Neural networks as mechanisms to regulate division of labor

In social insects, workers perform a multitude of tasks, such as foraging, nest construction, and brood rearing, without central control of how work is allocated among individuals. It has been suggested that workers choose a task by responding to stimuli gathered from the environment. Response-threshold models assume that individuals in a colony vary in the stimulus intensity (response threshold) at which they begin to perform the corresponding task. Here we highlight the limitations of these models with respect to colony performance in task allocation. First, we show with analysis and quantitative simulations that the deterministic response-threshold model constrains the workers' behavioral flexibility under some stimulus conditions. Next, we show that the probabilistic response-threshold model fails to explain precise colony responses to varying stimuli. Both of these limitations would be detrimental to colony performance when dynamic and precise task allocation is needed. To address these problems, we propose extensions of the response-threshold model by adding variables that weigh stimuli. We test the extended response-threshold model in a foraging scenario and show in simulations that it results in an efficient task allocation. Finally, we show that response-threshold models can be formulated as artificial neural networks, which consequently provide a comprehensive framework for modeling task allocation in social insects.     

Ventilation response thresholds do not change with age or self-reinforcement in workers of the bumble bee Bombus impatiens

The response threshold model is a potential mechanism for task allocation in social insects, and it assumes that workers vary in the levels of task stimuli to which they respond. Furthermore, response thresholds of individual workers may change over time through self-reinforcement (experience), such that workers become more sensitive to task stimuli. However, in addition to self-reinforcement, aging is another process that occurs through time. Distinguishing whether response thresholds change within workers due to self-reinforcement or aging may give insight into the flexibility of this task allocation mechanism. Using a ventilation paradigm, we manipulated workers of Bombus impatiens to have either repeated or lack of exposures to increases in nest air temperature, thereby allowing us to manipulate experience and thus self-reinforcement. Nest air temperature was the task stimulus, and ventilation (fanning) was the behavioral response. We found that ventilation response thresholds do not decrease either with age or experience in workers of B. impatiens, contrary to what has been reported for B. terrestris workers (Weidenmüller, 2004). Instead, we found high levels of intra-individual variation in response thresholds. Our results also show that workers with lower average response thresholds respond to heating events with higher probability than those with higher ventilation thresholds. These results provide insight into the role of the response threshold framework for task allocation; we also discuss how response probabilities may play a role in task allocation among workers.     

Thresholds of Response in Nest Thermoregulation by Worker Bumble Bees, Bombus bifarius nearcticus (Hymenoptera: Apidae)

Regulation of nest temperature is important to the fitness of eusocial insect colonies. To maintain appropriate conditions for the developing brood, workers must exhibit thermoregulatory responses to ambient temperature. Because nest-mate workers differ in task performance, thermoregulatory behavior provides an opportunity to test threshold of response models for the regulation of division of labor. We found that worker bumble bees ( Bombus bifarius nearcticus ) responded to changes in ambient temperature by altering their rates of performing two tasks – wing fanning and brood cell incubation. At the colony level, the rate of incubating decreased, and the rate of fanning increased, with increasing temperature. Changes in the number of workers performing these tasks were more important to the colony response than changes in workers' task performance rates. At the individual level, workers' lifetime rates of incubation and fanning were positively correlated, and most individuals did not specialize exclusively on either of these temperature-sensitive tasks. However, workers differed in the maximum temperature at which they incubated and in the minimum temperature at which they fanned. More individuals fanned at high and incubated at low temperatures. Most of the workers that began incubating at higher temperatures continued performing this task at lower temperatures, when additional nest-mates became active. The converse was true for fanning behavior. These data are consistent with a threshold of response model for thermoregulatory behavior of B. bifarius workers.     

The role of genetic diversity in nest cooling in a wild honey bee, Apis florea

Simulation studies of the task threshold model for task allocation in social insect colonies suggest that nest temperature homeostasis is enhanced if workers have slightly different thresholds for engaging in tasks related to nest thermoregulation. Genetic variance in task thresholds is one way a distribution of task thresholds can be generated. Apis mellifera colonies with large genetic diversity are able to maintain more stable brood nest temperatures than colonies that are genetically uniform. If this phenomenon is generalizable to other species, we would predict that patrilines should vary in the threshold in which they engage in thermoregulatory tasks. We exposed A. florea colonies to different temperatures experimentally, and retrieved fanning workers at these different temperatures. In many cases we found statistically significant differences in the proportion of fanning workers of different patrilines at different experimental temperatures. This suggests that genetically different workers have different thresholds for performing the thermoregulatory task of fanning. We suggest, therefore, that genetically based variance in task threshold is a widespread phenomenon in the genus Apis.     

Regulation of Brood-Care Behavior in the Dimorphic Castes of the Ant Pheidole morrisi (Hymenoptera: Formicidae): Effects of Caste Ratio, Colony Size, and Colony Needs

This study examines the social stimuli that regulate brood-care behavior in the two physical castes of the ant Pheidole morrisi. By increasing the proportion of major workers in a colony, brood-care behavior could be induced in individuals of this caste, which do not normally care for brood. Minor and major worker brood-care rates increased with the proportion of majors in the colony or as the need for brood care increased. Changes in colony size did not significantly affect the rate of either minor or major brood care. Major workers began to care for brood when the caste ratio reached a critical threshold but did not appear to be as efficient at rearing larvae as minor workers, which normally perform this task. After a perturbation that skewed the caste ratio toward majors, minor workers increased their rate of brood care, apparently to compensate for the inefficiency of brood care provided by majors. These results suggest that caste plasticity involves a social mechanism of ldquo;coupled compensation that maintains the efficiency of labor by ensuring that tasks are completed.     

Ants in a labyrinth: a statistical mechanics approach to the division of labour

Division of labour (DoL) is a fundamental organisational principle in human societies, within virtual and robotic swarms and at all levels of biological organisation. DoL reaches a pinnacle in the insect societies where the most widely used model is based on variation in response thresholds among individuals, and the assumption that individuals and stimuli are well-mixed. Here, we present a spatially explicit model of DoL. Our model is inspired by Pierre de Gennes' 'Ant in a Labyrinth' which laid the foundations of an entire new field in statistical mechanics. We demonstrate the emergence, even in a simplified one-dimensional model, of a spatial patterning of individuals and a right-skewed activity distribution, both of which are characteristics of division of labour in animal societies. We then show using a two-dimensional model that the work done by an individual within an activity bout is a sigmoidal function of its response threshold. Furthermore, there is an inverse relationship between the overall stimulus level and the skewness of the activity distribution. Therefore, the difference in the amount of work done by two individuals with different thresholds increases as the overall stimulus level decreases. Indeed, spatial fluctuations of task stimuli are minimised at these low stimulus levels. Hence, the more unequally labour is divided amongst individuals, the greater the ability of the colony to maintain homeostasis. Finally, we show that the non-random spatial distribution of individuals within biological and social systems could be caused by indirect (stigmergic) interactions, rather than direct agent-to-agent interactions. Our model links the principle of DoL with principles in the statistical mechanics and provides testable hypotheses for future experiments.     

The role of competition in task switching during colony emigration in the ant Leptothorax albipennis

The decision-making process that determines when an animal should switch between tasks is a fundamental issue in the study of animal behaviour. We investigated, for the first time, such task switching in terms of the dynamics of worker populations in ant colonies. During colony emigration in the ant Leptothorax albipennis, the colony has to carry out the following three tasks: (1) transport of brood and nestmates to the new nest; (2) sorting of the brood into its characteristic pattern; and (3) building the nest wall. At the beginning of the emigration, the stimuli for all three tasks increase simultaneously but the tasks are performed sequentially by populations of workers in the colony. The issue here is how decision making at the colony level is based on the behaviour of individual workers. We used a mathematical model to explore the hypothesis that such colony level task switching is based on tasks competing for workers. The essential feature of this model is that the sequence of tasks performed by an individual worker need not match the sequence of tasks on which the colony concentrates. We base the parameterization of our model on our detailed experimental study of eight emigrations, one for each of eight L. albipennis colonies. We compared our results with earlier work that emphasizes the role of response thresholds in task-related decisions. Copyright 2002 The Association for the Study of Animal Behaviour. Published by Elsevier Science Ltd. All rights reserved.     

Differences in the sensations of warmth on the anterior torso of normal and spinal-cord transected individuals

The threshold to warming was measured at 10 sites on the anterior torso between the umbilicus and the clavicle of normal and spinal-cord transected individuals. In normal individuals, thresholds were higher on the thorax than on the abdomen. Men had higher and more variable thresholds than women. Magnitude estimations of supra-threshold stimuli showed that men offer verbal estimates of warmth that are about half of the size of the estimates given by women to the same stimuli. The psychometric function shows that in women, the sensation of warmth grows more rapidly than in men after starting from a higher initial value. After spinal-cord injury, thresholds for detection of warming were elevated. This effect was most noticeable within 8 cm of the anesthetic zone, but farther away, thresholds were still elevated but uniform as a function of distance, being about 30% higher than in normal individuals. After spinal-cord injury, the psychometric functions show that small stimuli elicit relatively large sensations and that these sensations grow more slowly with increasing skin temperatures than for normal individuals. Thus, for small warm stimuli spinal-cord-injured patients (both men and women) have a response similar to normal women but the slope of the psychometric function is flat, being similar to the slope observed for normal men.     

Differences in the sensations of warmth on the anterior torso of normal and spinal-cord transected individuals

The threshold to warming was measured at 10 sites on the anterior torso between the umbilicus and the clavicle of normal and spinal-cord transected individuals. In normal individuals, thresholds were higher on the thorax than on the abdomen. Men had higher and more variable thresholds than women. Magnitude estimations of supra-threshold stimuli showed that men offer verbal estimates of warmth that are about half of the size of the estimates given by women to the same stimuli. The psychometric function shows that in women, the sensation of warmth grows more rapidly than in men after starting from a higher initial value. After spinal-cord injury, thresholds for detection of warming were elevated. This effect was most noticeable within 8 cm of the anesthetic zone, but farther away, thresholds were still elevated but uniform as a function of distance, being about 30% higher than in normal individuals. After spinal-cord injury, the psychometric functions show that small stimuli elicit relatively large sensations and that these sensations grow more slowly with increasing skin temperatures than for normal individuals. Thus, for small warm stimuli spinal-cord-injured patients (both men and women) have a response similar to normal women but the slope of the psychometric function is flat, being similar to the slope observed for normal men.     

Colony size affects collective decision-making in the ant Temnothorax albipennis

Social insects are well-known for their ability to achieve robust collective behaviours even when individuals have limited information. It is often assumed that such behaviours rely on very large group sizes, but many insect colonies start out with only a few workers. Here we investigate the influence of colony size on collective decision-making in the house-hunting of the ant Temnothorax albipennis. In experiments where colony size was manipulated by splitting colonies, we show that worker number has an influence on the speed with which colonies discover new nest sites, but not on the time needed to make a decision (achieve a quorum threshold) or total emigration time. This occurred because split colonies adopted a lower quorum threshold, in fact they adopted the same threshold in proportion to their size as full-size colonies. This indicates that ants may be measuring relative quorum, i.e. population in the new nest relative to that of the old nest, rather than the absolute number. Experimentally reduced colonies also seemed to gain more from experience through repeated emigrations, as they could then reduce nest discovery times to those of larger colonies. In colonies of different sizes collected from the field, total emigration time was also not correlated with colony size. However, quorum threshold was not correlated with colony size, meaning that individuals in larger colonies adopted relatively lower quorum thresholds. Since this is a different result to that from size-manipulated colonies, it strongly suggests that the differences between natural small and large colonies were not caused by worker number alone. Individual ants may have adjusted their behaviour to their colony’s size, or other factors may correlate with colony size in the field. Our study thus shows the importance of experimentally manipulating colony size if the effect of worker number on the emergence of collective behaviour is to be studied. Received 13 December 2005; revised 9 May 2006; accepted 15 May 2006.     

Division of labour and colony efficiency in social insects: effects of interactions between genetic architecture, colony kin structure and rate of perturbations

The efficiency of social insect colonies critically depends on their ability to efficiently allocate workers to the various tasks which need to be performed. While numerous models have investigated the mechanisms allowing an efficient colony response to external changes in the environment and internal perturbations, little attention has been devoted to the genetic architecture underlying task specialization. We used artificial evolution to compare the performances of three simple genetic architectures underlying within-colony variation in response thresholds of workers to five tasks. In the 'deterministic mapping' system, the thresholds of individuals for each of the five tasks is strictly genetically determined. In the second genetic architecture ('probabilistic mapping'), the genes only influence the probability of engaging in one of the tasks. Finally, in the 'dynamic mapping' system, the propensity of workers to engage in one of the five tasks depends not only on their own genotype, but also on the behavioural phenotypes of other colony members. We found that the deterministic mapping system performed well only when colonies consisted of unrelated individuals and were not subjected to perturbations in task allocation. The probabilistic mapping system performed well for colonies of related and unrelated individuals when there were no perturbations. Finally, the dynamic mapping system performed well under all conditions and was much more efficient than the two other mapping systems when there were perturbations. Overall, our simulations reveal that the type of mapping between genotype and individual behaviour greatly influences the dynamics of task specialization and colony productivity. Our simulations also reveal complex interactions between the mode of mapping, level of within-colony relatedness and risk of colony perturbations.     

Reappraising Social Insect Behavior through Aversive Responsiveness and Learning

Background

The success of social insects can be in part attributed to their division of labor, which has been explained by a response threshold model. This model posits that individuals differ in their response thresholds to task-associated stimuli, so that individuals with lower thresholds specialize in this task. This model is at odds with findings on honeybee behavior as nectar and pollen foragers exhibit different responsiveness to sucrose, with nectar foragers having higher response thresholds to sucrose concentration. Moreover, it has been suggested that sucrose responsiveness correlates with responsiveness to most if not all other stimuli. If this is the case, explaining task specialization and the origins of division of labor on the basis of differences in response thresholds is difficult.

Methodology

To compare responsiveness to stimuli presenting clear-cut differences in hedonic value and behavioral contexts, we measured appetitive and aversive responsiveness in the same bees in the laboratory. We quantified proboscis extension responses to increasing sucrose concentrations and sting extension responses to electric shocks of increasing voltage. We analyzed the relationship between aversive responsiveness and aversive olfactory conditioning of the sting extension reflex, and determined how this relationship relates to division of labor.

Principal Findings

Sucrose and shock responsiveness measured in the same bees did not correlate, thus suggesting that they correspond to independent behavioral syndromes, a foraging and a defensive one. Bees which were more responsive to shock learned and memorized better aversive associations. Finally, guards were less responsive than nectar foragers to electric shocks, exhibiting higher tolerance to low voltage shocks. Consequently, foragers, which are more sensitive, were the ones learning and memorizing better in aversive conditioning.

Conclusions

Our results constitute the first integrative study on how aversive responsiveness affects learning, memory and social organization in honeybees. We suggest that parallel behavioral modules (e.g. appetitive, aversive) coexist within each individual bee and determine its tendency to adopt a given task. This conclusion, which is at odds with a simple threshold model, should open new opportunities for exploring the division of labor in social insects.     

Worker connectivity: a simulation model of variation in worker communication and its effects on task performance

We develop a simulation model of worker connectivity to analyze how variation in worker communication can influence task performance. The model generates predictions about how colony demography, worker communicative behavior, and worker cognition will affect the rate of recruitment of workers to a new task. The model explores some mechanisms for modulating the recruitment of workers. Under the conditions of our model– probabilistic interactions that lower worker’s response thresholds to tasks– worker recruitment follows a logistic growth pattern. The rate of recruiting workers increases exponentially toward an inflection point when 50% of the available force has been activated, then decreases toward the upper asymptote (all workers recruited). Many relevant features of colony design and worker behavior, including group size, probability of interacting, and strength of interaction effects on receivers, show a positive but decelerating effect on the rate of worker recruitment. We also identify features of worker cognition that can influence task recruitment, focusing on the time course of worker’s memories about previous interactions. Both learning (e.g., sensitization) and forgetting about previous interactions can influence the rate of worker recruitment to a task. The model suggests that worker cognition may be shaped by natural selection on task performance at the colony level. Forgetting about interactions may be especially costly, because it leads to unpredictable patterns of worker recruitment. We also show that social inhibition, when coupled with excitatory interactions, can effectively modulate worker recruitment at the colony level. Received 9 December 2006; revised 23 May 2007; accepted 30 May 2007.     

The control of nest climate in bumblebee (Bombus terrestris) colonies: interindividual variability and self reinforcement in fanning response

Interindividual variability in response to environmental stimuliis believed to have a major impact on collective behaviors insocial insects. The present study presents a detailed investigationof the variability in individual fanning behavior underlyingthe collective control of nest climate in bumblebee (Bombusterrestris) colonies. Four colonies were repeatedly exposedto increasing temperature and CO₂ levels. The response thresholdof each worker (defined as the mean stimulus intensity at whicha worker responded by fanning) was determined. Temperature responsethresholds of 118 workers and CO₂ response thresholds of 88workers were analyzed. Workers differed in their response thresholds.Some consistently responded to low stimulus intensities, othersconsistently responded to high stimulus intensities. No consistentcorrelation between temperature and CO₂ thresholds was foundwithin individuals. Response thresholds of fanning bees decreasedover successive trials, providing empirical support for theidea of specialization through individual threshold reinforcement.In addition to variability in individual response thresholds,workers of a colony differed in two other parameters of responsiveness:response probability (the probability of responding to a stimulusonce it exceeded an individual's response threshold) and responseduration (the persistency with which fanning was performed oncean individual responded). The results of the present study suggestthat response threshold, response probability and response durationare important independent parameters of individual responsivenessin the collective control of nest climate in bumblebee colonies.     

Not one odour but two: A new model for nestmate recognition

Recognition systems play a key role in a range of biological processes, including mate choice, immune defence and altruistic behaviour. Social insects provide an excellent model for studying recognition systems because workers need to discriminate between nestmates and non-nestmates, enabling them to direct altruistic behaviour towards closer kin and to repel potential invaders. However, the level of aggression directed towards conspecific intruders can vary enormously, even among workers within the same colony. This is usually attributed to differences in the aggression thresholds of individuals or to workers having different roles within the colony. Recent evidence from the weaver ant Oecophylla smaragdina suggests that this does not tell the whole story. Here I propose a new model for nestmate recognition based on a vector template derived from both the individual’s innate odour and the shared colony odour. This model accounts for the recent findings concerning weaver ants, and also provides an alternative explanation for why the level of aggression expressed by a colony decreases as the diversity within the colony increases, even when odour is well-mixed. The model makes additional predictions that are easily tested, and represents a significant advance in our conceptualisation of recognition systems.     

Sucrose response thresholds of honey bee (Apis mellifera) foragers are not modulated by brood ester pheromone

Division of labor is a hallmark of eusocial insects and their ecological success can be attributed to it. Honey bee division of labor proceeds along a stereotypical ontogenetic path based on age, modulated by various internal and external stimuli. Brood pheromone is a major social pheromone of the honey bee that has been shown to affect honey bee division of labor. It elicits several physiological and behavioral responses; notably, regulating the timing of the switch from performing in-hive tasks to the initiation of foraging. Additionally, brood pheromone affects future foraging choice. In honey bees, sucrose response threshold is a physiological correlate of age of first foraging and foraging choice. Brood pheromone has been shown to modulate sucrose response threshold in young bees, but its effects on sucrose response thresholds of bees in advanced behavioral states (foragers) are not known. In this study we examined the sucrose response thresholds of two different task groups, foragers (pollen and non-pollen) and non-foraging bees, in response to honey bee brood pheromone. Sucrose response thresholds were not significantly different between brood pheromone treatment and controls among both non-pollen and pollen foragers. However, the sucrose response threshold of non-foraging bees was significantly higher in the brood pheromone treatment group than in the control group. The switch to foraging task is considered a terminal one, with honey bee lifespan being determined at least partially by risks and stress accompanying foraging. Our results indicate that foragers are physiologically resistant to brood pheromone priming of sucrose response thresholds.     

A trade-off in task allocation between sensitivity to the environment and response time

Task allocation is the process that adjusts the number of workers in each colony task in response to the environment. There is no central coordination of task allocation; instead workers use local cues from the environment and from other workers to decide which task to perform. We examine two aspects of task allocation: the sensitivity to the environment of task distribution, and the rate of response to environmental changes. We investigate how these two aspects are influenced by: (1) colony size, and (2) behavioral rules used by workers, i.e. how a worker uses cues from the environment and from social interactions with other workers in deciding which task to perform. We show that if workers use social cues in their choice of task, response time decreases with increasing colony size. Sensitivity of task distribution to the environment may decrease or not with colony size, depending on the behavioral rules used by workers. This produces a trade-off in task allocation: short response times can be achieved by increasing colony size, but at the cost of decreased sensitivity to the environment. We show that when a worker's response to social interactions depends on the local environment, sensitivity of task distribution to the environment is not affected by colony size and the trade-off is avoided.     

Flexible task allocation and the organization of work in ants

Flexibility in task performance is essential for a robust system of division of labour. We investigated what factors determine which social insect workers respond to colony-level changes in task demand. We used radio-frequency identification technology to compare the roles of corpulence, age, spatial location and previous activity (intra-nest/extra-nest) in determining whether worker ants (Temnothorax albipennis) respond to an increase in demand for foraging or brood care. The less corpulent ants took on the extra foraging, irrespective of their age, previous activity or location in the nest, supporting a physiological threshold model. We found no relationship between ants that tended the extra brood and corpulence, age, spatial location or previous activity, but ants that transported the extra brood to the main brood pile were less corpulent and had high previous intra-nest activity. This supports spatial task-encounter and physiological threshold models for brood transport. Our data suggest a flexible task-allocation system allowing the colony to respond rapidly to changing needs, using a simple task-encounter system for generalized tasks, combined with physiologically based response thresholds for more specialized tasks. This could provide a social insect colony with a robust division of labour, flexibly allocating the workforce in response to current needs.     

Sticking to their choice – honey bee subfamilies abandon declining food sources at a slow but uniform rate

Abstract. 1. The allocation of honey bee foragers among food patches is a result of decisions made by individual bees that are based on internal and external cues.
2. Decision-making processes are often based on internal thresholds. For example, if the quality of the food source is assessed by a forager as exceeding its internal threshold, the bee will continue foraging on that food source.
3. It is often assumed that all individuals have the same threshold and therefore use the same thresholds in decision-making, but because the honey bee queen mates with 12–30 males, the workers within a colony are genetically heterogeneous. Thus, the thresholds used by individual bees may be genetically variable within a colony.
4. Models of colony-level foraging behaviour of honey bees suggest that the rate of abandoning food sources is a critical parameter affecting foraging success. Moreover, these models show that variance among subfamilies in their abandonment rates may increase the colony's foraging efficiency.
5. Experimental data showing the relationship between the probability of abandoning a food source and its profitability are lacking, as is information on any variation in abandonment rates among subfamilies.
6. Abandonment rates were determined experimentally for four honey bee families for seven different sucrose concentrations. The results showed that abandonment rates appear to be invariant among (sub)families. The importance of forager fidelity to declining food sources is discussed with respect to foraging efficiency in a changing environment.