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Individual behavioural heterogeneity is key to understanding how natural populations adapt flexibly to environmental changes. In ant species like $\textit{Aphaenogaster senilis}$, two key roles in collective foraging are commonly recognised: scouts, who discover food patches, and recruits, who exploit these patches and transport food back to the nest. These roles involve distinct movement patterns and exploratory behaviours. In this chapter, we develop a correlated random walk model on the bounded honeycomb lattice to interpret and replicate empirical observations of foraging ants in an enclosed arena with honeycomb tiling. We do so by extending the theory of first-passage processes for $\mathcal{N}$ random walkers when individuals belong to a heterogeneous population. We apply this theory to examine how individual behavioural heterogeneity in ants affects collective foraging efficiency, focusing on first-passage time statistics for nest-to-patch and patch-to-patch movements. With the combined use of the mathematical model and the controlled experimental setup we evaluate (i) the impact of distinct movement strategies by scouts and recruits on finding food items and (ii) whether ants practice strict central place foraging or utilise previously discovered patches as starting points for further exploration., Comment: 28 pages, 8 figures

Dimensional data reduction methods are fundamental to explore and visualize large data sets. Basic requirements for unsupervised data exploration are simplicity, flexibility and scalability. However, current methods show complex parameterizations and strong computational limitations when exploring large data structures across scales. Here, we focus on the t-SNE algorithm and show that a simplified parameter setup with a single control parameter, namely the perplexity, can effectively balance local and global data structure visualization. We also designed a chunk\&mix protocol to efficiently parallelize t-SNE and explore data structure across a much wide range of scales than currently available. Our parallel version of the BH-tSNE, namely pt-SNE, converges to good global embedding, comparable to state-of-the-art solutions, though the chunk\&mix protocol adds little noise and decreases the accuracy at the local scale. Nonetheless, we show that simple post-processing can efficiently restore local scale visualization, without any loss of precision at the global scales. We expect the same approach to apply to faster embedding algorithms other than BH-tSNE, like FIt-SNE or UMAP, thus, extending the state-of-the-art and leading to more comprehensive data structure visualization and analysis., Comment: 32 pages, 11 figures

We introduce an improved unsupervised clustering protocol specially suited for large-scale structured data. The protocol follows three steps: a dimensionality reduction of the data, a density estimation over the low dimensional representation of the data, and a final segmentation of the density landscape. For the dimensionality reduction step we introduce a parallelized implementation of the well-known t-Stochastic Neighbouring Embedding (t-SNE) algorithm that significantly alleviates some inherent limitations, while improving its suitability for large datasets. We also introduce a new adaptive Kernel Density Estimation particularly coupled with the t-SNE framework in order to get accurate density estimates out of the embedded data, and a variant of the rainfalling watershed algorithm to identify clusters within the density landscape. The whole mapping protocol is wrapped in the bigMap R package, together with visualization and analysis tools to ease the qualitative and quantitative assessment of the clustering., Comment: 24 pages main text including 6 (full-page) figures; bigMap R-pacakge available at CRAN

Human mobility is becoming an accessible field of study thanks to the progress and availability of tracking technologies as a common feature of smart phones. We describe an example of a scalable experiment exploiting these circumstances at a public, outdoor fair in Barcelona (Spain). Participants were tracked while wandering through an open space with activity stands attracting their attention. We develop a general modeling framework based on Langevin Dynamics, which allows us to test the influence of two distinct types of ingredients on mobility: reactive or context-dependent factors, modelled by means of a force field generated by attraction points in a given spatial configuration, and active or inherent factors, modelled from intrinsic movement patterns of the subjects. The additive and constructive framework model accounts for the observed features. Starting with the simplest model (purely random walkers) as a reference, we progressively introduce different ingredients such as persistence, memory, and perceptual landscape, aiming to untangle active and reactive contributions and quantify their respective relevance. The proposed approach may help in anticipating the spatial distribution of citizens in alternative scenarios and in improving the design of public events based on a facts-based approach.

An efficient searcher needs to balance properly the tradeoff between the exploration of new spatial areas and the exploitation of nearby resources, an idea which is at the core of scale-free L\'evy search strategies. Here we study multi-scale 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 asymmetric regime, in which both nearby and faraway targets are available to the searcher. For this regime, we prove that the combination of only two movement scales can be enough to outperform both balistic and L\'evy 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 targets 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 in the asymmetric regime actually arise through the informed combination of only two walk scales (related to the exploitative and the explorative scale, respectively), expanding on the well-known result that optimal strategies in strictly uninformed scenarios are achieved through L\'evy paths (or, equivalently, through a hierarchical combination of multiple scales).

We present a variant of the well sounded Expectation-Maximization Clustering algorithm that is constrained to generate partitions of the input space into high and low values. The motivation of splitting input variables into high and low values is to favour the semantic interpretation of the final clustering. The Expectation-Maximization binary Clustering is specially useful when a bimodal conditional distribution of the variables is expected or at least when a binary discretization of the input space is deemed meaningful. Furthermore, the algorithm deals with the reliability of the input data such that the larger their uncertainty the less their role in the final clustering. We show here its suitability for behavioural annotation of movement trajectories. However, it can be considered as a general purpose algorithm for the clustering or segmentation of multivariate data or temporal series., Comment: 34 pages main text including 11 (full page) figures

Many attempts to relate animal foraging patterns to landscape heterogeneity are focused on the analysis of foragers movements. Resource detection patterns in space and time are not commonly studied, yet they are tightly coupled to landscape properties and add relevant information on foraging behavior. By exploring simple foraging models in unpredictable environments we show that the distribution of intervals between detected prey (detection statistics)is mostly determined by the spatial structure of the prey field and essentially distinct from predator displacement statistics. Detections are expected to be Poissonian in uniform random environments for markedly different foraging movements (e.g. L\'evy and ballistic). This prediction is supported by data on the time intervals between diving events on short-range foraging seabirds such as the thick-billed murre ({\it Uria lomvia}). However, Poissonian detection statistics is not observed in long-range seabirds such as the wandering albatross ({\it Diomedea exulans}) due to the fractal nature of the prey field, covering a wide range of spatial scales. For this scenario, models of fractal prey fields induce non-Poissonian patterns of detection in good agreement with two albatross data sets. We find that the specific shape of the distribution of time intervals between prey detection is mainly driven by meso and submeso-scale landscape structures and depends little on the forager strategy or behavioral responses., Comment: Submitted first to PLoS-ONE on 26/9/2011. Final version published on 14/04/2012