Octavio Miramontes

Lévy walk patterns in the foraging movements of spider monkeys ( Ateles geoffroyi )

Scale invariant patterns have been found in different biological systems, in many cases resembling what physicists have found in other, nonbiological systems. Here we describe the foraging patterns of free-ranging spider monkeys (Ateles geoffroyi) in the forest of the Yucatan Peninsula, Mexico and find that these patterns closely resemble what physicists know as Lévy walks. First, the length of a trajectory’s constituent steps, or continuous moves in the same direction, is best described by a power-law distribution in which the frequency of ever larger steps decreases as a negative power function of their length. The rate of this decrease is very close to that predicted by a previous analytical Lévy walk model to be an optimal strategy to search for scarce resources distributed at random. Second, the frequency distribution of the duration of stops or waiting times also approximates to a power-law function. Finally, the mean square displacement during the monkeys’ first foraging trip increases more rapidly than would be expected from a random walk with constant step length, but within the range predicted for Lévy walks. In view of these results, we analyze the different exponents characterizing the trajectories described by females and males, and by monkeys on their own and when part of a subgroup. We discuss the origin of these patterns and their implications for the foraging ecology of spider monkeys.

Scale-free foraging by primates emerges from their interaction with a complex environment

Scale-free foraging patterns are widespread among animals. These may be the outcome of an optimal searching strategy to find scarce, randomly distributed resources, but a less explored alternative is that this behaviour may result from the interaction of foraging animals with a particular distribution of resources. We introduce a simple foraging model where individual primates follow mental maps and choose their displacements according to a maximum efficiency criterion, in a spatially disordered environment containing many trees with a heterogeneous size distribution. We show that a particular tree-size frequency distribution induces non-Gaussian movement patterns with multiple spatial scales (Lévy walks). These results are consistent with field observations of tree-size variation and spider monkey (Ateles geoffroyi) foraging patterns. We discuss the consequences that our results may have for the patterns of seed dispersal by foraging primates.

Host-parasitoid metapopulations: The consequences of parasitoid aggregation on spatial dynamics and searching efficiency

Recent studies of host—parasitoid metapopulations have shown how uniform dispersal, from a patch to its neighbouring patches, can result in the persistence of an otherwise non-persistent interaction. Here these models are extended to include density-dependent parasitoid aggregation. The fraction of dispersing hosts colonize the neighbouring patches equally, whereas parasitoid dispersal is related to the relative density of healthy hosts in each surrounding patch. Interestingly, this shows that the degree of parasitoid aggregation is associated with the self-organization of spatial structures and, in particular, spiral waves. Regions where spirals are most pronounced correspond to minimal variance in population densities. It is demonstrated, however, that parasitoid searching efficiency is highest (and mean host densities lowest) for levels of aggregation where the spatial dynamics consist of an even mixture of spirals and disordered patterns. Using an algorithmic complexity measure, it is verified that spatial transitions are also reflected in the temporal dynamics. Finally, it is demonstrated that multiple episodes of parasitoid dispersal, within a host generation, can inhibit persistence, particularly for large parasitoid movement rates.

Intrinsically generated coloured noise in laboratory insect populations

What are the mechanisms responsible for generating the erratic fluctuations observed in natural populations? This question has been at the centre of a long debate in contemporary ecology. The irregularities in the patterns of population abundance were initially mostly attributed to environmental factors. In the mid–1970s, however, it was proposed that these fluctuations may be generated intrinsically, by the underlying nonlinearities inherent in population processes. More recently, the focus of this argument has turned increasingly towards the statistical properties of population fluctuations, with many studies showing that ecological systems tend to be dominated by low–frequency or long–term dynamics, termed ‘red’ noise. Currently, the source of the ‘redness’ in ecological time–series is hotly debated, with the general consensus being that environmental variables are the major driving force. Here we show that three classic laboratory populations known to display irregular fluctuations also have reddened spectra. Furthermore, the dynamics of these populations show very well–defined generic scaling properties in the form of power laws. These results imply that long–term influences in ecological systems can be the product of intrinsic dynamics.

Modeling the searching behavior of social monkeys

We discuss various features of the trajectories of spider monkeys looking for food in a tropical forest, as observed recently in an extensive in situ study. Some of the features observed can be interpreted as the result of social interactions. In addition, a simple model of deterministic walk in a random environment reproduces the observed angular correlations between successive steps, and in some cases, the emergence of Levy distributions for the length of the steps.

The Effects of Spatially Heterogeneous Prey Distributions on Detection Patterns in Foraging Seabirds

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. Lévy 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 (Uria lomvia). However, Poissonian detection statistics is not observed in long-range seabirds such as the wandering albatross (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.

Information at the edge of chaos in fluid neural networks

Abstract Fluid neural networks, defined as neural nets of mobile elements with random activation, are studied by means of several approaches. They are proposed as a theoretical framework for a wide class of systems as insect societies, collectives of robots or the immune system. The critical properties of this model are also analysed, showing the existence of a critical boundary in parameter space where maximum information transfer occurs. In this sense, this boundary is in fact an example of the “edge of chaos” in systems like those described in our approach. Recent experiments with ant colonies seem to confirm our result.

Estimating 1/fα scaling exponents from short time-series

In recent years, there has been a concerted effort to develop methods for estimating the scaling exponents of time-series data, thus permitting a characterisation of their underlying dynamical behaviour. This task becomes rather inaccurate with data of limited length (less than 100 points), as is the case in many real studies where observation time is constrained. In this paper, we explore a novel method for accurately calculating the scaling exponents of short-term data, using what we term the multiple segmenting method (MSM). This approach relies on maximising the available information within a time-series by generating pseudo-replicates. We believe this method is potentially useful, especially when applied to biological data.

Order‐disorder transitions in the behavior of ant societies

Systems of many interacting elements may exhibit both optimal information processing capabilities and optimal adaptive capacity when poised in a state at the boundary separating chaos from order. Ant societies, composed of interacting chaotic individuals, which can generate regular cycles in the activity of the colony, provide one of the very first examples of this phenomenon. They self-organize to attain nest densities at which the transfer of information, per capita activations and the information capacity of the colonies are maximal. At such densities, ant colonies are poised in the neighborhood of a chaos-order phase transition.

Origin of power-law distributions in deterministic walks: the influence of landscape geometry.

We investigate the properties of a deterministic walk, whose locomotion rule is always to travel to the nearest site. Initially the sites are randomly distributed in a closed rectangular (ALxL) landscape and, once reached, they become unavailable for future visits. As expected, the walker step lengths present characteristic scales in one (L-->0) and two (AL approximately L) dimensions. However, we find scale invariance for an intermediate geometry, when the landscape is a thin striplike region. This result is induced geometrically by a dynamical trapping mechanism, leading to a power-law distribution for the step lengths. The relevance of our findings in broader contexts--of both deterministic and random walks--is also briefly discussed.