Skip to main content
SpringerLink
Log in

An Environmental Model of Honey Bee Colony Collapse Due to Pesticide Contamination

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

We develop a model of honey bee colony collapse based on the contamination of forager bees in environmental regions contaminated with pesticides. An important feature of the model is the daily homing capacity each day of foragers bees. The model consists of difference equations describing the daily homing of uncontaminated and contaminated forager bees, with an increased homing failure of contaminated bees. The model quantifies colony collapse in terms of the fraction of contaminated bees subject to this increased homing failure. If the fraction is sufficiently high, then the hive falls below a viability threshold population size that leads to rapid disintegration. If the fraction is sufficiently low, then the hive can rise above the viability threshold and attain a stable population level.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Abou-Shaara HF (2014) The foraging behaviour of honey bees, Apis mellifera: a review. Vet Med 59(1):1–10

    Google Scholar 

  • American Society for Horticultural Science, U.S. states begin ban on neonicotinoids (2019) https://ashs.org/blogpost/1288786/251171/

  • Banks HT, Banks JE, Bommarco R et al (2017) Modeling bumble bee population dynamics with delay differential equations. Ecol Model 351:14–23

    Google Scholar 

  • Barron AB (2015) Death of the bee hive: understanding the failure of an insect society. Sci Direct 10:45–50

    Google Scholar 

  • Becher MA, Osborne JL, Thorbek P et al (2013) Towards a systems approach for understanding honeybee decline: a stocktaking and synthesis of existing models. J Appl Ecol 50:868–880

    Google Scholar 

  • Becher MA, Grimm V, Thorbek P et al (2014) BEEHAVE: a systems model of honeybee colony dynamics and foraging to explore multifactorial causes of colony failure. J Appl Ecol 51:470–482

    Google Scholar 

  • Becher MA, Twiston-Davies G, Penny TD (2018) Bumble-BEEHAVE: a systems model for exploring multifactorial causes of bumblebee decline at individual, colony, population and community level. J Appl Ecol 55:2797–2801

    Google Scholar 

  • Bee Informed Partnership, Total US managed honey bee colonies loss estimates (2018) https://beeinformd.org

  • Bernardi S, Venturino E (2016) Viral epidemiology of the adult Apis Mellifera infested by the Varroa destructor mite. Sci Direct 5:e00101

    Google Scholar 

  • Betti MI, Wahl LM, Zamir M (2014) Effects of infection on honey bee population dynamics: a model. PLoS ONE 9(10):e110237

    Google Scholar 

  • Betti M, LeClair J, Wahl LM et al (2017) Bee++: an object-oriented, agent-based simulator for honeybee colonies. Pop Sci 8:31

    Google Scholar 

  • Blacquiére T, Smagghe G, van Gestel CAM et al (2016) Neonicotinoids in bees: a review on concentrations, side-effects and risk assessment. Ecotoxicology 21(4):973–992

    Google Scholar 

  • Booten RD, Iwasa Y, Marshall JAR et al (2017) Stress-mediated Allee effects can cause the sudden collapse of honey bee colonies. J Theor Biol 420:213–219

    MathSciNet  MATH  Google Scholar 

  • Bryden J, Gill RJ, Mitton RAA et al (2013) Chronic sublethal stress causes bee colony failure. Ecol. Lett 16:1463–1469

    Google Scholar 

  • Chauzat M-P, Carpentier P, Martel A-C et al (2009) Influence of pesticide residues on honey bee (Hymenoptera: Apidae) colony health in France. Environ Entomol 38(3):514–543

    Google Scholar 

  • Cutler GC, Scott-Dupree CD (2007) Exposure to clothianidin seed-treated canola has no long-term impact on honey bees. J Econ Entomol 100(3):765–772

    Google Scholar 

  • Cutler GC, Scott-Dupree CD, Sultan M et al (2014) A large-scale field study examining effects of exposure to clothianidin seed-treated canola on honey bee colony health, development, and overwintering success. Peer J 2:e652

    Google Scholar 

  • Cutler GC, Scott-Dupree CD (2016) A field study examining the effects of exposure to neonicotinoid seed-treated corn on commercial bumble bee colonies. Ecotoxicology 23(9):1755–1763

    Google Scholar 

  • DeGrandi-Hoffman G, Roth SA, Loper GL, Erickson EH (1989) BEEPOP: a honeybee population dynamics simulation model. Ecol Model 45:133–150

    Google Scholar 

  • DeGrandi-Hoffman G, Curry R et al (2004) A mathematical model of Varroa mite (Varroa destructor Anderson and Trueman) and honeybee Apis mellifera L. population dynamics. Int J Acarol 30(3):259–274

    Google Scholar 

  • Dennis B, Kemp WP (2016) How hives collapse: Allee effects, ecological resilience, and the honey bee. PLoS ONE 11(2):e0150055

    Google Scholar 

  • Desneux N, Decourtye A, Delpuech JM (2007) The sublethal effects of pesticides on beneficial arthropods. Annu Rev Entomol 52:81–106

    Google Scholar 

  • Dively GP, Embrey MS, Kamel A et al (2015) Assessment of chronic sublethal effects of imidacloprid on honey bee colony health. PLoS ONE 10:e0118748

    Google Scholar 

  • Dukas R (2008) Mortality rates of honey bees in the wild. Insectes Sociaux 55(3):252–255

    Google Scholar 

  • European Food Safety Authority, Neonicotinoids: risks to bees confirmed (2018) https://doi.org/10.2903/sp.efsa.2018.EN-1378

  • European Food Safety Authority, Evaluation of the data on clothianidin, imidacloprid and thiamethoxam for the updated risk assessment to bees for seed treatments and granules in the EU (2018) https://doi.org/10.2903/sp.efsa.2018.EN-1378

  • Farley JD (2017) Evolutionary dynamics of bee colony collapse disorder: steps toward a mathematical model of the contagion hypothesis. J Adv Agric 7(2):1050–1056

    Google Scholar 

  • Gabbriellini G (2017) Seasonal effects on honey bee population dynamics: a nonautonomous system of difference equations. Int J Differ Equ 12(2):211–233

    MathSciNet  Google Scholar 

  • Goulson D, Nicholls E, Botas C, Rotheray EL (2015) Bee declines driven by combined stress from parasites, pesticides, and lack of flowers. Science 347:1255957

    Google Scholar 

  • H.R. 3040-Saving America’s Pollinators Act of 2017 (2018) https://www.congress.gov/bill /115th-congress/house-bill/3040/text

  • Henry M, Béguin M, Requier F et al (2012) A common pesticide decreases foraging success and survival in honey bees. Science 336(6079):348–350

    Google Scholar 

  • Henry M, Cerrutti N, Aupinel P et al (2015) Reconciling laboratory and field assessments of neonicotinoid toxicity to honeybees. Proc R Soc B Sci 282:20152110

    Google Scholar 

  • Huang ZY, Robinson GE (1974) Regulation of honey bee division of labor by colony age demography. Behav Ecol Sociobiol 39:147–158

    Google Scholar 

  • Kang Y, Theraulaz G (2016) Dynamical models of task organization in social insect colonies. Bull Math Biol 78(5):879–915

    MathSciNet  MATH  Google Scholar 

  • Kang Y, Blanco K, Davis T, Wang Y, DeGrandi-Hoffman G (2016) Disease dynamics of honeybees with Varroa destructor as parasite and virus vector. Math Biosci 275:71–92

    MathSciNet  MATH  Google Scholar 

  • Khoury DS, Myerscough MR, Barron AB (2011) A quantitative model of honey bee colony population dynamics. PLoS ONE 6(4):e18491

    Google Scholar 

  • Kribs-Zaleta CM, Mitchell C (2014) Modeling colony collapse disorder in honeybees as a contagion. Math Biosci Eng 11(6):1275–1294

    MathSciNet  MATH  Google Scholar 

  • Leoncini I, Le Conte Y, Costagliola G et al (2004) Regulation of behavioral maturation by a primer pheromone produced by adult worker honey bees. Proc Nat Acad Sci 101:17559–17564

    Google Scholar 

  • Martin SJ (2002) The role of Varroa and viral pathogens in the collapse of honeybee colonies: a modeling approach. J Appl Ecol 38:1082–1093

    Google Scholar 

  • Meikle WG, Adamczyk JJ, Weiss M et al (2016) Sublethal effects of imidacloprid on honey bee colony growth and activity at three sites in the US. PLoS ONE 11:e0168603

    Google Scholar 

  • Myerscough MR, Khoury DS, Ronzani S, Barron AB (2017) Why do hives die? Using mathematics to solve the problem of honey bee colony collapse. In: Anderssen B et al (eds) The role and importance of mathematics in innovation. Mathematics for industry, vol 25. Springer, Singapore

    Google Scholar 

  • Nguyen BK, Saegerman C, Picard C et al (2009) Does imidacloprid seed-treated maize have an impact on honey bee mortality? J Econ Entomol 102(2):616–623

    Google Scholar 

  • Pilling E, Cambell E, Coulson M et al (2013) A four-year field program investigating long-term effects of repeated exposure of honey bee colonies to flowering crops treated with thiamethoxam. PLoS ONE 8:e77193

    Google Scholar 

  • Ratti V, Kevan PG, Eberl HJ (2013) A mathematical model for population dynamics in honeybee colonies infested with Varroa destructor and the acute bee paralysis virus. Can Appl Math Q 21(1):63–93

    MathSciNet  MATH  Google Scholar 

  • Ratti V, Kevan PG, Eberl HJ (2015) A mathematical model of the honeybee-Varroa destructor-Acute bee paralysis virus system with seasonal effects. Bull Math Biol 77(8):1493–1520

    MathSciNet  MATH  Google Scholar 

  • Ratti V, Kevan PG, Eberl HJ (2017) A mathematical model of forager loss in honeybee colonies infested with Varroa destructor and the acute bee paralysis virus. Bull Math Biol 79(6):1218–1253

    MathSciNet  MATH  Google Scholar 

  • Rolke D, Fuchs S, Grunewald B et al (2016) Large-scale monitoring of effects of clothianidin-dressed oilseed rape seeds on pollinating insects in Northern Germany: effects on honey bees (Apis mellifera). Ecotoxicology 25(9):1648–1665

    Google Scholar 

  • Rundlof M, Andersson GKS, Bommarco R et al (2015) Seed coating with a neonicotinoid insecticide negatively affects wild bees. Nature 521:77–80

    Google Scholar 

  • Russell S, Barron AB, Harris D (2013) Dynamic modelling of honey bee (Apis mellifera) colony growth and failure. Ecol Model 265(10):158–169

    Google Scholar 

  • Sandrock C, Tanadini LG, Pettis JS et al (2014) Sublethal neonicotinoid insecticide exposure reduces solitary bee reproductive success. Agric For Entomol 16:119–128

    Google Scholar 

  • Schmickl T, Crailsheim K (2007) HoPoMo: a model of honeybee intracolonial population dynamics and resource management. Ecol Model 204:219–245

    Google Scholar 

  • Schneider CW, Tautz J, Grünewald B et al (2012) RFID tracking of sublethal effects of two neonicotinoid insecticides on the foraging behavior of Apis mellifera. PLoS ONE 7(1):e30023

    Google Scholar 

  • Stanley DA, Russell AL, Morrison SJ et al (2016) Investigating the impacts of field-realistic exposure to a neonicotinoid pesticide on bumblebee foraging, homing ability and colony growth. J Appl Ecol 53:1440–1449

    Google Scholar 

  • Sumpter DJ, Martin SJ (2004) The dynamics of virus epidemics in Varroa-infested honey bee colonies. J Animal Ecol 73(1):51–63

    Google Scholar 

  • Thompson HM, Wilkins S, Harkin S et al (2015) Neonicotinoids and bumblebees (Bombus terrestris): effects on nectar consumption in individual workers. Pest Manag Sci 71(7):946–950

    Google Scholar 

  • Torres DJ, Ricoy UM, Roybal S (2015) Modeling honey bee populations. PLoS ONE 10(7):e0130966

    Google Scholar 

  • Truitt LL, McArt SH, Vaughn AH, Ellner SP (2019) Trait-based modeling of multihost pathogen transmission: plant-pollinator networks. Am Nat 193(6):E149–E167

    Google Scholar 

  • United States Department of Agriculture Agricultural Research Service (2019) https://www.ars.usda.gov/oc/br/ccd/index/

  • United States Environmental Protection Agency, Schedule for Review of Neonicotinoid Pesticides (2019) https://www.epa.gov/pollinator-protection/schedule-review-neonicotinoid-pesticides

  • vanEngelsdorp D, Evans JD, Saegerman C et al (2009) Colony collapse disorder: a descriptive study. PLoS ONE 4(8):e6481

    Google Scholar 

  • Wikepedia (2019) https://en.wikipedia.org/wiki/Colony_collapse_disorder

  • Willkinson D, Smith GC (2002) A model of the mite parasite, Varroa destructor, on honeybees (Apis mellifera) to investigate parameters important to mite population growth. Ecol Model 148:263–275

    Google Scholar 

Download references

Acknowledgements

The authors express thanks to Dr. Frederic Barraquand, CNRS, IMB Bordeaux, France, for helpful assistance in the biological background of this work.

Author information

Authors and Affiliations

  1. Université de Bordeaux, Bordeaux, France

    P. Magal

  2. Vanderbilt University, Nashville, TN, USA

    G. F. Webb & Yixiang Wu

Authors
  1. P. Magal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. F. Webb
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yixiang Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. F. Webb.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Magal, P., Webb, G.F. & Wu, Y. An Environmental Model of Honey Bee Colony Collapse Due to Pesticide Contamination. Bull Math Biol 81, 4908–4931 (2019). https://doi.org/10.1007/s11538-019-00662-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-019-00662-5

Keywords

Mathematics Subject Classification

Search

Navigation