Jacques Gautrais

The formation of spatial patterns in social insects: from simple behaviours to complex structures.

Many of the collective activities performed by social insects result in the formation of complex spatio–temporal patterns. Without centralized control, workers are able to work together and collectively tackle tasks far beyond the abilities of any one individual. The resulting patterns produced by a colony are not explicitly coded at the individual level, but rather emerge from nonlinear interactions between individuals or between individuals and their environment. We present a few selected examples to illustrate some of the basic mechanisms used by social insects, such as templates, stigmergy and self–organization. These mechanisms can be used in combination to organize pattern formation at the colony level.

Deciphering Interactions in Moving Animal Groups

Collective motion phenomena in large groups of social organisms have long fascinated the observer, especially in cases, such as bird flocks or fish schools, where large-scale highly coordinated actions emerge in the absence of obvious leaders. However, the mechanisms involved in this self-organized behavior are still poorly understood, because the individual-level interactions underlying them remain elusive. Here, we demonstrate the power of a bottom-up methodology to build models for animal group motion from data gathered at the individual scale. Using video tracks of fish shoal in a tank, we show how a careful, incremental analysis at the local scale allows for the determination of the stimulus/response function governing an individuals moving decisions. We find in particular that both positional and orientational effects are present, act upon the fish turning speed, and depend on the swimming speed, yielding a novel schooling model whose parameters are all estimated from data. Our approach also leads to identify a density-dependent effect that results in a behavioral change for the largest groups considered. This suggests that, in confined environment, the behavioral state of fish and their reaction patterns change with group size. We debate the applicability, beyond the particular case studied here, of this novel framework for deciphering interactions in moving animal groups.

Collective decision-making in white-faced capuchin monkeys

In group-living animals, collective movements are a widespread phenomenon and occur through consensus decision. When one animal proposes a direction for group movement, the others decide to follow or not and hence take part in the decision-making process. This paper examines the temporal spread of individual responses after the departure of a first individual (the initiator) in a semi-free ranging group of white-faced capuchins (Cebus capucinus). We analysed 294 start attempts, 111 succeeding and 183 failing. Using a modelling approach, we have demonstrated that consensus decision-making for group movements is based on two complementary phenomena in this species: firstly, the joining together of group members thanks to a mimetic process; and secondly, a modulation of this phenomenon through the propensity of the initiator to give up (i.e. cancellation rate). This cancellation rate seems to be directly dependent upon the number of followers: the greater this number is, the lower the cancellation rate is seen to be. The coupling between joining and cancellation rates leads to a quorum: when three individuals join the initiator, the group collectively moves. If the initiator abandons the movement, this influences the joining behaviour of the other group members, which in return influences the initiators behaviour. This study demonstrates the synergy between the initiators behaviour and the self-organized mechanisms underlying group movements.

From behavioural analyses to models of collective motion in fish schools

Fish schooling is a phenomenon of long-lasting interest in ethology and ecology, widely spread across taxa and ecological contexts, and has attracted much interest from statistical physics and theoretical biology as a case of self-organized behaviour. One topic of intense interest is the search of specific behavioural mechanisms at stake at the individual level and from which the school properties emerges. This is fundamental for understanding how selective pressure acting at the individual level promotes adaptive properties of schools and in trying to disambiguate functional properties from non-adaptive epiphenomena. Decades of studies on collective motion by means of individual-based modelling have allowed a qualitative understanding of the self-organization processes leading to collective properties at school level, and provided an insight into the behavioural mechanisms that result in coordinated motion. Here, we emphasize a set of paradigmatic modelling assumptions whose validity remains unclear, both from a behavioural point of view and in terms of quantitative agreement between model outcome and empirical data. We advocate for a specific and biologically oriented re-examination of these assumptions through experimental-based behavioural analysis and modelling.

Nest excavation in ants: group size effects on the size and structure of tunneling networks

Collective digging activity was studied in the ant Messor sancta Forel in laboratory conditions and with a two dimensional set-up. We analyzed the digging dynamics and topology of tunneling networks excavated by groups of workers ranging from 50 to 200 individuals over 3xa0days. In all conditions, the dynamics of excavated sand volume were clearly non-linear. Excavation began with an exponential growth and after 3xa0days reached a saturation phase in which activity was almost totally stopped. The final volume of sand excavated was positively correlated with the number of workers. At the end of the experiments, the two-dimensional tunneling networks were mapped onto planar graphs where the vertices represent small chambers or intersections between tunnels and the edges represent tunnels. We found that all the networks belonged to a same topological family and exhibited several striking invariants such as the distribution of vertex degree that follows a power law. When increasing the number of ants, some changes occurred in the network structure, mainly an increase in the number of edges and vertices, and the progressive emergence of enlarged and highly connected vertices.

Stigmergic construction and topochemical information shape ant nest architecture

Significance Social insects build some of the most complex nests found in the animal kingdom. Here, we use experiments and modeling to decipher the mechanisms involved in the coordination of nest building in the ant Lasius niger: we first characterize nest architecture and its growth with 3D imaging techniques; then, we test the building responses of individual ants to artificial stimuli. A model entirely based on experimental data confirms that the individual level interactions and building rules are sufficient to reproduce the nest growth dynamics and the spatial patterns observed for real ant nests. Our results show that a pheromone added by ants to the building material is a key factor that controls the growth and form of nest architecture. The nests of social insects are not only impressive because of their sheer complexity but also because they are built from individuals whose work is not centrally coordinated. A key question is how groups of insects coordinate their building actions. Here, we use a combination of experimental and modeling approaches to investigate nest construction in the ant Lasius niger. We quantify the construction dynamics and the 3D structures built by ants. Then, we characterize individual behaviors and the interactions of ants with the structures they build. We show that two main interactions are involved in the coordination of building actions: (i) a stigmergic-based interaction that controls the amplification of depositions at some locations and is attributable to a pheromone added by ants to the building material; and (ii) a template-based interaction in which ants use their body size as a cue to control the height at which they start to build a roof from existing pillars. We then develop a 3D stochastic model based on these individual behaviors to analyze the effect of pheromone presence and strength on construction dynamics. We show that the model can quantitatively reproduce key features of construction dynamics, including a large-scale pattern of regularly spaced pillars, the formation and merging of caps over the pillars, and the remodeling of built structures. Finally, our model suggests that the lifetime of the pheromone is a highly influential parameter that controls the growth and form of nest architecture.

Modeling Collective Animal Behavior with a Cognitive Perspective: A Methodological Framework

The last decades have seen an increasing interest in modeling collective animal behavior. Some studies try to reproduce as accurately as possible the collective dynamics and patterns observed in several animal groups with biologically plausible, individual behavioral rules. The objective is then essentially to demonstrate that the observed collective features may be the result of self-organizing processes involving quite simple individual behaviors. Other studies concentrate on the objective of establishing or enriching links between collective behavior researches and cognitive or physiological ones, which then requires that each individual rule be carefully validated. Here we discuss the methodological consequences of this additional requirement. Using the example of corpse clustering in ants, we first illustrate that it may be impossible to discriminate among alternative individual rules by considering only observational data collected at the group level. Six individual behavioral models are described: They are clearly distinct in terms of individual behaviors, they all reproduce satisfactorily the collective dynamics and distribution patterns observed in experiments, and we show theoretically that it is strictly impossible to discriminate two of these models even in the limit of an infinite amount of data whatever the accuracy level. A set of methodological steps are then listed and discussed as practical ways to partially overcome this problem. They involve complementary experimental protocols specifically designed to address the behavioral rules successively, conserving group-level data for the overall model validation. In this context, we highlight the importance of maintaining a sharp distinction between model enunciation, with explicit references to validated biological concepts, and formal translation of these concepts in terms of quantitative state variables and fittable functional dependences. Illustrative examples are provided of the benefits expected during the often long and difficult process of refining a behavioral model, designing adapted experimental protocols and inversing model parameters.

Transition from isotropic to digitated growth modulates network formation in Physarum polycephalum

Some organisms, including fungi, ants, and slime molds, explore their environment and forage by forming interconnected networks. The plasmodium of the slime mold Physarum polycephalum is a large unicellular amoeboid organism that grows a tubular spatial network through which nutrients, body mass, and chemical signals are transported. Individual plasmodia are capable of sophisticated behaviours such as optimizing their network connectivity and dynamics using only decentralized information processing. In this study, we used a population of plasmodia that interconnect through time to analyse the dynamical interactions between growth of individual plasmodia and global network formation. Our results showed how initial conditions, such as the distance between plasmodia, their size, or the presence and quality of food, affect the emerging network connectivity.

Addressing nonlinearities in Monte Carlo

Monte Carlo is famous for accepting model extensions and model refinements up to infinite dimension. However, this powerful incremental design is based on a premise which has severely limited its application so far: a state-variable can only be recursively defined as a function of underlying state-variables if this function is linear. Here we show that this premise can be alleviated by projecting nonlinearities onto a polynomial basis and increasing the configuration space dimension. Considering phytoplankton growth in light-limited environments, radiative transfer in planetary atmospheres, electromagnetic scattering by particles, and concentrated solar power plant production, we prove the real-world usability of this advance in four test cases which were previously regarded as impracticable using Monte Carlo approaches. We also illustrate an outstanding feature of our method when applied to acute problems with interacting particles: handling rare events is now straightforward. Overall, our extension preserves the features that made the method popular: addressing nonlinearities does not compromise on model refinement or system complexity, and convergence rates remain independent of dimension.