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.     

A single-chain-based multidimensional Markov chain model for subsurface characterization

Multidimensional Markov chain models in geosciences were often built on multiple chains, one in each direction, and assumed these 1-D chains to be independent of each other. Thus, unwanted transitions (i.e., transitions of multiple chains to the same location with unequal states) inevitably occur and have to be excluded in estimating the states at unobserved locations. This consequently may result in unreliable estimates, such as underestimation of small classes (i.e., classes with smaller than average areas) in simulated realizations. This paper presents a single-chain-based multidimensional Markov chain model for estimation (i.e., prediction and conditional stochastic simulation) of spatial distribution of subsurface formations with borehole data. The model assumes that a single Markov chain moves in a lattice space, interacting with its nearest known neighbors through different transition probability rules in different cardinal directions. The conditional probability distribution of the Markov chain at the location to be estimated is formulated in an explicit form by following the Bayes’ Theorem and the conditional independence of sparse data in cardinal directions. Since no unwanted transitions are involved, the model can estimate all classes fairly. Transiogram models (i.e., 1-D continuous Markov transition probability diagrams) are used to provide transition probability input with needed lags to generalize the model. Therefore, conditional simulation can be conducted directly and efficiently. The model provides an alternative for heterogeneity characterization of subsurface formations.

Behavioural switching in a central place forager: patterns of diving behaviour in the macaroni penguin (Eudyptes chrysolophus)

Recording the activity of animals as they migrate or forage has proven hugely advantageous to understanding how animals use their environment. Where animals cannot be directly observed, the problem remains of how to identify distinct behaviours that represent an animal’s decision-making process. An excellent example of this problem is that of foraging penguins, which travel to sea to find prey to provision their young. Without direct sampling of the prey field, we cannot calibrate patterns of movement with prey capture, and therefore we cannot determine how different activities link to decision-making. To overcome this, we use a hidden markov model (HMM), which is a machine-learning technique that seeks to identify the underlying states of a system from observable outputs. We apply HMM to determine classes of behaviour from repetitive dives. We take dive data from 103 breeding macaroni penguins at Bird Island, South Georgia, for which we have measures of weight gain over a trip. We identify two classes of behaviour; those of short-shallow and long-deep dives. Using these two behaviours, we calculate the transition probabilities between these states and analyse these data to determine what predicts variation in the transition probabilities. We found that the stage of reproduction during a season, the sex and year of an individual influenced the probability of transition between long-deep and short-shallow sequential dives. We also found differences in the hourly transition rates between the four reproductive stages (incubation, broodguard, crèche and premoult) over a daily cycle. We conclude that this application of HMMs for behavioural switching is potentially useful for other species and other types of recorded behaviour.     

Effects of tour boats on dolphin activity examined with sensitivity analysis of Markov chains

In Patagonia, Argentina, watching dolphins, especially dusky dolphins (Lagenorhynchus obscurus), is a new tourist activity. Feeding time decreases and time to return to feeding after feeding is abandoned and time it takes a group of dolphins to feed increase in the presence of boats. Such effects on feeding behavior may exert energetic costs on dolphins and thus reduce an individual's survival and reproductive capacity or maybe associated with shifts in distribution. We sought to predict which behavioral changes modify the activity pattern of dolphins the most. We modeled behavioral sequences of dusky dolphins with Markov chains. We calculated transition probabilities from one activity to another and arranged them in a stochastic matrix model. The proportion of time dolphins dedicated to a given activity (activity budget) and the time it took a dolphin to resume that activity after it had been abandoned (recurrence time) were calculated. We used a sensitivity analysis of Markov chains to calculate the sensitivity of the time budget and the activity-resumption time to changes in behavioral transition probabilities. Feeding-time budget was most sensitive to changes in the probability of dolphins switching from traveling to feeding behavior and of maintaining feeding behavior. Thus, an increase in these probabilities would be associated with the largest reduction in the time dedicated to feeding. A reduction in the probability of changing from traveling to feeding would also be associated with the largest increases in the time it takes dolphins to resume feeding. To approach dolphins when they are traveling would not affect behavior less because presence of the boat may keep dolphins from returning to feeding. Our results may help operators of dolphin-watching vessels minimize negative effects on dolphins.     

Effects of Tour Boats on the Behavior of Bottlenose Dolphins: Using Markov Chains to Model Anthropogenic Impacts

Abstract:   Nature-based tourism activities have been developing over the last decade, but it is still difficult to manage these activities sustainably. This sector is increasingly focusing on whales and dolphins in coastal communities, but the exact effects of these tourism activities are unclear. Markov chain modeling may help researchers assess the effects of tourism activities on the behavioral budget of small cetaceans. Matrix models have been used widely in population ecology to provide successful management guidelines. From June 2000 to August 2001, I collected information on the behavioral state of bottlenose dolphin (  Tursiops spp.) schools from a population residing in Doubtful Sound, Fiordland, New Zealand. In addition, I recorded the occurrence of boat and dolphin interactions. I then calculated the transition probabilities of passing from one behavior to another by using a first-order, time-discrete Markov chain model. Behavioral transitions during which a boat-dolphin interaction occurred were compiled in an "impact" chain. All other transitions were tallied in a control chain. I then quantified the effect of boat-dolphin interactions during behavioral transitions by comparing the behavioral transition probabilities of both chains. Socializing and resting behaviors were disrupted by interactions with boats to a level that raises concern. Both the duration of bouts and the total amount of time spent in both these behavioral states were substantially decreased. Dolphins were significantly more likely to be traveling after an interaction with a boat. However, the overall behavioral budget of the population was not significantly affected. Therefore, the bottlenose dolphin population seems to be able to sustain the present level of boat interactions because of its low intensity. More effort is needed to develop prognosis analyses in order to understand how the effect of boat interactions on dolphins changes with variations in intensity.     

Using hidden Markov chains and empirical Bayes change-point estimation for transect data

Consider a lattice of locations in one dimension at which data are observed. We model the data as a random hierarchical process. The hidden process is assumed to have a (prior) distribution that is derived from a two-state Markov chain. The states correspond to the mean values (high and low) of the observed data. Conditional on the states, the observations are modelled, for example, as independent Gaussian random variables with identical variances. In this model, there are four free parameters: the Gaussian variance, the high and low mean values, and the transition probability in the Markov chain. A parametric empirical Bayes approach requires estimation of these four parameters from the marginal (unconditional) distribution of the data and we use the EM-algorithm to do this. From the posterior of the hidden process, we use simulated annealing to find the maximum a posteriori (MAP) estimate. Using a Gibbs sampler, we also obtain the maximum marginal posterior probability (MMPP) estimate of the hidden process. We use these methods to determine where change-points occur in spatial transects through grassland vegetation, a problem of considerable interest to plant ecologists.     

Estimation methods for nonlinear state-space models in ecology

The use of nonlinear state-space models for analyzing ecological systems is increasing. A wide range of estimation methods for such models are available to ecologists, however it is not always clear, which is the appropriate method to choose. To this end, three approaches to estimation in the theta logistic model for population dynamics were benchmarked by Wang (2007). Similarly, we examine and compare the estimation performance of three alternative methods using simulated data. The first approach is to partition the state-space into a finite number of states and formulate the problem as a hidden Markov model (HMM). The second method uses the mixed effects modeling and fast numerical integration framework of the AD Model Builder (ADMB) open-source software. The third alternative is to use the popular Bayesian framework of BUGS. The study showed that state and parameter estimation performance for all three methods was largely identical, however with BUGS providing overall wider credible intervals for parameters than HMM and ADMB confidence intervals.     

Development of an individual-based model to evaluate elk (Cervus elaphus nelsoni) movement and distribution patterns following the Cerro Grande Fire in north central New Mexico, USA

Though studies have modeled the effects of fires on elk, no studies have related the effects of post-fire landscape succession on ungulate movements and distribution using dynamic modeling techniques. The purpose of this study was to develop and test a spatially-explicit, stochastic, individual-based model (IBM) to evaluate potential movement and distribution patterns of elk (Cervus elaphus nelsoni) in relation to spatial and temporal aspects of the Cerro Grande Fire that burned north central New Mexico in May of 2000. Following extensive literature review, the SAVANNA Ecosystem Model was selected to simulate the underlying post-fire successional processes driving elk movement and distribution. Standard logisitic regression was used to analyze habitat-use patterns of ten elk from data collected using global positioning system radio collars while an additional five animals were used as an independent test set during model validation. Static variables in the form of roads, buildings, fences, and habitual use/memory were used to modify a map of impedance values based on the logistic regression of slope, aspect, and elevation. Integration with SAVANNA came through the application of a habitat suitability index (HSI), which combined movement rules written for the IBM and variables modified and produced by the dynamic ecological processes run in SAVANNA. Overall pattern analysis indicated that realistic migrational processes and habitat-use patterns emerged from movement rules incorporated into the IBM in response to advancing and receding snow when compared to the independent test set. Primary and secondary movement pathways emerged from the collective responses of simulated individuals. Using regression analyses, no significant differences between simulated animals and animals used in either model development or an independent test set revealed any differences in response to snow patterns. These considerations suggest the model was adequately corroborated based on existing data and outlined objectives.     

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.     

Using multistate mark-recapture methods to model adult salmonid migration in an industrialized river

A multistate mark-recapture (MSMR) model of the adult salmonid migration through the lower Columbia River and into the Snake River was developed, designed for radiotelemetry detections at dams and tributary mouths. The model focuses on upstream-directed travel, with states determined from observed fish movement patterns indicating directed upstream travel, downstream travel (fallback), and use of non-natal tributaries. The model was used to analyze telemetry data from 846 migrating adult spring-summer Chinook salmon (Oncorhynchus tshawytscha) tagged in 1996 at Bonneville Dam on the Columbia River. We used the model to test competing hypotheses regarding delayed effects of fallback at dams and visits to tributaries, and to define and estimate migration summary measures. Tagged fish had an average probability of 0.755 () of ending migration at a tributary or upstream of Lower Granite Dam on the Snake River, and a probability of 0.245 () of unaccountable loss (i.e., mortality or mainstem spawning) between the release site downstream of Bonneville Dam and Lower Granite Dam. The highest probability of unaccountable loss (0.092; ) was in the reach between Bonneville Dam and The Dalles Dam. Study fish used the tributaries primarily as exits from the hydrosystem, and visits to non-natal tributaries had no significant effect on subsequent movement upriver (P = 0.4245). However, fallback behavior had a small effect on subsequent tributary entry and exit (P = 0.0530), with fish using tributaries as resting areas after reascending Bonneville Dam after fallback. The spatial MSMR model developed here can be adapted to address additional questions about the interaction of migrating organisms with their environment, or for the study of migrations in other river systems.     

Efficient Markov chain Monte Carlo sampling for hierarchical hidden Markov models

Traditional Markov chain Monte Carlo (MCMC) sampling of hidden Markov models (HMMs) involves latent states underlying an imperfect observation process, and generates posterior samples for top-level parameters concurrently with nuisance latent variables. When potentially many HMMs are embedded within a hierarchical model, this can result in prohibitively long MCMC runtimes. We study combinations of existing methods, which are shown to vastly improve computational efficiency for these hierarchical models while maintaining the modeling flexibility provided by embedded HMMs. The methods include discrete filtering of the HMM likelihood to remove latent states, reduced data representations, and a novel procedure for dynamic block sampling of posterior dimensions. The first two methods have been used in isolation in existing application-specific software, but are not generally available for incorporation in arbitrary model structures. Using the NIMBLE package for R, we develop and test combined computational approaches using three examples from ecological capture–recapture, although our methods are generally applicable to any embedded discrete HMMs. These combinations provide several orders of magnitude improvement in MCMC sampling efficiency, defined as the rate of generating effectively independent posterior samples. In addition to being computationally significant for this class of hierarchical models, this result underscores the potential for vast improvements to MCMC sampling efficiency which can result from combinations of known algorithms.     

Predator and prey space use: dragonflies and tadpoles in an interactive game

Predator and prey spatial distributions have important population and community level consequences. However, little is known either theoretically or empirically about behavioral mechanisms that underlie the spatial patterns that emerge when predators and prey freely interact. We examined the joint space use and behavioral rules governing movement of freely interacting groups of odonate (dragonfly) predators and two size classes of anuran (tadpole) prey in arenas containing two patches with different levels of the prey's resource. Predator and prey movement and space use was quantified both when they were apart and together. When apart from predators, large tadpoles strongly preferred the high resource patch. When apart from prey, dragonflies weakly preferred the high resource patch. When together, large prey shifted to a uniform distribution, while predators strongly preferred the high resource patch. These patterns qualitatively fit the predictions of several three trophic level, ideal free distribution models. In contrast, the space use of small prey and predators did not deviate from uniform. Three measures of joint space use (spatial correlations, overlap, and co-occurrence) concurred in suggesting that prey avoidance of predators was more important than predator attraction to prey in determining overall spatial patterns. To gain additional insight into behavioral mechanisms, we used a model selection approach to identify behavioral movement rules that can potentially explain the observed, emergent patterns of space use. Prey were more likely to leave patches with more predators and more conspecific competitors; resources had relatively weak effects on prey movements. In contrast, predators were more likely to leave patches with low resources (that they do not consume) and more competing predators; prey had relatively little effect on predator movements. These results highlight the importance of investigating freely interacting predators and prey, the potential for simple game theory models to predict joint spatial distributions, and the utility of using model choice methods to identify potential key factors that govern movement.     

Lotka-Volterra competition models for sessile organisms

Markov models are widely used to describe the dynamics of communities of sessile organisms, because they are easily fitted to field data and provide a rich set of analytical tools. In typical ecological applications, at any point in time, each point in space is in one of a finite set of states (e.g., species, empty space). The models aim to describe the probabilities of transitions between states. In most Markov models for communities, these transition probabilities are assumed to be independent of state abundances. This assumption is often suspected to be false and is rarely justified explicitly. Here, we start with simple assumptions about the interactions among sessile organisms and derive a model in which transition probabilities depend on the abundance of destination states. This model is formulated in continuous time and is equivalent to a Lotka-Volterra competition model. We fit this model and a variety of alternatives in which transition probabilities do not depend on state abundances to a long-term coral reef data set. The Lotka-Volterra model describes the data much better than all models we consider other than a saturated model (a model with a separate parameter for each transition at each time interval, which by definition fits the data perfectly). Our approach provides a basis for further development of stochastic models of sessile communities, and many of the methods we use are relevant to other types of community. We discuss possible extensions to spatially explicit models.     

Changes of movement patterns from early dispersal to settlement

Moving and spatial learning are two intertwined processes: (a) changes in movement behavior determine the learning of the spatial environment, and (b) information plays a crucial role in several animal decision-making processes like movement decisions. A useful way to explore the interactions between movement decisions and learning of the spatial environment is by comparing individual behaviors during the different phases of natal dispersal (when individuals move across more or less unknown habitats) with movements and choices of breeders (who repeatedly move within fixed home ranges), that is, by comparing behaviors between individuals who are still acquiring information vs. individuals with a more complete knowledge of their surroundings. When analyzing movement patterns of eagle owls, Bubo bubo, belonging to three status classes (floaters wandering across unknown environments, floaters already settled in temporary settlement areas, and territory owners with a well-established home range), we found that: (1) wandering individuals move faster than when established in a more stable or fixed settlement area, traveling larger and straighter paths with longer move steps; and (2) when floaters settle in a permanent area, then they show movement behavior similar to territory owners. Thus, movement patterns show a transition from exploratory strategies, when animals have incomplete environmental information, to a more familiar way to exploit their activity areas as they get to know the environment better.     

A General Model for Analyzing Data from Mark-recapture Experiments with an Application to the Pacific Halibut

A general model is developed to examine the patterns of the regional movement of tagged and released fish from mark-recapture experiments. It is a stochastic model that incorporates fishing mortality, natural mortality, fish movement, tag-shedding, and different rates of reporting. A likelihood function is constructed for estimating its parameters. We used this model to analyze data on the Pacific halibut from mark-recapture experiments conducted by the International Pacific Halibut Commission (IPHC), with a total of 36,058 releases from 1982 to 1986 and 5,826 recoveries from 1982 to 2000. We estimated their rates of movement among IPHC management areas, along with their instantaneous rates of natural and fishing mortalities. Our analysis revealed that fish movement was not significant among areas, with a resident probability of > 0.92. This lends support to the IPHC catch-at-age stock assessment model (which has no built-in movement components). The estimated instantaneous rate of natural mortality (0.198 year⁻¹) lies between that assumed in all IPHC stock assessments before 1998 (0.20 year⁻¹) and that from 1999 onwards (0.15 year⁻¹). The estimates of the instantaneous rates of fishing mortality were consistent with those from the IPHC stock assessment model. Received: April 2003 / Revised: May 2005     

Habitat fragmentation affects movement behavior of migrating juvenile common toads

Displacement characteristics in animals are crucial drivers of successful movement decisions in resources acquisition, migration, and dispersal. As landscape structure is modified by human activity, mobility patterns are likely to evolve in response to habitat fragmentation. In species with complex life cycles that involve obligatory migrations between different habitats, one can predict that movement propensity would be promoted by fragmentation as long as it allows to reaching a habitat patch. Here, we compare the movement characteristics of naive toadlets sampled in populations distributed over a fragmentation gradient to test the hypothesis of a positive correlation between fragmentation and mobility levels. We studied toadlet movement in experimental arenas providing small patches of suitable conditions. We recorded the use of these patches (patch behavior) or the absence of their use (overtaking behavior). The more fragmented the original landscape, the more prone the toadlets were to combine these two behaviors, thus showing a higher motivation to explore. Moreover, the more fragmented the original landscape, the less the toadlets exhibited patch behavior. As the toadlets were reared in a common environment, the behavioral differences detected, relating to the level of fragmentation, resulted from inheritance. Our results thus illustrate that fragmentation is likely to create cross-generational transmittable variations in movement characteristics.     

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.     

Modeling Diapause Termination of Rhipicephalus Appendiculatus using Statistical Tools to Detect Sudden Behavioral Changes and Time Dependencies

This paper presents statistical methodology to analyze longitudinal binary responses for which a sudden change in the response occurs in time. Probability plots, transition matrices, and change-point models and more advanced techniques such as generalized auto-regression models and hidden Markov chains are presented and applied on a study on the activity of Rhipicephalus appendiculatus, the major vector of Theileria parva, a fatal disease in cattle. This study presents individual measurements on female R. appendiculatus, which are terminating their diapause (resting status) and become active. Comprehending activity patterns is very important to better understand the ecology of R. appendiculatus. The model indicates that activity and non-activity act in an absorbing way meaning that once a tick becomes active it shows a tendency to remain active. The change-point model estimates that the sudden change in activity happens on December 10. The reaction of ticks on acceleration and changes in rainfall and temperature indicates that ticks can sense climatic changes. The study revealed the underlying not visually observable states during diapause development of the adult tick of R. appendiculatus. These states could be related to phases during the dynamic event of diapause development and post-diapause activity in R. appendiculatus.     

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).