Task Allocation of Wasps Governed by Common Stomach: A Model Based on Electric Circuits

RESEARCH ARTICLE Task Allocation of Wasps Governed by Common Stomach: A Model Based on Electric Circuits Allison Hilbun1☯, Istvan Karsai2☯* 1 Department of Biomedical Sciences, East Tennessee State University, Johnson City, Tennessee, United States of America, 2 Department of Biological Sciences, East Tennessee State University, Johnson City, Tennessee, United States of America ☯ These authors contributed equally to this work. * Abstract a11111 OPEN ACCESS Citation: Hilbun A, Karsai I (2016) Task Allocation of Wasps Governed by Common Stomach: A Model Based on Electric Circuits. PLoS ONE 11 (11): e0167041. doi:10.1371/journal. pone.0167041 Editor: Fabio S. Nascimento, Universidade de Sao Paulo Faculdade de Filosofia Ciencias e Letras de Ribeirao Preto, BRAZIL Received: July 22, 2016 Accepted: November 8, 2016 Published: November 18, 2016 Copyright: © 2016 Hilbun, Karsai. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All relevant data are within the paper. Funding: The authors received no specific funding for this work. Competing Interests: The authors have declared that no competing interests exist. Simple regulatory mechanisms based on the idea of the saturable ‘common stomach’ can control the regulation of construction behavior and colony-level responses to environmental perturbations in Metapolybia wasp societies. We mapped the different task groups to mutual inductance electrical circuits and used Kirchoff’s basic voltage laws to build a model that uses master equations from physics, yet is able to provide strong predictions for this complex biological phenomenon. Similar to real colonies, independently of the initial conditions, the system shortly sets into an equilibrium, which provides optimal task allocation for a steady construction, depending on the influx of accessible water. The system is very flexible and in the case of perturbations, it reallocates its workforce and adapts to the new situation with different equilibrium levels. Similar to the finding of field studies, decreasing any task groups caused decrease of construction; increasing or decreasing water inflow stimulated or reduced the work of other task groups while triggering compensatory behavior in water foragers. We also showed that only well connected circuits are able to produce adequate construction and this agrees with the finding that this type of task partitioning only exists in larger colonies. Studying the buffer properties of the common stomach and its effect on the foragers revealed that it provides stronger negative feedback to the water foragers, while the connection between the pulp foragers and the common stomach has a strong fixedpoint attractor, as evidenced by the dissipative trajectory. Introduction Insect societies function as superorganisms [1] in which parallel processing is ubiquitous. The parallel processing not only makes the system more reliable [2], but it also makes possible the emergence of a complex system of the network of specialized units [3]. Division of labor is one of the most studied,debated, and intriguing phenomena in insect societies [4,5,6]. One of the most complex types of labor organization mechanisms is called task partitioning, which describes a situation when a given task, such as nest construction, is partitioned into subtasks. PLOS ONE | DOI:10.1371/journal.pone.0167041 November 18, 2016 1 / 18 Task Allocation of Wasps: An Electric Circuit Model These subtasks are commonly connected sequentially and carried out by different more or less specialized individuals, such that it can be observed on the working process of the bucket brigade [7]. The assignment of a given worker to a given subtask is commonly dynamic, because it depends on the progress of the work, the number of participants, and other factors, and it poses a decision problem at the individual level for task switching [8]. In the insect society, each agent has only a local perception and only local information about the overall situation, and these societies have no foreman or other central task allocation unit, therefore the whole system is self-organizing itself to establish efficient performance via allocating different numbers of workers to different task groups [9,10,1,11]. Swarm founding Metapolybia wasps exhibit flexible and adaptive task specialization, in which distinct subsets of the complex nest construction task is partitioned between cooperative teams of nest mates [3,12,13]. The building task is partitioned into four subtasks, and all subtasks are carried out by generally different individuals. Some workers specialize in water collecting and bring the water to the nest, where it is stored in the crop of other wasps. These water storer wasps form a “common stomach” where the water can be downloaded or taken out, if needed. Other specialized wasps called pulp foragers collect water from the common stomach and fly out to collect wooden pulp. The water they bring from the nest is needed to macerate the plant materials (cellulose) into building material. This building material then is transported to the nest, where it will be distributed to builder wasps, which built the pulp into the nest. Field experiments and modeling of this system revealed that the saturation of the common stomach is used by the wasp as an information center [14]. For example, if the common stomach is saturated with water, the water foragers have difficulty downloading their water load, while the pulp foragers can take water from the common stomach very easily. This indicates that in the colony, there would be more water providers than necessary. Consequently, some of the water foragers would give up water foraging and switch into water users such as pulp foragers or builders. However, these switches also have costs [15]; therefore a large common stomach also can play a role as a buffer [16], so small fluctuations would not trigger task switching, and the wasps would operate with high task fidelity [17]. This would in turn ensure additional benefits to the colony, such as the ability to learn the position of water and pulp resources. Task partitioning itself is an old and general challenge not only in insect societies [18–20], but also in computational distributed systems [21–22] or in robot groups [23–24]. Due to the hiatus of master equations in biology, task partitioning is commonly described and modeled with agent-based approaches or by the use of empirical functions. For example the ‘‘response threshold models” assume that workers vary intrinsically in task preference [25] and these threshold functions are commonly described by some form of sigmoid curve [26]. Karsai and Balazsi [27] used a Weibull function, commonly used to describe stress and aging processes, for modeling task (...truncated)