Distinguishing Between Long-Transient and Asymptotic States in a Biological Aggregation Model.

Aggregations are emergent features common to many biological systems. Mathematical models to understand their emergence are consequently widespread, with the aggregation-diffusion equation being a prime example. Here we study the aggregation-diffusion equation with linear diffusion in one spatial dimension. This equation is known to support solutions that involve both single and multiple aggregations. However, numerical evidence suggests that the latter, which we term 'multi-peaked solutions' may often be long-transient solutions rather than asymptotic steady states. We develop a novel technique for distinguishing between long transients and asymptotic steady states via an energy minimisation approach. The technique involves first approximating our study equation using a limiting process and a moment closure procedure. We then analyse local minimum energy states of this approximate system, hypothesising that these will correspond to asymptotic patterns in the aggregation-diffusion equation. Finally, we verify our hypotheses through numerical investigation, showing that our approximate analytic technique gives good predictions as to whether a state is asymptotic or transient. Overall, we find that almost all twin-peaked, and by extension multi-peaked, solutions are transient, except for some very special cases. We demonstrate numerically that these transients can be arbitrarily long-lived, depending on the parameters of the system.

Nonviral Liver Disease Burden in People Living With HIV and Elevated Transaminases: A Cross-Sectional Study.

INTRODUCTION: Because of improved life expectancy in people living with HIV (PLWH), liver disease is increasingly being recognized. We assessed nonviral chronic liver disease burden in PLWH. METHODS: The HIV non-virAL liver disease study (2014-2021) prospectively recruited PLWH with elevated serum alanine aminotransferase levels and negative hepatitis serology. Clinically significant hepatic fibrosis (CSHF) was defined as liver stiffness measurement of >7.1 kPa and hazardous alcohol use as Alcohol Use Disorders Identification Test score ≥ 8. Primary outcome was prevalence/predictors of CSHF. RESULTS: Total recruited were n = 274, 92% male, median age 52 (45-59) years, and 96% having undetectable HIV viral load. Overall, n = 97 (35%) had hazardous alcohol use, n = 72 (26%) had metabolic syndrome, and 17%-27% had exposure to hepatotoxic antiretrovirals. Prevalence of CSHF was 20% (n = 54), prevalence of cirrhosis (liver stiffness measurement > 12.5 kPa) being 7% (19/274). Risk factors for CSHF were hazardous alcohol use in 44% (n = 24), metabolic syndrome in 46% (n = 25), and hepatotoxic antiretrovirals in 56% (n = 30), most having more than one risk factor. Independent predictors of CSHF were serum high-density lipoprotein (odds ratio [OR] 0.220; 95% confidence interval [CI]: 0.061 to 0.790, P = 0.020) (inverse relationship); serum aspartate aminotransferase (OR 1.033, 95% CI: 1.001 to 1.067, P = 0.045), and didanosine use (OR 2.878, 95% CI: 1.228 to 6.774, P = 0.015). Moderate-severe hepatic steatosis was identified in 52% (n = 142). FIB-4 and aspartate aminotransferase-to-platelet ratio index performed poorly in predicting CSHF (positive predictive value 27.3% and 30.6%, respectively) and advanced fibrosis (≥F3) (positive predictive value 17.6% and 5.9%, respectively). CONCLUSION: In this study, 20% of PLWH had CSHF associated with high prevalence of hazardous alcohol use/metabolic syndrome/potentially hepatotoxic antiretrovirals. These potentially modifiable risk factors need addressing.

How to scale up from animal movement decisions to spatiotemporal patterns: An approach via step selection.

Uncovering the mechanisms behind animal space use patterns is of vital importance for predictive ecology, thus conservation and management of ecosystems. Movement is a core driver of those patterns so understanding how movement mechanisms give rise to space use patterns has become an increasingly active area of research. This study focuses on a particular strand of research in this area, based around step selection analysis (SSA). SSA is a popular way of inferring drivers of movement decisions, but, perhaps less well appreciated, it also parametrises a model of animal movement. Of key interest is that this model can be propagated forwards in time to predict the space use patterns over broader spatial and temporal scales than those that pertain to the proximate movement decisions of animals. Here, we provide a guide for understanding and using the various existing techniques for scaling up step selection models to predict broad-scale space use patterns. We give practical guidance on when to use which technique, as well as specific examples together with code in R and Python. By pulling together various disparate techniques into one place, and providing code and instructions in simple examples, we hope to highlight the importance of these techniques and make them accessible to a wider range of ecologists, ultimately helping expand the usefulness of SSA.

Detecting minimum energy states and multi-stability in nonlocal advection-diffusion models for interacting species.

Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations, these emergent patterns sometimes appear as local minimisers of a corresponding energy functional. Here we give methods for determining the qualitative structure of local minimum energy states of a broad class of multi-species nonlocal advection-diffusion models, recently proposed for modelling the spatial structure of ecosystems. We show that when each pair of species respond to one another in a symmetric fashion (i.e. via mutual avoidance or mutual attraction, with equal strength), the system admits an energy functional that decreases in time and is bounded below. This suggests that the system will eventually reach a local minimum energy steady state, rather than fluctuating in perpetuity. We leverage this energy functional to develop tools, including a novel application of computational algebraic geometry, for making conjectures about the number and qualitative structure of local minimum energy solutions. These conjectures give a guide as to where to look for numerical steady state solutions, which we verify through numerical analysis. Our technique shows that even with two species, multi-stability with up to four classes of local minimum energy states can emerge. The associated dynamics include spatial sorting via aggregation and repulsion both within and between species. The emerging spatial patterns include a mixture of territory-like segregation as well as narrow spike-type solutions. Overall, our study reveals a general picture of rich multi-stability in systems of moving and interacting species.

Highlighting when animals expend excessive energy for travel using dynamic body acceleration.

Travel represents a major cost for many animals so there should be selection pressure for it to be efficient - at minimum cost. However, animals sometimes exceed minimum travel costs for reasons that must be correspondingly important. We use Dynamic Body Acceleration (DBA), an acceleration-based metric, as a proxy for movement-based power, in tandem with vertical velocity (rate of change in depth) in a shark (Rhincodon typus) to derive the minimum estimated power required to swim at defined vertical velocities. We show how subtraction of measured DBA from the estimated minimum power for any given vertical velocity provides a "proxy for power above minimum" metric (PPAmin), highlighting when these animals travel above minimum power. We suggest that the adoption of this metric across species has value in identifying where and when animals are subject to compelling conditions that lead them to deviate from ostensibly judicious energy expenditure.

Energy-based step selection analysis: Modelling the energetic drivers of animal movement and habitat use.

The energetic gains from foraging and costs of movement are expected to be key drivers of animal decision-making, as their balance is a large determinant of body condition and survival. This fundamental perspective is often missing from habitat selection studies, which mainly describe correlations between space use and environmental features, rather than the mechanisms behind these correlations. To address this gap, we present a novel parameterisation of step selection functions (SSFs), that we term the energy selection function (ESF). In this model, the likelihood of an animal selecting a movement step depends directly on the corresponding energetic gains and costs, and we can therefore assess how moving animals choose habitat based on energetic considerations. The ESF retains the mathematical convenience and practicality of other SSFs and can be quickly fitted using standard software. In this article, we outline a workflow, from data gathering to statistical analysis, and use a case study of polar bears Ursus maritimus to demonstrate application of the model. We explain how defining gains and costs at the scale of the movement step allows us to include information about resource distribution, landscape resistance and movement patterns. We further demonstrate this process with a case study of polar bears and show how the parameters can be interpreted in terms of selection for energetic gains and against energetic costs. The ESF is a flexible framework that combines the energetic consequences of both movement and resource selection, thus incorporating a key mechanism into habitat selection analysis. Further, because it is based on familiar habitat selection models, the ESF is widely applicable to any study system where energetic gains and costs can be derived, and has immense potential for methodological extensions.

Differences in the temporal scale of reproductive investment across the slow-fast continuum in a passerine.

Life-history strategies differ with respect to investment in current versus 'future' reproduction, but when is this future? Under the novel 'temporality in reproductive investment hypothesis', we postulate variation should exist in the time frame over which reproductive costs are paid. Slow-paced individuals should pay reproductive costs over short (e.g. inter-annual) time scales to prevent reproductive costs accumulating, whereas fast-paced individuals should allow costs to accumulate (i.e. senescence). Using Fourier transforms, we quantify adjustments in clutch size with age, across four populations of blue tits (Cyanistes caeruleus). Fast populations had more prevalent and stronger long-term changes in reproductive investment, whereas slower populations had more prevalent short-term adjustments. Inter-annual environmental variation partly accounted for short-, but not long-term changes in reproductive investment. Our study reveals individuals differ in when they pay the cost of reproduction and that failure to partition this variation across different temporal scales and environments could underestimate reproductive trade-offs.

Diagnostic accuracy and interobserver agreement of digital single-operator cholangioscopy for indeterminate biliary strictures.

BACKGROUND AND AIMS: Digital single-operator cholangioscopy (d-SOC) with cholangioscopic biopsy sampling has shown promise in the evaluation of indeterminate biliary strictures. Some studies have suggested higher sensitivity for visual impression compared with biopsy sampling, although assessors were not blinded to previous investigations. We aimed to investigate the diagnostic accuracy and interobserver agreement (IOA) of d-SOC in the visual appraisal of biliary strictures when blinded to additional information. METHODS: A multicenter, international cohort study was performed. Cholangioscopic videos in patients with a known final diagnosis were systematically scored. Pseudonymized videos were reviewed by 19 experts in 2 steps: blinded for patient history and investigations and unblinded. RESULTS: Forty-four high-quality videos were reviewed of 19 benign and 25 malignant strictures. The sensitivity and specificity for the diagnosis of malignancy was 74.2% and 46.9% (blinded) and 72.7% and 62.5% (unblinded). Cholangioscopic certainty of a malignant diagnosis led to overdiagnosis (sensitivity, 90.6%; specificity, 33%), especially if no additional information was provided. The IOA for the presence of malignancy was fair for both assessments (Fleiss' κ = .245 [blinded] and κ = .321 [unblended]). For individual visual features, the IOA ranged from slight to moderate for both assessments (κ = .059-.400 vs κ = .031-.452). CONCLUSIONS: This study showed low sensitivity and specificity for blinded and unblinded d-SOC video appraisal of indeterminate biliary strictures, with considerable interobserver variation. Although reaching a consensus on the optical features of biliary strictures remains important, optimizing visually directed biopsy sampling may be the most important role of cholangioscopy in biliary stricture assessment.

Mechanistic home range analysis reveals drivers of space use patterns for a non-territorial passerine.

Home ranging is a near-ubiquitous phenomenon in the animal kingdom. Understanding the behavioural mechanisms that give rise to observed home range patterns is thus an important general question, and mechanistic home range analysis (MHRA) provides the tools to address it. However, such analysis has hitherto been principally restricted to scent-marking territorial animals, so its potential breadth of application has not been tested. Here, we apply MHRA to a population of long-tailed tits Aegithalos caudatus, a non-territorial passerine, in the non-breeding season where there is no clear 'central place' near which birds need to remain. The aim is to uncover the principal movement mechanisms underlying observed home range formation. Our foundational models consist of memory-mediated conspecific avoidance between flocks, combined with attraction to woodland. These are then modified to incorporate the effects of flock size and relatedness (i.e. kinship), to uncover the effect of these on the mechanisms of home range formation. We found that a simple model of spatial avoidance, together with attraction to the central parts of woodland areas, accurately captures long-tailed tit home range patterns. Refining these models further, we show that the magnitude of spatial avoidance by a flock is negatively correlated to both the relative size of the flock (compared to its neighbour) and the relatedness of the flock with its neighbour. Our study applies MHRA beyond the confines of scent-marking, territorial animals, so paves the way for much broader taxonomic application. These could potentially help uncover general properties underlying the emergence of animal space use patterns. This is also the first study to apply MHRA to questions of relatedness and flock size, thus broadening the potential possible applications of this suite of analytic techniques.

An "orientation sphere" visualization for examining animal head movements.

Animal behavior is elicited, in part, in response to external conditions, but understanding how animals perceive the environment and make the decisions that bring about these behavioral responses is challenging.Animal heads often move during specific behaviors and, additionally, typically have sensory systems (notably vision, smell, and hearing) sampling in defined arcs (normally to the front of their heads). As such, head-mounted electronic sensors consisting of accelerometers and magnetometers, which can be used to determine the movement and directionality of animal heads (where head "movement" is defined here as changes in heading [azimuth] and/or pitch [elevation angle]), can potentially provide information both on behaviors in general and also clarify which parts of the environment the animals might be prioritizing ("environmental framing").We propose a new approach to visualize the data of such head-mounted tags that combines the instantaneous outputs of head heading and pitch in a single intuitive spherical plot. This sphere has magnetic heading denoted by "longitude" position and head pitch by "latitude" on this "orientation sphere" (O-sphere).We construct the O-sphere for the head rotations of a number of vertebrates with contrasting body shape and ecology (oryx, sheep, tortoises, and turtles), illustrating various behaviors, including foraging, walking, and environmental scanning. We also propose correcting head orientations for body orientations to highlight specific heading-independent head rotation, and propose the derivation of O-sphere-metrics, such as angular speed across the sphere. This should help identify the functions of various head behaviors.Visualizations of the O-sphere provide an intuitive representation of animal behavior manifest via head orientation and rotation. This has ramifications for quantifying and understanding behaviors ranging from navigation through vigilance to feeding and, when used in tandem with body movement, should provide an important link between perception of the environment and response to it in free-ranging animals.

Optimizing the use of biologgers for movement ecology research.

The paradigm-changing opportunities of biologging sensors for ecological research, especially movement ecology, are vast, but the crucial questions of how best to match the most appropriate sensors and sensor combinations to specific biological questions and how to analyse complex biologging data, are mostly ignored. Here, we fill this gap by reviewing how to optimize the use of biologging techniques to answer questions in movement ecology and synthesize this into an Integrated Biologging Framework (IBF). We highlight that multisensor approaches are a new frontier in biologging, while identifying current limitations and avenues for future development in sensor technology. We focus on the importance of efficient data exploration, and more advanced multidimensional visualization methods, combined with appropriate archiving and sharing approaches, to tackle the big data issues presented by biologging. We also discuss the challenges and opportunities in matching the peculiarities of specific sensor data to the statistical models used, highlighting at the same time the large advances which will be required in the latter to properly analyse biologging data. Taking advantage of the biologging revolution will require a large improvement in the theoretical and mathematical foundations of movement ecology, to include the rich set of high-frequency multivariate data, which greatly expand the fundamentally limited and coarse data that could be collected using location-only technology such as GPS. Equally important will be the establishment of multidisciplinary collaborations to catalyse the opportunities offered by current and future biologging technology. If this is achieved, clear potential exists for developing a vastly improved mechanistic understanding of animal movements and their roles in ecological processes and for building realistic predictive models.

Spatial Memory and Taxis-Driven Pattern Formation in Model Ecosystems.

Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, significant arrangement in space can occur on shorter timescales, where births and deaths are negligible. This phenomenon is particularly prevalent in populations of larger, vertebrate animals who often reproduce only once per year or less. To understand spatial arrangements of animal communities on such timescales, we use a class of diffusion-taxis equations for modelling inter-population movement responses between [Formula: see text] populations. These systems of equations incorporate the effect on animal movement of both the current presence of other populations and the memory of past presence encoded either in the environment or in the minds of animals. We give general criteria for the spontaneous formation of both stationary and oscillatory patterns, via linear pattern formation analysis. For [Formula: see text], we classify completely the pattern formation properties using a combination of linear analysis and nonlinear energy functionals. In this case, the only patterns that can occur asymptotically in time are stationary. However, for [Formula: see text], oscillatory patterns can occur asymptotically, giving rise to a sequence of period-doubling bifurcations leading to patterns with no obvious regularity, a hallmark of chaos. Our study highlights the importance of understanding between-population animal movement for understanding spatial species distributions, something that is typically ignored in species distribution modelling, and so develops a new paradigm for spatial population dynamics.

Making sense of ultrahigh-resolution movement data: A new algorithm for inferring sites of interest.

Decomposing the life track of an animal into behavioral segments is a fundamental challenge for movement ecology. The proliferation of high-resolution data, often collected many times per second, offers much opportunity for understanding animal movement. However, the sheer size of modern data sets means there is an increasing need for rapid, novel computational techniques to make sense of these data. Most existing methods were designed with smaller data sets in mind and can thus be prohibitively slow. Here, we introduce a method for segmenting high-resolution movement trajectories into sites of interest and transitions between these sites. This builds on a previous algorithm of Benhamou and Riotte-Lambert (2012). Adapting it for use with high-resolution data. The data's resolution removed the need to interpolate between successive locations, allowing us to increase the algorithm's speed by approximately two orders of magnitude with essentially no drop in accuracy. Furthermore, we incorporate a color scheme for testing the level of confidence in the algorithm's inference (high = green, medium = amber, low = red). We demonstrate the speed and accuracy of our algorithm with application to both simulated and real data (Alpine cattle at 1 Hz resolution). On simulated data, our algorithm correctly identified the sites of interest for 99% of "high confidence" paths. For the cattle data, the algorithm identified the two known sites of interest: a watering hole and a milking station. It also identified several other sites which can be related to hypothesized environmental drivers (e.g., food). Our algorithm gives an efficient method for turning a long, high-resolution movement path into a schematic representation of broadscale decisions, allowing a direct link to existing point-to-point analysis techniques such as optimal foraging theory. It is encoded into an R package called SitesInterest, so should serve as a valuable tool for making sense of these increasingly large data streams.

In vivo imaging of hepatic neutrophil migration in severe alcoholic hepatitis with 111In-radiolabelled leucocytes.

The study's aim was to image severe alcoholic hepatitis (SAH) using 111In-labelled leucocytes with two objectives in mind: firstly for non-invasive diagnosis and secondly to provide a platform for experimental therapies aiming to inhibit intrahepatic neutrophil migration. 111In-leucocyte scintigraphy was performed 30 min and 24 h post-injection in 19 patients with SAH, 14 abstinent patients with alcohol-related cirrhosis and 11 normal controls. Eleven with SAH and seven with cirrhosis also had 99mTc-nanocolloid scintigraphy. Change in hepatic 111In radioactivity was expressed as decay-corrected 24 h:30 min count ratio and, in SAH, compared with histological grading of steatohepatitis and expression of granulocyte marker, CD15. Hepatic microautoradiography on biopsy specimens obtained 24 h post-injection of 111In-leucocytes was performed in one patient. Median 24 h:30 min hepatic 111In activity ratio was higher in SAH (2.5 (interquartile range (IQR): 1.7-4.0) compared with cirrhotics and normal controls (1.0 (0.8-1.1) and 0.8 (0.7-0.9) respectively, P<0.0001). In SAH, it correlated with CD15 expression (r = 0.62, P=0.023) and was higher in marked compared with mild/moderate steatohepatitis (4.0 (3.0-4.6) compared with 1.8 (1.5-2.6), P=0.006). Hepatic-to-splenic 99mTc count rate ratio was reduced in SAH (0.5 (0.4-1.4)) compared with cirrhotics (2.3( 0.6-3.0)) and three historic normal controls (4.2 (3.8-5.0); P=0.003), consistent with impaired hepatic reticuloendothelial function. Scintigraphic findings in SAH included prominent lung radioactivity at 30 min, likely the result of neutrophil primimg. Microautoradiography demonstrated cell-associated 111In in areas of parenchymal neutrophil infiltration. In conclusion, 111In-leucocyte scintigraphy can non-invasively diagnose SAH and could provide a platform for evaluation of novel treatments aiming to inhibit intrahepatic neutrophil migration.

Fortune favours the brave: Movement responses shape demographic dynamics in strongly competing populations.

Animal movement is a key mechanism for shaping population dynamics. The effect of interactions between competing animals on a population's survival has been studied for many decades. However, interactions also affect an animal's subsequent movement decisions. Despite this, the indirect effect of these decisions on animal survival is much less well-understood. Here, we incorporate movement responses to foreign animals into a model of two competing populations, where inter-specific competition is greater than intra-specific competition. When movement is diffusive, the travelling wave moves from the stronger population to the weaker. However, by incorporating behaviourally induced directed movement towards the stronger population, the weaker one can slow the travelling wave down, even reversing its direction. Hence movement responses can switch the predictions of traditional mechanistic models. Furthermore, when environmental heterogeneity is combined with aggressive movement strategies, it is possible for spatially segregated co-existence to emerge. In this situation, the spatial patterns of the competing populations have the unusual feature that they are slightly out-of-phase with the environmental patterns. Finally, incorporating dynamic movement responses can also enable stable co-existence in a homogeneous environment, giving a new mechanism for spatially segregated co-existence.

Partial differential equation techniques for analysing animal movement: A comparison of different methods.

Recent advances in animal tracking have allowed us to uncover the drivers of movement in unprecedented detail. This has enabled modellers to construct ever more realistic models of animal movement, which aid in uncovering detailed patterns of space use in animal populations. Partial differential equations (PDEs) provide a popular tool for mathematically analysing such models. However, their construction often relies on simplifying assumptions which may greatly affect the model outcomes. Here, we analyse the effect of various PDE approximations on the analysis of some simple movement models, including a biased random walk, central-place foraging processes and movement in heterogeneous landscapes. Perhaps the most commonly-used PDE method dates back to a seminal paper of Patlak from 1953. However, our results show that this can be a very poor approximation in even quite simple models. On the other hand, more recent methods, based on transport equation formalisms, can provide more accurate results, as long as the kernel describing the animal's movement is sufficiently smooth. When the movement kernel is not smooth, we show that both the older and newer methods can lead to quantitatively misleading results. Our detailed analysis will aid future researchers in the appropriate choice of PDE approximation for analysing models of animal movement.

Circulating granulocyte lifespan in compensated alcohol-related cirrhosis: a pilot study.

Although granulocyte dysfunction is known to occur in cirrhosis, in vivo studies of granulocyte lifespan have not previously been performed. The normal circulating granulocyte survival half-time (G - t½), determined using indium-111 ((111)In)-radiolabeled granulocytes, is ~7 h. In this pilot study, we aimed to measure the in vivo G - t½ in compensated alcohol-related cirrhosis. Sequential venous blood samples were obtained in abstinent subjects with alcohol-related cirrhosis over 24 h post injection (PI) of minimally manipulated (111)In-radiolabeled autologous mixed leukocytes. Purified granulocytes were isolated from each sample using a magnetic microbead-antibody technique positively selecting for the marker CD15. Granulocyte-associated radioactivity was expressed relative to peak activity, plotted over time, and G - t½ estimated from data up to 12 h PI This was compared with normal neutrophil half-time (N - t½), determined using a similar method specifically selecting neutrophils in healthy controls at a collaborating center. Seven patients with cirrhosis (six male, aged 57.8 ± 9.4 years, all Child-Pugh class A) and seven normal controls (three male, 64.4 ± 5.6 years) were studied. Peripheral blood neutrophil counts were similar in both groups (4.6 (3.5 - 5.5) × 10(9)/L vs. 2.8 (2.7 - 4.4) × 10(9)/L, respectively, P = 0.277). G - t½ in cirrhosis was significantly lower than N - t½ in controls (2.7 ± 0.5 h vs. 4.4 ± 1.0 h, P = 0.007). Transient rises in granulocyte and neutrophil-associated activities occurred in four patients from each group, typically earlier in cirrhosis (4-6 h PI) than in controls (8-10 h), suggesting recirculation of radiolabeled cells released from an unidentified focus. Reduced in vivo granulocyte survival in compensated alcohol-related cirrhosis is a novel finding and potentially another mechanism for immune dysfunction in chronic liver disease. Larger studies are needed to corroborate these pilot data and assess intravascular neutrophil residency in other disease etiologies.

Flexible characterization of animal movement pattern using net squared displacement and a latent state model.

BACKGROUND: Characterizing the movement patterns of animals is an important step in understanding their ecology. Various methods have been developed for classifying animal movement at both coarse (e.g., migratory vs. sedentary behavior) and fine (e.g., resting vs. foraging) scales. A popular approach for classifying movements at coarse resolutions involves fitting time series of net-squared displacement (NSD) to models representing different conceptualizations of coarse movement strategies (i.e., migration, nomadism, sedentarism, etc.). However, the performance of this method in classifying actual (as opposed to simulated) animal movements has been mixed. Here, we develop a more flexible method that uses the same NSD input, but relies on an underlying discrete latent state model. Using simulated data, we first assess how well patterns in the number of transitions between modes of movement and the duration of time spent in a mode classify movement strategies. We then apply our approach to elucidate variability in the movement strategies of eight giant tortoises (Chelonoidis sp.) using a multi-year (2009-2014) GPS dataset from three different Galapagos Islands. RESULTS: With respect to patterns of time spent and the number of transitions between modes, our approach out-performed previous efforts to distinguish among migration, dispersal, and sedentary behavior. We documented marked inter-individual variation in giant tortoise movement strategies, with behaviors indicating migration, dispersal, nomadism and sedentarism, as well as hybrid behaviors such as "exploratory residence". CONCLUSIONS: Distilling complex animal movement into discrete modes remains a fundamental challenge in movement ecology, a problem made more complex by the ever-longer duration, ever-finer resolution, and gap-ridden trajectories recorded by GPS devices. By clustering into modes, we derived information on the time spent within one mode and the number of transitions between modes which enabled finer differentiation of movement strategies over previous methods. Ultimately, the techniques developed here address limitations of previous approaches and provide greater insights with respect to characterization of movement strategies across scales by more fully utilizing long-term GPS telemetry datasets.

How memory of direct animal interactions can lead to territorial pattern formation.

Mechanistic home range analysis (MHRA) is a highly effective tool for understanding spacing patterns of animal populations. It has hitherto focused on populations where animals defend their territories by communicating indirectly, e.g. via scent marks. However, many animal populations defend their territories using direct interactions, such as ritualized aggression. To enable application of MHRA to such populations, we construct a model of direct territorial interactions, using linear stability analysis and energy methods to understand when territorial patterns may form. We show that spatial memory of past interactions is vital for pattern formation, as is memory of 'safe' places, where the animal has visited but not suffered recent territorial encounters. Additionally, the spatial range over which animals make decisions to move is key to understanding the size and shape of their resulting territories. Analysis using energy methods, on a simplified version of our system, shows that stability in the nonlinear system corresponds well to predictions of linear analysis. We also uncover a hysteresis in the process of territory formation, so that formation may depend crucially on initial space-use. Our analysis, in one dimension and two dimensions, provides mathematical groundwork required for extending MHRA to situations where territories are defended by direct encounters.

Spatial Patterning of Prey at Reproduction to Reduce Predation Risk: What Drives Dispersion from Groups?

Group living is a widespread behavior thought to be an evolutionary adaptation for reducing predation risk. Many group-living species, however, spend a portion of their life cycle as dispersed individuals, suggesting that the costs and benefits of these opposing behaviors vary temporally. Here, we evaluated mechanistic hypotheses for explaining individual dispersion as a tactic for reducing predation risk at reproduction (i.e., birthing) in an otherwise group-living animal. Using simulation analyses parameterized by empirical data, we assessed whether dispersion increases reproductive success by (i) increasing predator search time, (ii) reducing predator encounter rates because individuals are inconspicuous relative to groups, or (iii) eliminating the risk of multiple kills per encounter. Simulations indicate that dispersion becomes favorable only when detectability increases with group size and there is risk of multiple kills per encounter. This latter effect, however, is likely the primary mechanism driving females to disperse at reproduction because group detectability effects are presumably constant year-round. We suggest that the risk of multiple kills imposed by highly vulnerable offspring may be an important factor influencing dispersive behavior in many species, and conservation strategies for such species will require protecting sufficient space to allow dispersion to effectively reduce predation risk.