Animal dispersal modelling: Handling landscape features and related animal choices

Animal dispersal in a fragmented landscape depends on the complex interaction between landscape structure and animal behavior. To better understand how individuals disperse, it is important to explicitly represent the properties of organisms and the landscape in which they move. A common approach to modelling dispersal includes representing the landscape as a grid of equal sized cells and then simulating individual movement as a correlated random walk. This approach uses a priori scale of resolution, which limits the representation of all landscape features and how different dispersal abilities are modelled.We develop a vector-based landscape model coupled with an object-oriented model for animal dispersal. In this spatially explicit dispersal model, landscape features are defined based on their geographic and thematic properties and dispersal is modelled through consideration of an organism's behavior, movement rules and searching strategies (such as visual cues). We present the model's underlying concepts, its ability to adequately represent landscape features and provide simulation of dispersal according to different dispersal abilities. We demonstrate the potential of the model by simulating two virtual species in a real Swiss landscape. This illustrates the model's ability to simulate complex dispersal processes and provides information about dispersal such as colonization probability and spatial distribution of the organism's path.     

Analyzing animal movements using Brownian bridges

By studying animal movements, researchers can gain insight into many of the ecological characteristics and processes important for understanding population-level dynamics. We developed a Brownian bridge movement model (BBMM) for estimating the expected movement path of an animal, using discrete location data obtained at relatively short time intervals. The BBMM is based on the properties of a conditional random walk between successive pairs of locations, dependent on the time between locations, the distance between locations, and the Brownian motion variance that is related to the animal's mobility. We describe two critical developments that enable widespread use of the BBMM, including a derivation of the model when location data are measured with error and a maximum likelihood approach for estimating the Brownian motion variance. After the BBMM is fitted to location data, an estimate of the animal's probability of occurrence can be generated for an area during the time of observation. To illustrate potential applications, we provide three examples: estimating animal home ranges, estimating animal migration routes, and evaluating the influence of fine-scale resource selection on animal movement patterns.     

Hidden process models for animal population dynamics.

Hidden process models are a conceptually useful and practical way to simultaneously account for process variation in animal population dynamics and measurement errors in observations and estimates made on the population. Process variation, which can be both demographic and environmental, is modeled by linking a series of stochastic and deterministic subprocesses that characterize processes such as birth, survival, maturation, and movement. Observations of the population can be modeled as functions of true abundance with realistic probability distributions to describe observation or estimation error. Computer-intensive procedures, such as sequential Monte Carlo methods or Markov chain Monte Carlo, condition on the observed data to yield estimates of both the underlying true population abundances and the unknown population dynamics parameters. Formulation and fitting of a hidden process model are demonstrated for Sacramento River winter-run chinook salmon (Oncorhynchus tshawytsha).     

Using accelerometer,high sample rate GPS and magnetometer data to develop a cattle movement and behaviour model

The study described in this paper developed a model of animal movement, which explicitly recognised each individual as the central unit of measure. The model was developed by learning from a real dataset that measured and calculated, for individual cows in a herd, their linear and angular positions and directional and angular speeds. Two learning algorithms were implemented: a Hidden Markov model (HMM) and a long-term prediction algorithm. It is shown that a HMM can be used to describe the animal's movement and state transition behaviour within several “stay” areas where cows remained for long periods. Model parameters were estimated for hidden behaviour states such as relocating, foraging and bedding. For cows’ movement between the “stay” areas a long-term prediction algorithm was implemented. By combining these two algorithms it was possible to develop a successful model, which achieved similar results to the animal behaviour data collected. This modelling methodology could easily be applied to interactions of other animal species.     

Analysis of behavioral changes of zebrafish (Danio rerio) in response to formaldehyde using Self-organizing map and a hidden Markov model

Two computational methods were applied to classification of movement patterns of zebrafish (Danio rerio) to elucidate Markov processes in behavioral changes before and after treatment of formaldehyde (0.1 mg/L) in semi-natural conditions. The complex data of the movement tracks were initially classified by the Self-organizing map (SOM) to present different behavioral states of test individuals. Transition probabilities between behavioral states were further evaluated to fit Markov processes by using the hidden Markov model (HMM). Emission transition probability was also obtained from the observed variables (i.e., speed) for training with the HMM. Experimental transition and emission probability matrices were successfully estimated with the HMM for recognizing sequences of behavioral states with accuracy rates in acceptable ranges at central and boundary zones before (77.3-81.2%) and after (70.1-76.5%) treatment. A heuristic algorithm and a Markov model were efficiently combined to analyze movement patterns and could be a means of in situ behavioral monitoring tool.     

Measurement error causes scale-dependent threshold erosion of biological signals in animal movement data.

Recent advances in telemetry technology have created a wealth of tracking data available for many animal species moving over spatial scales from tens of meters to tens of thousands of kilometers. Increasingly, such data sets are being used for quantitative movement analyses aimed at extracting fundamental biological signals such as optimal searching behavior and scale-dependent foraging decisions. We show here that the location error inherent in various tracking technologies reduces the ability to detect patterns of behavior within movements. Our analyses endeavored to set out a series of initial ground rules for ecologists to help ensure that sampling noise is not misinterpreted as a real biological signal. We simulated animal movement tracks using specialized random walks known as Lévy flights at three spatial scales of investigation: 100-km, 10-km, and 1-km maximum daily step lengths. The locations generated in the simulations were then blurred using known error distributions associated with commonly applied tracking methods: the Global Positioning System (GPS), Argos polar-orbiting satellites, and light-level geolocation. Deviations from the idealized Lévy flight pattern were assessed for each track after incrementing levels of location error were applied at each spatial scale, with additional assessments of the effect of error on scale-dependent movement patterns measured using fractal mean dimension and first-passage time (FPT) analyses. The accuracy of parameter estimation (Lévy mu, fractal mean D, and variance in FPT) declined precipitously at threshold errors relative to each spatial scale. At 100-km maximum daily step lengths, error standard deviations of > or = 10 km seriously eroded the biological patterns evident in the simulated tracks, with analogous thresholds at the 10-km and 1-km scales (error SD > or = 1.3 km and 0.07 km, respectively). Temporal subsampling of the simulated tracks maintained some elements of the biological signals depending on error level and spatial scale. Failure to account for large errors relative to the scale of movement can produce substantial biases in the interpretation of movement patterns. This study provides researchers with a framework for understanding the limitations of their data and identifies how temporal subsampling can help to reduce the influence of spatial error on their conclusions.     

Reliance of mobile species on sensitive habitats: a case study of manta rays (Manta alfredi) and lagoons

Quantifying the ecological importance of individual habitats to highly mobile animals is challenging because patterns of habitat reliance for these taxa are complex and difficult to observe. We investigated the importance of lagoons to the manta ray, Manta alfredi, a wide-ranging and vulnerable species in a less-disturbed atoll ecosystem. Lagoons are highly sensitive to anthropogenic disturbance and are known to be ecologically important to a wide variety of mobile species. We used a novel combination of research tools to examine the reliance of M. alfredi on lagoon habitats. Stable isotope analysis was used to assay the recent energetic importance of lagoons to M. alfredi; high-resolution tracking data provided information about how M. alfredi utilised lagoonal habitats over long and short time periods; acoustic cameras logged patterns of animal entrances and departures from lagoons; and photo identification/laser photogrammetry provided some insight into why they may be using this habitat. M. alfredi showed strong evidence of energetic dependence on lagoon resources during the course of the study and spent long periods of residence within lagoons or frequently transited into them from elsewhere. While within lagoons, they demonstrated affinities for particular structural features within this habitat and showed evidence of temporal patterning in habitat utilization. This work sheds light on how and why M. alfredi uses lagoons and raises questions about how this use may be altered in disturbed settings. More generally, these observations contribute to our knowledge of how to assess the ecological importance of particular habitats situated within the broader home range of mobile consumers.     

Predicting functional response and size selectivity of juvenile Notonecta maculata foraging on Daphnia magna

A mechanistic model was developed to assess the impact of predation of juvenile Notonecta maculata on size structured Daphnia magna populations and to provide a framework for quantifying the backswimmers uptake of food. Results of experiments and model predictions clearly demonstrate selective predation of backswimmers when fed with a choice of daphnid size classes, with patterns of selectivity differing across N. maculata instars. The model describes the foraging process empirically on the base of a general predation cycle including four conditional events instead of using classic functional response curves. For model parameterisation components of predation, namely probability of encounter, attack and success as well as time spent on handling prey was directly observed by means of video tracking experiments. Since attack rate, capture success and handling time appeared to be a function of prey size differing between Notonecta instars, the model takes into account ontogenic changes in both predator and prey characteristics. Independent data of functional response and size selectivity experiments were used for model validation and proved the model outcome to be consistent with observations.     

Estimating behavioral parameters in animal movement models using a state-augmented particle filter

Data on fine-scale animal movement are being collected worldwide, with the number of species being tagged and the resolution of data rapidly increasing. In this study, a general methodology is proposed to understand the patterns in these high-resolution movement time series that relate to marine animal behavior. The approach is illustrated with dive data from a northern fur seal (Callorhinus ursinus) tagged on the Pribilof Islands, Alaska, USA. We apply a state-space model composed of a movement model and corresponding high-resolution vertical movement data. The central goal is to estimate parameters of this movement model, particularly their variation on appropriate time scales, thereby providing a direct link to behavior. A particle filter with state augmentation is used to jointly estimate the movement parameters and the state. A multiple iterated filter using overlapping data segments is implemented to match the parameter time scale with the behavioral inference. The time variation in the auto-covariance function facilitates identification of a movement model, allows separation of observation and process noise, and provides for validation of results. The analysis yields fitted parameters that show distinct time-evolving changes in fur seal behavior over time, matching well what is observed in the original data set.     

Modeling amphibian energetics, habitat suitability, and movements of western toads, Anaxyrus (=Bufo) boreas, across present and future landscapes

Effective conservation of amphibian populations requires the prediction of how amphibians use and move through a landscape. Amphibians are closely coupled to their physical environment. Thus an approach that uses the physiological attributes of amphibians, together with knowledge of their natural history, should be helpful. We used Niche Mapper™ to model the known movements and habitat use patterns of a population of Western toads (Anaxyrus (=Bufo) boreas) occupying forested habitats in southeastern Idaho. Niche Mapper uses first principles of environmental biophysics to combine features of topography, climate, land cover, and animal features to model microclimates and animal physiology and behavior across landscapes. Niche Mapper reproduced core body temperatures (T_c) and evaporation rates of live toads with average errors of 1.6 ± 0.4 °C and 0.8 ± 0.2 g/h, respectively. For four different habitat types, it reproduced similar mid-summer daily temperature patterns as those measured in the field and calculated evaporation rates (g/h) with an average error rate of 7.2 ± 5.5%. Sensitivity analyses indicate these errors do not significantly affect estimates of food consumption or activity. Using Niche Mapper we predicted the daily habitats used by free-ranging toads; our accuracy for female toads was greater than for male toads (74.2 ± 6.8% and 53.6 ± 15.8%, respectively), reflecting the stronger patterns of habitat selection among females. Using these changing to construct a cost surface, we also reconstructed movement paths that were consistent with field observations. The effect of climate warming on toads depends on the interaction of temperature and atmospheric moisture. If climate change occurs as predicted, results from Niche Mapper suggests that climate warming will increase the physiological cost of landscapes thereby limiting the activity for toads in different habitats.     

Consideration of translocation into a growth model of a plant organ

Taking account of the Bertalanffy's differential equation on animal growth, plant growth is also considered as the net result of anabolism and catabolism. When we, however, consider the growth of a plant organ, it is necessary to add a term of translocation because it plays an important role in the growth of plant organs, such as leaf and fruit. Considering translocation, therefore, a growth model of a plant organ was proposed on the basis of the compartment model for estimating the carbon balance in the organ by using the experimental data on translocation, photosynthesis and respiration of a tropical fruit of durian (Durio zibethinus Murray). The present growth model of a plant organ belongs to an extended Bertalanffy's growth equation, and was possible to be transformed into the simple Bertalanffy's growth equation on the basis of the proportionality between the growth and translocation rates. The Bertalanffy's growth equation of a plant organ was also possible to apply to that of the whole plant on the assumption of the allomeric relationship between a plant organ and the whole plant.     

GPS tracking a marine predator: the effects of precision,resolution and sampling rate on foraging tracks of African Penguins

We used a prototype GPS logger to track the movements of breeding African Penguins (Spheniscus demersus). The loggers also recorded temperature and water depth, which allowed us to reconstruct foraging tracks in three dimensions, although GPS signals are interrupted when the birds dive. Here we report the loggers performance in the field and assess the effects of GPS error, resolution and sampling rate on estimates of foraging track length and speed. There is a trade-off between sampling rate and battery lifespan. We tested loggers at sampling intervals of 1 s, 10 s, 1 min, 2 min and 10 min. Sampling less frequently increases the chance of tracking an entire foraging trip, but it slows uplink times, slightly decreases the accuracy of positional fixes, and significantly reduces the ability to measure fine-scale aspects of foraging behaviour. Compared with radio or satellite tracking, GPS loggers offer unprecedented detail about animal movements. The results of our analysis suggest that techniques that sample relatively infrequently, such as satellite tracking, underestimate actual track lengths by up to 50%. However, caution is needed when interpreting fine-scale sampling for relatively slow-moving organisms. Re-sampling 1-s tracks suggests that c. 35% of apparent movements at this scale are due to measurement error and, more importantly, the limited spatial resolution of GPS (1.85×1.54 m at the study area). We recommend that researchers use a 1-s sampling rate for fine-scale studies, but resample at less frequent intervals to remove spurious noise for slow-moving animals. At current levels of resolution, animals should move at least 4 m per sampling interval. We provide empirical correction factors to compare inferred track length sampled at different rates, but caution that these are idiosyncratic and strongly dependent on the animals behaviour. Overall, GPS loggers offer a significant advance for studies of fine-scale animal movement patterns.Communicated by O. Kinne, Oldendorf/Luhe     

Spatio-temporal modeling of striped-bass egg, larval movement, and fate in the San Francisco Bay-Delta

Most models developed for the movement and fate of eggs and larvae of aquatic species are based on a particle tracking approach. Although this method has many advantages due to its high flexibility, particle tracking may become computationally intensive for complex geometries and when large numbers of particles are needed to simulate the population properly. In continuous models based on advection and dispersion mechanisms, the computational burden is independent of the size of the population. We developed a continuous fate and transport model for striped bass eggs and larvae in the San Francisco Bay-Delta. The model predicts the concentration of eggs and larvae at any location over time. The method of moments was used to account for the effect of temperature and age on the transition of eggs to larvae and larvae to juveniles. Egg and larval mortality were represented as functions of temperature, and eggs also experienced settling mortality. The fate and transport model used the same one-dimensional spatial grid as the existing Delta Simulation Model II (DSM2) hydrodynamics model. DSM2 output of flow rates, water depths, and cross-sectional areas were inputted into the fate and transport model to determine transport. The model was applied to striped bass eggs and larvae data collected during years 1990-1994; agreement between the modeled and the measured data was acceptable in most cases. Exploratory simulations were performed to demonstrate how the model could be used to evaluate the effects on egg and larval survival and total juvenile production of water diversions for supply and agricultural use and changes in the long-term mean water temperature. The model can be further used to examine the impact of various operation strategies in the San Francisco Bay-Delta, where diversion losses of early life stages of fishes remain a major management issue.     

Radio-acoustic positioning as a tool for studying site-specific behavior of the white shark and other large marine species

We describe a method, radio-acoustic-positioning (RAP), for continuously monitoring the movements and behavior of large marine animals. An ultrasonic transmitter on the animal can be localized with high spatial accuracy (2 to 10?m) within an area of 1?km², based on when the same pulse arrives at three hydrophones on sonobuoys aligned in a triangular array. Radio transceivers communicate with the base station, where the x and y coordinates of the subject are calculated using hyperbolic equations. The base station plots the individual's position and displays information from the tag's sensors in real time on a computer monitor before saving the data on a disk. The base station must be situated either on land or on a vessel within the reception range of the three buoys. We used a RAP system to monitor the movements and behavior of white sharks (Carcharodon carcharias) near the elephant seal rookery at Año Nuevo Island in central California. This type of system is an ideal tool to study the predatory behavior of the white shark because individuals patrol for seal prey within a zone <1300?m from shore. We describe the operation of the system, including acoustic triangulation, range of detection and positioning, data acquisition and analysis, and positional accuracy. We illustrate the implementation of the method and its advantages and disadvantages by describing an ongoing study of white shark hunting-behavior. Sample data from this study are presented to illustrate specific points. We describe the movements of five sharks within the receiving range and their behavior relative to each other. The RAP system is compared to other complementary tracking methods. We conclude that this system has great potential for monitoring the movements and behavior of large marine animals within a relatively small zone, where feeding or reproduction takes place.     

Modeling and inference of animal movement using artificial neural networks

Movement of animals in relation to objects in their environment is important in many areas of ecology and wildlife conservation. Tools for analysis of movement data, however, still remain rather limited. In previous work, we developed nonlinear regression models for movement in relation to a single landscape feature. Here we greatly expand these previous models by using artificial neural networks. The new models add substantial flexibility and capabilities, including the ability to incorporate multiple factors and covariates. We devise a likelihood-based model fitting procedure that utilizes genetic algorithms and demonstrate the approach with movement data for red diamond rattlesnakes. The proposed methodology can be useful for global positioning system tracking data that are becoming more common in studies of animal movement behavior.     

Incorporating the perceptual range of animals into connectivity models

The perceptual range of an animal towards different landscape elements affects its movements through heterogeneous landscapes. However, empirical knowledge and modeling tools are lacking to assess the consequences of variation in the perceptual range for movement patterns and connectivity. In this study we tested how changes in the assumed perception of different landscape elements affect the outcomes of a connectivity model. We used an existing individual-based, spatially explicit model for the dispersal of Eurasian lynx (Lynx lynx). We systematically altered the perceptual range in which animals recognize forest fragments, water bodies or cities, as well as the probability that they respond to these landscape elements. Overall, increasing the perceptual range of the animals enhanced connectivity substantially, both qualitatively and quantitatively. An enhanced range of attraction to forests had the strongest impact, doubling immigration success; an enhanced range of attraction to rivers had a slightly lower impact; and an enhanced range of avoidance of cities had the lowest impact. Correcting the enhancement in connectivity by the abundance of each of the landscape elements in question reversed the results, indicating the potential sensitivity of connectivity models to rare landscape elements (in our case barriers such as cities). Qualitatively, the enhanced perception resulted in strong changes in movement patterns and connectivity. Furthermore, model results were highly parameter-specific and patch-specific. These results emphasize the need for further empirical research on the perceptual capabilities of different animals in different landscapes and conditions. They further indicate the usefulness of spatially explicit individual-based simulation models for recognizing consistent patterns that emerge, despite uncertainty regarding animals’ movement behavior. Altogether, this study demonstrates the need to extend the concept of ‘perceptual ranges’ beyond patch detection processes, to encompass the wide range of elements that can direct animal movements during dispersal through heterogeneous landscapes.     

Estimating dyad association probability under imperfect and heterogeneous detection

In animal behaviour studies, association indices estimate the proportion of time two individuals (i.e. a dyad) spend in association. In terms of dyads, all association indices can be interpreted as estimators of the probability that a dyad is associated. However, traditional indices rely on the assumptions that the probability to detect a particular individual (p) is either approximately one and/or homogeneous between associated and not associated individuals. Based on marked individuals we develop a likelihood based model to estimate the probability a dyad is associated (ψ) accounting for p < 1 and possibly varying between associated and not associated individuals. The proposed likelihood based model allows for both individual and dyadic missing observations. In addition, the model can easily be extended to incorporate covariate information for modeling p and ψ. A simulation study showed that the likelihood based model approach yield reasonably unbiased estimates, even for low and heterogeneous individual detection probabilities, while, in contrast, traditional indices showed moderate to strong biases. The application of the proposed approach is illustrated using a real data set collected from a population of Commerson's dolphin (Cephalorhynchus commersonii) in Patagonia Argentina. Finally, we discuss possible extensions of the proposed model and its applicability in animal behaviour and ecological studies.     

Incorporating multidimensional behavior into a risk management tool for a critically endangered and migratory species

Conservation of migratory species exhibiting wide-ranging and multidimensional behaviors is challenged by management efforts that only utilize horizontal movements or produce static spatial–temporal products. For the deep-diving, critically endangered eastern Pacific leatherback turtle, tools that predict where turtles have high risks of fisheries interactions are urgently needed to prevent further population decline. We incorporated horizontal–vertical movement model results with spatial–temporal kernel density estimates and threat data (gear-specific fishing) to develop monthly maps of spatial risk. Specifically, we applied multistate hidden Markov models to a biotelemetry data set (n = 28 leatherback tracks, 2004–2007). Tracks with dive information were used to characterize turtle behavior as belonging to 1 of 3 states (transiting, residential with mixed diving, and residential with deep diving). Recent fishing effort data from Global Fishing Watch were integrated with predicted behaviors and monthly space-use estimates to create maps of relative risk of turtle–fisheries interactions. Drifting (pelagic) longline fishing gear had the highest average monthly fishing effort in the study region, and risk indices showed this gear to also have the greatest potential for high-risk interactions with turtles in a residential, deep-diving behavioral state. Monthly relative risk surfaces for all gears and behaviors were added to South Pacific TurtleWatch (SPTW) ( https://www.upwell.org/sptw ), a dynamic management tool for this leatherback population. These modifications will refine SPTW's capability to provide important predictions of potential high-risk bycatch areas for turtles undertaking specific behaviors. Our results demonstrate how multidimensional movement data, spatial–temporal density estimates, and threat data can be used to create a unique conservation tool. These methods serve as a framework for incorporating behavior into similar tools for other aquatic, aerial, and terrestrial taxa with multidimensional movement behaviors.