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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Territorial pattern formation in the absence of an attractive potential.

Territoriality is a phenomenon exhibited throughout nature. On the individual level, it is the processes by which organisms exclude others of the same species from certain parts of space. On the population level, it is the segregation of space into separate areas, each used by subsections of the population. Proving mathematically that such individual-level processes can cause observed population-level patterns to form is necessary for linking these two levels of description in a non-speculative way. Previous mathematical analysis has relied upon assuming animals are attracted to a central area. This can either be a fixed geographical point, such as a den- or nest-site, or a region where they have previously visited. However, recent simulation-based studies suggest that this attractive potential is not necessary for territorial pattern formation. Here, we construct a partial differential equation (PDE) model of territorial interactions based on the individual-based model (IBM) from those simulation studies. The resulting PDE does not rely on attraction to spatial locations, but purely on conspecific avoidance, mediated via scent-marking. We show analytically that steady-state patterns can form, as long as (i) the scent does not decay faster than it takes the animal to traverse the terrain, and (ii) the spatial scale over which animals detect scent is incorporated into the PDE. As part of the analysis, we develop a general method for taking the PDE limit of an IBM that avoids destroying any intrinsic spatial scale in the underlying behavioral decisions.

Stigmergy, collective actions, and animal social spacing.

Collective animal behavior studies have led the way in developing models that account for a large number of individuals, but mostly have considered situations in which alignment and attraction play a key role, such as in schooling and flocking. By quantifying how animals react to one another's presence, when interaction is via conspecific avoidance rather than alignment or attraction, we present a mechanistic insight that enables us to link individual behavior and space use patterns. As animals respond to both current and past positions of their neighbors, the assumption that the relative location of individuals is statistically and history independent is not tenable, underscoring the limitations of traditional space use studies. We move beyond that assumption by constructing a framework to analyze spatial segregation of mobile animals when neighbor proximity may elicit a retreat, and by linking conspecific encounter rate to history-dependent avoidance behavior. Our approach rests on the knowledge that animals communicate by modifying the environment in which they live, providing a method to analyze social cohesion as stigmergy, a form of mediated animal-animal interaction. By considering a population of animals that mark the terrain as they move, we predict how the spatiotemporal patterns that emerge depend on the degree of stigmergy of the interaction processes. We find in particular that nonlocal decision rules may generate a nonmonotonic dependence of the animal encounter rate as a function of the tendency to retreat from locations recently visited by other conspecifics, which has fundamental implications for epidemic disease spread and animal sociality.

How do animal territories form and change? Lessons from 20 years of mechanistic modelling.

Territory formation is ubiquitous throughout the animal kingdom. At the individual level, various behaviours attempt to exclude conspecifics from regions of space. At the population level, animals often segregate into distinct territorial areas. Consequently, it should be possible to derive territorial patterns from the underlying behavioural processes of animal movements and interactions. Such derivations are an important element in the development of an ecological theory that can predict the effects of changing conditions on territorial populations. Here, we review the approaches developed over the past 20 years or so, which go under the umbrella of 'mechanistic territorial models'. We detail the two main strands to this research: partial differential equations and individual-based approaches, showing what each has offered to our understanding of territoriality and how they can be unified. We explain how they are related to other approaches to studying territories and home ranges, and point towards possible future directions.

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.

Quantifying behavioral changes in territorial animals caused by sudden population declines.

Although territorial animals are able to maintain exclusive use of certain regions of space, movement data from neighboring individuals often suggest overlapping home ranges. To explain and unify these two aspects of animal space use, we use recently developed mechanistic models of collective animal movement. We apply our approach to a natural experiment on an urban red fox (Vulpes vulpes) population that underwent a rapid decline in population density due to a sarcoptic mange epizooty. By extracting details of movement and interaction strategies from location data, we show how foxes alter their behavior, taking advantage of sudden population-level changes by acquiring areas vacated due to neighbor mortality, while ensuring territory boundaries remain contiguous. The rate of territory border movement increased eightfold as the population declined and the foxes' response time to neighboring scent reduced by a third. By demonstrating how observed, fluctuating territorial patterns emerge from movements and interactions of individual animals, our results give the first data-validated, mechanistic explanation of the elastic disc hypothesis, proposed nearly 80 years ago.

Hepatotoxicity from anabolic androgenic steroids marketed as dietary supplements: contribution from ATP8B1/ABCB11 mutations?

BACKGROUND: Though possession of androgenic anabolic steroids (AAS) is illegal, non-prescription use of AAS persists. METHODS: We describe two Caucasian males (aged 25 and 45 years) with cholestatic hepatitis following ingestion of the dietary supplement Mass-Drol ('Celtic Dragon') containing the AAS 2α-17α-dimethyl-etiocholan-3-one,17ß-ol. RESULTS: Despite substantial hyperbilirubinaemia peak gamma-glutamyl transferase (GGT) remained normal. Besides 'bland' intralobular cholestasis, liver biopsy in both found deficiency of canalicular expression of ectoenzymes as seen in ATP8B1 disease. In the older patient, bile salt export pump marking (encoded by ABCB11) was focally diminished. We hypothesized that AAS had either induced inhibition of normal ATP8B1/ABCB11 expression or triggered initial episodes of benign recurrent intrahepatic cholestasis (BRIC) type 1/or 2. On sequencing, ATP8B1 was normal in both patients although the younger was heterozygous for the c.2093G>A mutation in ABCB11, a polymorphism previously encountered in drug-induced liver injury. CONCLUSION: AAS marketed as dietary supplements continue to cause hepatotoxicity in the UK; underlying mechanisms may include unmasking of genetic cholestatic syndromes.

Animal interactions and the emergence of territoriality.

Inferring the role of interactions in territorial animals relies upon accurate recordings of the behaviour of neighbouring individuals. Such accurate recordings are rarely available from field studies. As a result, quantification of the interaction mechanisms has often relied upon theoretical approaches, which hitherto have been limited to comparisons of macroscopic population-level predictions from un-tested interaction models. Here we present a quantitative framework that possesses a microscopic testable hypothesis on the mechanism of conspecific avoidance mediated by olfactory signals in the form of scent marks. We find that the key parameters controlling territoriality are two: the average territory size, i.e. the inverse of the population density, and the time span during which animal scent marks remain active. Since permanent monitoring of a territorial border is not possible, scent marks need to function in the temporary absence of the resident. As chemical signals carried by the scent only last a finite amount of time, each animal needs to revisit territorial boundaries frequently and refresh its own scent marks in order to deter possible intruders. The size of the territory an animal can maintain is thus proportional to the time necessary for an animal to move between its own territorial boundaries. By using an agent-based model to take into account the possible spatio-temporal movement trajectories of individual animals, we show that the emerging territories are the result of a form of collective animal movement where, different to shoaling, flocking or herding, interactions are highly heterogeneous in space and time. The applicability of our hypothesis has been tested with a prototypical territorial animal, the red fox (Vulpes vulpes).