Animal Trajectories Research Articles

Evaluating State Space Discovery by Persistent Cohomology in the Spatial Representation System.

Persistent cohomology is a powerful technique for discovering topological structure in data. Strategies for its use in neuroscience are still undergoing development. We comprehensively and rigorously assess its performance in simulated neural recordings of the brain's spatial representation system. Grid, head direction, and conjunctive cell populations each span low-dimensional topological structures embedded in high-dimensional neural activity space. We evaluate the ability for persistent cohomology to discover these structures for different dataset dimensions, variations in spatial tuning, and forms of noise. We quantify its ability to decode simulated animal trajectories contained within these topological structures. We also identify regimes under which mixtures of populations form product topologies that can be detected. Our results reveal how dataset parameters affect the success of topological discovery and suggest principles for applying persistent cohomology, as well as persistent homology, to experimental neural recordings.

Spatiotemporal Large-Scale Networks Shaped by Air Mass Movements

The movement of atmospheric air masses can be seen as a continuous flow of gases and particles hovering over our planet, and it can be locally simplified by means of three-dimensional trajectories. These trajectories can hence be seen as a way of connecting distant areas of the globe during a given period of time. In this paper we present a mathematical formalism to construct spatial and spatiotemporal networks where the nodes represent the subsets of a partition of a geographical area and the links between them are inferred from sampled trajectories of air masses passing over and across them. We propose different estimators of the intensity of the links, relying on different bio-physical hypotheses and covering adjustable time periods. This construction leads to a new definition of spatiotemporal networks characterized by adjacency matrices giving, e.g., the probability of connection between distant areas during a chosen period of time. We applied our methodology to characterize tropospheric connectivity in two real geographical contexts: the watersheds of the French region Provence-Alpes-Côte d’Azur and the coastline of the Mediterranean Sea. The analysis of the constructed networks allowed identifying a marked seasonal pattern in air mass movements in the two study areas. If our methodology is applied to samples of air-mass trajectories, with potential implications in aerobiology and plant epidemiology, it could be applied to other types of trajectories, such as animal trajectories, to characterize connectivity between different components of the landscape hosting the animals.

Deep learning-assisted comparative analysis of animal trajectories with DeepHL

A comparative analysis of animal behavior (e.g., male vs. female groups) has been widely used to elucidate behavior specific to one group since pre-Darwinian times. However, big data generated by new sensing technologies, e.g., GPS, makes it difficult for them to contrast group differences manually. This study introduces DeepHL, a deep learning-assisted platform for the comparative analysis of animal movement data, i.e., trajectories. This software uses a deep neural network based on an attention mechanism to automatically detect segments in trajectories that are characteristic of one group. It then highlights these segments in visualized trajectories, enabling biologists to focus on these segments, and helps them reveal the underlying meaning of the highlighted segments to facilitate formulating new hypotheses. We tested the platform on a variety of trajectories of worms, insects, mice, bears, and seabirds across a scale from millimeters to hundreds of kilometers, revealing new movement features of these animals.

Episodic Memory: What's Consciousness Got to Do with It?

Episodic memory is the memory for experienced events. A peak competence of episodic memory is the mental combination of experienced events to infer commonalities. This enables adequate interpretation and behavior. Inferring commonalities in episodic memory may proceed with and without consciousness of events. Yet, what distinguishes conscious from unconscious event encoding? This question inspired nine experiments that featured strongly and weakly masked cartoon clips presented for unconscious and conscious encoding and inference. Each clip featured a scene with a visually impenetrable hiding place. Five animals crossed the scene one-by-one consecutively. One animal trajectory represented one event. The animals moved through the hiding place, where they might linger or not. Participants’ task was to observe the animals’ entrances and exits to maintain a mental record of which animals hid simultaneously. We manipulated information load to explore capacity limits of conscious/unconscious encoding. Memory of inferences was tested immediately or 3.5 or 6 minutes following encoding. Participants retrieved inferences well when encoding was conscious. When encoding was unconscious, participants needed to give retrieval responses intuitively. Only habitually intuitive decision-makers exhibited significant delayed retrieval of inferences drawn unconsciously. Hippocampal activity increased with correct retrieval responses and correlated with retrieval success at both consciousness levels. With increasing information load, delayed retrieval performance remained only stable when encoding had been unconscious. A strong hippocampal-neocortical functional connectivity hallmarked conscious memories. A sparse coding hallmarked unconscious memories. Sparse coding may have enlarged memory capacity. Hence, levels of consciousness influenced the memories’ behavioral impact, representational code, and memory capacity.

A framework for pre-processing individual location telemetry data for freshwater fish in a river section

Animal movement study often relies on individual tracking. The data scale (in time and space) varies according to the species, the environment where individuals live, or the exogenous processes that drive movement. To explore freshwater fish movement in rivers, fine-scale data are needed. Also, in rivers, recorded telemetry frequently shows missing data and location errors. The irregular time-steps, huge amount of data, environmental complexity (river section) and how fish move in such anisotropic environments undermine the use of statistical frameworks such as state-space models. To deal with these specificities, data pre-treatment can be required. We propose a generic method of telemetry data pre-processing, which can be transposed to other datasets. This framework includes interpolation to handle trajectories at fine time scales and performs data analysis within a state-space model.We combined analyses on observed and simulated data at various interpolation time-steps to choose the one that best preserves the general movement while reducing the total amount of data required. First, we directly compared raw and interpolated data, and the results of parameter inference of a simple state-space model using the interpolated data. The state-space model infers behavioural state based on speed and turning angle between successive locations in animal trajectories. We also included two additional variables computed from raw data: a quantitative indicator of the correspondence between the interpolated trajectory and the raw data, and the variance of turning angles of raw data within the interpolation time-step. We were finally able to determine the most appropriate time-step to obtain locations that were regularly spaced in time and to reduce the amount of data while maintaining the precision of the raw data. Computational time was reduced 12-fold by using a 30-second time-step to interpolate data simulated at 3-second intervals. The inclusion of the two variables derived from raw data compensated for the loss of information in interpolated trajectories and allowed more efficient discrimination between behaviours.

Parametrizing diffusion‐taxis equations from animal movement trajectories using step selection analysis

Abstract Mathematical analysis of partial differential equations (PDEs) has led to many insights regarding the effect of organism movements on spatial population dynamics. However, their use has mainly been confined to the community of mathematical biologists, with less attention from statistical and empirical ecologists. We conjecture that this is principally due to the inherent difficulties in fitting PDEs to data. To help remedy this situation, in the context of movement ecology, we show how the popular technique of step selection analysis (SSA) can be used to parametrize a class of PDEs, called diffusion‐taxis models, from an animal's trajectory. We examine the accuracy of our technique on simulated data, then demonstrate the utility of diffusion‐taxis models in two ways. First, for non‐interacting animals, we derive the steady‐state utilization distribution in a closed analytic form. Second, we give a recipe for deriving spatial pattern formation properties that emerge from interacting animals: specifically, do those interactions cause heterogeneous spatial distributions to emerge and if so, do these distributions oscillate at short times or emerge without oscillations? The second question is applied to data on concurrently tracked bank voles Myodes glareolus. Our results show that SSA can accurately parametrize diffusion‐taxis equations from location data, providing the frequency of the data is not too low. We show that the steady‐state distribution of our diffusion‐taxis model, where it is derived, has an identical functional form to the utilization distribution given by resource selection analysis (RSA), thus formally linking (fine scale) SSA with (broad scale) RSA. For the bank vole data, we show how our SSA‐PDE approach can give predictions regarding the spatial aggregation and segregation of different individuals, which are difficult to predict purely by examining results of SSA. Our methods provide a user‐friendly way into the world of PDEs, via a well‐used statistical technique, which should lead to tighter links between the findings of mathematical ecology and observations from empirical ecology. By providing a non‐speculative link between observed movement behaviours and space use patterns on larger spatio‐temporal scales, our findings will also aid integration of movement ecology into understanding spatial species distributions.

Analysis of temporal patterns in animal movement networks

Abstract Understanding how animal movements change across space and time is a fundamental question in ecology. While classical analyses of trajectories give insightful descriptors of spatial patterns, a satisfying method for assessing the temporal succession of such patterns is lacking. Network analyses are increasingly used to capture properties of complex animal trajectories in simple graphical metrics. Here, building on this approach, we introduce a method that incorporates time into movement network analyses based on temporal sequences of network motifs. We illustrate our method using four example trajectories (bumblebee, black kite, roe deer, wolf) collected with different technologies (harmonic radar, platform terminal transmitter, global positioning system). First, we transformed each trajectory into a spatial network by defining the animal's coordinates as nodes and movements in between as edges. Second, we extracted temporal sequences of network motifs from each movement network and compared the resulting behavioural profiles to topological features of the original trajectory. Finally, we compared each sequence of motifs with simulated Brownian and Lévy random motions to statistically determine differences between trajectories and classical movement models. Our analysis of the temporal sequences of network motifs in individual movement networks revealed successions of spatial patterns corresponding to changes in behavioural modes that can be attributed to specific spatio‐temporal events of each animal trajectory. Future applications of our method to multi‐layered movement and social network analysis yield considerable promises for extending the study of complex movement patterns at the population level.

Using time-series similarity measures to compare animal movement trajectories in ecology

Identifying and understanding patterns in movement data are amongst the principal aims of movement ecology. By quantifying the similarity of movement trajectories, inferences can be made about diverse processes, ranging from individual specialisation to the ontogeny of foraging strategies. Movement analysis is not unique to ecology however, and methods for estimating the similarity of movement trajectories have been developed in other fields but are currently under-utilised by ecologists. Here, we introduce five commonly used measures of trajectory similarity: dynamic time warping (DTW), longest common subsequence (LCSS), edit distance for real sequences (EDR), Fréchet distance and nearest neighbour distance (NND), of which only NND is routinely used by ecologists. We investigate the performance of each of these measures by simulating movement trajectories using an Ornstein-Uhlenbeck (OU) model in which we varied the following parameters: (1) the point of attraction, (2) the strength of attraction to this point and (3) the noise or volatility added to the movement process in order to determine which measures were most responsive to such changes. In addition, we demonstrate how these measures can be applied using movement trajectories of breeding northern gannets (Morus bassanus) by performing trajectory clustering on a large ecological dataset. Simulations showed that DTW and Fréchet distance were most responsive to changes in movement parameters and were able to distinguish between all the different parameter combinations we trialled. In contrast, NND was the least sensitive measure trialled. When applied to our gannet dataset, the five similarity measures were highly correlated despite differences in their underlying calculation. Clustering of trajectories within and across individuals allowed us to easily visualise and compare patterns of space use over time across a large dataset. Trajectory clusters reflected the bearing on which birds departed the colony and highlighted the use of well-known bathymetric features. As both the volume of movement data and the need to quantify similarity amongst animal trajectories grow, the measures described here and the bridge they provide to other fields of research will become increasingly useful in ecology.Significance statementAs the use of tracking technology increases, there is a need to develop analytical techniques to process such large volumes of data. One area in which this would be useful is the comparison of individual movement trajectories. In response, a variety of measures of trajectory similarity have been developed within the information sciences. However, such measures are rarely used by ecologists who may be unaware of them. To remedy this, we apply five common measures of trajectory similarity to both simulated data and real ecological dataset comprising of movement trajectories of breeding northern gannets. Dynamic time warping and Fréchet distance performed best on simulated data. Using trajectory similarity measures on our gannet dataset, we identified distinct foraging clusters centred on different bathymetric features, demonstrating one application of such similarity measures. As new technology and analysis techniques proliferate across ecology and the information sciences, closer ties between these fields promise further innovative analysis of movement data.

STEFTR: A Hybrid Versatile Method for State Estimation and Feature Extraction From the Trajectory of Animal Behavior.

Animal behavior is the final and integrated output of brain activity. Thus, recording and analyzing behavior is critical to understand the underlying brain function. While recording animal behavior has become easier than ever with the development of compact and inexpensive devices, detailed behavioral data analysis requires sufficient prior knowledge and/or high content data such as video images of animal postures, which makes it difficult for most of the animal behavioral data to be efficiently analyzed. Here, we report a versatile method using a hybrid supervised/unsupervised machine learning approach for behavioral state estimation and feature extraction (STEFTR) only from low-content animal trajectory data. To demonstrate the effectiveness of the proposed method, we analyzed trajectory data of worms, fruit flies, rats, and bats in the laboratories, and penguins and flying seabirds in the wild, which were recorded with various methods and span a wide range of spatiotemporal scales—from mm to 1,000 km in space and from sub-seconds to days in time. We successfully estimated several states during behavior and comprehensively extracted characteristic features from a behavioral state and/or a specific experimental condition. Physiological and genetic experiments in worms revealed that the extracted behavioral features reflected specific neural or gene activities. Thus, our method provides a versatile and unbiased way to extract behavioral features from simple trajectory data to understand brain function.

Biologging Tags Reveal Links Between Fine-Scale Horizontal and Vertical Movement Behaviors in Tiger Sharks (Galeocerdo cuvier)

An understanding of the role that large marine predators play in structuring trophic flow and nutrient cycling in marine ecosystems requires knowledge of their fine-scale (m-km) movement behaviours. In this study, biologging tags were used to reveal new insights into the three-dimensional fine-scale movement ecology of tiger sharks (Galeocerdo cuvier) at Ningaloo Reef, Western Australia. Tags deployed on 21 sharks in April-May 2017 for durations of 5-48 hours recorded both physical parameters such as depth and temperature, and, through the use of accelerometers, gyroscopes and compasses, in-situ measurements of animal trajectory and locomotion. Animal-borne-video enabled the validation of behavioural signatures, mapping of habitat, and recording of interactions with prey. Collectively, these data were used to examine the link between vertical (oscillations) and horizontal (tortuosity) movements, and link sensor data to prey interactions recorded by the video. This biologging approach revealed complex movements that would otherwise be invisible within the time-depth records provided by traditional tagging techniques. The rate of horizontal turning was not related to vertical oscillations, suggesting that vertical movements occur independently of searching behaviours in tiger sharks. These animals displayed tortuous movements possibly associated with prey searching for 27% of their tracks, and interactions with prey elicited varied responses including highly tortuous paths and burst movements. Accurate speed measurements and GPS anchor points will considerably enhance the value of magnetometer data in future studies by facilitating more accurate dead-reckoning and geo-referencing of area-restricted search behaviours.

Accounting for phenology in the analysis of animal movement.

The analysis of animal tracking data provides important scientific understanding and discovery in ecology. Observations of animal trajectories using telemetry devices provide researchers with information about the way animals interact with their environment and each other. For many species, specific geographical features in the landscape can have a strong effect on behavior. Such features may correspond to a single point (eg, dens or kill sites), or to higher dimensional subspaces (eg, rivers or lakes). Features may be relatively static in time (eg, coastlines or home-range centers), or may be dynamic (eg, sea ice extent or areas of high-quality forage for herbivores). We introduce a novel model for animal movement that incorporates active selection for dynamic features in a landscape. Our approach is motivated by the study of polar bear (Ursus maritimus) movement. During the sea ice melt season, polar bears spend much of their time on sea ice above shallow, biologically productive water where they hunt seals. The changing distribution and characteristics of sea ice throughout the year mean that the location of valuable habitat is constantly shifting. We develop a model for the movement of polar bears that accounts for the effect of this important landscape feature. We introduce a two-stage procedure for approximate Bayesian inference that allows us to analyze over 300 000 observed locations of 186 polar bears from 2012 to 2016. We use our model to estimate a spatial boundary of interest to wildlife managers that separates two subpopulations of polar bears from the Beaufort and Chukchi seas.

Context-based semantical vector representations for animal trajectories

ABSTRACTBehaviour could be expressed as a set of specific movement patterns in time. An animal's movement or trajectory could characterise its behaviours and provide information about its internal states. Recent advances in GPS-based sensor technologies led to drastic increase in volume of the data collected from animals' movements which enables researchers to analyse and model their behaviours using data-driven methods. However, having compact, discriminative, semantical and independent numerical representations of trajectories as features, is essential for employing the most of available off-the-shelf machine learning and deep learning techniques. Inspired by language processing, the approach presented in this study utilizes Skip-gram model to create contextual vector embeddings or representations of key-points in animal trajectories to be used as input features. Here, a key-point is defined as a location which represents a trajectory segment. It is assumed that these key-points encapsulate contextual information which is attributed to a certain behaviour or specific group of animals with similar behavioural features. So, the vector embeddings could be interpreted as contextual semantical representations of trajectory key-points independent of their spatial coordinates. With these representations, it would be possible to predict likelihood of preceding or subsequent key-points given a context or an internal state, or vice versa. To test this hypothesis, an experiment was conducted on birds' trajectories logged from a seabird species, Streaked Shearwater (Calonectris leucomelas). In this experiment, vector representations of the key-points in birds' trajectories were constructed and optimized using candidate sampling. The experimental results showcased the utility of these vector embeddings in both exploration of Streaked Shearwater trajectory data and improvement of gender-based trajectory classification. In summary, the proposed method provided a novel approach for numerical representation of animal trajectories and, it was illustrated to be semantically more explanatory for analysis as well as being more informative as features for modelling of animal movement data.

Efficient learning algorithm for sparse subsequence pattern-based classification and applications to comparative animal trajectory data analysis

ABSTRACTRecent advances in robotics and measurement technologies have enabled biologists to record the trajectories created by animal movements. In this paper, we convert time series of animal trajectories into sequences of finite symbols, and then propose a machine learning method for gaining biological insight from the trajectory data in the form of symbol sequences. The proposed method is used for training a classifier which differentiates between the trajectories of two groups of animals such as male and female. The classifier is represented in the form of a sparse linear combination of subsequence patterns, and we call the classifier an S3P-classifier. The trained S3P-classifier is easy to interpret because each coefficient represents the specificity of the subsequence patterns in either of the two classes of animal trajectories. However, fitting an S3P-classifier is computationally challenging because the number of subsequence patterns is extremely large. The main technical contribution in this paper is the development of a novel algorithm for overcoming this computational difficulty by combining a sequential mining technique with a recently developed convex optimization technique called safe screening. We demonstrate the effectiveness of the proposed method by applying it to three animal trajectory data analysis tasks.

Can AI predict animal movements? Filling gaps in animal trajectories using inverse reinforcement learning

AbstractFocal animal sampling and continuous recording of behavior in situ are essential in the study of ecology. However, observation gaps and missing records are unavoidable because the focal individual can move out of sight and recording devices do not always work properly. Using an inverse reinforcement learning (IRL) framework, we have developed a novel gap‐filling method to predict the most likely route that an animal would have traveled; within this framework, an algorithm learns a reward function from animal trajectories to find the environmental features preferred by the animal. We applied this approach to GPS trajectories obtained from streaked shearwaters (Calonectris leucomelas) and provide evidence of the advantages of the IRL approach over previously used interpolation methods. These advantages are as follows: (1) No assumptions about the parametric distribution governing movements are needed, (2) no assumptions regarding landscape preferences and restrictions are needed, and (3) large spatiotemporal gaps can be filled. This work demonstrates how IRL can enhance the ability to fill gaps in animal trajectories and construct reward‐space maps in heterogeneous environments. The proposed methodology can assist movement research, which seeks to understand phenomena that are ecologically and evolutionarily significant, such as habitat selection and migration.

Conservation conundrum: Endangered predators eating endangered prey

Conservation conundrum: Endangered predators eating endangered prey

Probabilistic models of individual and collective animal behavior

Recent developments in automated tracking allow uninterrupted, high-resolution recording of animal trajectories, sometimes coupled with the identification of stereotyped changes of body pose or other behaviors of interest. Analysis and interpretation of such data represents a challenge: the timing of animal behaviors may be stochastic and modulated by kinematic variables, by the interaction with the environment or with the conspecifics within the animal group, and dependent on internal cognitive or behavioral state of the individual. Existing models for collective motion typically fail to incorporate the discrete, stochastic, and internal-state-dependent aspects of behavior, while models focusing on individual animal behavior typically ignore the spatial aspects of the problem. Here we propose a probabilistic modeling framework to address this gap. Each animal can switch stochastically between different behavioral states, with each state resulting in a possibly different law of motion through space. Switching rates for behavioral transitions can depend in a very general way, which we seek to identify from data, on the effects of the environment as well as the interaction between the animals. We represent the switching dynamics as a Generalized Linear Model and show that: (i) forward simulation of multiple interacting animals is possible using a variant of the Gillespie’s Stochastic Simulation Algorithm; (ii) formulated properly, the maximum likelihood inference of switching rate functions is tractably solvable by gradient descent; (iii) model selection can be used to identify factors that modulate behavioral state switching and to appropriately adjust model complexity to data. To illustrate our framework, we apply it to two synthetic models of animal motion and to real zebrafish tracking data.

Light-guided running behavior induces direction selective spikes of hippocampal neurons

The hippocampus consists of place cells that preferentially show spike activity when animals visit a limited area of the environment. A widely used behavioral task for characterizing place cells is a foraging task in which rats freely explore an open two-dimensional space in search of randomly dispersed food pellets. In this task, firing of place cells tends to be largely independent of movement direction. On the other hand, in spatial task on radial arm maze and linear track where animals develop goal-directed behavioral strategies, place-selective firing of hippocampal cells is biased in a specific direction of movement. Thus, the hippocampal circuit employs distinct encoding modes for space depending on ongoing task demands and the presence of goals. In this study, we recorded the firing patterns of hippocampal cells, and the rats performed goal related tasks and random foraging tasks in open field. In the goal-related task, the rat had to run towards a light-cued goal to obtain a food reward in the field. Enhancing the degree of freedom of moving directions by utilizing the two-dimensional space allowed us to analyze animal's trajectories from various provenance toward goals, including errors, which could not be parsed in a stereotyped one-dimensional path, such as a linear track. We found a certain population of hippocampal cells in the goal-directed task fired only while rats approached to a specific future goal independent of moving directions. These goal-directed place-selective firing cells showed similar firing patterns to those observed in the same locations in the foraging task only when the animals ran fast. In the random foraging task, these cells also showed goal-directed activity by accelerating their firing rates as a function of their speeds when the animals moved to the goal location. The evidence advances our understanding of how place-selective firing of hippocampal cells is modified by goal-directed movement in an open field.

Sensorimotor computation underlying phototaxis in zebrafish

Animals continuously gather sensory cues to move towards favourable environments. Efficient goal-directed navigation requires sensory perception and motor commands to be intertwined in a feedback loop, yet the neural substrate underlying this sensorimotor task in the vertebrate brain remains elusive. Here, we combine virtual-reality behavioural assays, volumetric calcium imaging, optogenetic stimulation and circuit modelling to reveal the neural mechanisms through which a zebrafish performs phototaxis, i.e. actively orients towards a light source. Key to this process is a self-oscillating hindbrain population (HBO) that acts as a pacemaker for ocular saccades and controls the orientation of successive swim-bouts. It further integrates visual stimuli in a state-dependent manner, i.e. its response to visual inputs varies with the motor context, a mechanism that manifests itself in the phase-locked entrainment of the HBO by periodic stimuli. A rate model is developed that reproduces our observations and demonstrates how this sensorimotor processing eventually biases the animal trajectory towards bright regions.

Guest Editor’s Introduction to the Special Issue on “Animal Movement Modeling”

In this introduction, we provide a brief overview to statistical models for animal trajectories and then summarize the set of invited articles that comprise the issue.

Idiothetic Path Integration in the Fruit Fly Drosophila melanogaster

After discovering a small drop of food, hungry flies exhibit a peculiar behavior in which they repeatedly stray from, but then return to, the newly discovered resource. To study this behavior in more detail, we tracked hungry Drosophila as they explored a large arena, focusing on the question of how flies remain near the food. To determine whether flies use external stimuli, we individually eliminated visual, olfactory, and pheromonal cues. In all cases, flies still exhibited a centralized search behavior, suggesting that none of these cues are absolutely required for navigation back to the food. To simultaneously eliminate visual and olfactory cues associated with the position of the food, we constructed an apparatus in which the food could be rapidly translated from the center of the arena. Flies continued to search around the original location, even after the food was moved to a new position. A random search model based on measured locomotor statistics could not reproduce the centered nature of the animal's trajectory. We conclude that this behavior is best explained by a form of path integration in which the flies use idiothetic cues to search near the location of the food. We argue that the use of path integration to perform a centered local search is not a specialization of Drosophila but rather represents an ancient behavioral mode that is homologous to the more elaborate foraging strategies of central place foragers such as ants.