Collective Behavior by Bernd Meyer
Swarm Intelligence, 2020
Social insects allocate their workforce in a decentralised fashion, addressing multiple tasks and... more Social insects allocate their workforce in a decentralised fashion, addressing multiple tasks and responding effectively to environmental changes. This process is fundamental to their ecological success, but the mechanisms behind it are not well understood. While most models focus on internal and individual factors, empirical evidence highlights the importance of ecology and social interactions. To address this gap, we propose a game theoretical model of task allocation. Our main findings are twofold: Firstly, the specialisation emerging from self-organised task allocation can be largely determined by the ecology. Weakly specialised colonies in which all individuals perform more than one task emerge when foraging is cheap; in contrast, harsher environments with high foraging costs lead to strong specialisation in which each individual fully engages in a single task. Secondly, social interactions lead to important differences in dynamic environments. Colonies whose individuals rely on their own experience are predicted to be more flexible when dealing with change than colonies relying on social information. We also find that, counter to intuition, strongly specialised colonies may perform suboptimally, whereas the group performance of weakly specialised colonies approaches optimality. Our simulation results fully agree with the predictions of the mathematical model for the regions where the latter is analytically tractable. Our results are useful in framing relevant and important empirical questions, where ecology and interactions are key elements of hypotheses and predictions.
Reconsidering Response Threshold Models --- Short-term Response Patterns in Thermoregulating Bumblebees
Behavioral Ecology and Sociobiology, 2019
Social insect colonies distribute their workforce with amazing flexibility across a large array o... more Social insect colonies distribute their workforce with amazing flexibility across a large array of diverse tasks under fluctuating external conditions and internal demands. Deciphering the individual rules of task selection and task performance is at the heart of understanding how colonies can achieve this collective feature. Models play an important role in this endeavor, as they allow us to investigate how the rules of individual behavior give rise to emergent patterns at the colony level. Modulation of individual behavior occurs at many different timescales and to successfully use a model we need to ensure that it applies on the timescale under observation. Here, we focus on short timescales and ask the question whether the most commonly used class of models (response threshold models) adequately describes behavioral modulation on this timescale. We study the fanning behavior of bumblebees on temperature-controlled brood dummies and investigate the effect of (i) stimulus intensity, (ii) repeated task performance, and (iii) task performance feedback. We analyze the timing patterns (rates of task engagement and task disengagement) using survival analysis. Our results show that stimulus intensity does not significantly influence individual task investment at these comparably short timescales. In contrast, repeated task performance and task performance feedback affect individual task investment. We propose an explicitly time-resolved individual-based model and simulate this model to study how patterns of individual task engagement influence task involvement at the group level, finding support for the hypothesis that regulation mechanisms at different timescales can improve performance at the group level in dynamic environments.
Infrastructure construction without information exchange: the trail clearing mechanism in Atta leafcutter ants
Proceedings of the Royal Society B, 2019
A wide range of group-living animals construct tangible infrastructure networks, often of remarka... more A wide range of group-living animals construct tangible infrastructure networks, often of remarkable size and complexity. In ant colonies, infrastructure construction may require tens of thousands of work hours distributed among many thousand individuals. What are the individual behaviours involved in the construction and what level of complexity in inter-individual interaction is required to organize this effort? We investigate this question in one of the most sophisticated trail builders in the animal world: the leafcutter ants, which remove leaf litter, cut through overhangs and shift soil to level the path of trail networks that may cumulatively extend for kilometres. Based on obstruction experiments in the field and the laboratory, we identify and quantify different individual trail clearing behaviours. Via a computational model, we further investigate the presence of recruitment, which—through direct or indirect information transfer between individuals—is one of the main organizing mechanisms of many collective behaviours in ants. We show that large-scale transport networks can emerge purely from the stochastic process of workers encountering obstructions and subsequently engaging in removal behaviour with a fixed probability. In addition to such incidental removal, we describe a dedicated clearing behaviour in which workers remove additional obstructions independent of chance encounters. We show that to explain the dynamics observed in the experiments, no information exchange (e.g. via recruitment) is required, and propose that large-scale infrastructure construction of this type can be achieved without coordination between individuals.
Optimal information transfer and stochastic resonance in collective decision making
Swarm Intelligence , 2017
Self-organised collective decision making is one of the core components of swarm intelligence, an... more Self-organised collective decision making is one of the core components of swarm intelligence, and numerous swarm algorithms that are widely used in optimisation and optimal control have been inspired by the biological mechanisms driving it. Beyond the life sciences and bio-inspired engineering, collective decision making is important in a number of other disciplines, most prominently economics and the social sciences. A paradigmatic model system for collective decision making is the foraging behaviour of mass recruiting ant colonies. While this system has been investigated extensively, our knowledge about its function in dynamic environments is still incomplete at best. We show that the mathematical model of mass foraging is really just a specific instance of a very general class of rational group decision making processes. We analyse this general class using an information-theoretic framework, which allows us to abstract from the specific details of a fixed model system. We specifically investigate how noisy communication can enable groups to share information about changes in an environment more efficiently. In the present paper, we show that an optimal noise level exists and that this optimal level depends on the rate of change in the environment. We explain this on the basis of stochastic resonance theory and show why stochastic attractor switching is a suitable base mechanism for adaptive group decision making in dynamic environments.
PLoS One, 2017
Self-organized mechanisms are frequently encountered in nature and known to achieve flexible, ada... more Self-organized mechanisms are frequently encountered in nature and known to achieve flexible, adaptive control and decision-making. Noise plays a crucial role in such systems: It can enable a self-organized system to reliably adapt to short-term changes in the environment while maintaining a generally stable behavior. This is fundamental in biological systems because they must strike a delicate balance between stable and flexible behavior. In the present paper we analyse the role of noise in the decision-making of the true slime mold Physarum polycephalum, an important model species for the investigation of computational abilities in simple organisms. We propose a simple biological experiment to investigate the reaction of P. polycephalum to time-variant risk factors and present a stochastic extension of an established mathematical model for P. polycephalum to analyze this experiment. It predicts that—due to the mechanism of stochastic resonance—noise can enable P. polycephalum to correctly assess time-variant risk factors, while the corresponding noise-free system fails to do so. Beyond the study of P. polycephalum we demonstrate that the influence of noise on self-organized decision-making is not tied to a specific organism. Rather it is a general property of the underlying process dynamics, which appears to be universal across a wide range of systems. Our study thus provides further evidence that stochastic resonance is a fundamental component of the decision-making in self-organized macroscopic and microscopic groups and organisms.
Energetics of trail clearing in the leaf-cutter ant Atta
Behavioral Ecology and Sociobiology, 2017
Few ant species construct cleared trails. Among those that do, leaf-cutting Atta ants build the m... more Few ant species construct cleared trails. Among those that do, leaf-cutting Atta ants build the most prominent networks, with single colonies clearing debris and obstructions from hundreds of meters of trails annually. Workers on cleared paths move at higher speed than they do over uncleared litter, and one measurement of the time and energetic costs of trail clearance suggests that benefits of trail usage far outweigh the investment costs of trail clearing. The ecological basis of trail clearing remains uncertain, however, because no full account has been made of benefits and costs in common units that allow comparison. We make such an account using a scalable, integrative model of trail investment and foraging energetics. Contrary to assumptions in previous work, we find that trail clearing needs not always be energetically profitable for leaf-cutting ants. Profitability depends on the workforce composition, specifically, on how many ants in a traffic stream act as maintenance workforce to respond to sudden and unpredictable obstructions, such as leaf fall. Such maintenance patrols have not previously been recognized as a cost of trail building. If the patrolling workforce is not too large, the energetic savings from foraging over cleared trails offset the investment and maintenance costs within a few days. Under some conditions, however, amortization can take weeks or months, or trail clearing can become unprofitable altogether. This suggests that Atta colonies must have a mechanism to regulate the intensity of their trail clearing behavior. We explore possible mechanisms and make testable predictions for future research.
Parallel foraging cycles for different resources in leaf-cutting ants: a clue to the mechanisms of rhythmic activity
Ecological Entomology, 2017
Leaf‐cutting ants display regular diel cycles of foraging, but the regulatory mechanisms underlyi... more Leaf‐cutting ants display regular diel cycles of foraging, but the regulatory mechanisms underlying these cycles are not well known. There are, however, some indications in the literature that accumulation of leaf tissue inside a nest dampens recruitment of foragers, thereby providing a negative feedback that can lead to periodic foraging. We investigated two foraging cycles occurring simultaneously in an Atta colombica colony, one involving leaf harvesting and the other exploiting an ephemeral crop of ripe fruit.
Leaf harvesting followed a typical diel pattern of a 10–12 h foraging bout followed by a period of inactivity, while fruit harvesting occurred continuously, but with a regular pre‐dawn dip in activity that marked a 24 h cycle.
Although the results of the present study are drawn from a single field colony, the difference found is consistent with a mechanism of negative feedback regulation acting in parallel on two resources that differ in their rates of distribution and processing, creating cycles of formation and depletion of material caches.
This hypothesis should provoke further interest from students of ant behaviour and some simple manipulative experiments that would begin to test it are outlined. Any role of resource caches in regulating foraging by Atta colonies may have similarities to the logistics of warehouse inventories in human economic activity.
Trail clearing behaviour in leaf-cutter ants: regulatory mechanism and stochastic simulation
Conference on Complex Systems, 2016
ALife XV Workshop on multidisciplinary applications of evolutionary game theory, 2016
We investigate the effects of social interactions in task al- location using Evolutionary Game Th... more We investigate the effects of social interactions in task al- location using Evolutionary Game Theory (EGT). We propose a simple task-allocation game and study how different learning mechanisms can give rise to specialised and non- specialised colonies under different ecological conditions. By combining agent-based simulations and adaptive dynamics we show that social learning can result in colonies of generalists or specialists, depending on ecological parameters. Agent-based simulations further show that learning dynamics play a crucial role in task allocation. In particular, introspective individual learning readily favours the emergence of specialists, while a process resembling task recruitment favours the emergence of generalists.
Int. Conf. on Bio-inspired Information and Communications Technologies (formerly BIONETICS), 2016
One of the main factors behind the amazing ecological success of social insects is their ability ... more One of the main factors behind the amazing ecological success of social insects is their ability to flexibly allocate the colony's workforce to all the different tasks it has to address. Insights into the self-organised task allocation methods used for this have given rise to the design of an important class of bio-inspired algorithms for network control, industrial optimisation, and other applications. The most widely used class of models for self-organised task allocation, which also forms the core of these algorithms, are response threshold models.
We revisit response threshold models with new experiments using temperature regulation in bumblebee colonies as the model system. We show that standard response threshold models do not fit our experiments and present an alternative behavioural model. This captures a fine-grained, time resolved picture of task engagement, which enables us to investigate task allocation with a different set of statistical methods. Using these we show that our model fits the experiment well and explains its salient aspects.
We compare the effectiveness of our model behaviour with that of response threshold models and demonstrate that it can lead to more efficient task management when demands fluctuate. Our results have the potential to provide a basis for the design of more efficient task allocation algorithms for dynamic environments and to elucidate important biological questions, such as the functional role of inter-individual variation.
Origin of high variability in colony odor representation in the ants' brain
11th Göttingen Meeting of the German Neuroscience Society, 2015
PLoS ONE, 2014
We present a unified approach to describing certain types of collective decision making in swarm ... more We present a unified approach to describing certain types of collective decision making in swarm robotics that bridges from a microscopic individual-based description to aggregate properties. Our approach encompasses robot swarm experiments, microscopic and probabilistic macroscopic-discrete simulations as well as an analytic mathematical model. Following up on previous work, we identify the symmetry parameter, a measure of the progress of the swarm towards a decision, as a fundamental integrated swarm property and formulate its time evolution as a continuous-time Markov process. Contrary to previous work, which justified this approach only empirically and a posterior,I, we justify it from first principles and drive hard limits on the parameter regime in which it is applicable
PLoS ONE, 2012
We present a method for mesoscopic, dynamic Monte Carlo simulations of pattern formation in excit... more We present a method for mesoscopic, dynamic Monte Carlo simulations of pattern formation in excitable reaction–diffusion systems. Using a two-level parallelization approach, our simulations cover the whole range of the parameter space, from the noise-dominated low-particle number regime to the quasi-deterministic high-particle number limit. Three qualitatively different case studies are performed that stand exemplary for the wide variety of excitable systems. We present mesoscopic stochastic simulations of the Gray-Scott model, of a simplified model for intracellular Ca2+ oscillations and, for the first time, of the Oregonator model. We achieve simulations with up to 10^10 particles. The software and the model files are freely available and researchers can use the models to reproduce our results or adapt and refine them for further exploration
PLoS ONE, 2012
For many biological applications, a macroscopic (deterministic) treatment of reaction-drift-diffu... more For many biological applications, a macroscopic (deterministic) treatment of reaction-drift-diffusion systems is insufficient. Instead, one has to properly handle the stochastic nature of the problem and generate true sample paths of the underlying probability distribution. Unfortunately, stochastic algorithms are computationally expensive and, in most cases, the large number of participating particles renders the relevant parameter regimes inaccessible. In an attempt to address this problem we present a genuine stochastic, multi-dimensional algorithm that solves the inhomogeneous, non-linear, drift-diffusion problem on a mesoscopic level. Our method improves on existing implementations in being multi-dimensional and handling inhomogeneous drift and diffusion. The algorithm is well suited for implementation on data-parallel hardware architectures such as general-purpose graphics processing units (GPUs). We integrate the method into an operator-splitting approach that decouples chemical reactions from the spatial evolution. We demonstrate the validity and applicability of our algorithm with a comprehensive suite of standard test problems that also serve to quantify the numerical accuracy of the method. We provide a freely available, fully functional GPU implementation. Integration into Inchman, a user-friendly web service, that allows researchers to perform parallel simulations of reaction-drift-diffusion systems on GPU clusters is underway.
Towards accessible tera-scale individual-based simulations of collective behaviour
European Conference on Complex Systems, 2011
Reaction-diffusion systems can be used to model a large variety of complex self-organized phenome... more Reaction-diffusion systems can be used to model a large variety of complex self-organized phenomena occurring in biological, chemical, and social systems.
The common macroscopic description of these systems, based on a Fokker-Planck equation (FPE), suffers from major limitations. Most importantly, it fails at low particle densities and it is impossible to incorporate individual-level experimental observations.
A microscopic Langevin-type individual-based description can – in principle – address these issues but is challenging and computationally expensive to the point that hardware limitations severely restrict their applicability to models of realistic size.
We present a graphics-processor accelerated stochastic simulation solver that obtains performance gains of up to two orders of magnitude even on workstations. We provide a versatile web-interface allowing researcher to perform complex experiments and parameter studies on a dedicated GPU cluster.
Bioinformatics, 2011
We present a massively parallel stochastic simulation algorithm (SSA) for reaction-diffusion syst... more We present a massively parallel stochastic simulation algorithm (SSA) for reaction-diffusion systems implemented on Graphics Processing Units (GPUs). These are designated chips optimized to process a high number of floating point operations in parallel, rendering them well-suited for a range of scientifichigh-performance computations. Newer GPU generations provide a high-level programming interface which turns them into General-Purpose Graphics Processing Units ( GPGPUs). Our SSA exploits GPGPU architecture to achieve a performance gain of two orders of magnitude over the fastest existing implementations on conventional hardware.
Estimation of time-variant risks by the slime mold Physarum polycephalum
European Conference on Complex Systems, 2010
Self-organized mechanisms are widely used in nature to achieve flexible, adaptive control and dec... more Self-organized mechanisms are widely used in nature to achieve flexible, adaptive control and decision-making. It has recently been shown that noise can play a crucial functional role in such systems. Essentially, noise can enable a self-organized system to reliably adapt to short-term changes in the environment while maintaining a generally stable behavior. This is fundamental in biological systems because they must strike a delicate balance between stable and flexible behavior. We investigate the question how noise influences the decision-making of the true slime mold Physarum polycephalum, an important model species for the investigation of computational abilities in simple organisms. We propose a simple biological experiment to investigate the reaction of P. polycephalum to time-variant risk factors. We present a stochastic extension of an established mathematical model for P. polycephalum to analyze this experiment. It predicts that noise can enable P. polycephalum to correctly assess time-variant risk factors, while the corresponding noise-free system fails to do so. Importantly, our analysis holds interest beyond the study of P. polycephalum. In conjunction with earlier work it demonstrates that the influence of noise on self-organized decision-making is not tied to a specific self-organized mechanism or its physical realization. Rather it is a general property of the underlying process dynamics, which appears to be universal across a wide range of systems. Our study thus provides further evidence that stochastic resonance is a fundamental component of the decision-making in self-organized macroscopic groups and organisms.
Lecture Notes in Computer Science, 2010
Symmetry breaking is commonly found in self-organized collective decision making. It serves an im... more Symmetry breaking is commonly found in self-organized collective decision making. It serves an important functional role, specifically in biological and bio-inspired systems. The analysis of symmetry breaking is thus an important key to understanding self-organized decision making. However, in many systems of practical importance avail-able analytic methods cannot be applied due to the complexity of the scenario and consequentially the model. This applies specifically to self-organization in bio-inspired engineering. We propose a new modelling approach which allows us to formally analyze important properties of such processes. The core idea of our approach is to infer a compact model based on stochastic processes for a one-dimensional symmetry parameter. This enables us to analyze the fundamental properties of even complex collective decision making processes via Fokker–Planck theory. We are able to quantitatively address the effectiveness of symmetry breaking, the stability, the time taken to reach a consensus, and other parameters. This is demonstrated with two examples from swarm robotics
Proceedings of the Royal Society B: Biological Sciences, 2009
Recruitment via pheromone trails by ants is arguably one of the best-studied examples of self-org... more 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.
A Tale of two Wells: Noise-Induced Adaptiveness in Self-Organized Systems
IEEE International Conference on Self-Adaptive and Self-Organizing Systems, 2008
One of the core aspects that make self-organized systems an interesting engineering paradigm is t... more One of the core aspects that make self-organized systems an interesting engineering paradigm is their potential to behave adaptively. Unravelling the fundamental mechanisms that drive this adaptiveness is of prime importance for understanding and designing such systems. The present paper demonstrates that noise is one of the core ingredients that enable self-organized systems to behave adaptively. This suggests that noise should be taken into account as a constructive component when engineering them. Our study analyses two different but closely related self-organized systems: a man-made system, Ant Colony Optimization algorithms (ACO), and real ant colonies, the natural system that inspired ACO. We demonstrate that the conventionally used mean-field analysis is not a correct description of their behavior in dynamic environments. This can only be achieved by a stochastic analysis that quantitatively takes noise into account. We present such an analysis based on Ito-Diffusions and Fokker-Planck equations and show it to be consistent with experimental data. Real ant colonies and ACO are both controlled by coupled self-limiting feedback loops. Decision making in such systems can be understood as stochastic attractor switching. This is the basis of our analysis. As coupled feedback mechanism are a universal control mechanism found in many types of self-organized systems, we expect our approach to be applicable to a vast array of other natural and man-made self-organized systems.
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Collective Behavior by Bernd Meyer
Leaf harvesting followed a typical diel pattern of a 10–12 h foraging bout followed by a period of inactivity, while fruit harvesting occurred continuously, but with a regular pre‐dawn dip in activity that marked a 24 h cycle.
Although the results of the present study are drawn from a single field colony, the difference found is consistent with a mechanism of negative feedback regulation acting in parallel on two resources that differ in their rates of distribution and processing, creating cycles of formation and depletion of material caches.
This hypothesis should provoke further interest from students of ant behaviour and some simple manipulative experiments that would begin to test it are outlined. Any role of resource caches in regulating foraging by Atta colonies may have similarities to the logistics of warehouse inventories in human economic activity.
We revisit response threshold models with new experiments using temperature regulation in bumblebee colonies as the model system. We show that standard response threshold models do not fit our experiments and present an alternative behavioural model. This captures a fine-grained, time resolved picture of task engagement, which enables us to investigate task allocation with a different set of statistical methods. Using these we show that our model fits the experiment well and explains its salient aspects.
We compare the effectiveness of our model behaviour with that of response threshold models and demonstrate that it can lead to more efficient task management when demands fluctuate. Our results have the potential to provide a basis for the design of more efficient task allocation algorithms for dynamic environments and to elucidate important biological questions, such as the functional role of inter-individual variation.
The common macroscopic description of these systems, based on a Fokker-Planck equation (FPE), suffers from major limitations. Most importantly, it fails at low particle densities and it is impossible to incorporate individual-level experimental observations.
A microscopic Langevin-type individual-based description can – in principle – address these issues but is challenging and computationally expensive to the point that hardware limitations severely restrict their applicability to models of realistic size.
We present a graphics-processor accelerated stochastic simulation solver that obtains performance gains of up to two orders of magnitude even on workstations. We provide a versatile web-interface allowing researcher to perform complex experiments and parameter studies on a dedicated GPU cluster.