An important application involving two-species reaction-diffusion systems relates to the problem of finding the best statistical strategy for optimizing the encounter rate between organisms. We investigate the general problem of how the encounter rate depends on whether organisms move in Lévy or Brownian random walks. By simulating a limiting generalized searcher-target model (e.g., predator-prey, mating partner, pollinator-flower), we find that Lévy walks confer a significant advantage for increasing encounter rates when the searcher is larger or moves rapidly relative to the target, and when the target density is low.

Search and capture in space and time: How immunological T cells scan target cells for ligands is poorly understood. Cai et al. examined microvillar dynamics in living T cells in three dimensions and real time. The T cells palpated all spots on a surface within about 1 min through rapid movements of their microvilli. The time it took to scan the surface matched the movement rate of cells through tissues. These contacts took place in the absence of T cell receptor recognition and were stabilized independently of signaling or the cytoskeleton. Instead, stabilization depended on ligand affinity. The findings explain why many of the previously described components of the immunological synapse and T cell receptor signaling reside on three-dimensional microvillar-derived projections. Science , this issue p. eaal3118

The searching trajectories of different animals can be described with a broad class of flight length ( l _j ) distributions with P ( l _j ) = l _j ^–μ . Theoretical studies have shown that changes in these distributions (i.e., different μ values) are key to optimizing the long-term encounter statistics under certain searcher–resource scenarios. In particular, they predict the advantage of Lévy searching (μ ≈ 2) over Brownian motion (μ ≥ 3) for low-prey-density scenarios. Here, we present experimental evidence of predicted optimal changes in the flight-time distribution of a predator's walk in response to gradual density changes of its moving prey. Flight times of the dinoflagellate Oxyrrhis marina switched from an exponential to an inverse square power-law distribution when the prey ( Rhodomonas sp.) decreased in abundance. Concomitantly, amplitude and frequency of the short-term helical path increased. The specific biological mechanisms involved in these searching behavioral changes are discussed. We suggest that, in a three-dimensional environment, a stronger helical component combined with a Lévy walk searching strategy enhances predator's encounter rates. Our results support the idea of universality of the statistical laws in optimal searching processes despite variations in the biological details of the organisms.

Whereas the Asian tiger mosquito (Aedes albopictus) has low active dispersal capabilities, its worldwide colonization has been rapid. Indirect evidence and informal reports have long implicated passive transportation in cars, but this has not previously been studied systematically given the difficulties of real-time roadside surveys. Here we report the first sampling study confirming that adult tiger mosquitoes travel with humans in cars and enabling us to estimate the frequency of these events. We combine the results with citizen science data to model the car-facilitated dispersal of Aedes albopictus at a nationwide level. During the summer of 2015, we sampled 770 cars in north-eastern Spain, discovering 4 adult female tiger mosquitoes that had entered cars prior to sampling. Our Bayesian model suggests that of the 6.5 million daily car trips in the Barcelona metropolitan area, between 13,000 and 71,500 facilitate tiger mosquito movement, and that Barcelona is the largest source of inter-province tiger mosquito transfers in Spain. Our results are supported by expert-validated citizen science data, and will contribute to better understanding the tiger mosquito’s invasion process and ultimately lead to more effective vector control strategies.