Reconsidering response threshold models—short-term response patterns in thermoregulating bumblebees

  • Anja WeidenmüllerEmail author
  • Rui Chen
  • Bernd Meyer
Original Article


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.

Significance statement

Social insect colonies distribute their workforce flexibly across a wide range of tasks. In the absence of a central command structure, it is crucial for our understanding of collective task allocation that we decipher the rules according to which individuals regulate their task engagement. Here, we explore bumblebee thermoregulation. Using temperature-controlled brood dummies. we analyze how temperature, repeated task performance, and performance feedback modulate the timing of individual fanning behavior. We show behavioral modulation in response to task performance. Contrary to common expectation, our results show that in some cases the inability to experience success in performing a task (here cooling the brood when fanning) can result in increased individual task engagement. Based on our analysis, we construct and simulate a detailed model for individual task response to show how this individual-level behavior can impact on group-level performance.


Task allocation Temporal influence Timing of behavior Task feedback Behavioral flexibility 



We thank Linda Garrison and Christoph Kleineidam for comments on an early version of the manuscript.

Funding information

This work was supported by a DAAD grant (Division of Labour and Collective Homeostasis in Dynamic Environments, DAAD PPP Australia, joint project C.K. and B.M.) and by the German Research Foundation (DFG, WE 4252/2-1 to A.W.; and the Centre of Excellence 2117 “Centre for the Advanced Study of Collective Behaviour” (ID: 422037984)).


  1. Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19:716–723CrossRefGoogle Scholar
  2. Beshers SN, Fewell JH (2001) Models of division of labor in social insects. Annu Rev Entomol 46:413–440CrossRefGoogle Scholar
  3. Bonabeau E, Theraulaz G, Deneubourg JL (1996) Quantitative study of the fixed threshold model for the regulation of division of labour in insect societies. Proc R Soc Lond B 263:1565–1569CrossRefGoogle Scholar
  4. Charbonneau D, Dornhaus A (2015) When doing nothing is something. How task allocation strategies compromise between flexibility, efficiency, and inactive agents. J Bioecon 17:217–242CrossRefGoogle Scholar
  5. Cook CN, Breed MD (2013) Social context influences the initiation and threshold of thermoregulatory behaviour in honeybees. Anim Behav 86:323–329CrossRefGoogle Scholar
  6. Cox DR (1972) Regression models and life-tables. J R Stat Soc B Methodol 34:187–220Google Scholar
  7. Dornhaus A (2008) Specialization does not predict individual efficiency in an ant. PLoS Biol 6:e285CrossRefGoogle Scholar
  8. Duarte A, Weissing FJ, Pen I, Keller L (2011) An evolutionary perspective on self-organized division of labor in social insects. Annu Rev Ecol Evol Syst 42:91–110CrossRefGoogle Scholar
  9. Dukas R, Visscher PK (1994) Lifetime learning by foraging honey bees. Anim Behav 48:1007–1012CrossRefGoogle Scholar
  10. Duong N, Dornhaus A (2012) Ventilation response thresholds do not change with age or self-reinforcement in workers of the bumble bee Bombus impatiens. Insect Soc 59:25–32CrossRefGoogle Scholar
  11. Fewell JH, Harrison JF (2016) Scaling of work and energy use in social insect colonies. Behav Ecol Sociobiol 70:1047–1061CrossRefGoogle Scholar
  12. Gardner KE, Foster RL, O’Donnell S (2007) Experimental analysis of worker division of labor in bumblebee nest thermoregulation (Bombus huntii, Hymenoptera: Apidae). Behav Ecol Sociobiol 61:783–792CrossRefGoogle Scholar
  13. Garrison LK, Kleineidam CJ, Weidenmüller A (2018) Behavioral flexibility promotes collective consistency in a social insect. Sci Rep 8:15836CrossRefGoogle Scholar
  14. Gautrais J, Theraulaz G, Deneubourg JL, Anderson C (2002) Emergent polyethism as a consequence of increased colony size in insect societies. J Theor Biol 215:363–373CrossRefGoogle Scholar
  15. Gillespie DT (1976) A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J Comput Phys 22:403–434CrossRefGoogle Scholar
  16. Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81:2340–2361CrossRefGoogle Scholar
  17. Gordon DM (1996) The organization of work in social insect colonies. Nature 380:121–124CrossRefGoogle Scholar
  18. Gordon DM (2016) From division of labor to the collective behavior of social insects. Behav Ecol Sociobiol 70:1101–1108CrossRefGoogle Scholar
  19. Goulson D (2010) Bumblebees: behaviour, ecology, and conservation, 2nd edn. Oxford University Press, New York CityCrossRefGoogle Scholar
  20. Grimaldi D, Engel MS (2005) Evolution of the insects. Cambridge University Press, New York CityGoogle Scholar
  21. Heinrich B (1979) Bumblebee economics. Harvard University Press, CambridgeGoogle Scholar
  22. Hölldobler B, Wilson EO (1990) The ants. Belknap Press of Harvard University Press, CambridgeCrossRefGoogle Scholar
  23. Hölldobler B, Wilson EO (2009) The superorganism: the beauty, elegance, and strageness of insect societies. W. W. Norton & Company, New York CityGoogle Scholar
  24. Jeanne RL (2016) Division of labor is not a process or a misleading concept. Behav Ecol Sociobiol 70:1109–1112CrossRefGoogle Scholar
  25. Jeanson R, Weidenmüller A (2014) Interindividual variability in social insects—proximate causes and ultimate consequences. Biol Rev 89:671–687CrossRefGoogle Scholar
  26. Johnson BR (2009) A self-organizing model for task allocation via frequent task quitting and random walks in the honeybee. Am Nat 174:537–547CrossRefGoogle Scholar
  27. Kleinbaum DG, Klein M (2012) Survival analysis: a self-learning text, 3rd edn. Springer, New York CityCrossRefGoogle Scholar
  28. Leighton GM, Charbonneau D, Dornhaus A (2017) Task switching is associated with temporal delays in Temnothorax rugatulus ants. Behav Ecol 28:319–327CrossRefGoogle Scholar
  29. Liu X (2012) Survival analysis: models and applications. Wiley, West SussexCrossRefGoogle Scholar
  30. Mattila HR, Seeley TD (2010) Promiscuous honeybee queens generate colonies with a critical minority of waggle-dancing foragers. Behav Ecol Sociobiol 64:875–889CrossRefGoogle Scholar
  31. Meyer B, Weidenmüller A, Chen R, García J (2015) Collective homeostasis and time-resolved models of self-organised task allocation. In: BICT. ACM, New York City, pp 469–478Google Scholar
  32. Myerscough MR, Oldroyd BP (2004) Simulation models of the role of genetic variability in social insect task allocation. Insect Soc 51:146–152CrossRefGoogle Scholar
  33. Naug D (2016) From division of labor to collective behavior: behavioral analyses at different levels. Behav Ecol Sociobiol 70:1113–1115CrossRefGoogle Scholar
  34. O’Donnell S, Foster RL (2001) Thresholds of response in nest thermoregulation by worker bumble bees, Bombus bifarius nearcticus (Hymenoptera: Apidae). Ethology 107:387–399CrossRefGoogle Scholar
  35. O’Donnell S, Jeanne RL (1992) Forager success increases with experience in Polybia occidentalis (Hymenoptera: Vespidae). Insectes Sociaux 39:451–454CrossRefGoogle Scholar
  36. Oster GF, Wilson EO (1978) Caste and ecology in the social insects. Princeton University Press, PrincetonGoogle Scholar
  37. Page RE, Mitchell SD (1990) Self organization and adaptation in insect societies. PSA 2:289–298Google Scholar
  38. Page RE, Mitchell SD (1998) Self-organization and the evolution of division of labor. Apidologie 29:171–190CrossRefGoogle Scholar
  39. Plowright RC, Plowright CMS (1988) Elitism in social insects: a positive feedback model. In: Jeanne R L (ed) Interindividual behavioral variability in social insects. Westview Press, Boulder, pp 419–431CrossRefGoogle Scholar
  40. Ravary F, Lecoutey E, Kaminski G, Châline N, Jaisson P (2007) Individual experience alone can generate lasting division of labor in ants. Curr Biol 17:1308–1312CrossRefGoogle Scholar
  41. Robinson GE (1992) Regulation of division of labor in insect societies. Annu Rev Entomol 37:637–665CrossRefGoogle Scholar
  42. Robson SKA, Traniello JFA (2016) Division of labor in complex societies: a new age of conceptual expansion and integrative analysis. Behav Ecol Sociobiol 70:995–998CrossRefGoogle Scholar
  43. Schoenfeld D (1982) Partial residuals for the proportional hazards regression model. Biometrika 69:239–241CrossRefGoogle Scholar
  44. Schultze-Motel P (1991) Heat loss and thermoregulation in a nest of the bumblebee Bombus lapidarius (hymenoptera, apidae). Thermochim Acta 193:57–66CrossRefGoogle Scholar
  45. Schwander T, Rosset H, Chapuisat M (2005) Division of labour and worker size polymorphism in ant colonies: the impact of social and genetic factors. Behav Ecol Sociobiol 59:215–221CrossRefGoogle Scholar
  46. Theraulaz G, Bonabeau E, Deneubourg JL (1998) Response threshold reinforcements and division of labour in insect societies. Proc R Soc Lond B 265:327–332CrossRefGoogle Scholar
  47. Tripet F, Nonacs P (2004) Foraging for work and age-based polyethism: the roles of age and previous experience on task choice in ants. Ethology 110:863–877CrossRefGoogle Scholar
  48. Trumbo ST, Robinson G E (1997) Learning and task interference by corpse-removal specialists in honey bee colonies. Ethology 103:966–975CrossRefGoogle Scholar
  49. Weidenmüller A (2004) The control of nest climate in bumblebee (Bombus terrestris) colonies: interindividual variability and self reinforcement in fanning response. Behav Ecol 15:120– 128CrossRefGoogle Scholar
  50. Weidenmüller A, Kleineidam C, Tautz J (2002) Collective control of nest climate parameters in bumblebee colonies. Anim Behav 63:1065–1071CrossRefGoogle Scholar
  51. Westhus C, Kleineidam C J, Roces F, Weidenmüller A (2013) Behavioural plasticity in the fanning response of bumblebee workers: impact of experience and rate of temperature change. Anim Behav 85:27–34CrossRefGoogle Scholar
  52. Wilson EO (1971) The insect societies. Belknap Press of Harvard University Press, CambridgeGoogle Scholar
  53. Wilson EO (1985) The sociogenesis of insect colonies. Science 228:1489–1495CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Centre for the Advanced Study of Collective Behaviour & Department of BiologyUniversity of KonstanzKonstanzGermany
  2. 2.Faculty of ITMonash UniversityCaulfield EastAustralia

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