Modeling seasonal changes and death rate of hive bee in honey bee colony

Document Type : Original Paper

Authors

1 Department of Applied Mathematics, Tarbiat Modares University, Tehran, Iran.

2 Department of Applied Mathematics, Tarbiat Modares University, Tehran, Iran

Abstract

Honey bee is the insect that mainly pollens agricultural products. In recent decades, colony failure rates as a global concern have increased. Some mathematical models have been proposed. In one of the first models the impact of bee death rates on population dynamics was studied and then the food availability and the rate of broods added to the model. Here we improve the model by considering seasonal changes and death rate of hive bees. Our results show that death rates higher than 0.41 lead to colony collapse. At higher death rates, despite of colony failure, food stored in colony and this is instance of colony collapse. Additionally, the model predicts the minimum food needed for colony in various death rates.

Keywords

Main Subjects

References

[1] Betti, M., Wahl, L. and Zamir,M. ,(2017). Reproduction Number and Asymptotic Stability for the Dynamics of a Honey Bee Colony with Continuous Age Structure, Bulletin of mathematical biology, 79, 1586-1611.
[2] Gervasi, D. D. and Schiestl, F. P. (2017). Real-time divergent evolution in plants driven by pollinators, Nature Communications,8, 14691.
[3] Evans, J.D., Saegerman, C.C. Mullin, Haubruge, E., Nguyen, B.K. and Frazier, M. (2009). Colony collapse disorder: a descriptive study, PloS one,4, e6481.
[4] Winston, M. L. (1992). The biology and management of Africanized honey bees, Annual Review of Entomology, 37, 173-193.
[5] Khoury, D. S., Myerscough, M. R. and Barron, A. B. (2011).A quantitative model of honey bee colony population dynamics, PloS one, 6, 18491.
[6] Schmickl, T. and Karsai, I. (2017). Resilience of honeybee colonies via common stomach: A model of self-regulation of foraging, PloS one, 12, 0188004.
[7] Messan, M. R., Page Jr M. R. and Kang, Y. (2018). Effects of vitellogenin in age polyethism and population dynamics of honeybees, Ecological Modelling, 388, 88-107.
[8] Perry, C. J., Søvik, E., Myerscough, M. R. and Barron, A. B. (2015). Rapid behavioral maturation accelerates failure of stressed honey bee colonies, Proceedings of the National Academy of Sciences, 112 (11), 3427-3432.
[9] Betti, M. I., Wahl, M. I. and Zamir, M. (2014). Effects of infection on honey bee population dynamics: a model, PloS one, 9, 110237.
[10] Ratti, V., Kevan, P. G. and Eberl, H. J. (2017). A mathematical model of forager loss in honeybee colonies infested with Varroa destructor and the acute bee paralysis virus, Bulletin of mathematical biology, 79, 1218-1253.
[11] Khoury, D. S., Barron, A. B. and Myerscough, M. R. (2013). Modelling food and population dynamics in honey bee colonies, PloS one, 8, 59084.
[12] Higes. M., Martín‐Hernández, R., Botías, C., Bailón, E. G., González‐Porto, A. V. and Barrios, L. (2008). How natural infection by Nosema ceranae causes honeybee colony collapse, Environmental microbiology, 10, 2659-2669.
[13] Ratnieks, F. L. and Carreck, N. L. (2010). Clarity on honey bee collapse, Science, 327, 152-153.
[14] Oldroyd, B. P. (1999). Coevolution while you wait: Varroa jacobsoni, a new parasite of western honeybees, Trends in Ecology & Evolution,14, 312-315.
[15] Fahrbach, S. E. and Robinson, G. E. (1996). Juvenile hormone, behavioral maturation, and brain structure in the honey bee, Developmental neuroscience, 18, 102-114.
[16] Robinson, G. E., Page Jr, R. E., Strambi, C. and Strambi, A. (1992). Colony integration in honey bees: mechanisms of behavioral reversion, Ethology, 90, 336-348.
[17] Schulz, D. J., Huang, Z.Y. and Robinson, G. E. (1998). Effects of colony food shortage on behavioral development in honey bees, Behavioral Ecology and Sociobiology,42, 295-303.
Journal of Advanced Mathematical Modeling
Volume 9, Issue 2
September 2019
Pages 77-92

Files

History

  • Receive Date: 01 August 2018
  • Revise Date: 10 December 2018
  • Accept Date: 02 February 2019

Share

How to cite

Statistics