Universality in ant behaviour

Tree size distribution as the stationary limit of an evolutionary master equation

The diameter distribution of a given species of deciduous trees is well approximated by a Gamma distribution. Here we give new experimental evidence for this conjecture by analyzing deciduous tree size data in mature semi-natural forest and ancient, traditionally managed wood-pasture from Central Europe. These distribution functions collapse on a universal shape if the tree sizes are normalized to the mean value in the considered sample. A new evolutionary master equation is used to model the observed distribution. The model incorporates four ecological processes: tree growth, mortality, recruitment, and diversification. Utilizing simple and realistic kernel functions describing the first three, along with an assumed multiplicative dilution due to diversification, the stationary solution of the master equation yields the experimentally observed Gamma distribution. The model as it is formulated allows an analytically compact solution and has only two fitting parameters whose values are consistent with the experimental data related to these processes. We found that the equilibrium size distribution of tree species with different ecology, originating from two contrastingly different semi-natural ecosystem types can be accurately described by a single dynamical mean-field model.

Animal intermittent locomotion: A null model for the probability of moving forward in bounded space

We present a null model to be compared with biological data to test for intrinsic persistence in movement between stops during intermittent locomotion in bounded space with different geometries and boundary conditions. We describe spatio-temporal properties of the sequence of stopping points r₁,r₂,r₃,… visited by a Random Walker within a bounded space. The path between stopping points is not considered, only the displacement. Since there are no intrinsic correlations in the displacements between stopping points, there is no intrinsic persistence in the movement between them. Hence, this represents a null-model against which to compare empirical data for directional persistence in the movement between stopping points when there is external bias due to the bounded space. This comparison is a necessary first step in testing hypotheses about the function of the stops that punctuate intermittent locomotion in diverse organisms. We investigate the probability of forward movement, defined as a deviation of less than 90° between two successive displacement vectors, as a function of the ratio between the largest displacement between stops that could be performed by the random walker and the system size, α=Δℓ/L_max. As expected, the probability of forward movement is 1/2 when α→0. However, when α is finite, this probability is less than 1/2 with a minimum value when α=1. For certain boundary conditions, the minimum value is between 1/3 and 1/4 in 1D while it can be even lower in 2D. The probability of forward movement in 1D is calculated exactly for all values 0<α⩽1 for several boundary conditions. Analytical calculations for the probability of forward movement are performed in 2D for circular and square bounded regions with one boundary condition. Numerical results for all values 0<α⩽1 are presented for several boundary conditions. The cases of rectangle and ellipse are also considered and an approximate model of the dependence of the forward movement probability on the aspect ratio is provided. Finally, some practical points are presented on how these results can be utilised in the empirical analysis of animal movement in two-dimensional bounded space.

Sources of intraspecific variation in the collective tempo and synchrony of ant societies

Populations of independently oscillating agents can sometimes synchronize. In the context of animal societies, conspicuous synchronization of activity is known in some social insects. However, the causes of variation in synchrony within and between species have received little attention. We repeatedly assessed the short-term activity cycle of ant colonies (Temnothorax rugatulus) and monitored the movements of individual workers and queens within nests. We detected persistent differences between colonies in the waveform properties of their collective activity oscillations, with some colonies consistently oscillating much more erratically than others. We further demonstrate that colony crowding reduces the rhythmicity (i.e., the consistent timing) of oscillations. Workers in both erratic and rhythmic colonies spend less time active than completely isolated workers, but workers in erratic colonies oscillate out of phase with one another. We further show that the queen's absence can impair the ability of colonies to synchronize worker activity and that behavioral differences between queens are linked with the waveform properties of their societies.

How ants move: individual and collective scaling properties

The motion of social insects is often used as a paradigmatic example of complex adaptive dynamics arising from decentralized individual behaviour. In this paper, we revisit the topic of the ruling laws behind the burst of activity in ants. The analysis, done over previously reported data, reconsiders the causation arrows, proposed at individual level, not finding any link between the duration of the ants' activity and their moving speed. Secondly, synthetic trajectories created from steps of different ants demonstrate that a Markov process can explain the previously reported speed shape profile. Finally, we show that as more ants enter the nest, the faster they move, which implies a collective property. Overall, these results provide a mechanistic explanation for the reported behavioural laws, and suggest us a formal way to further study the collective properties in these scenarios.

Recurrence analysis of ant activity patterns

In this study, we used recurrence quantification analysis (RQA) and recurrence plots (RPs) to compare the movement activity of individual workers of three ant species, as well as a gregarious beetle species. RQA and RPs quantify the number and duration of recurrences of a dynamical system, including a detailed quantification of signals that could be stochastic, deterministic, or both. First, we found substantial differences between the activity dynamics of beetles and ants, with the results suggesting that the beetles have quasi-periodic dynamics and the ants do not. Second, workers from different ant species varied with respect to their dynamics, presenting degrees of predictability as well as stochastic signals. Finally, differences were found among minor and major caste of the same (dimorphic) ant species. Our results underscore the potential of RQA and RPs in the analysis of complex behavioral patterns, as well as in general inferences on animal behavior and other biological phenomena.

Ants determine their next move at rest: motor planning and causality in complex systems

To find useful work to do for their colony, individual eusocial animals have to move, somehow staying attentive to relevant social information. Recent research on individual Temnothorax albipennis ants moving inside their colony's nest found a power-law relationship between a movement's duration and its average speed; and a universal speed profile for movements showing that they mostly fluctuate around a constant average speed. From this predictability it was inferred that movement durations are somehow determined before the movement itself. Here, we find similar results in lone T. albipennis ants exploring a large arena outside the nest, both when the arena is clean and when it contains chemical information left by previous nest-mates. This implies that these movement characteristics originate from the same individual neural and/or physiological mechanism(s), operating without immediate regard to social influences. However, the presence of pheromones and/or other cues was found to affect the inter-event speed correlations. Hence we suggest that ants' motor planning results in intermittent response to the social environment: movement duration is adjusted in response to social information only between movements, not during them. This environmentally flexible, intermittently responsive movement behaviour points towards a spatially allocated division of labour in this species. It also prompts more general questions on collective animal movement and the role of intermittent causation from higher to lower organizational levels in the stability of complex systems.

A social mechanism facilitates ant colony emigrations over different distances

Behavioural responses enable animals to react rapidly to fluctuating environments. In eusocial organisms, such changes are often enacted at the group level, but may be organised in a decentralised fashion by the actions of individuals. However, the contributions of different group members are rarely homogenous, and there is evidence to suggest that certain ‘keystone’ individuals are important in shaping collective responses. Accordingly, investigations of the dynamics and structuring of behavioural changes at both the group and individual level, are crucial for evaluating the relative influence of different individuals. Here, we examine the composition of tandem running behaviour during colony emigrations in the ant species Temnothorax albipennis. Tandem running is modulated in response to emigration distance, with more runs being conducted when a more distant nest site must be reached. We show that certain individuals are highly active in the tandem running process, attempting significantly more work in the task. Contrary to expectations, however, such individuals are in fact no more successful at conducting tandem runs than their less active nest mates. Instead, it seems that when more tandem runs are required, colonies rely on greater recruitment of workers into the process. The implications of our study are that in some cases, even when apparently ‘key’ individuals exist within a group, their relative contribution to task performance may be far from decisive.

How we move is universal: Scaling in the average shape of human activity

Human motor activity is constrained by the rhythmicity of the 24 hours circadian cycle, including the usual 12-15 hours sleep-wake cycle. However, activity fluctuations also appear over a wide range of temporal scales, from days to a few seconds, resulting from the concatenation of a myriad of individual smaller motor events. Furthermore,  individuals present different propensity to wakefulness and thus to motor activity throughout the circadian cycle.  Are activity fluctuations across temporal scales intrinsically different, or is there a universal description encompassing them? Is this description also universal across individuals, considering the aforementioned variability?  Here we establish the presence of universality in motor activity fluctuations based on the empirical study of a month of continuous wristwatch accelerometer recordings. We study the scaling of average fluctuations across temporal scales and determine a universal law characterized by critical exponents $\alpha$, $\tau$ and $1/{ \mu}$. Results are highly reminiscent of the universality described for the average shape of avalanches in systems exhibiting crackling noise. Beyond its theoretical relevance, the present results can be important for developing objective markers of healthy  as well as pathological human motor behavior.Received: 18 October 2015,  Accepted: 10 November 2015; Edited by: E. Mizraji; Reviewed by: J. Lin, Department of Physics, Washington College, Maryland, USA.; DOI: http://dx.doi.org/10.4279/PIP.070017Cite as: D R Chialvo, A M Gonzalez Torrado, E Gudowska-Nowak, J K Ochab, P Montoya, M A Nowak, E Tagliazucchi, Papers in Physics 7, 070017 (2015)This paper, by D R Chialvo, A M Gonzalez Torrado, E Gudowska-Nowak, J K Ochab, P Montoya, M A Nowak, E Tagliazucchi, is licensed under the Creative Commons Attribution License 3.0.