A mathematical model of honey bee colony dynamics to predict the effect of pollen on colony failure

1. Gervasi DD, Schiestl FP. Real-time divergent evolution in plants driven by pollinators. Nature Communications. 2017;8:14691. doi: 10.1038/ncomms14691 28291771

2. Huang Z. Pollen nutrition affects honey bee stress resistance. Terrestrial Arthropod Reviews. 2012;5(2):175–89.

3. Evans JD, Saegerman C, Mullin C, Haubruge E, Nguyen BK, Frazier M, et al. Colony collapse disorder: a descriptive study. PloS one. 2009;4(8):e6481. doi: 10.1371/journal.pone.0006481 19649264

4. Henry M, Beguin M, Requier F, Rollin O, Odoux J-F, Aupinel P, et al. A common pesticide decreases foraging success and survival in honey bees. Science. 2012;336(6079):348–50. doi: 10.1126/science.1215039 22461498

5. Moore J, Jironkin A, Chandler D, Burroughs N, Evans DJ, Ryabov EV. Recombinants between Deformed wing virus and Varroa destructor virus-1 may prevail in Varroa destructor-infested honeybee colonies. Journal of General Virology. 2011;92(1):156–61.

6. Higes M, Meana A, Bartolomé C, Botías C, Martín‐Hernández R. Nosema ceranae (Microsporidia), a controversial 21st century honey bee pathogen. Environmental microbiology reports. 2013;5(1):17–29. doi: 10.1111/1758-2229.12024 23757127

7. Dainat B, Evans JD, Chen YP, Gauthier L, Neumann P. Predictive markers of honey bee colony collapse. PLoS one. 2012;7(2):e32151. doi: 10.1371/journal.pone.0032151 22384162

8. Alaux C, Ducloz F, Crauser D, Le Conte Y. Diet effects on honeybee immunocompetence. Biology letters. 2010;6(4):562–5. doi: 10.1098/rsbl.2009.0986 20089536

9. Oldroyd BP. What's killing American honey bees? PLoS biology. 2007;5(6):e168. doi: 10.1371/journal.pbio.0050168 17564497

10. Huang Z. The colony collapse disorder crisis for honey bees. Encyclopedia of Life Science. 2008;1:15–8.

11. Johnson RM, Dahlgren L, Siegfried BD, Ellis MD. Acaricide, fungicide and drug interactions in honey bees (Apis mellifera). PloS one. 2013;8(1):e54092. doi: 10.1371/journal.pone.0054092 23382869

12. Wu JY, Anelli CM, Sheppard WS. Sub-lethal effects of pesticide residues in brood comb on worker honey bee (Apis mellifera) development and longevity. PloS one. 2011;6(2):e14720. doi: 10.1371/journal.pone.0014720 21373182

13. Crailsheim K. The flow of jelly within a honeybee colony. Journal of comparative physiology B. 1992;162(8):681–9.

14. Robinson GE, Page RE. Genetic determination of nectar foraging, pollen foraging, and nest-site scouting in honey bee colonies. Behavioral Ecology and Sociobiology. 1989;24(5):317–23.

15. Pankiw T, Page RE Jr. Response thresholds to sucrose predict foraging division of labor in honeybees. Behavioral Ecology and Sociobiology. 2000;47(4):265–7.

16. Schmickl T, Karsai I. How regulation based on a common stomach leads to economic optimization of honeybee foraging. Journal of theoretical biology. 2016;389:274–86. doi: 10.1016/j.jtbi.2015.10.036 26576492

17. Scheiner R, Toteva A, Reim T, Søvik E, Barron AB. Differences in the phototaxis of pollen and nectar foraging honey bees are related to their octopamine brain titers. Frontiers in physiology. 2014;5:116–. doi: 10.3389/fphys.2014.00116 24734024.

18. Carroll MJ, Duehl AJ. Collection of volatiles from honeybee larvae and adults enclosed on brood frames. Apidologie. 2012;43(6):715–30.

19. Schmickl T, Crailsheim K. Inner nest homeostasis in a changing environment with special emphasis on honey bee brood nursing and pollen supply. Apidologie. 2004;35(3):249–63.

20. Schmickl T, Crailsheim K. How honeybees (Apis mellifera L.) change their broodcare behaviour in response to non-foraging conditions and poor pollen conditions. Behavioral Ecology and Sociobiology. 2002;51(5):415–25.

21. Requier F, Odoux JF, Henry M, Bretagnolle V. The carry‐over effects of pollen shortage decrease the survival of honeybee colonies in farmlands. Journal of applied ecology. 2017;54(4):1161–70.

22. Keller I, Fluri P, Imdorf A. Pollen nutrition and colony development in honey bees: part 1. Bee World. 2005;86(1):3–10.

23. Kleinschmidt G, Kondos A. Influence of crude protein levels on colony production. Australasian Beekeeper. 1976.

24. Haydak M. Bee nutrition and pollen substitutes. Apiacta. 1967;1:3–8.

25. Knox DA, Shimanuki H, Herbert E. Diet and the longevity of adult honey bees. Journal of Economic Entomology. 1971;64(6):1415–6.

26. Becher MA, Osborne JL, Thorbek P, Kennedy PJ, Grimm V. Towards a systems approach for understanding honeybee decline: a stocktaking and synthesis of existing models. Journal of Applied Ecology. 2013;50(4):868–80. doi: 10.1111/1365-2664.12112 24223431

27. Becher MA, Grimm V, Thorbek P, Horn J, Kennedy PJ, Osborne JL. BEEHAVE: a systems model of honeybee colony dynamics and foraging to explore multifactorial causes of colony failure. Journal of Applied Ecology. 2014;51(2):470–82. doi: 10.1111/1365-2664.12222 25598549

28. Francis RM, Nielsen SL, Kryger P. Varroa-virus interaction in collapsing honey bee colonies. PloS one. 2013;8(3):e57540. doi: 10.1371/journal.pone.0057540 23526946

29. Ramsey SD, Ochoa R, Bauchan G, Gulbronson C, Mowery JD, Cohen A, et al. Varroa destructor feeds primarily on honey bee fat body tissue and not hemolymph. Proceedings of the National Academy of Sciences. 2019;116(5):1792–801.

30. Janmaat AF, Winston ML. Removal of Varroa jacobsoni infested brood in honey bee colonies with differing pollen stores. Apidologie. 2000;31(3):377–85.

31. Mattila H, Otis G. Effects of pollen availability and Nosema infection during the spring on division of labor and survival of worker honey bees (Hymenoptera: Apidae). Environmental entomology. 2006;35(3):708–17.

32. Scofield HN, Mattila HR. Honey bee workers that are pollen stressed as larvae become poor foragers and waggle dancers as adults. Plos one. 2015;10(4):e0121731. doi: 10.1371/journal.pone.0121731 25853902

33. Khoury DS, Myerscough MR, Barron AB. A quantitative model of honey bee colony population dynamics. PloS one. 2011;6(4):e18491. doi: 10.1371/journal.pone.0018491 21533156

34. Khoury DS, Barron AB, Myerscough MR. Modelling food and population dynamics in honey bee colonies. PloS one. 2013;8(5):e59084. doi: 10.1371/journal.pone.0059084 23667418

35. Paiva JPLM, Paiva HM, Esposito E, Morais MM. On the effects of artificial feeding on bee colony dynamics: a mathematical model. PloS one. 2016;11(11):e0167054. doi: 10.1371/journal.pone.0167054 27875589

36. Perry CJ, Søvik E, Myerscough MR, Barron AB. Rapid behavioral maturation accelerates failure of stressed honey bee colonies. Proceedings of the National Academy of Sciences. 2015;112(11):3427–32.

37. Betti MI, Wahl LM, Zamir M. Effects of infection on honey bee population dynamics: a model. PloS one. 2014;9(10):e110237. doi: 10.1371/journal.pone.0110237 25329468

38. Russell S, Barron AB, Harris D. Dynamic modelling of honey bee (Apis mellifera) colony growth and failure. Ecological Modelling. 2013;265:158–69.

39. Schmickl T, Crailsheim K. HoPoMo: A model of honeybee intracolonial population dynamics and resource management. Ecological modelling. 2007;204(1–2):219–45.

40. Karsai I, Schmickl T. Regulation of task partitioning by a “common stomach”: a model of nest construction in social wasps. Behavioral Ecology. 2011;22(4):819–30.

41. Karsai I, Phillips MD. Regulation of task differentiation in wasp societies: A bottom-up model of the “common stomach”. Journal of theoretical biology. 2012;294:98–113. doi: 10.1016/j.jtbi.2011.10.037 22079942

42. Ade PA, Aghanim N, Armitage-Caplan C, Arnaud M, Ashdown M, Atrio-Barandela F, et al. Planck 2013 results. XVI. Cosmological parameters. Astronomy & Astrophysics. 2014;571:A16.

43. Schmickl T, Karsai I. Sting, carry and stock: How corpse availability can regulate de-centralized task allocation in a Ponerine ant colony. PloS one. 2014;9(12):e114611. doi: 10.1371/journal.pone.0114611 25493558

44. Karsai I, Wenzel JW. Organization and regulation of nest construction behavior in Metapolybia wasps. Journal of Insect Behavior. 2000;13(1):111–40.

45. Knisley J, Schmickl T, Karsai I. Compartmental models of migratory dynamics. Mathematical Modelling of Natural Phenomena. 2011;6(6):245–59.

46. Seeley TD. The wisdom of the hive: the social physiology of honey bee colonies: Harvard University Press; 2009.

47. Booton RD, Iwasa Y, Marshall JA, Childs DZ. Stress-mediated Allee effects can cause the sudden collapse of honey bee colonies. Journal of theoretical biology. 2017;420:213–9. doi: 10.1016/j.jtbi.2017.03.009 28288794

48. Bodenheimer F. Studies in animal populations. II. Seasonal population-trends of the honey-bee. The Quarterly Review of Biology. 1937;12(4):406–25.

49. Seeley TD. Honeybee democracy: Princeton University Press; 2010.

50. Jay S. Seasonal development of honeybee colonies started from package bees. Journal of Apicultural Research. 1974;13(2):149–52.

51. Leoncini I, Le Conte Y, Costagliola G, Plettner E, Toth AL, Wang M, et al. Regulation of behavioral maturation by a primer pheromone produced by adult worker honey bees. Proceedings of the National Academy of Sciences. 2004;101(50):17559–64.

52. Huang Z-Y, Robinson GE. Regulation of honey bee division of labor by colony age demography. Behavioral Ecology and Sociobiology. 1996;39(3):147–58.

53. Jeffree E, Allen DM. The annual cycle of pollen storage by honey bees. Journal of Economic Entomology. 1957;50(2):211–2.

54. Camazine S, Sneyd J, Jenkins MJ, Murray J. A mathematical model of self-organized pattern formation on the combs of honeybee colonies. Journal of Theoretical Biology. 1990;147(4):553–71.

55. Eckert C, Winston M, Ydenberg R. The relationship between population size, amount of brood, and individual foraging behaviour in the honey bee, Apis mellifera L. Oecologia. 1994;97(2):248–55. doi: 10.1007/BF00323157 28313936

56. Horn J, Becher MA, Kennedy PJ, Osborne JL, Grimm V. Multiple stressors: using the honeybee model BEEHAVE to explore how spatial and temporal forage stress affects colony resilience. Oikos. 2016;125(7):1001–16.