Rationalizing spatial exploration patterns of wild animals and humans through a temporal discounting framework

Differences in time perception in patients with obstructive sleep apnea

BACKGROUND

Obstructive sleep apnea (OSA) is a condition that occurs due to complete (apnea) and partial (hypopnea) obstruction in the upper airways during sleep. Hypoxia is one of the key factors contributing to the development of symptoms of obstructive sleep apnea and OSA-related diseases.

OBJECTIVE

The present study aimed to evaluate time perception differences between patients with OSA and healthy individuals, as well as among different OSA severity groups.

METHODS

Twenty severe OSA, twenty moderate OSA, twenty mild OSA patients, and twenty healthy volunteers without OSA were included in the study. Scales were administered to the participants. Time perception tests were administered to evaluate perceptual timing.

RESULTS

In the paced motor timing test, a difference was observed between the OSA ( +) group and the OSA (-) group. In the Time Estimation Test, a difference was observed between the OSA ( +) group and the OSA (-) group and their subgroups.

CONCLUSION

The internal clock works slower in the OSA ( +) group. When subgroups were compared based on the degree of OSA, the internal clock worked slower as we transitioned from the OSA (-) group to the severe OSA group. It is considered that as you move from the OSA (-) group to the severe OSA group, the switch between pacemaker and accumulator is disrupted due to the decrease in attention. Recurrent hypoxia observed in OSA may alter the perception of time by affecting attention.

Individual exploration and selective social learning: balancing exploration-exploitation trade-offs in collective foraging

Search requires balancing exploring for more options and exploiting the ones previously found. Individuals foraging in a group face another trade-off: whether to engage in social learning to exploit the solutions found by others or to solitarily search for unexplored solutions. Social learning can better exploit learned information and decrease the costs of finding new resources, but excessive social learning can lead to over-exploitation and too little exploration for new solutions. We study how these two trade-offs interact to influence search efficiency in a model of collective foraging under conditions of varying resource abundance, resource density and group size. We modelled individual search strategies as Lévy walks, where a power-law exponent (μ) controlled the trade-off between exploitative and explorative movements in individual search. We modulated the trade-off between individual search and social learning using a selectivity parameter that determined how agents responded to social cues in terms of distance and likely opportunity costs. Our results show that social learning is favoured in rich and clustered environments, but also that the benefits of exploiting social information are maximized by engaging in high levels of individual exploration. We show that selective use of social information can modulate the disadvantages of excessive social learning, especially in larger groups and when individual exploration is limited. Finally, we found that the optimal combination of individual exploration and social learning gave rise to trajectories with μ ≈ 2 and provide support for the general optimality of such patterns in search. Our work sheds light on the interplay between individual search and social learning, and has broader implications for collective search and problem-solving.

Learning and Animal Movement

Integrating diverse concepts from animal behavior, movement ecology, and machine learning, we develop an overview of the ecology of learning and animal movement. Learning-based movement is clearly relevant to ecological problems, but the subject is rooted firmly in psychology, including a distinct terminology. We contrast this psychological origin of learning with the task-oriented perspective on learning that has emerged from the field of machine learning. We review conceptual frameworks that characterize the role of learning in movement, discuss emerging trends, and summarize recent developments in the analysis of movement data. We also discuss the relative advantages of different modeling approaches for exploring the learning-movement interface. We explore in depth how individual and social modalities of learning can matter to the ecology of animal movement, and highlight how diverse kinds of field studies, ranging from translocation efforts to manipulative experiments, can provide critical insight into the learning process in animal movement.

Dopamine and the interdependency of time perception and reward

Time is a fundamental dimension of our perception of the world and is therefore of critical importance to the organization of human behavior. A corpus of work - including recent optogenetic evidence - implicates striatal dopamine as a crucial factor influencing the perception of time. Another stream of literature implicates dopamine in reward and motivation processes. However, these two domains of research have remained largely separated, despite neurobiological overlap and the apothegmatic notion that "time flies when you're having fun". This article constitutes a review of the literature linking time perception and reward, including neurobiological and behavioral studies. Together, these provide compelling support for the idea that time perception and reward processing interact via a common dopaminergic mechanism.

Power Laws Derived from a Bayesian Decision-Making Model in Non-Stationary Environments

The frequency of occurrence of step length in the migratory behaviour of various organisms, including humans, is characterized by the power law distribution. This pattern of behaviour is known as the Lévy walk, and the reason for this phenomenon has been investigated extensively. Especially in humans, one possibility might be that this pattern reflects the change in self-confidence in one’s chosen behaviour. We used simulations to demonstrate that active assumptions cause changes in the confidence level in one’s choice under a situation of lack of information. More specifically, we presented an algorithm that introduced the effects of learning and forgetting into Bayesian inference, and simulated an imitation game in which two decision-making agents incorporating the algorithm estimated each other’s internal models. For forgetting without learning, each agents’ confidence levels in their own estimation remained low owing to a lack of information about the counterpart, and the agents changed their hypotheses about the opponent frequently, and the frequency distribution of the duration of the hypotheses followed an exponential distribution for a wide range of forgetting rates. Conversely, when learning was introduced, high confidence levels occasionally occurred even at high forgetting rates, and exponential distributions universally turned into power law distribution.

The Free-movement pattern Y-maze: A cross-species measure of working memory and executive function

Numerous neurodegenerative and psychiatric disorders are associated with deficits in executive functions such as working memory and cognitive flexibility. Progress in developing effective treatments for disorders may benefit from targeting these cognitive impairments, the success of which is predicated on the development of animal models with validated behavioural assays. Zebrafish offer a promising model for studying complex brain disorders, but tasks assessing executive function are lacking. The Free-movement pattern (FMP) Y-maze combines aspects of the common Y-maze assay, which exploits the inherent motivation of an organism to explore an unknown environment, with analysis based on a series of sequential two-choice discriminations. We validate the task as a measure of working memory and executive function by comparing task performance parameters in adult zebrafish treated with a range of glutamatergic, cholinergic and dopaminergic drugs known to impair working memory and cognitive flexibility. We demonstrate the cross-species validity of the task by assessing performance parameters in adapted versions of the task for mice and Drosophila, and finally a virtual version in humans, and identify remarkable commonalities between vertebrate species' navigation of the maze. Together, our results demonstrate that the FMP Y-maze is a sensitive assay for assessing working memory and cognitive flexibility across species from invertebrates to humans, providing a simple and widely applicable behavioural assay with exceptional translational relevance.

Efficient Lévy walks in virtual human foraging

Efficient foraging depends on decisions that account for the costs and benefits of various activities like movement, perception, and planning. We conducted a virtual foraging experiment set in the foothills of the Himalayas to examine how time and energy are expended to forage efficiently, and how foraging changes when constrained to a home range. Two hundred players foraged the human-scale landscape with simulated energy expenditure in search of naturally distributed resources. Results showed that efficient foragers produced periods of locomotion interleaved with perception and planning that approached theoretical expectations for Lévy walks, regardless of the home-range constraint. Despite this constancy, efficient home-range foraging trajectories were less diffusive by virtue of restricting locomotive search and spending more time instead scanning the environment to plan movement and detect far-away resources. Altogether, results demonstrate that humans can forage efficiently by arranging and adjusting Lévy-distributed search activities in response to environmental and task constraints.

Tuning movement for sensing in an uncertain world

While animals track or search for targets, sensory organs make small unexplained movements on top of the primary task-related motions. While multiple theories for these movements exist-in that they support infotaxis, gain adaptation, spectral whitening, and high-pass filtering-predicted trajectories show poor fit to measured trajectories. We propose a new theory for these movements called energy-constrained proportional betting, where the probability of moving to a location is proportional to an expectation of how informative it will be balanced against the movement's predicted energetic cost. Trajectories generated in this way show good agreement with measured trajectories of fish tracking an object using electrosense, a mammal and an insect localizing an odor source, and a moth tracking a flower using vision. Our theory unifies the metabolic cost of motion with information theory. It predicts sense organ movements in animals and can prescribe sensor motion for robots to enhance performance.

Functional advantages of Lévy walks emerging near a critical point

A special class of random walks, so-called Lévy walks, has been observed in a variety of organisms ranging from cells, insects, fishes, and birds to mammals, including humans. Although their prevalence is considered to be a consequence of natural selection for higher search efficiency, some findings suggest that Lévy walks might also be epiphenomena that arise from interactions with the environment. Therefore, why they are common in biological movements remains an open question. Based on some evidence that Lévy walks are spontaneously generated in the brain and the fact that power-law distributions in Lévy walks can emerge at a critical point, we hypothesized that the advantages of Lévy walks might be enhanced by criticality. However, the functional advantages of Lévy walks are poorly understood. Here, we modeled nonlinear systems for the generation of locomotion and showed that Lévy walks emerging near a critical point had optimal dynamic ranges for coding information. This discovery suggested that Lévy walks could change movement trajectories based on the magnitude of environmental stimuli. We then showed that the high flexibility of Lévy walks enabled switching exploitation/exploration based on the nature of external cues. Finally, we analyzed the movement trajectories of freely moving Drosophila larvae and showed empirically that the Lévy walks may emerge near a critical point and have large dynamic range and high flexibility. Our results suggest that the commonly observed Lévy walks emerge near a critical point and could be explained on the basis of these functional advantages.

Optimal searching behaviour generated intrinsically by the central pattern generator for locomotion

Efficient searching for resources such as food by animals is key to their survival. It has been proposed that diverse animals from insects to sharks and humans adopt searching patterns that resemble a simple Lévy random walk, which is theoretically optimal for 'blind foragers' to locate sparse, patchy resources. To test if such patterns are generated intrinsically, or arise via environmental interactions, we tracked free-moving Drosophila larvae with (and without) blocked synaptic activity in the brain, suboesophageal ganglion (SOG) and sensory neurons. In brain-blocked larvae, we found that extended substrate exploration emerges as multi-scale movement paths similar to truncated Lévy walks. Strikingly, power-law exponents of brain/SOG/sensory-blocked larvae averaged 1.96, close to a theoretical optimum (µ ≅ 2.0) for locating sparse resources. Thus, efficient spatial exploration can emerge from autonomous patterns in neural activity. Our results provide the strongest evidence so far for the intrinsic generation of Lévy-like movement patterns.

Search as a simple take-the-best heuristic

Humans commonly engage in a variety of search behaviours, for example when looking for an object, a partner, information or a solution to a complex problem. The success or failure of a search strategy crucially depends on the structure of the environment and the constraints it imposes on the individuals. Here, we focus on environments in which individuals have to explore the solution space gradually and where their reward is determined by one unique solution they choose to exploit. This type of environment has been relatively overlooked in the past despite being relevant to numerous real-life situations, such as spatial search and various problem-solving tasks. By means of a dedicated experimental design, we show that the search behaviour of experimental participants can be well described by a simple heuristic model. Both in rich and poor solution spaces, a take-the-best procedure that ignores all but one cue at a time is capable of reproducing a diversity of observed behavioural patterns. Our approach, therefore, sheds lights on the possible cognitive mechanisms involved in human search.

Prefrontal Dynamics Associated with Efficient Detours and Shortcuts: A Combined Functional Magnetic Resonance Imaging and Magnetoencenphalography Study

Central to the concept of the “cognitive map” is that it confers behavioral flexibility, allowing animals to take efficient detours, exploit shortcuts, and avoid alluring, but unhelpful, paths. The neural underpinnings of such naturalistic and flexible behavior remain unclear. In two neuroimaging experiments, we tested human participants on their ability to navigate to a set of goal locations in a virtual desert island riven by lava, which occasionally spread to block selected paths (necessitating detours) or receded to open new paths (affording real shortcuts or false shortcuts to be avoided). Detours activated a network of frontal regions compared with shortcuts. Activity in the right dorsolateral PFC specifically increased when participants encountered tempting false shortcuts that led along suboptimal paths that needed to be differentiated from real shortcuts. We also report modulation in event-related fields and theta power in these situations, providing insight to the temporal evolution of response to encountering detours and shortcuts. These results help inform current models as to how the brain supports navigation and planning in dynamic environments.

Lévy foraging patterns of rural humans

Movement patterns resembling Lévy walks, often attributed to the execution of an advantageous probabilistic searching strategy, are found in a wide variety of organisms, from cells to human hunter-gatherers. It has been suggested that such movement patterns may be fundamental to how humans interact and experience the world and that they may have arisen early in our genus with the evolution of a hunting and gathering lifestyle. Here we show that Lévy walks are evident in the Me’Phaa of Mexico, in Brazilian Cariri farmers and in Amazonian farmers when gathering firewood, wild fruit and nuts. Around 50% of the search patterns resemble Lévy walks and these are characterized by Lévy exponents close to 1.7. The other search patterns more closely resemble bi-phasic walks. We suggest potential generative mechanisms for the occurrence of these ubiquitous Lévy walks which can be used to guide future studies on human mobility. We show that frequent excursions and meanderings from pre-existing trails can account for our observations.

Current status and future directions of Lévy walk research

Lévy walks are a mathematical construction useful for describing random patterns of movement with bizarre fractal properties that seem to have no place in biology. Nonetheless, movement patterns resembling Lévy walks have been observed at scales ranging from the microscopic to the ecological. They have been seen in the molecular machinery operating within cells during intracellular trafficking, in the movement patterns of T cells within the brain, in DNA, in some molluscs, insects, fish, birds and mammals, in the airborne flights of spores and seeds, and in the collective movements of some animal groups. Lévy walks are also evident in trace fossils (ichnofossils) – the preserved form of tracks made by organisms that occupied ancient sea beds about 252-66 million years ago. And they are utilised by algae that originated around two billion years ago, and still exist today. In September of 2017, leading researchers from across the life sciences, along with mathematicians and physicists, got together at a Company of Biologists' Workshop to discuss the origins and biological significance of these movement patterns. In this Review the essence of the technical and sometimes heated discussions is distilled and made accessible for all. In just a few pages, the reader is taken from a gentle introduction to the frontiers of a very active field of scientific enquiry. What emerges is a fascinating story of a truly inter-disciplinary scientific endeavour that is seeking to better understand movement patterns occurring across all biological scales.

Summary: Movement patterns resembling Lévy walks are found in a wide variety of organisms, from cells to humans. In this Review the latest research into their origins and biological significance is discussed.

The evolutionary origins of Lévy walk foraging

We study through a reaction-diffusion algorithm the influence of landscape diversity on the efficiency of search dynamics. Remarkably, the identical optimal search strategy arises in a wide variety of environments, provided the target density is sparse and the searcher’s information is restricted to its close vicinity. Our results strongly impact the current debate on the emergentist vs. evolutionary origins of animal foraging. The inherent character of the optimal solution (i.e., independent on the landscape for the broad scenarios assumed here) suggests an interpretation favoring the evolutionary view, as originally implied by the Lévy flight foraging hypothesis. The latter states that, under conditions of scarcity of information and sparse resources, some organisms must have evolved to exploit optimal strategies characterized by heavy-tailed truncated power-law distributions of move lengths. These results strongly suggest that Lévy strategies—and hence the selection pressure for the relevant adaptations—are robust with respect to large changes in habitat. In contrast, the usual emergentist explanation seems not able to explain how very similar Lévy walks can emerge from all the distinct non-Lévy foraging strategies that are needed for the observed large variety of specific environments. We also report that deviations from Lévy can take place in plentiful ecosystems, where locomotion truncation is very frequent due to high encounter rates. So, in this case normal diffusion strategies—performing as effectively as the optimal one—can naturally emerge from Lévy. Our results constitute the strongest theoretical evidence to date supporting the evolutionary origins of experimentally observed Lévy walks.

How organisms improve the search for food, mates, etc., is a key factor to their survival. Mathematically, the best strategy to look for randomly distributed re-visitable resources—under scarce information and sparse conditions—results from Lévy distributions of move lengths (the probability of taking a step ℓ is proportional to 1/ℓ²). Today it is well established that many animal species in different habitats do perform Lévy foraging. This fact has raised a heated debate, viz., the emergent versus evolutionary hypotheses. For the former, a Lévy foraging is an emergent property, a consequence of searcher-environment interactions: certain landscapes induce Lévy patterns, but others not. In this view, the optimal strategy depends on the particular habitat. The evolutionary explanation, in contrast, is that Lévy foraging strategies are adaptations that evolved via natural selection. In this article, through simulations we exhaustively analyze the influence of distinct environments on the foraging efficiency. We find that the optimal procedure is the same in all situations, provided density is low and landscape information is scarce. So, the best search strategy is remarkably independent of details. These results constitute the strongest theoretical evidence to date supporting the evolutionary origins of experimentally observed Lévy walks.

The hunt for the perfect discounting function and a reckoning of time perception

Making decisions that factor the cost of time is fundamental to survival. Yet, while it is readily appreciated that our perception of time is intimately involved in this process, theories regarding intertemporal decision-making and theories regarding time perception are treated, largely, independently. Even within these respective domains, models providing good fits to data fail to provide insight as to why, from a normative sense, those fits should take their apparent form. Conversely, normative models that proffer a rationalization for why an agent should weigh options in a particular way, or to perceive time in a particular way, fail to account for the full body of well-established experimental evidence. Here we review select, yet key advances in our understanding, identifying conceptual breakthroughs in the fields of intertemporal decision-making and in time perception, as well as their limits and failings in the face of hard-won experimental observation. On this background of accrued knowledge, a new conception unifying the domains of decision-making and time perception is put forward (Training-Integrated Maximization of Reinforcement Rate, TIMERR) to provide a better fit to observations and a more parsimonious reckoning of why we make choices, and thereby perceive time, the way we do.