Feedbacks, nonlinearities and nonequilibria: A thermodynamic perspective.

The feedback circuit approach to nonlinear dynamical systems pioneered by Thomas and coworkers is revisited in a thermodynamical perspective. The role of nonequilibrium conditions and of other types of constraints such as mass action kinetics or microscopic reversibility around thermodynamic equilibrium in the way positive feedback circuits are operating is analyzed. It is shown that the appearance of non-trivial steady-state and time-dependent behaviors necessitates that the strengths of the feedback loops present exceed some well-defined critical values. Illustrations are provided on prototypical systems giving rise to multiple steady states.

Collective choice in ants: the role of protein and carbohydrates ratios.

In a foraging context, social insects make collective decisions from individuals responding to local information. When faced with foods varying in quality, ants are known to be able to select the best food source using pheromone trails. Until now, studies investigating collective decisions have focused on single nutrients, mostly carbohydrates. In the environment, the foods available are a complex mixture and are composed of various nutrients, available in different forms. In this paper, we explore the effect of protein to carbohydrate ratio on ants' ability to detect and choose between foods with different protein characteristics (free amino acids or whole proteins). In a two-choice set up, Argentine ants Linepithema humile were presented with two artificial foods containing either whole protein or amino acids in two different dietary conditions: high protein food or high carbohydrate food. At the collective level, when ants were faced with high carbohydrate foods, they did not show a preference between free amino acids or whole proteins, while a preference for free amino acids emerged when choosing between high protein foods. At the individual level, the probability of feeding was higher for high carbohydrates food and for foods containing free amino acids. Two mathematical models were developed to evaluate the importance of feeding probability in collective food selection. A first model in which a forager deposits pheromone only after feeding, and a second model in which a forager always deposits pheromone, but with greater intensity after feeding. Both models were able to predict free amino acid selection, however the second one was better able to reproduce the experimental results suggesting that modulating trail strength according to feeding probability is likely the mechanism explaining amino acid preference at a collective level in Argentine ants.

Foraging at the edge of chaos: internal clock versus external forcing.

Activity rhythms in animal groups arise both from external changes in the environment, as well as from internal group dynamics. These cycles are reminiscent of physical and chemical systems with quasiperiodic and even chaotic behavior resulting from "autocatalytic" mechanisms. We use nonlinear differential equations to model how the coupling between the self-excitatory interactions of individuals and external forcing can produce four different types of activity rhythms: quasiperiodic, chaotic, phase locked, and displaying over or under shooting. At the transition between quasiperiodic and chaotic regimes, activity cycles are asymmetrical, with rapid activity increases and slower decreases and a phase shift between external forcing and activity. We find similar activity patterns in ant colonies in response to varying temperature during the day. Thus foraging ants operate in a region of quasiperiodicity close to a cascade of transitions leading to chaos. The model suggests that a wide range of temporal structures and irregularities seen in the activity of animal and human groups might be accounted for by the coupling between collectively generated internal clocks and external forcings.

Information flow and information production in a population system.

An approach aiming to quantify the dynamics of information within a population is developed based on the mapping of the processes underlying the system's evolution into a birth and death type stochastic process and the derivation of a balance equation for the information entropy. Information entropy flux and information entropy production are identified and their time-dependent properties, as well as their dependence on the parameters present in the problem, are analyzed. States of minimum information entropy production are shown to exist for appropriate parameter values. Furthermore, uncertainty and information production are transiently intensified when the population traverses the inflexion point stage of the logisticlike growth process.

Resource exploitation strategies in the presence of traffic between food sources.

A mathematical model of food recruitment and resource exploitation in group-living organisms accounting for direct traffic of individuals between the available sources is developed. It is shown that traffic between sources gives rise to the enhancement of the range of stability of the homogeneous mode of exploitation and of the range of coexistence of homogeneous and semi-inhomogeneous ones, as well as the appearance of symmetry breaking transitions leading to fully inhomogeneous exploitation modes.

The selfish to egalitarian transition in young children: developmental processes versus cooperative interactions.

There is evidence that a tendency to share resources equitably among members of a social group emerges in middle childhood. It is regarded by many investigators as a central and unique feature of human social life. In this work the relative roles of developmental processes and collective effects generated by interindividual interactions on the selfish to egalitarian transition observed in middle childhood are analyzed. Using mathematical modeling, conditions are identified under which the transition becomes sharp and gives rise to hysteretic behavior.

Propagation of extremes in space.

The propagation of extreme events in space is analyzed for a class of dynamical systems giving rise to spatiotemporal chaos. It is shown that this process can be mapped into a generalized random walk, whereby the mean square displacement increases linearly in time and there is a nonvanishing probability for jumps beyond first neighbors. The relative roles of the local dynamics and of the spatial coupling are identified.

Noise improves collective decision-making by ants in dynamic environments.

Recruitment via pheromone trails by ants is arguably one of the best-studied examples of self-organization in animal societies. Yet it is still unclear if and how trail recruitment allows a colony to adapt to changes in its foraging environment. We study foraging decisions by colonies of the ant Pheidole megacephala under dynamic conditions. Our experiments show that P. megacephala, unlike many other mass recruiting species, can make a collective decision for the better of two food sources even when the environment changes dynamically. We developed a stochastic differential equation model that explains our data qualitatively and quantitatively. Analysing this model reveals that both deterministic and stochastic effects (noise) work together to allow colonies to efficiently track changes in the environment. Our study thus suggests that a certain level of noise is not a disturbance in self-organized decision-making but rather serves an important functional role.

The role of multiple pheromones in food recruitment by ants.

In this paper we investigate the foraging activity of an invasive ant species, the big headed ant Pheidole megacephala. We establish that the ants' behavior is consistent with the use of two different pheromone signals, both of which recruit nestmates. Our experiments suggest that during exploration the ants deposit a long-lasting pheromone that elicits a weak recruitment of nestmates, while when exploiting food the ants deposit a shorter lasting pheromone eliciting a much stronger recruitment. We further investigate experimentally the role of these pheromones under both static and dynamic conditions and develop a mathematical model based on the hypothesis that exploration locally enhances exploitation, while exploitation locally suppresses exploration. The model and the experiments indicate that exploratory pheromone allows the colony to more quickly mobilize foragers when food is discovered. Furthermore, the combination of two pheromones allows colonies to track changing foraging conditions more effectively than would a single pheromone. In addition to the already known causes for the ecological success of invasive ant species, our study suggests that their opportunistic strategy of rapid food discovery and ability to react to changes in the environment may have strongly contributed to their dominance over native species.

Extreme events in bimodal systems.

The extreme value statistics of systems possessing a two-hump probability density of the relevant variable, in which the left peak is more pronounced than the right one, is studied. It is shown that systems of this type display a nontrivial transient behavior in the form of anomalous fluctuations around the mean, for certain (finite) ranges of observational time windows. The results are illustrated on independent identically distributed random variables, systems possessing two locally stable states and subjected to additive white noise, and dynamical systems in the regime of deterministic chaos.

Collective decision-making and behavioral polymorphism in group living organisms.

Collective foraging in group living animal populations displaying behavioral polymorphism is considered. Using mathematical modeling it is shown that symmetric, spatially homogeneous (food sources are used equally) and asymmetric, spatially inhomogeneous (only one food source is used) regimes can coexist, as a result of differential amplification of choice depending on behavioral type. The model accounts for recent experimental results on social caterpillars not only confirming this coexistence, but also showing the relationship between the two types of regime and the ratio of active to inactive individuals.

Kinetics of aggregate formation in social insects.

A model for the kinetics of aggregation in social insects which accounts for stochastic effects arising from individual variability and covers both the early and the mature stages of the process is developed. Different aggregation scenarios are studied, depending on the degree of cooperativity and the mean population density. It is shown that under certain conditions, the system evolves slowly to a single cluster incorporating all individuals, or to two coexisting clusters of similar sizes.

Optimality of collective choices: a stochastic approach.

Amplifying communication is a characteristic of group-living animals. This study is concerned with food recruitment by chemical means, known to be associated with foraging in most ant colonies but also with defence or nest moving. A stochastic approach of collective choices made by ants faced with different sources is developed to account for the fluctuations inherent to the recruitment process. It has been established that ants are able to optimize their foraging by selecting the most rewarding source. Our results not only confirm that selection is the result of a trail modulation according to food quality but also show the existence of an optimal quantity of laid pheromone for which the selection of a source is at the maximum, whatever the difference between the two sources might be. In terms of colony size, large colonies more easily focus their activity on one source. Moreover, the selection of the rich source is more efficient if many individuals lay small quantities of pheromone, instead of a small group of individuals laying a higher trail amount. These properties due to the stochasticity of the recruitment process can be extended to other social phenomena in which competition between different sources of information occurs.