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Parallel vector memories in the brain of a bee as foundation for flexible navigation

Insects rely on path integration (vector-based navigation) and landmark guidance to perform sophisticated navigational feats, rivaling those seen in mammals. Bees in particular exhibit complex navigation behaviors including creating optimal routes and novel shortcuts between locations, an ability historically indicative of the presence of a cognitive map. A mammalian cognitive map has been widely accepted. However, in insects, the existence of a centralized cognitive map is highly contentious. Using a controlled laboratory assay that condenses foraging behaviors to short distances in walking bumblebees, we reveal that vectors learned during path integration can be transferred to long-term memory, that multiple such vectors can be stored in parallel, and that these vectors can be recalled at a familiar location and used for homeward navigation. These findings demonstrate that bees meet the two fundamental requirements of a vector-based analog of a decentralized cognitive map: Home vectors need to be stored in long-term memory and need to be recalled from remembered locations. Thus, our data demonstrate that bees possess the foundational elements for a vector-based map. By utilizing this relatively simple strategy for spatial organization, insects may achieve high-level navigation behaviors seen in vertebrates with the limited number of neurons in their brains, circumventing the computational requirements associated with the cognitive maps of mammals.

Spatiotemporal structure of foraging and path integration errors by fiddler crabs, Leptuca pugilator

Path integration is the navigational process by which animals construct a memory of a previous location by continuously measuring and summing their movements to form a single home vector pointing to the starting location. It is intrinsically error prone, subject to random errors and, potentially, to systematic errors in either measurement or the summing algorithm. Both types of errors lead to an incorrect vector memory and thus to an error in homing. Because the errors are incurred when animals move, they are theoretically predictable from the movements. We analyzed the behavior of fiddler crabs (Leptuca pugilator) as they performed foraging excursions followed by homing with varying degrees of error. From video recordings we measured body orientations and locations and computed these spatiotemporal path characteristics: duration, distance, turns, bearing and arc sector. These were analyzed for their effect on, separately, the magnitude, and the direction, of crabs’ homing error. The magnitude of the homing error was predicted by arc sector, Δbearing and path length, and several interactions. The direction of the homing error was predicted by interactions including arc sector x Δbearing, arc sector x turns, and Δbearing x turns. Covariance among these factors results in a path that traces a large arc while maintaining body orientation toward the burrow direction and leads to an error with the same clockwise/counterclockwise sign as the arc and the body turns. These results place L. pugilator’s path integration mechanism among others with known systematic errors.

Eye Movement Reflexes Indicate the Homing Direction in the Path-Integrating Fiddler Crab, Uca pugilator

As animals execute essential behaviors like foraging, they must orient with respect to the space around them, requiring some neural/behavioral mechanism for spatial navigation. One such navigation mechanism is path integration, whereby animals recall their starting point by creating a memory-stored home vector. In some animals, this is stored in an egocentric frame of reference; however, it remains unclear what comprises this in animals’ spatial memory. The fiddler crab Uca pugilator makes an excellent model to investigate the nature of the egocentric frame of reference because they appear to path integrate using self-motion cues to form an egocentric vector. We hypothesized that the home vector direction is governed by the optokinetic system, since the eye–body angle explicitly reflects the deviation of the body axis from home direction as optokinetic eye movements stabilize the eyes against body rotation. To test this hypothesis, we monitored eye and body movements during foraging excursions of crabs showing varying degrees of visual stabilization. We found that crabs with good eye stability had more accurate home vectors than those with poor eye stability, and the quantitative degree of stability accurately predicted the crabs’ perception of home direction. These results suggest that eye movement reflexes may establish the homing direction in path integrating fiddler crabs.

The balbyter ant Camponotus fulvopilosus combines several navigational strategies to support homing when foraging in the close vicinity of its nest.

Many insects rely on path integration to define direct routes back to their nests. When shuttling hundreds of meters back and forth between a profitable foraging site and a nest, navigational errors accumulate unavoidably in this compass- and odometer-based system. In familiar terrain, terrestrial landmarks can be used to compensate for these errors and safely guide the insect back to its nest with pin-point precision. In this study, we investigated the homing strategies employed by Camponotus fulvopilosus ants when repeatedly foraging no more than 1.25 m away from their nest. Our results reveal that the return journeys of the ants, even when setting out from a feeder from which the ants could easily get home using landmark information alone, are initially guided by path integration. After a short run in the direction given by the home vector, the ants then switched strategies and started to steer according to the landmarks surrounding their nest. We conclude that even when foraging in the close vicinity of its nest, an ant still benefits from its path-integrated vector to direct the start of its return journey.

Vector navigation in walking bumblebees

Path integration is a computational strategy that allows an animal to maintain an internal estimate of its position relative to a point of origin. Many species use path integration to navigate back to specific locations, typically their homes, after lengthy and convoluted excursions. Hymenopteran insects are impressive path integrators, directly returning to their hives after hundreds of meters of outward travel. Recent neurobiological insights have established hypotheses for how path integration vectors could be encoded in the brains of bees, but clear ways to test these hypotheses in the laboratory are currently unavailable. Here, we report that the bumblebee, Bombus terrestris, uses path integration while walking over short distances in an indoor arena. They estimate accurate vector distances after displacement and orient by artificial celestial cues. Walking bumblebees also exhibited systematic search patterns when home vectors failed to lead them accurately back to the nest, closely resembling searches performed by other species under natural conditions. We thus provide a robust experimental system to test navigation behavior in the laboratory that reflects most aspects of natural path integration. Importantly, we established this assay in an animal that is both readily available and resilient to invasive manipulations, as we demonstrate with the retention of the homing behavior post-anesthesia and surgery. In the future, our behavioral assay can therefore be combined with current electrophysiological techniques, opening a path toward directly probing the neural basis of the sophisticated vector navigation abilities of bees.

Anesthesia disrupts distance, but not direction, of path integration memory

Solitary foraging insects, such as ants, maintain an estimate of the direction and distance to their starting location as they move away from it, in a process known as path integration. This estimate, commonly known as the "home vector," is updated continuously as the ant moves1-4 and is reset as soon as it enters its nest,5 yet ants prevented from returning to their nest can still use their home vector when released several hours later.6,7 This conjunction of fast update and long persistence of the home vector memory does not directly map to existing accounts of short-, mid-, and long-term memory;2,8-12 hence, the substrate of this memory remains unknown. Chill-coma anesthesia13-15 has previously been shown to affect associative memory retention in fruit flies14,16 and honeybees.9,17,18 We investigate the nature of path integration memory by anesthetizing ants after they have accumulated home vector information and testing if the memory persists on recovery. We show that after anesthesia the memory of the distance ants have traveled is degraded, but the memory of the direction is retained. We also show that this is consistent with models of path integration that maintain the memory in a redundant Cartesian coordinate system and with the hypothesis that chill-coma produces a proportional reduction of the memory, rather than a subtractive reduction or increase of noise. The observed effect is not compatible with a memory based on recurrent circuit activity and points toward an activity-dependent molecular process as the basis of path integration memory.

Cold-induced anesthesia impairs path integration memory in dung beetles

Path integration is a general mechanism used by many animals to maintain an updated record of their position in relation to a set reference point.1-11 To do this, they continually integrate direction and distance information into a memorized home vector. What remains unclear is how this vector is stored, maintained, and utilized for successful navigation. A recent computational model based on the neuronal circuitry of the insect central complex suggests that home vector memories are encoded across a set of putative memory neurons and maintained through ongoing recurrent neural activity.12 To better understand the nature of the home vector memory and experimentally assess underlying mechanisms for maintaining it, we performed a series of experiments on the path integrating dung beetle Scarabaeus galenus.13 We found that, while the directional component of the home vector was maintained for up to 1 h, the distance component of the vector memory decreased gradually over time. Using cold-induced anesthesia, we disrupted the neural activity of beetles that had stored a home vector of known length and direction. This treatment diminished both components of the home vector memory, but by different amounts-the homing beetles lost their distance memory before their directional memory. Together, these findings present new insights into the functional properties of home vector memories and provide the first empirical evidence that a biological process that can be disrupted by cold-induced anesthesia is essential to support homing by path integration.

Role of the pheromone for navigation in the group foraging ant, Veromessor pergandei.

Navigation is comprised of a variety of strategies which rely on multiple external cues to shape a navigator's behavioral output. Here, we explored in the ant Veromessor pergandei, the interactions between the information provided by the pheromone trail and the home vector guided by the celestial compass. We found that a cross sensory interaction between the pheromone cue and the path integrator underlies correct orientation during the inbound journey. The celestial compass provides directional information, while the presence of the trail pheromone acts as a critical context cue, triggering distinct behaviors (vector orientation, search, and backtracking). While exposed to the pheromone, foragers orient to the vector direction regardless of vector state, while in the pheromone's absence, the current remaining vector determines the forager's navigational behavior. This interaction also occurs in foragers with no remaining path integrator, relying on the activation of a celestial compass-based memory of the previous trip. Such cue interactions maximize the foragers' return to the nest and inhibit movement off the pheromone trail. Finally, our manipulations continuously rotated foragers away from their desired heading, yet foragers were proficient at counteracting these changes, steering to maintain a correct compass heading even at rotational speeds of ~ 40°/s.

Spatial inference without a cognitive map: the role of higher-order path integration.

The cognitive map has been taken as the standard model for how agents infer the most efficient route to a goal location. Alternatively, path integration - maintaining a homing vector during navigation - constitutes a primitive and presumably less-flexible strategy than cognitive mapping because path integration relies primarily on vestibular stimuli and pace counting. The historical debate as to whether complex spatial navigation is ruled by associative learning or cognitive map mechanisms has been challenged by experimental difficulties in successfully neutralizing path integration. To our knowledge, there are only three studies that have succeeded in resolving this issue, all showing clear evidence of novel route taking, a behaviour outside the scope of traditional associative learning accounts. Nevertheless, there is no mechanistic explanation as to how animals perform novel route taking. We propose here a new model of spatial learning that combines path integration with higher-order associative learning, and demonstrate how it can account for novel route taking without a cognitive map, thus resolving this long-standing debate. We show how our higher-order path integration (HOPI) model can explain spatial inferences, such as novel detours and shortcuts. Our analysis suggests that a phylogenetically ancient, vector-based navigational strategy utilizing associative processes is powerful enough to support complex spatial inferences.

Non-visual homing and the current status of navigation in scorpions

Within arthropods, the investigation of navigational aspects including homing abilities has mainly focused on insect representatives, while other arthropod taxa have largely been ignored. As such, scorpions are rather underrepresented concerning behavioral studies for reasons such as low participation rates and motivational difficulties. Here, we review the sensory abilities of scorpions related to navigation. Furthermore, we present an improved laboratory setup to shed light on navigational abilities in general and homing behavior in particular. We tracked directed movements towards home shelters of the lesser Asian scorpion Mesobuthus eupeus to give a detailed description of their departure and return movements. To do so, we analyzed the departure and return angles as well as measures of directness like directional deviation, lateral displacement, and straightness indices. We compared these parameters under different light conditions and with blinded scorpions. The motivation of scorpions to leave their shelter depends strongly upon the light condition and the starting time of the experiment; highest participation rates were achieved with infrared conditions or blinded scorpions, and close to dusk. Naïve scorpions are capable of returning to a shelter object in a manner that is directionally consistent with the home vector. The first-occurring homing bouts are characterized by paths consisting of turns about 10 cm to either side of the straightest home path and a distance efficiency of roughly three-quarters of the maximum efficiency. Our results show that neither chemosensation nor vision, but rather path integration based on proprioception, plays a superior role in the homing of scorpions.

A generalized multi-snapshot model for 3D homing and route following

Inspired by the learning walks of the ant Ocymyrmex robustior, the original multi-snapshot model was introduced, which—in contrast to the classical “single snapshot at the goal” model—collects multiple snapshots in the vicinity of the goal location that subsequently can be used for homing, that is, for guiding the return to the goal. In this study, we show that the multi-snapshot model can be generalized to homing in three dimensions. In addition to capturing snapshots at positions shifted in all three dimensions, we suggest to decouple the home direction from the orientation of snapshots and to associate a home vector with each snapshot. We then propose a modification of the multi-snapshot model for three-dimensional route following and evaluate its performance in an accurate reconstruction of a real environment. As an illumination-invariant alternative to grayscale images, we also examine sky-segmented images. We use spherical harmonics as efficient representation of panoramic images enabling low memory usage and fast similarity estimation of rotated images. The results show that our approach can steer an agent reliably along a route, making it also suitable for robotic applications using on-board computers with limited resources.

이미지 특징점 가중치 학습을 통한 내비게이션

Visual navigation is a challenging subject in robotics, which is involved estimating the target position and direction at an arbitrary location. In this study, we follow the snapshot model, a bio-inspired model to determine the target direction with the snapshots taken at the current location and the target location. From the snapshots, we collect landmarks with three different features, the corner landmarks with SURF (Speeded Up Robust Features), the vertical edge landmarks with HOG (Histogram of Gradient) and the Haar-like feature landmarks. Those methods can play significant roles in finding appropriate visual features depending on the environment. A linear combination of those landmarks, that is, weighted feature landmarks are more suitable to find homing vector than landmarks found with one method alone. We propose that the gradient-descent method should be applied to the weighted feature landmarks to improve the homing performance. The homing results with ALV (Average Landmark Vector) model are demonstrated to show the effectiveness of the method.

New Results on Vector and Homing Vector Automata

We present several new results and connections between various extensions of finite automata through the study of vector automata and homing vector automata. We show that homing vector automata outperform extended finite automata when both are defined over [Formula: see text] integer matrices. We study the string separation problem for vector automata and demonstrate that generalized finite automata with rational entries can separate any pair of strings using only two states. Investigating stateless homing vector automata, we prove that a language is recognized by stateless blind deterministic real-time version of finite automata with multiplication iff it is commutative and its Parikh image is the set of nonnegative integer solutions to a system of linear homogeneous Diophantine equations.

The Central Complex as a Potential Substrate for Vector Based Navigation.

Insects use path integration (PI) to maintain a home vector, but can also store and recall vector-memories that take them from home to a food location, and even allow them to take novel shortcuts between food locations. The neural circuit of the Central Complex (a brain area that receives compass and optic flow information) forms a plausible substrate for these behaviors. A recent model, grounded in neurophysiological and neuroanatomical data, can account for PI during outbound exploratory routes and the control of steering to return home. Here, we show that minor, hypothetical but neurally plausible, extensions of this model can additionally explain how insects could store and recall PI vectors to follow food-ward paths, take shortcuts, search at the feeder and re-calibrate their vector-memories with experience. In addition, a simple assumption about how one of multiple vector-memories might be chosen at any point in time can produce the development and maintenance of efficient routes between multiple locations, as observed in bees. The central complex circuitry is therefore well-suited to allow for a rich vector-based navigational repertoire.

A simple mathematical model using centred loops and random perturbations accurately reconstructs search patterns observed in desert ants

This paper describes a new mathematical model that is based on centred loops to reconstruct the “Systematic Search” behaviour of Cataglyphis desert ants. The notable advantage of this model is the combination of simplicity, efficiency and performance. All model input is kept to a minimum, using only parameters that previous research has shown to be available to the animals at all times: distance from the origin, direction of the last step and home vector. Outbound and inbound search paths are being combined into loops that return to the origin, sampling this area more intensely. A stochastic element is added by random perturbations during the next step, mimicking unsystematic errors during the process of path integration and yielding the typical search patterns observed in Cataglyphis desert ants. The model output is compared to runs observed in the field.

Exclusive shift from path integration to visual cues during the rapid escape run of fiddler crabs

Animals are equipped with sophisticated guidance systems that enable them to navigate efficiently. Previous studies suggest that foraging animals such as desert ants tend to combine guidance systems in a weighted manner, where the weight given to each cue gradually changes during the approach to the goal. However, when subjected to rapid enforced decision making (e.g. under predation risk), the animal may use alternative mechanisms, as recently suggested for ecologically relevant decisions involving time constraints in humans. We show here that fiddler crabs, Uca perplexa, scuttling to their burrows when threatened, responded to visual cues only if their path integration (PI) systems indicated nearness to their burrows. When homing errors were imposed by placing fake entrances (visual cues) along their homing paths and masking their true burrows (the goal of PI), the threatened crabs altered their behaviour towards visual cues according to the remaining PI vector length; if it was long, they continued running until they arrived at the masked true burrow, ignoring the visual cue, but if it was short, they suddenly stopped at the fake entrance. Our results suggest that, for fiddler crabs, PI and the view are mutually exclusive cues and that they instantly shift from one to the other if they approach the end of the home vector, instead of combining systems in a weighted manner. This could enable them to avoid entering the wrong burrow, where they would be ejected by the resident crab and be subject to predation.

The Geomagnetic Field Is a Compass Cue in Cataglyphis Ant Navigation

Desert ants (Cataglyphis) are famous insect navigators. During their foraging lives, the ants leave their underground colonies for long distances and return to their starting point with fair accuracy [1, 2]. Their incessantly running path integrator provides them with a continually updated home vector [3-5]. Directional input to their path integrator is provided by avisual compass based on celestial cues [6, 7]. However, as path integration is prone to cumulative errors, the ants additionally employ landmark guidance routines [8-11]. At the start of their foraging lives, they acquire the necessary landmark information by performing well-structured learning walks [12, 13], including turns about their vertical body axes [14]. When Cataglyphis noda performs these pirouettes, it always gazes at the nest entrance during the longest of several short stopping phases [14]. As the small nest entrance is not visible, the ants can adjust their gaze direction only by reading out their path integrator. However, recent experiments have shown that, for adjusting the goal-centered gaze directions during learning walks, skylight cues are not required [15]. A most promising remaining compass cue is the geomagnetic field, which is used for orientation in one way or the other by a variety of animal species [16-25]. Here, we show that the gaze directions during the look-back-to-the-nest behavior change in a predictable way to alterations of the horizontal component of the magnetic field. This is the first demonstration that, in insects, a geomagnetic compass cue is both necessary and sufficient for accomplishing a well-defined navigational task.

Towards efficient and scalable visual homing

Visual homing describes the ability of a robot to autonomously return to its starting position along a previously traversed path using visual information. In this paper, we propose a method for visual homing that is solely based on bearing angles to landmarks. During the first traversal of a path, the robot creates a sequence of viewframes, which are rotationally aligned landmark angle configurations at certain locations. While homing, the robot calculates homing vectors which subsequently align the currently perceived set of landmark observations with the reference viewframe until the home location is reached. This paper discusses methods for homing vector calculation and proposes new methods which are more robust and yield straighter homing paths in non-isotropic landmark distributions and false landmark matches. Furthermore, we present the Trail-Map, which is a novel data structure for storing a sequence of viewframes in a non-redundant and scalable way. The Trail-Map exploits the fact that the bearing angles to both distant landmarks and landmarks in the direction of movement hardly change when the robot moves, whereas close landmarks change their bearing angles quickly. Thus, the Trail-Map enables easy downscaling by deleting observations that correspond to nearby, fast-changing landmarks and, thus, retains the stable, translation invariant landmark information. We demonstrate the memory efficiency and scalability of the data structure in simulations and in real-world indoor and outdoor experiments. This makes the proposed method for visual homing suitable for mobile robots with limited computational and memory resources.

High-Order Moment Models of Landmark Distribution for Local Homing Navigation

For local homing navigation, a mobile robot is supposed to return home using snapshots of the surrounding environment. It basically follows the snapshot model, comparing the home snapshot and the current view to determine the homing direction. In this paper, we suggest a high-order moment potential to describe the landmark feature distribution for local homing navigation. The moment potential function calculates the sum of products of the feature and the distance of landmark particles as a holistic view, allowing a high order of the distance. It effectively combines the range sensor values of landmarks in the current view and the visual features. By analogy with the moment in physics, the center of the moment is estimated as the reference point, which is the unique convergence point in the convex moment potential from any view, and using the property, the gradient of moment potential at the current position and home location can derive the homing vector. We provide a proof of convergence for any moment potential with order greater than or equal to one. Also, we demonstrate homing performances with various moment models in real environments to validate our models. The suggested moment models combining both landmark distance and visual feature have better performances than the visual information alone, and high-order moment potentials can be searched to obtain a better description of landmark distribution for a given environment.

Local Homing Navigation Based on the Moment Model for Landmark Distribution and Features.

For local homing navigation, an agent is supposed to return home based on the surrounding environmental information. According to the snapshot model, the home snapshot and the current view are compared to determine the homing direction. In this paper, we propose a novel homing navigation method using the moment model. The suggested moment model also follows the snapshot theory to compare the home snapshot and the current view, but the moment model defines a moment of landmark inertia as the sum of the product of the feature of the landmark particle with the square of its distance. The method thus uses range values of landmarks in the surrounding view and the visual features. The center of the moment can be estimated as the reference point, which is the unique convergence point in the moment potential from any view. The homing vector can easily be extracted from the centers of the moment measured at the current position and the home location. The method effectively guides homing direction in real environments, as well as in the simulation environment. In this paper, we take a holistic approach to use all pixels in the panoramic image as landmarks and use the RGB color intensity for the visual features in the moment model in which a set of three moment functions is encoded to determine the homing vector. We also tested visual homing or the moment model with only visual features, but the suggested moment model with both the visual feature and the landmark distance shows superior performance. We demonstrate homing performance with various methods classified by the status of the feature, the distance and the coordinate alignment.