Animal path integration: a model of positional uncertainty along tortuous paths

No Need for Landmarks: An Embodied Neural Controller for Robust Insect-Like Navigation Behaviors

Bayesian filters have been considered to help refine and develop theoretical views on spatial cell functions for self-localization. However, extending a Bayesian filter to reproduce insect-like navigation behaviors (e.g., home searching) remains an open and challenging problem. To address this problem, we propose an embodied neural controller for self-localization, foraging, backward homing (BH), and home searching of an advanced mobility sensor (AMOS)-driven insect-like robot. The controller, comprising a navigation module for the Bayesian self-localization and goal-directed control of AMOS and a locomotion module for coordinating the 18 joints of AMOS, leads to its robust insect-like navigation behaviors. As a result, the proposed controller enables AMOS to perform robust foraging, BH, and home searching against various levels of sensory noise, compared to conventional controllers. Its implementation relies only on self-localization and heading perception, rather than global positioning and landmark guidance. Interestingly, the proposed controller makes AMOS achieve spiral searching patterns comparable to those performed by real insects. We also demonstrated the performance of the controller for real-time indoor and outdoor navigation in a real insect-like robot without any landmark and cognitive map.

A connectome of the Drosophila central complex reveals network motifs suitable for flexible navigation and context-dependent action selection

Flexible behaviors over long timescales are thought to engage recurrent neural networks in deep brain regions, which are experimentally challenging to study. In insects, recurrent circuit dynamics in a brain region called the central complex (CX) enable directed locomotion, sleep, and context- and experience-dependent spatial navigation. We describe the first complete electron microscopy-based connectome of the Drosophila CX, including all its neurons and circuits at synaptic resolution. We identified new CX neuron types, novel sensory and motor pathways, and network motifs that likely enable the CX to extract the fly's head direction, maintain it with attractor dynamics, and combine it with other sensorimotor information to perform vector-based navigational computations. We also identified numerous pathways that may facilitate the selection of CX-driven behavioral patterns by context and internal state. The CX connectome provides a comprehensive blueprint necessary for a detailed understanding of network dynamics underlying sleep, flexible navigation, and state-dependent action selection.

Drosophila re-zero their path integrator at the center of a fictive food patch

The ability to keep track of one's location in space is a critical behavior for animals navigating to and from a salient location, and its computational basis is now beginning to be unraveled. Here, we tracked flies in a ring-shaped channel as they executed bouts of search triggered by optogenetic activation of sugar receptors. Unlike experiments in open field arenas, which produce highly tortuous search trajectories, our geometrically constrained paradigm enabled us to monitor flies' decisions to move toward or away from the fictive food. Our results suggest that flies use path integration to remember the location of a food site even after it has disappeared, and flies can remember the location of a former food site even after walking around the arena one or more times. To determine the behavioral algorithms underlying Drosophila search, we developed multiple state transition models and found that flies likely accomplish path integration by combining odometry and compass navigation to keep track of their position relative to the fictive food. Our results indicate that whereas flies re-zero their path integrator at food when only one feeding site is present, they adjust their path integrator to a central location between sites when experiencing food at two or more locations. Together, this work provides a simple experimental paradigm and theoretical framework to advance investigations of the neural basis of path integration.

The Critical Role of Head Movements for Spatial Representation During Bumblebees Learning Flight

Bumblebees perform complex flight maneuvers around the barely visible entrance of their nest upon their first departures. During these flights bees learn visual information about the surroundings, possibly including its spatial layout. They rely on this information to return home. Depth information can be derived from the apparent motion of the scenery on the bees' retina. This motion is shaped by the animal's flight and orientation: Bees employ a saccadic flight and gaze strategy, where rapid turns of the head (saccades) alternate with flight segments of apparently constant gaze direction (intersaccades). When during intersaccades the gaze direction is kept relatively constant, the apparent motion contains information about the distance of the animal to environmental objects, and thus, in an egocentric reference frame. Alternatively, when the gaze direction rotates around a fixed point in space, the animal perceives the depth structure relative to this pivot point, i.e., in an allocentric reference frame. If the pivot point is at the nest-hole, the information is nest-centric. Here, we investigate in which reference frames bumblebees perceive depth information during their learning flights. By precisely tracking the head orientation, we found that half of the time, the head appears to pivot actively. However, only few of the corresponding pivot points are close to the nest entrance. Our results indicate that bumblebees perceive visual information in several reference frames when they learn about the surroundings of a behaviorally relevant location.

Towards a multi-level understanding in insect navigation

To understand the brain is to understand behaviour. However, understanding behaviour itself requires consideration of sensory information, body movements and the animal's ecology. Therefore, understanding the link between neurons and behaviour is a multi-level problem, which can be achieved when considering Marr's three levels of understanding: behaviour, computation, and neural implementation. Rather than establishing direct links between neurons and behaviour, the matter boils down to understanding two transitions: the link between neurons and brain computation on one hand, and the link between brain computations and behaviour on the other hand. The field of insect navigation illustrates well the power of such two-sided endeavour. We provide here examples revealing that each transition requires its own approach with its own intrinsic difficulties, and show how modelling can help us reach the desired multi-level understanding.

Path integration error and adaptable search behaviors in a mantis shrimp

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.

Principles of Insect Path Integration

Continuously monitoring its position in space relative to a goal is one of the most essential tasks for an animal that moves through its environment. Species as diverse as rats, bees, and crabs achieve this by integrating all changes of direction with the distance covered during their foraging trips, a process called path integration. They generate an estimate of their current position relative to a starting point, enabling a straight-line return, following what is known as a home vector. While in theory path integration always leads the animal precisely back home, in the real world noise limits the usefulness of this strategy when operating in isolation. Noise results from stochastic processes in the nervous system and from unreliable sensory information, particularly when obtaining heading estimates. Path integration, during which angular self-motion provides the sole input for encoding heading (idiothetic path integration), results in accumulating errors that render this strategy useless over long distances. In contrast, when using an external compass this limitation is avoided (allothetic path integration). Many navigating insects indeed rely on external compass cues for estimating body orientation, whereas they obtain distance information by integration of steps or optic-flow-based speed signals. In the insect brain, a region called the central complex plays a key role for path integration. Not only does the central complex house a ring-attractor network that encodes head directions, neurons responding to optic flow also converge with this circuit. A neural substrate for integrating direction and distance into a memorized home vector has therefore been proposed in the central complex. We discuss how behavioral data and the theoretical framework of path integration can be aligned with these neural data.

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 Neurocomputational Model of Goal-Directed Navigation in Insect-Inspired Artificial Agents

Despite their small size, insect brains are able to produce robust and efficient navigation in complex environments. Specifically in social insects, such as ants and bees, these navigational capabilities are guided by orientation directing vectors generated by a process called path integration. During this process, they integrate compass and odometric cues to estimate their current location as a vector, called the home vector for guiding them back home on a straight path. They further acquire and retrieve path integration-based vector memories globally to the nest or based on visual landmarks. Although existing computational models reproduced similar behaviors, a neurocomputational model of vector navigation including the acquisition of vector representations has not been described before. Here we present a model of neural mechanisms in a modular closed-loop control—enabling vector navigation in artificial agents. The model consists of a path integration mechanism, reward-modulated global learning, random search, and action selection. The path integration mechanism integrates compass and odometric cues to compute a vectorial representation of the agent's current location as neural activity patterns in circular arrays. A reward-modulated learning rule enables the acquisition of vector memories by associating the local food reward with the path integration state. A motor output is computed based on the combination of vector memories and random exploration. In simulation, we show that the neural mechanisms enable robust homing and localization, even in the presence of external sensory noise. The proposed learning rules lead to goal-directed navigation and route formation performed under realistic conditions. Consequently, we provide a novel approach for vector learning and navigation in a simulated, situated agent linking behavioral observations to their possible underlying neural substrates.

Probabilistic Learning by Rodent Grid Cells

Mounting evidence shows mammalian brains are probabilistic computers, but the specific cells involved remain elusive. Parallel research suggests that grid cells of the mammalian hippocampal formation are fundamental to spatial cognition but their diverse response properties still defy explanation. No plausible model exists which explains stable grids in darkness for twenty minutes or longer, despite being one of the first results ever published on grid cells. Similarly, no current explanation can tie together grid fragmentation and grid rescaling, which show very different forms of flexibility in grid responses when the environment is varied. Other properties such as attractor dynamics and grid anisotropy seem to be at odds with one another unless additional properties are assumed such as a varying velocity gain. Modelling efforts have largely ignored the breadth of response patterns, while also failing to account for the disastrous effects of sensory noise during spatial learning and recall, especially in darkness. Here, published electrophysiological evidence from a range of experiments are reinterpreted using a novel probabilistic learning model, which shows that grid cell responses are accurately predicted by a probabilistic learning process. Diverse response properties of probabilistic grid cells are statistically indistinguishable from rat grid cells across key manipulations. A simple coherent set of probabilistic computations explains stable grid fields in darkness, partial grid rescaling in resized arenas, low-dimensional attractor grid cell dynamics, and grid fragmentation in hairpin mazes. The same computations also reconcile oscillatory dynamics at the single cell level with attractor dynamics at the cell ensemble level. Additionally, a clear functional role for boundary cells is proposed for spatial learning. These findings provide a parsimonious and unified explanation of grid cell function, and implicate grid cells as an accessible neuronal population readout of a set of probabilistic spatial computations.

Cells in the mammalian hippocampal formation are thought to be central for spatial learning and stable spatial representations. Of the known spatial cells, grid cells form strikingly regular and stable patterns of activity, even in darkness. Hence, grid cells may provide the universal metric upon which spatial cognition is based. However, a more fundamental problem is how grids themselves may form and stabilise, since sensory information is noisy and can vary tremendously with environmental conditions. Furthermore, the same grid cell can display substantially different yet stable patterns of activity in different environments. Currently, no model explains how vastly different sensory cues can give rise to the diverse but stable grid patterns. Here, a new probabilistic model is proposed which combines information encoded by grid cells and boundary cells. This noise-tolerant model performs robust spatial learning, under a variety of conditions, and produces varied yet stable grid cell response patterns like rodent grid cells. Across numerous experimental manipulations, rodent and probabilistic grid cell responses are similar or even statistically indistinguishable. These results complement a growing body of evidence suggesting that mammalian brains are inherently probabilistic, and suggest for the first time that grid cells may be involved.

Morphological differences between habitats are associated with physiological and behavioural trade-offs in stickleback (Gasterosteus aculeatus)

Local specialization can be advantageous for individuals and may increase the resilience of the species to environmental change. However, there may be trade-offs between morphological responses and physiological performance and behaviour. Our aim was to test whether habitat-specific morphology of stickleback (Gasterosteus aculeatus) interacts with physiological performance and behaviour at different salinities. We rejected the hypothesis that deeper body shape of fish from habitats with high predation pressure led to decreases in locomotor performance. However, there was a trade-off between deeper body shape and muscle quality. Muscle of deeper-bodied fish produced less force than that of shallow-bodied saltmarsh fish. Nonetheless, saltmarsh fish had lower swimming performance, presumably because of lower muscle mass overall coupled with smaller caudal peduncles and larger heads. Saltmarsh fish performed better in saline water (20 ppt) relative to freshwater and relative to fish from freshwater habitats. However, exposure to salinity affected shoaling behaviour of fish from all habitats and shoals moved faster and closer together compared with freshwater. We show that habitat modification can alter phenotypes of native species, but local morphological specialization is associated with trade-offs that may reduce its benefits.

Early ant trajectories: spatial behaviour before behaviourism

In the beginning of the twentieth century, when Jacques Loeb's and John Watson's mechanistic view of life started to dominate animal physiology and behavioural biology, several scientists with different academic backgrounds got engaged in studying the wayfinding behaviour of ants. Largely unaffected by the scientific spirit of the time, they worked independently of each other in different countries: in Algeria, Tunisia, Spain, Switzerland and the United States of America. In the current literature on spatial cognition these early ant researchers--Victor Cornetz, Felix Santschi, Charles Turner and Rudolf Brun--are barely mentioned. Moreover, it is virtually unknown that the great neuroanatomist Santiago Ramón y Cajal had also worked on spatial orientation in ants. This general neglect is certainly due to the fact that nearly all these ant researchers were scientific loners, who did their idiosyncratic investigations outside the realm of comparative physiology, neurobiology and the behavioural sciences of the time, and published their results in French, German, and Spanish at rather inaccessible places. Even though one might argue that much of their work resulted in mainly anecdotal evidence, the conceptual approaches of these early ant researchers preempt much of the present-day discussions on spatial representation in animals.

Spatial cognition in bats and rats: from sensory acquisition to multiscale maps and navigation

Spatial orientation and navigation rely on the acquisition of several types of sensory information. This information is then transformed into a neural code for space in the hippocampal formation through the activity of place cells, grid cells and head-direction cells. These spatial representations, in turn, are thought to guide long-range navigation. But how the representations encoded by these different cell types are integrated in the brain to form a neural 'map and compass' is largely unknown. Here, we discuss this problem in the context of spatial navigation by bats and rats. We review the experimental findings and theoretical models that provide insight into the mechanisms that link sensory systems to spatial representations and to large-scale natural navigation.

Estimating location without external cues

The ability to determine one's location is fundamental to spatial navigation. Here, it is shown that localization is theoretically possible without the use of external cues, and without knowledge of initial position or orientation. With only error-prone self-motion estimates as input, a fully disoriented agent can, in principle, determine its location in familiar spaces with 1-fold rotational symmetry. Surprisingly, localization does not require the sensing of any external cue, including the boundary. The combination of self-motion estimates and an internal map of the arena provide enough information for localization. This stands in conflict with the supposition that 2D arenas are analogous to open fields. Using a rodent error model, it is shown that the localization performance which can be achieved is enough to initiate and maintain stable firing patterns like those of grid cells, starting from full disorientation. Successful localization was achieved when the rotational asymmetry was due to the external boundary, an interior barrier or a void space within an arena. Optimal localization performance was found to depend on arena shape, arena size, local and global rotational asymmetry, and the structure of the path taken during localization. Since allothetic cues including visual and boundary contact cues were not present, localization necessarily relied on the fusion of idiothetic self-motion cues and memory of the boundary. Implications for spatial navigation mechanisms are discussed, including possible relationships with place field overdispersion and hippocampal reverse replay. Based on these results, experiments are suggested to identify if and where information fusion occurs in the mammalian spatial memory system.

Spatial navigation is one of the most important functions of animal brains. Multiple regions and cell types encode the current location in mammalian brains, but the underlying interactions between sensory and memory information remain unclear. Recent experimental and theoretical evidence have been found to suggest that the presence of a boundary fundamentally alters the task of navigation. In this paper, evidence is provided that it is possible to determine the location inside any familiar arena with 1-fold rotational symmetry, while completely ignoring sensory cues from the outside world. Surprisingly, the results show that the mere knowledge of the boundary's existence is enough, without requiring direct physical contact. Localization is robust despite the presence of noise modelled from the rodent head direction system, and even inaccuracies in the navigation system's memory of the boundary or internal models of noise. In circular arenas, rotational asymmetry can arise from interior structures such as barriers or voids, also without contact information. This theoretical evidence highlights the need to distinguish arena-based navigation common to most experimental studies, from open field navigation. These findings also point to novel ways to study information fusion in mammalian brains.