Search times with arbitrary detection constraints

Foraging behaviour and patch size distribution jointly determine population dynamics in fragmented landscapes

Increased fragmentation caused by habitat loss represents a major threat to the persistence of animal populations. How fragmentation affects populations depends on the rate at which individuals move between spatially separated patches. Whereas negative effects of habitat loss on biodiversity are well known, the effects of fragmentation per se on population dynamics and ecosystem stability remain less well understood. Here, we use a spatially explicit predator-prey model to investigate how the interplay between fragmentation and optimal foraging behaviour affects predator-prey interactions and, subsequently, ecosystem stability. We study systems wherein prey occupies isolated patches and are consumed by predators that disperse following Lévy random walks. Our results show that the Lévy exponent and the degree of fragmentation jointly determine coexistence probabilities. In highly fragmented landscapes, Brownian and ballistic predators go extinct and only scale-free predators can coexist with prey. Furthermore, our results confirm that predation causes irreversible habitat loss in fragmented landscapes owing to overexploitation of smaller patches of prey. Moreover, we show that predator dispersal can reduce, but not prevent or minimize, the amount of lost habitat. Our results suggest that integrating optimal foraging theory into population and landscape ecology is crucial to assessing the impact of fragmentation on biodiversity and ecosystem stability.

Optimal escape-and-feeding dynamics of random walkers: Rethinking the convenience of ballistic strategies

Excited random walks represent a convenient model to study food intake in a media which is progressively depleted by the walker. Trajectories in the model alternate between (i) feeding and (ii) escape (when food is missed and so it must be found again) periods, each governed by different movement rules. Here, we explore the case where the escape dynamics is adaptive, so at short times an area-restricted search is carried out, and a switch to extensive or ballistic motion occurs later if necessary. We derive for this case explicit analytical expressions of the mean escape time and the asymptotic growth of the depleted region in one dimension. These, together with numerical results in two dimensions, provide surprising evidence that ballistic searches are detrimental in such scenarios, a result which could explain why ballistic movement is barely observed in animal searches at microscopic and millimetric scales, therefore providing significant implications for biological foraging.

Foraging success under uncertainty: search tradeoffs and optimal space use

Understanding the structural complexity and the main drivers of animal search behaviour is pivotal to foraging ecology. Yet, the role of uncertainty as a generative mechanism of movement patterns is poorly understood. Novel insights from search theory suggest that organisms should collect and assess new information from the environment by producing complex exploratory strategies. Based on an extension of the first passage time theory, and using simple equations and simulations, we unveil the elementary heuristics behind search behaviour. In particular, we show that normal diffusion is not enough for determining optimal exploratory behaviour but anomalous diffusion is required. Searching organisms go through two critical sequential phases (approach and detection) and experience fundamental search tradeoffs that may limit their encounter rates. Using experimental data, we show that biological search includes elements not fully considered in contemporary physical search theory. In particular, the need to consider search movement as a non-stationary process that brings the organism from one informational state to another. For example, the transition from remaining in an area to departing from it may occur through an exploratory state where cognitive search is challenged. Therefore, a more comprehensive view of foraging ecology requires including current perspectives about movement under uncertainty.

T cell migration, search strategies and mechanisms

T cell migration is essential for T cell responses; it allows for the detection of cognate antigen at the surface of antigen-presenting cells and for interactions with other cells involved in the immune response. Although appearing random, growing evidence suggests that T cell motility patterns are strategic and governed by mechanisms that are optimized for both the activation stage of the cell and for environment-specific cues. In this Opinion article, we discuss how the combined effects of T cell-intrinsic and -extrinsic forces influence T cell motility patterns in the context of highly complex tissues that are filled with other cells involved in parallel motility. In particular, we examine how insights from 'search theory' can be used to describe T cell movement across an 'exploitation-exploration trade-off' in the context of activation versus effector function and lymph nodes versus peripheral tissues.

First-passage times in multiscale random walks: The impact of movement scales on search efficiency

An efficient searcher needs to balance properly the trade-off between the exploration of new spatial areas and the exploitation of nearby resources, an idea which is at the core of scale-free Lévy search strategies. Here we study multiscale random walks as an approximation to the scale-free case and derive the exact expressions for their mean-first-passage times in a one-dimensional finite domain. This allows us to provide a complete analytical description of the dynamics driving the situation in which both nearby and faraway targets are available to the searcher, so the exploration-exploitation trade-off does not have a trivial solution. For this situation, we prove that the combination of only two movement scales is able to outperform both ballistic and Lévy strategies. This two-scale strategy involves an optimal discrimination between the nearby and faraway targets which is only possible by adjusting the range of values of the two movement scales to the typical distances between encounters. So, this optimization necessarily requires some prior information (albeit crude) about target distances or distributions. Furthermore, we found that the incorporation of additional (three, four, …) movement scales and its adjustment to target distances does not improve further the search efficiency. This allows us to claim that optimal random search strategies arise through the informed combination of only two walk scales (related to the exploitative and the explorative scales, respectively), expanding on the well-known result that optimal strategies in strictly uninformed scenarios are achieved through Lévy paths (or, equivalently, through a hierarchical combination of multiple scales).

Optimal search strategies of space-time coupled random walkers with finite lifetimes

We present a simple paradigm for detection of an immobile target by a space-time coupled random walker with a finite lifetime. The motion of the walker is characterized by linear displacements at a fixed speed and exponentially distributed duration, interrupted by random changes in the direction of motion and resumption of motion in the new direction with the same speed. We call these walkers "mortal creepers." A mortal creeper may die at any time during its motion according to an exponential decay law characterized by a finite mean death rate ω(m). While still alive, the creeper has a finite mean frequency ω of change of the direction of motion. In particular, we consider the efficiency of the target search process, characterized by the probability that the creeper will eventually detect the target. Analytic results confirmed by numerical results show that there is an ω(m)-dependent optimal frequency ω=ω(opt) that maximizes the probability of eventual target detection. We work primarily in one-dimensional (d=1) domains and examine the role of initial conditions and of finite domain sizes. Numerical results in d=2 domains confirm the existence of an optimal frequency of change of direction, thereby suggesting that the observed effects are robust to changes in dimensionality. In the d=1 case, explicit expressions for the probability of target detection in the long time limit are given. In the case of an infinite domain, we compute the detection probability for arbitrary times and study its early- and late-time behavior. We further consider the survival probability of the target in the presence of many independent creepers beginning their motion at the same location and at the same time. We also consider a version of the standard "target problem" in which many creepers start at random locations at the same time.

Detection of rare antigen-presenting cells through T cell-intrinsic meandering motility, mediated by Myo1g

To mount an immune response, T lymphocytes must successfully search for foreign material bound to the surface of antigen-presenting cells. How T cells optimize their chances of encountering and responding to these antigens is unknown. T cell motility in tissues resembles a random or Levy walk and is regulated in part by external factors including chemokines and lymph-node topology, but motility parameters such as speed and propensity to turn may also be cell intrinsic. Here we found that the unconventional myosin 1g (Myo1g) motor generates membrane tension, enforces cell-intrinsic meandering search, and enhances T-DC interactions during lymph-node surveillance. Increased turning and meandering motility, as opposed to ballistic motility, is enhanced by Myo1g. Myo1g acts as a "turning motor" and generates a form of cellular "flânerie." Modeling and antigen challenges show that these intrinsically programmed elements of motility search are critical for the detection of rare cognate antigen-presenting cells.

Optimal search in interacting populations: Gaussian jumps versus Lévy flights

We investigated the relationships between search efficiency, movement strategy, and nonlocal communication in the biological context of animal foraging. We considered situations where the members of a population of foragers perform either Gaussian jumps or Lévy flights, and show that the search time is minimized when communication among individuals occurs at intermediate ranges, independently of the type of movement. Additionally, while Brownian strategies are more strongly influenced by the communication mechanism, Lévy flights still result in shorter overall search durations.

Evanescent continuous-time random walks

We study how an evanescence process affects the number of distinct sites visited by a continuous-time random walker in one dimension. We distinguish two very different cases, namely, when evanescence can only occur concurrently with a jump, and when evanescence can occur at any time. The first is characteristic of trapping processes on a lattice, whereas the second is associated with spontaneous death processes such as radioactive decay. In both of these situations we consider three different forms of the waiting time distribution between jumps, namely, exponential, long tailed, and ultraslow.