How do insects use path integration for their navigation?

 We combine experimental findings on ants and bees, and build on earlier models, to give an account of how these insects navigate using path integration, and how path integration interacts with other modes of navigation. At the core of path integration is an accumulator. This is set to an initial state at the nest and is updated as the insect moves so that it always reports the insect's current position relative to the nest. Navigation that uses path integration requires, in addition, a way of storing states of the accumulator at significant places for subsequent recall as goals, and a means of computing the direction to such goals. We discuss three models of how path integration might be used for this process, which we call vector navigation. Vector navigation is the principal means of navigating over unfamiliar terrain, or when landmarks are unavailable. Under other conditions, insects often navigate by landmarks, and ignore the output of the vector navigation system. Landmark navigation does not interfere with the updating of the accumulator. There is an interesting symmetry in the use of landmarks and path integration. In the short term, vector navigation can be independent of landmarks, and landmark navigation needs no assistance from path integration. In the longer term, visual landmarks help keep path vector navigation calibrated, and the learning of visual landmarks is guided by path integration. Received: 6 June 1999 / Accepted in revised form: 20 March 2000     

Sensory feedback in a bump attractor model of path integration

Mammalian spatial navigation systems utilize several different sensory information channels. This information is converted into a neural code that represents the animal’s current position in space by engaging place cell, grid cell, and head direction cell networks. In particular, sensory landmark (allothetic) cues can be utilized in concert with an animal’s knowledge of its own velocity (idiothetic) cues to generate a more accurate representation of position than path integration provides on its own (Battaglia et al. The Journal of Neuroscience 24(19):4541–4550 (2004)). We develop a computational model that merges path integration with feedback from external sensory cues that provide a reliable representation of spatial position along an annular track. Starting with a continuous bump attractor model, we explore the impact of synaptic spatial asymmetry and heterogeneity, which disrupt the position code of the path integration process. We use asymptotic analysis to reduce the bump attractor model to a single scalar equation whose potential represents the impact of asymmetry and heterogeneity. Such imperfections cause errors to build up when the network performs path integration, but these errors can be corrected by an external control signal representing the effects of sensory cues. We demonstrate that there is an optimal strength and decay rate of the control signal when cues appear either periodically or randomly. A similar analysis is performed when errors in path integration arise from dynamic noise fluctuations. Again, there is an optimal strength and decay of discrete control that minimizes the path integration error.     

Path integration — a network model

Path integration is a primary means of navigation for a number of animals. We present a model which performs path integration with a neural network. This model is based on a neural structure called a sinusoidal array, which allows an efficient representation of vector information with neurons. We show that exact path integration can easily be achieved by a neural network. Thus deviations from the direct home trajectory, found previously in experiments with ants, can not be explained by computational limitations of the nervous system. Instead we suggest that the observed deviations are caused by a strategy to simplify landmark navigation.     

A new navigational mechanism mediated by ant ocelli

Many animals rely on path integration for navigation and desert ants are the champions. On leaving the nest, ants continuously integrate their distance and direction of travel so that they always know their current distance and direction from the nest and can take a direct path to home. Distance information originates from a step-counter and directional information is based on a celestial compass. So far, it has been assumed that the directional information obtained from ocelli contribute to a single global path integrator, together with directional information from the dorsal rim area (DRA) of the compound eyes and distance information from the step-counter. Here, we show that ocelli mediate a distinct compass from that mediated by the compound eyes. After travelling a two-leg outbound route, untreated foragers headed towards the nest direction, showing that both legs of the route had been integrated. In contrast, foragers with covered compound eyes but uncovered ocelli steered in the direction opposite to the last leg of the outbound route. Our findings suggest that, unlike the DRA, ocelli cannot by themselves mediate path integration. Instead, ocelli mediate a distinct directional system, which buffers the most recent leg of a journey.     

The hidden spiral: systematic search and path integration in desert ants,Cataglyphis fortis

The main navigational mechanism used by foraging desert ants of the genus Cataglyphis is path integration (dead reckoning). Any such egocentric system of navigation is prone to cumulative navigational errors. Hence, while homing Cataglyphis might have reset its path integration system and yet not arrived at the start of its foraging excursion, the nest entrance. Then it resorts to piloting or performs a systematic search for the nest. The search pattern consists of a system of loops of ever increasing size centred about the origin, i.e. the start of the search. Here we show that underlying the system of loops is a spiral search programme that gets transformed into the observed pattern of loops by the ant's idiosyncratic path-integration algorithm. The ant starts to follow a spiral course, then breaks off this course and walks towards the centre, i.e. to what its path-integration system has computed to be the origin of the search. This reset episode is followed by another spiral course, which is terminated by the next reset, and so forth. After each reset, the spiral gets wider, so that the whole pattern expands. Futhermore, every now and then the spiral might change its sign. Computer simulations based on these simple rules lead to search patterns of the kind actually recorded in Cataglyphis ants. These patterns ensure that those parts of the area in which the target (nest entrance) is most likely to be located are searched most heavily; in other words: the search density profile is adapted to the probability density function of the target.     

Navigation without vision: bumblebee orientation in complete darkness

In flight cages, worker bumblebees (Bombus impatiens) spontaneously explored the surroundings of their nest and foraged in complete darkness, by walking instead of flying, from feeders up to 150 cm away from the nest. This behaviour was wholly unexpected in these classically visual foragers. The finding provides a controlled system for dissecting possible non-visual components of navigation used in daylight. It also allows us to isolate navigation mechanisms used in naturally dark situations, such as in the nest. Using infrared video, we mapped walking trails. We found that bumblebees laid odour marks. When such odour cues were eliminated, bees maintained correct directionality, suggesting a magnetic compass. They were also able to assess travel distance correctly, using an internal, non-visual, measure of path length. Path integration was not employed. Presumably, this complex navigational skill requires visual input in bees.     

Evidence for Resetting the Directional Component of Path Integration in the House Mouse (Mus musculus)

Path integration is the animal's running computation of its position relative to a starting point based on recording all displacements. This process is known to be prone to cumulative errors and hence must somehow be corrected with the help of local spatial cues. In the reported experiments, the relative role of local spatial cues at two target locations was appraised. These two targets were the peripheral box of a female house mouse (Mus musculus) and a central box from where she retrieved her pups over a distance of 50 cm. The experimental conditions required the mouse to navigate between the two targets solely by means of path integration. To find out whether the mice continued integrating at the two target locations, directional misinformation was fed into their path integrating system. Hence, passive rotation of 90° proved to be sufficient to decide unambiguously whether the mice were misdirected. Such experimental interference consistently documented ongoing path integration at the target location outside the residential nest. In contrast, the same interference when the mouse was in the residential nest documented discontinuation of path integration in most cases. It is inferred that mice, when departing from residential nests, initially direct themselves by means of local guiding stimuli.     

Long-distance navigation in the wandering desert spider<Emphasis Type="Italic"> Leucorchestris arenicola</Emphasis>: can the slope of the dune surface provide a compass cue?

Males of the nocturnal spider Leucorchestris arenicola (Araneae: Sparassidae) wander long distances over seemingly featureless dune surfaces in the Namib Desert searching for females. The spiders live in burrows to which they return after nearly every such excursion. While the outward path of an excursion may be a meandering search, the return path is often a nearly straight line leading towards the burrow. This navigational behaviour resembles that of path integration known from other arthropods, though on a much larger scale (over tens to hundreds of meters). Theoretically, precise navigation by path integration over long distances requires an external compass in order to adjust for inevitable accumulation of navigational errors. As a first step towards identifying any nocturnal compass cues used by the male spiders, a method for detailed 3-D recordings of the spiders paths was developed. The 3-D reconstructions of the paths revealed details about the processes involved in the spiders nocturnal way of navigation. Analyses of the reconstructed paths suggest that gravity (slope of the dune surface) is an unlikely parameter used in path integration by the L. arenicola spiders.     

Path integration controls nest-plume following in desert ants

The desert ant Cataglyphis fortis is equipped with sophisticated navigational skills for returning to its nest after foraging. The ant's primary means for long-distance navigation is path integration, which provides a continuous readout of the ant's approximate distance and direction from the nest. The nest is pinpointed with the aid of visual and olfactory landmarks. Similar landmark cues help ants locate familiar food sites. Ants on their outward trip will position themselves so that they can move upwind using odor cues to find food. Here we show that homing ants also move upwind along nest-derived odor plumes to approach their nest. The ants only respond to odor plumes if the state of their path integrator tells them that they are near the nest. This influence of path integration is important because we could experimentally provoke ants to follow odor plumes from a foreign, conspecific nest and enter that nest. We identified CO(2) as one nest-plume component that can by itself induce plume following in homing ants. Taken together, the results suggest that path-integration information enables ants to avoid entering the wrong nest, where they would inevitably be killed by resident ants.     

Ageing effects on path integration and landmark navigation

Navigation abilities show marked decline in both normal ageing and dementia. Path integration may be particularly affected, as it is supported by the hippocampus and entorhinal cortex, both of which show severe degeneration with ageing. Age differences in path integration based on kinaesthetic and vestibular cues have been clearly demonstrated, but very little research has focused on visual path integration, based only on optic flow. Path integration is complemented by landmark navigation, which may also show age differences, but has not been well studied either. Here we present a study using several simple virtual navigation tasks to explore age differences in path integration both with and without landmark information. We report that, within a virtual environment that provided only optic flow information, older participants exhibited deficits in path integration in terms of distance reproduction, rotation reproduction, and triangle completion. We also report age differences in triangle completion within an environment that provided landmark information. In all tasks, we observed a more restricted range of responses in the older participants, which we discuss in terms of a leaky integrator model, as older participants showed greater leak than younger participants. Our findings begin to explain the mechanisms underlying age differences in path integration, and thus contribute to an understanding of the substantial decline in navigation abilities observed in ageing.     

Robust path integration in the entorhinal grid cell system with hippocampal feed-back

Animals are able to update their knowledge about their current position solely by integrating the speed and the direction of their movement, which is known as path integration. Recent discoveries suggest that grid cells in the medial entorhinal cortex might perform some of the essential underlying computations of path integration. However, a major concern over path integration is that as the measurement of speed and direction is inaccurate, the representation of the position will become increasingly unreliable. In this paper, we study how allothetic inputs can be used to continually correct the accumulating error in the path integrator system. We set up the model of a mobile agent equipped with the entorhinal representation of idiothetic (grid cell) and allothetic (visual cells) information and simulated its place learning in a virtual environment. Due to competitive learning, a robust hippocampal place code emerges rapidly in the model. At the same time, the hippocampo-entorhinal feed-back connections are modified via Hebbian learning in order to allow hippocampal place cells to influence the attractor dynamics in the entorhinal cortex. We show that the continuous feed-back from the integrated hippocampal place representation is able to stabilize the grid cell code. This research was supported by the EU Framework 6 ICEA project (IST-4-027819-IP).     

Spatial cognition and neuro-mimetic navigation: a model of hippocampal place cell activity

 A computational model of hippocampal activity during spatial cognition and navigation tasks is presented. The spatial representation in our model of the rat hippocampus is built on-line during exploration via two processing streams. An allothetic vision-based representation is built by unsupervised Hebbian learning extracting spatio-temporal properties of the environment from visual input. An idiothetic representation is learned based on internal movement-related information provided by path integration. On the level of the hippocampus, allothetic and idiothetic representations are integrated to yield a stable representation of the environment by a population of localized overlapping CA3-CA1 place fields. The hippocampal spatial representation is used as a basis for goal-oriented spatial behavior. We focus on the neural pathway connecting the hippocampus to the nucleus accumbens. Place cells drive a population of locomotor action neurons in the nucleus accumbens. Reward-based learning is applied to map place cell activity into action cell activity. The ensemble action cell activity provides navigational maps to support spatial behavior. We present experimental results obtained with a mobile Khepera robot. Received: 02 July 1999 / Accepted in revised form: 20 March 2000     

Two spatial memories for honeybee navigation

Insect navigation is thought to be based on an egocentric reference system which relates vector information derived from path integration to views of landmarks experienced en route and at the goal. Here we show that honeybees also possess an allocentric form of spatial memory which allows localization of multiple places relative to the intended goal, the hive. The egocentric route memory, which is called the specialized route memory (SRM) here, initially dominates navigation when an animal is first trained to a feeding site and then released at an unexpected site and this is why it is the only reference system detected so far in experiments with bees. However, the SRM can be replaced by an allocentric spatial memory called the general landscape memory (GLM). The GLM is directly accessible to the honeybee (and to the experimenter) if no SRM exists, for example, if bees were not trained along a route before testing. Under these conditions bees return to the hive from all directions around the hive at a speed comparable to that of an equally long flight along a trained route. The flexible use of the GLM indicates that bees may store relational information on places, connections between landmarks and the hive and/or views of landmarks from different directions and, thus, the GLM may have a graph structure, at least with respect to one goal, i.e. the hive.     

Which coordinate system for modelling path integration?

Path integration is a navigation strategy widely observed in nature where an animal maintains a running estimate, called the home vector, of its location during an excursion. Evidence suggests it is both ancient and ubiquitous in nature, and has been studied for over a century. In that time, canonical and neural network models have flourished, based on a wide range of assumptions, justifications and supporting data. Despite the importance of the phenomenon, consensus and unifying principles appear lacking. A fundamental issue is the neural representation of space needed for biological path integration. This paper presents a scheme to classify path integration systems on the basis of the way the home vector records and updates the spatial relationship between the animal and its home location. Four extended classes of coordinate systems are used to unify and review both canonical and neural network models of path integration, from the arthropod and mammalian literature. This scheme demonstrates analytical equivalence between models which may otherwise appear unrelated, and distinguishes between models which may superficially appear similar. A thorough analysis is carried out of the equational forms of important facets of path integration including updating, steering, searching and systematic errors, using each of the four coordinate systems. The type of available directional cue, namely allothetic or idiothetic, is also considered. It is shown that on balance, the class of home vectors which includes the geocentric Cartesian coordinate system, appears to be the most robust for biological systems. A key conclusion is that deducing computational structure from behavioural data alone will be difficult or impossible, at least in the absence of an analysis of random errors. Consequently it is likely that further theoretical insights into path integration will require an in-depth study of the effect of noise on the four classes of home vectors.     

Inhibition, not excitation, is the key to multimodal sensory integration

Multimodal neuronal maps, combining input from two or more sensory systems, play a key role in the processing of sensory and motor information. For such maps to be of any use, the input from all participating modalities must be calibrated so that a stimulus at a specific spatial location is represented at an unambiguous position in the multimodal map. Here we discuss two methods based on supervised spike-timing-dependent plasticity (STDP) to gauge input from different sensory modalities so as to ensure a proper map alignment. The first uses an excitatory teacher input. It is therefore called excitation-mediated learning. The second method is based on an inhibitory teacher signal, as found in the barn owl, and is called inhibition-mediated learning. Using detailed analytical calculations and numerical simulations, we demonstrate that inhibitory teacher input is essential if high-quality multimodal integration is to be learned rapidly. Furthermore, we show that the quality of the resulting map is not so much limited by the quality of the teacher signal but rather by the accuracy of the input from other sensory modalities.     

Information integration: its relevance to brain function and consciousness

A proper understanding of cognitive functions cannot be achieved without an understanding of consciousness, both at the empirical and at the theoretical level. This paper argues that consciousness has to do with a system's capacity for information integration. In this approach, every causal mechanism capable of choosing among alternatives generates information, and information is integrated to the extent that it is generated by a system above and beyond its parts. The set of integrated informational relationships generated by a complex of mechanisms--its quale--specify both the quantity and the quality of experience. As argued below, depending on the causal structure of a system, information integration can reach a maximum value at a particular spatial and temporal grain size. It is also argued that changes in information integration reflect a system's ability to match the causal structure of the world, both on the input and the output side. After a brief review suggesting that this approach is consistent with several experimental and clinical observations, the paper concludes with some prospective remarks about the relevance of understanding information integration for analyzing cognitive function, both normal and pathological.     

Calibration of vector navigation in desert ants.

Desert ants (Cataglyphis sp.) monitor their position relative to the nest using a form of dead reckoning [1] [2] [3] known as path integration (PI) [4]. They do this with a sun compass and an odometer to update an accumulator that records their current position [1]. Ants can use PI to return to the nest [2] [3]. Here, we report that desert ants, like honeybees [5] and hamsters [6], can also use PI to approach a previously visited food source. To navigate to a goal using only PI information, a forager must recall a previous state of the accumulator specifying the goal, and compare it with the accumulator's current state [4]. The comparison - essentially vector subtraction - gives the direction to the goal. This whole process, which we call vector navigation, was found to be calibrated at recognised sites, such as the nest and a familiar feeder, throughout the life of a forager. If a forager was trained around a one-way circuit in which the result of PI on the return route did not match the result on the outward route, calibration caused the ant's trajectories to be misdirected. We propose a model of vector navigation to suggest how calibration could produce such trajectories.     

Accurate Path Integration in Continuous Attractor Network Models of Grid Cells

Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal''s position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rat''s velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model networks can accurately integrate velocity inputs over a maximum of ∼10–100 meters and ∼1–10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in the dorsolateral medial entorhinal cortex. The simulations also generate pertinent upper bounds on the accuracy of integration that may be achieved by continuous attractor dynamics in the grid cell network. We suggest experiments to test the continuous attractor model and differentiate it from models in which single cells establish their responses independently of each other.     

Finding the way with a noisy brain

Successful navigation is fundamental to the survival of nearly every animal on earth, and achieved by nervous systems of vastly different sizes and characteristics. Yet surprisingly little is known of the detailed neural circuitry from any species which can accurately represent space for navigation. Path integration is one of the oldest and most ubiquitous navigation strategies in the animal kingdom. Despite a plethora of computational models, from equational to neural network form, there is currently no consensus, even in principle, of how this important phenomenon occurs neurally. Recently, all path integration models were examined according to a novel, unifying classification system. Here we combine this theoretical framework with recent insights from directed walk theory, and develop an intuitive yet mathematically rigorous proof that only one class of neural representation of space can tolerate noise during path integration. This result suggests many existing models of path integration are not biologically plausible due to their intolerance to noise. This surprising result imposes significant computational limitations on the neurobiological spatial representation of all successfully navigating animals, irrespective of species. Indeed, noise-tolerance may be an important functional constraint on the evolution of neuroarchitectural plans in the animal kingdom.