Dynamical Models of Task Organization in Social Insect Colonies

Foraging dynamics in social insect colonies: Mechanisms of backward bifurcations and impacts of stochasticity

This investigation presents a two-dimensional collective foraging model alongside its stochastic counterpart, simplifying the previous more complex three-dimensional framework utilized to examine foraging behaviors within social insect colonies. We first conduct a thorough examination of the global dynamics of the deterministic model. The results show that the two-dimensional model exhibits equilibrium dynamics, with the possibility of coexistence between non-foraging and foraging equilibrium states. This finding highlights the parallelism between the two-dimensional model and the traditional three-dimensional framework. Following this, an extensive exploration into the long-term collective foraging dynamics within a stochastic environment is conducted, elucidating the interplay between stochasticity and the transitions across distinct stable foraging states. Additionally, the investigation assesses the risk of foraging cessation across varying initial worker populations, subsequently delineating foraging termination warning thresholds. The findings illuminate the multifaceted influence of environmental stochasticity on the collective foraging dynamics observed in harvester ant colonies. Grasping these dynamics furnishes valuable understanding of ecological resilience and the adaptive strategies deployed by collective entities in navigating environmental fluctuations.

Noise-Driven Transitions in Collective Foraging of Ant Colonies

Understanding the collective foraging strategies of ant colonies is essential for studying self-organization and collective behavior in biological systems. This study introduces a simplified foraging model that classifies worker roles into two functional groups-available workers and active foragers-providing a concise yet effective framework for analyzing foraging dynamics. Our model effectively reproduces the foraging dynamics observed in more complex three-dimensional models, while taking a more tractable form that is more conducive to mathematical analysis. We examine the effects of stochasticity in mortality rates of foragers and workers on foraging state transitions, with a particular emphasis on the critical noise threshold, transition probability, and transition time. While the critical noise threshold is reduced by stochasticity in either of the two mortality rates, that of active foragers has the greatest effect. We find that slight increases in the arrival rate of available workers and the recruitment rate of active foragers enhance the colony's resilience to environmental stochasticity, suggesting that colonies can self-regulate via a feedback loop of foraging and recruitment to maintain their foraging while their environment changes around them. In contrast, varying the mortality rate of available workers had little effect on this resilience, analogously to experimental observations that older or unhealthy worker ants disproportionately transition into foraging roles. This study not only advances our understanding of ant foraging dynamics by simplifying complex models but also provides valuable insights into the robustness of foraging activities under varying environmental conditions.

A quantitative Apis mellifera hazard and risk assessment model (AMHRA) illustrated with the insecticide sulfoxaflor: sulfoxaflor environmental science review part VI

In this paper, conceptual models of the exposure pathways outside the hive and the in-hive distribution of pesticide residues brought to the honeybee hive are presented. The conceptual model is based on the natural life history, behavior and diet of individual honeybees (Apis mellifera). Receptor groups of bees with similar diets and potential exposure are defined. From the conceptual model, a quantitative A. mellifera hazard and risk assessment model (AMHRA) is developed and illustrated using sulfoxaflor (SFX) as a case study. The model estimates the exposure of the receptor groups of honeybees within a colony via various routes of exposure. The user selects a deterministic mode to obtain hazard quotients (HQ) or a probabilistic mode to obtain risk quotients (RQ). The model was run in the deterministic mode using the pesticide concentrations in nectar and pollen from a field experiment in which SFX was applied to cotton crops at the highest permitted application rate of 101 g a.i. ha-1. Acute and chronic exposure HQ values were calculated for the adult and larval receptor groups. The results showed that the SFX applied at the highest single application rate following the label directions was not hazardous to honeybees. The probabilistic mode was described but not run.

Spatiotemporal organization of ant foraging from a complex systems perspective

We use complex systems science to explore the emergent behavioral patterns that typify eusocial species, using collective ant foraging as a paradigmatic example. Our particular aim is to provide a methodology to quantify how the collective orchestration of foraging provides functional advantages to ant colonies. For this, we combine (i) a purpose-built experimental arena replicating ant foraging across realistic spatial and temporal scales, and (ii) a set of analytical tools, grounded in information theory and spin-glass approaches, to explore the resulting data. This combined approach yields computational replicas of the colonies; these are high-dimensional models that store the experimental foraging patterns through a training process, and are then able to generate statistically similar patterns, in an analogous way to machine learning tools. These in silico models are then used to explore the colony performance under different resource availability scenarios. Our findings highlight how replicas of the colonies trained under constant and predictable experimental food conditions exhibit heightened foraging efficiencies, manifested in reduced times for food discovery and gathering, and accelerated transmission of information under similar conditions. However, these same replicas demonstrate a lack of resilience when faced with new foraging conditions. Conversely, replicas of colonies trained under fluctuating and uncertain food conditions reveal lower efficiencies at specific environments but increased resilience to shifts in food location.

Unraveling the forces shaping foraging dynamics in harvester ant colonies: Recruitment efficiency and environmental variability

The collective foraging behavior of ant colonies is a central focus in behavioral ecology. This paper enhances the classical model of foraging dynamics in harvester ant colonies by introducing a nonlinear recruitment rate and considering environmental variability. Initially, we analyze the existence and stability of steady states in the deterministic model. The results suggest that an increase in mean recruitment time can reduce the foraging threshold, leading to both forward and backward bifurcations. Furthermore, both average recruitment time and the interference intensity of recruiters impact the number of workers in each subgroup. Subsequently, we conduct an analysis of the long-term and transient dynamics of collective foraging in random environments, providing sufficient conditions for the colony to sustain foraging activity. The findings emphasize the scene-dependent impact of environmental stochasticity on foraging dynamics. When ant colonies deterministically cease foraging, environmental stochasticity may unexpectedly prolong the foraging state. Conversely, when colonies deterministically persist in foraging, environmental stochasticity may disrupt this continuity. Additionally, the effect of environmental stochasticity on foraging status varies with the initial worker size. Sizes near the boundary of the basin of attraction between non-foraging and foraging states exhibit greater sensitivity to environmental stochasticity, and sufficiently large stochasticity can impact foraging dynamics across a broader range of initial worker sizes. These findings underscore the intricate interplay between intrinsic factors (e.g., recruitment efficiency and interference intensity) and extrinsic factors (e.g., environmental stochasticity) in shaping the collective foraging dynamics of ant colonies.

A modeling framework for adaptive collective defense: crisis response in social-insect colonies

Living systems, from cells to superorganismic insect colonies, have an organizational boundary between inside and outside and allocate resources to defend it. Whereas the micro-scale dynamics of cell walls can be difficult to study, the adaptive allocation of workers to defense in social-insect colonies is more conspicuous. This is particularly the case for Tetragonisca angustula stingless bees, which combine different defensive mechanisms found across other colonial animals: (1) morphological specialization (distinct soldiers (majors) are produced over weeks); (2) age-based polyethism (young majors transition to guarding tasks over days); and (3) task switching (small workers (minors) replace soldiers within minutes under crisis). To better understand how these timescales of reproduction, development, and behavior integrate to balance defensive demands with other colony needs, we developed a demographic Filippov ODE system to study the effect of these processes on task allocation and colony size. Our results show that colony size peaks at low proportions of majors, but colonies die if minors are too plastic or defensive demands are too high or if there is a high proportion of quickly developing majors. For fast maturation, increasing major production may decrease defenses. This model elucidates the demographic factors constraining collective defense regulation in social insects while also suggesting new explanations for variation in defensive allocation at smaller scales where the mechanisms underlying defensive processes are not easily observable. Moreover, our work helps to establish social insects as model organisms for understanding other systems where the transaction costs for component turnover are nontrivial, as in manufacturing systems and just-in-time supply chains.

Variation in environmental stochasticity dramatically affects viability and extinction time in a predator-prey system with high prey group cohesion

Understanding how tipping points arise is critical for population protection and ecosystem robustness. This work evaluates the impact of environmental stochasticity on the emergence of tipping points in a predator-prey system subject to the Allee effect and Holling type IV functional response, modeling an environment in which the prey has high group cohesion. We analyze the relationship between stochasticity and the probability and time that predator and prey populations in our model tip between different steady states. We evaluate the safety from extinction of different population values for each species, and accordingly assign extinction warning levels to these population values. Our analysis suggests that the effects of environmental stochasticity on tipping phenomena are scenario-dependent but follow a few interpretable trends. The probability of tipping towards a steady state in which one or both species go extinct generally monotonically increased with noise intensity, while the probability of tipping towards a more favorable steady state (in which more species were viable) usually peaked at intermediate noise intensity. For tipping between two equilibria where a given species was at risk of extinction in one equilibrium but not the other, noise affecting that species had greater impact on tipping probability than noise affecting the other species. Noise in the predator population facilitated quicker tipping to extinction equilibria, whereas prey noise instead often slowed down extinction. Changes in warning level for initial population values due to noise were most apparent near attraction basin boundaries, but noise of sufficient magnitude (especially in the predator population) could alter risk even far away from these boundaries. Our model provides critical theoretical insights for the conservation of population diversity: management criteria and early warning signals can be developed based on our results to keep populations away from destructive critical thresholds.

Social Learning versus Individual Learning in the Division of Labour

Division of labour, or the differentiation of the individuals in a collective across tasks, is a fundamental aspect of social organisations, such as social insect colonies. It allows for efficient resource use and improves the chances of survival for the entire collective. The emergence of large inactive groups of individuals in insect colonies sometimes referred to as laziness, has been a puzzling and hotly debated division-of-labour phenomenon in recent years that is counter to the intuitive notion of effectiveness. It has previously been shown that inactivity can be explained as a by-product of social learning without the need to invoke an adaptive function. While highlighting an interesting and important possibility, this explanation is limited because it is not yet clear whether the relevant aspects of colony life are governed by social learning. In this paper, we explore the two fundamental types of behavioural adaptation that can lead to a division of labour, individual learning and social learning. We find that inactivity can just as well emerge from individual learning alone. We compare the behavioural dynamics in various environmental settings under the social and individual learning assumptions, respectively. We present individual-based simulations backed up by analytic theory, focusing on adaptive dynamics for the social paradigm and cross-learning for the individual paradigm. We find that individual learning can induce the same behavioural patterns previously observed for social learning. This is important for the study of the collective behaviour of social insects because individual learning is a firmly established paradigm of behaviour learning in their colonies. Beyond the study of inactivity, in particular, the insight that both modes of learning can lead to the same patterns of behaviour opens new pathways to approach the study of emergent patterns of collective behaviour from a more generalised perspective.

Explaining workers' inactivity in social colonies from first principles

Social insects are among the ecologically most successful collectively living organisms, with efficient division of labour a key feature of this success. Surprisingly, these efficient colonies often have a large proportion of inactive workers in their workforce, sometimes referred to as lazy workers. The dominant hypotheses explaining this are based on specific life-history traits, specific behavioural features or uncertain environments where inactive workers can provide a 'reserve' workforce that can spring into action quickly. While there is a number of experimental studies that show and investigate the presence of inactive workers, mathematical and computational models exploring specific hypotheses are not common. Here, using a simple mathematical model, we show that a parsimonious hypothesis can explain this puzzling social phenomenon. Our model incorporates social interactions and environmental influences into a game-theoretical framework and captures how individuals react to environment by allocating their activity according to environmental conditions. This model shows that inactivity can emerge under specific environmental conditions as a by-product of the task allocation process. Our model confirms the empirical observation that in the case of worker loss, prior homeostatic balance is re-established by replacing some of the lost force with previously inactive workers. Most importantly, our model shows that inactivity in social colonies can be explained without the need to assume an adaptive function for this phenomenon.

When being flexible matters: Ecological underpinnings for the evolution of collective flexibility and task allocation

A central problem in evolutionary biology is explaining variation in the organization of task allocation across collective systems. Why do human cells irreversibly adopt a task during development (e.g., kidney vs. liver cell), while sponge cells switch between different cell types? And why have only some ant species evolved specialized castes of workers for particular tasks? Although it seems reasonable to suppose that such differences reflect, at least partially, the different ecological pressures that systems face, there is no general understanding of how a system’s dynamic environment shapes its task allocation. To this end, we develop a general mathematical framework that reveals how simple ecological considerations could potentially explain cross-system variation in task allocation—including in flexibility, specialization, and (in)activity.

Task allocation is a central feature of collective organization. Living collective systems, such as multicellular organisms or social insect colonies, have evolved diverse ways to allocate individuals to different tasks, ranging from rigid, inflexible task allocation that is not adjusted to changing circumstances to more fluid, flexible task allocation that is rapidly adjusted to the external environment. While the mechanisms underlying task allocation have been intensely studied, it remains poorly understood whether differences in the flexibility of task allocation can be viewed as adaptive responses to different ecological contexts—for example, different degrees of temporal variability. Motivated by this question, we develop an analytically tractable mathematical framework to explore the evolution of task allocation in dynamic environments. We find that collective flexibility is not necessarily always adaptive, and fails to evolve in environments that change too slowly (relative to how long tasks can be left unattended) or too quickly (relative to how rapidly task allocation can be adjusted). We further employ the framework to investigate how environmental variability impacts the internal organization of task allocation, which allows us to propose adaptive explanations for some puzzling empirical observations, such as seemingly unnecessary task switching under constant environmental conditions, apparent task specialization without efficiency benefits, and high levels of individual inactivity. Altogether, this work provides a general framework for probing the evolved diversity of task allocation strategies in nature and reinforces the idea that considering a system’s ecology is crucial to explaining its collective organization.

Wolf Pack's Role Matching Labor Division Model for Dynamic Task Allocation of Swarm Robotics

First, through in-depth analysis of the diversified collective behaviors in wolf pack, this study summarizes four remarkable features of wolf pack's labor division. Second, the wolf pack's role-task matching labor division mechanism is investigated, namely the individual wolves perform specific tasks that match their respective roles, and then a novel role matching labor division model is proposed. Finally, the performances of RMM are tested and evaluated with two swarm robotics task allocation scenarios. It is proved that RMM has higher solving efficiency and faster calculation speed for the concerned problem than the compared approach. Moreover, the proposed model shows advantages in the task allocation balance, robustness, and real time, especially in the dynamic response capability to the complex and changing environments.

Movement, Encounter Rate, and Collective Behavior in Ant Colonies

Spatial patterns of movement regulate many aspects of social insect behavior, because how workers move around, and how many are there, determines how often they meet and interact. Interactions are usually olfactory; for example, in ants, by means of antennal contact in which one worker assesses the cuticular hydrocarbons of another. Encounter rates may be a simple outcome of local density: a worker experiences more encounters, the more other workers there are around it. This means that encounter rate can be used as a cue for overall density even though no individual can assess global density. Encounter rate as a cue for local density regulates many aspects of social insect behavior, including collective search, task allocation, nest choice, and traffic flow. As colonies grow older and larger, encounter rates change, which leads to changes in task allocation. Nest size affects local density and movement patterns, which influences encounter rate, so that nest size and connectivity influence colony behavior. However, encounter rate is not a simple function of local density when individuals change their movement in response to encounters, thus influencing further encounter rates. Natural selection on the regulation of collective behavior can draw on variation within and among colonies in the relation of movement patterns, encounter rate, and response to encounters.

Nutritional regulation influencing colony dynamics and task allocations in social insect colonies

In this paper, we use an adaptive modeling framework to model and study how nutritional status (measured by the protein to carbohydrate ratio) may regulate population dynamics and foraging task allocation of social insect colonies. Mathematical analysis of our model shows that both investment to brood rearing and brood nutrition are important for colony survival and dynamics. When division of labour and/or nutrition are in an intermediate value range, the model undergoes a backward bifurcation and creates multiple attractors due to bistability. This bistability implies that there is a threshold population size required for colony survival. When the investment in brood is large enough or nutritional requirements are less strict, the colony tends to survive, otherwise the colony faces collapse. Our model suggests that the needs of colony survival are shaped by the brood survival probability, which requires good nutritional status. As a consequence, better nutritional status can lead to a better survival rate of larvae and thus a larger worker population.

Dynamics of task allocation in social insect colonies: scaling effects of colony size versus work activities

The mechanisms through which work is organized are central to understanding how complex systems function. Previous studies suggest that task organization can emerge via nonlinear dynamical processes wherein individuals interact and modify their behavior through simple rules. However, there is very limited theory about how those processes are shaped by behavioral variation within social groups. In this work, we propose an adaptive modeling framework on task allocation by incorporating variation both in task performance and task-related metabolic rates. We study the scaling effects of colony size on the resting probability as well as task allocation. We also numerically explore the effects of stochastic noise on task allocation in social insect colonies. Our theoretical and numerical results show that: (a) changes in colony size can regulate the probability of colony resting and the allocation of tasks, and the direction of regulation depends on the nonlinear metabolic scaling effects of tasks; (b) increased response thresholds may cause colonies to rest in varied patterns such as periodicity. In this case, we observed an interesting bubble phenomenon in the task allocation of social insect colonies for the first time; (c) stochastic noise can cause work activities and task demand to fluctuate within a range, where the amplitude of the fluctuation is positively correlated with the intensity of noise.

A spatial model of honey bee colony collapse due to pesticide contamination of foraging bees

We develop a model of honey bee colony collapse based on contamination of forager bees in pesticide contaminated spatial environments. The model consists of differential and difference equations for the spatial distributions of the uncontaminated and contaminated forager bees. A key feature of the model is incorporation of the return to the hive each day of forager bees. The model quantifies colony collapse in terms of two significant properties of honey bee colonies: (1) the fraction of contaminated forager bees that fail to return home due to pesticide contamination, and (2) the fraction of forager bees in the total forager bee population that return to the sites visited on the previous day. If the fraction of contaminated foragers failing to return home is high, then the total population falls below a critical threshold and colony collapse ensues. If the fraction of all foragers that return to previous foraging sites is high, then foragers who visit contaminated sites multiple times have a higher probability of becoming contaminated, and colony collapse ensues. This quantification of colony collapse provides guidance for implementing measures for its avoidance.

How Approaches to Animal Swarm Intelligence Can Improve the Study of Collective Intelligence in Human Teams

Researchers of team behavior have long been interested in the essential components of effective teamwork. Much existing research focuses on examining correlations between team member traits, team processes, and team outcomes, such as collective intelligence or team performance. However, these approaches are insufficient for providing insight into the dynamic, causal mechanisms through which the components of teamwork interact with one another and impact the emergence of team outcomes. Advances in the field of animal behavior have enabled a precise understanding of the behavioral mechanisms that enable groups to perform feats that surpass the capabilities of the individuals that comprise them. In this manuscript, we highlight how studies of animal swarm intelligence can inform research on collective intelligence in human teams. By improving the ability to obtain precise, time-varying measurements of team behaviors and outcomes and building upon approaches used in studies of swarm intelligence to analyze and model individual and group-level behaviors, researchers can gain insight into the mechanisms underlying the emergence of collective intelligence. Such understanding could inspire targeted interventions to improve team effectiveness and support the development of a comparative framework of group-level intelligence in animal and human groups.

A computational model of task allocation in social insects: ecology and interactions alone can drive specialisation

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.

The Ecology of Collective Behavior in Ants

Nest choice in Temnothorax spp.; task allocation and the regulation of activity in Pheidole dentata, Pogonomyrmex barbatus, and Atta spp.; and trail networks in Monomorium pharaonis and Cephalotes goniodontus all provide examples of correspondences between the dynamics of the environment and the dynamics of collective behavior. Some important aspects of the dynamics of the environment include stability, the threat of rupture or disturbance, the ratio of inflow and outflow of resources or energy, and the distribution of resources. These correspond to the dynamics of collective behavior, including the extent of amplification, how feedback instigates and inhibits activity, and the extent to which the interactions that provide the information to regulate behavior are local or spatially centralized.