Social and seasonal variation in dwarf mongoose home-range size, daily movements, and burrow use.

When making decisions about resource use, social species must integrate not only environmental factors but also the influence of opportunities and costs associated with group living. Bigger groups are expected to move further and to need access to larger areas for adequate food acquisition, but the relationships with group size can vary seasonally and with reproductive stage. Shelters are often more consistent in availability than food, but their use relates to factors such as predator defense and parasite transmission that are themselves influenced by group size and seasonality.

Exact spatiotemporal dynamics of lattice random walks in hexagonal and honeycomb domains.

A variety of transport processes in natural and man-made systems are intrinsically random. To model their stochasticity, lattice random walks have been employed for a long time, mainly by considering Cartesian lattices. However, in many applications in bounded space the geometry of the domain may have profound effects on the dynamics and ought to be accounted for.

Subdiffusion in the Presence of Reactive Boundaries: A Generalized Feynman-Kac Approach.

We derive, through subordination techniques, a generalized Feynman-Kac equation in the form of a time fractional Schrödinger equation. We relate such equation to a functional which we name the subordinated local time. We demonstrate through a stochastic treatment how this generalized Feynman-Kac equation describes subdiffusive processes with reactions.

Sociogenesis in unbounded space: modelling self-organised cohesive collective motion.

Maintaining cohesion between randomly moving agents in unbounded space is an essential functionality for many real-world applications requiring distributed multi-agent systems. We develop a bio-inspired collective movement model in 1D unbounded space to ensure such functionality. Using an internal agent belief to estimate the mesoscopic state of the system, agent motion is coupled to a dynamically self-generated social ranking variable.

Closed-form solutions to the dynamics of confined biased lattice random walks in arbitrary dimensions.

Biased lattice random walks (BLRW) are used to model random motion with drift in a variety of empirical situations in engineering and natural systems such as phototaxis, chemotaxis, or gravitaxis. When motion is also affected by the presence of external borders resulting from natural barriers or experimental apparatuses, modelling biased random movement in confinement becomes necessary. To study these scenarios, confined BLRW models have been employed but so far only through computational techniques due to the lack of an analytic framework.

Toward Engineering Biosystems With Emergent Collective Functions.

Many complex behaviors in biological systems emerge from large populations of interacting molecules or cells, generating functions that go beyond the capabilities of the individual parts. Such collective phenomena are of great interest to bioengineers due to their robustness and scalability. However, engineering emergent collective functions is difficult because they arise as a consequence of complex multi-level feedback, which often spans many length-scales.

Fokker-Planck representations of non-Markov Langevin equations: application to delayed systems.

Noise and time delays, or history-dependent processes, play an integral part in many natural and man-made systems. The resulting interplay between random fluctuations and time non-locality are essential features of the emerging complex dynamics in non-Markov systems. While stochastic differential equations in the form of Langevin equations with additive noise for such systems exist, the corresponding probabilistic formalism is yet to be developed.

Making ecological models adequate.

Critical evaluation of the adequacy of ecological models is urgently needed to enhance their utility in developing theory and enabling environmental managers and policymakers to make informed decisions. Poorly supported management can have detrimental, costly or irreversible impacts on the environment and society. Here, we examine common issues in ecological modelling and suggest criteria for improving modelling frameworks.

Identifying influential neighbors in animal flocking.

Schools of fish and flocks of birds can move together in synchrony and decide on new directions of movement in a seamless way. This is possible because group members constantly share directional information with their neighbors. Although detecting the directionality of other group members is known to be important to maintain cohesion, it is not clear how many neighbors each individual can simultaneously track and pay attention to, and what the spatial distribution of these influential neighbors is.

Localization Transition Induced by Learning in Random Searches.

We solve an adaptive search model where a random walker or Lévy flight stochastically resets to previously visited sites on a d-dimensional lattice containing one trapping site. Because of reinforcement, a phase transition occurs when the resetting rate crosses a threshold above which nondiffusive stationary states emerge, localized around the inhomogeneity. The threshold depends on the trapping strength and on the walker's return probability in the memoryless case.

Measuring site fidelity and spatial segregation within animal societies.

Animals often display a marked tendency to return to previously visited locations that contain important resources, such as water, food, or developing brood that must be provisioned. A considerable body of work has demonstrated that this tendency is strongly expressed in ants, which exhibit fidelity to particular sites both inside and outside the nest. However, thus far many studies of this phenomena have taken the approach of reducing an animal's trajectory to a summary statistic, such as the area it covers.

Flying foxes create extensive seed shadows and enhance germination success of pioneer plant species in deforested Madagascan landscapes.

Seed dispersal plays a significant role in forest regeneration and maintenance. Flying foxes are often posited as effective long-distance seed dispersers due to their large home ranges and ability to disperse seeds when flying. We evaluate the importance of the Madagascan flying fox Pteropus rufus in the maintenance and regeneration of forests in one of the world's priority conservation areas.

Bumblebees can discriminate between scent-marks deposited by conspecifics.

Bumblebees secrete a substance from their tarsi wherever they land, which can be detected by conspecifics. These secretions are referred to as scent-marks, which bumblebees are able to use as social cues. Although it has been found that bumblebees can detect and associate scent-marks with rewarding or unrewarding flowers, their ability at discriminating between scent-marks from bumblebees of differing relatedness is unknown.

Delayed response and biosonar perception explain movement coordination in trawling bats.

Animal coordinated movement interactions are commonly explained by assuming unspecified social forces of attraction, repulsion and alignment with parameters drawn from observed movement data. Here we propose and test a biologically realistic and quantifiable biosonar movement interaction mechanism for echolocating bats based on spatial perceptual bias, i.e.

Consequences of animal interactions on their dynamics: emergence of home ranges and territoriality.

Animal spacing has important implications for population abundance, species demography and the environment. Mechanisms underlying spatial segregation have their roots in the characteristics of the animals, their mutual interaction and their response, collective as well as individual, to environmental variables. This review describes how the combination of these factors shapes the patterns we observe and presents a practical, usable framework for the analysis of movement data in confined spaces.

Exact dynamics of stochastic linear delayed systems: application to spatiotemporal coordination of comoving agents.

Delayed dynamics result from finite transmission speeds of a signal in the form of energy, mass, or information. In stochastic systems the resulting lagged dynamics challenge our understanding due to the rich behavioral repertoire encompassing monotonic, oscillatory, and unstable evolution. Despite the vast literature, quantifying this rich behavior is limited by a lack of explicit analytic studies of high-dimensional stochastic delay systems.

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.

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.

Encounter times in overlapping domains: application to epidemic spread in a population of territorial animals.

We develop an analytical method to calculate encounter times of two random walkers in one dimension when each individual is segregated in its own spatial domain and shares with its neighbor only a fraction of the available space, finding very good agreement with numerically exact calculations. We model a population of susceptible and infected territorial individuals with this spatial arrangement, and which may transmit an epidemic when they meet. We apply the results on encounter times to determine analytically the macroscopic propagation speed of the epidemic as a function of the microscopic characteristics: the confining geometry, the animal diffusion constant, and the infection transmission probability.

Quasi-one-dimensional waves in rodent populations in heterogeneous habitats: a consequence of elevational gradients on spatio-temporal dynamics.

Wave propagation can be clearly discerned in data collected on mouse populations in the Cibola National Forest (New Mexico, USA) related to seasonal changes. During an exploration of the construction of a methodology for investigations of the spread of the Hantavirus epidemic in mice we have built a system of interacting reaction diffusion equations of the Fisher-Kolmogorov-Petrovskii-Piskunov type. Although that approach has met with clear success recently in explaining Hantavirus refugia and other spatiotemporal correlations, we have discovered that certain observed features of the wave propagation observed in the data we mention are impossible to explain unless modifications are made.

Bacterial secretion and the role of diffusive and subdiffusive first passage processes.

By funneling protein effectors through needle complexes located on the cellular membrane, bacteria are able to infect host cells during type III secretion events. The spatio-temporal mechanisms through which these events occur are however not fully understood, due in part to the inherent challenges in tracking single molecules moving within an intracellular medium. As a result, theoretical predictions of secretion times are still lacking.

Territorial dynamics and stable home range formation for central place foragers.

Uncovering the mechanisms behind territory formation is a fundamental problem in behavioural ecology. The broad nature of the underlying conspecific avoidance processes are well documented across a wide range of taxa. Scent marking in particular is common to a large range of terrestrial mammals and is known to be fundamental for communication.

Linking animal movement to site fidelity.

Site fidelity, the recurrent visit of an animal to a previously occupied area is a wide-spread behavior in the animal kingdom. The relevance of site fidelity to territoriality, successful breeding, social associations, optimal foraging and other ecological processes, demands accurate quantification. Here we generalize previous theory that connects site fidelity patterns to random walk parameters within the framework of the space-time fractional diffusion equation.