails variables that encompass the limbs in coordination, such as global phase, and not variables at the level of the single limb, such as step length and step number, as traditionally assumed.

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

Foraging fiddler crabs (Uca spp.) monitor the location of, and are able to return to, their burrows by employing path integration. This requires them to accurately measure both the directions and distances of their locomotory movements. Even though most fiddler crabs inhabit relatively flat terrain, they must cope with vertical features of their environment, such as sloping beaches, mounds and shells, which may represent significant obstacles. To determine whether fiddler crabs can successfully perform path integration among such three-dimensional obstacles, we tested their ability to measure distance while we imposed a vertical detour. By inserting a large hill in the homeward path of foraging crabs we show that fiddler crabs can cope with vertical detours: they accurately travel the correct horizontal distance,despite the fact that the shape of the hill forces them to change their gait from what would be used on flat ground. Our results demonstrate a flexible path integrator capable of measuring, and either integrating or discarding,the vertical dimension.

Estimation of homing distance in desert ants,Cataglyphis fortis, remains unaffected by disturbance of walking behaviour

Desert ants, Cataglyphis fortis, use a stride integrator as a distance gauge in their well-studied path integration system (while a skylight compass provides the direction gauge). To further scrutinize the mechanisms of the ant odometer, we tried to disturb the stride integrator by interfering with normal walking behaviour. First, legs that contribute to one of the two leg tripods alternately used in normal walking were selectively amputated. This prevented the normal tripod gait and should interfere with both the normal walking programme controlled by the central nervous system, and normal sensory feedback from the legs. Second, manipulation of the walking substrate in the form of regular corrugations was observed to interfere with normal walking behaviour, at least for corrugation wavelengths (12–25 mm) in the range of normal stride lengths. The animals fell and stumbled, or footfall patterns were entrained to the corrugation wavelength. The relationship between stride length and stride frequency was altered in several situations. Surprisingly, distance estimation and homing performance remained virtually unaffected even by the most severe interferences with walking behaviour. This demonstrates a remarkable robustness of walking behaviour and homing, and it suggests that stride length is determined by robust signals of leg sense organs.