Food and environmental degradation as causative agents of honey bee colonies decline: Mathematical model approach
Keywords:Honey Bees, Colony Collapse Disorder, degradation, Environment
In this research, a new compartment model of honey bee population is developed to study the effects of gradual change of food availability and environmental degradation on bee population growth and development. The model is proved to be mathematical well posed and a non-trivial equilibrium point is shown to exist and asymptotically stable under certain conditions. The model predicts a critical threshold environmental degradation rate above which the population size of bees decline and subsequently collapse. Low environmental degradation and high food availability leads to stable bee population. Global sensitivity analysis is conducted to determine the most sensitive parameters of the model that can lead to colony collapse disorder. Numerical simulations are conducted to illustrate all the results.
T. D. Seeley, Honeybee Ecology: A Study of Adaptation in Social Life, Princeton University Press, Princeton, NJ, 1985. DOI: https://doi.org/10.1515/9781400857876
F. A. Eischen, W. C. Rothenbuhler & J. M. Kulicevic, “Length of life and dry weight of worker honeybees reared in colonies with di erent workerlarva ratios”, Journal of Apicultural Research, 21 (1982) 19. DOI: https://doi.org/10.1080/00218839.1982.11100511
S. Russell, A. B. Barron & D. Harris, “Dynamic modelling of honey bee (Apis mellifera) colony growth and failure”, Ecological Modelling 265 (2013) 158. DOI: https://doi.org/10.1016/j.ecolmodel.2013.06.005
F. S. Bodenheimer, “Studies in animal populations II. Seasonal population-trends in the honey-bee”, Quat. Rev. Zool. 12 (1937) 406. DOI: https://doi.org/10.1086/394540
D. J. T. Sumpter & S. J. Martin, “The dynamics of virus epidemics in Varroa-infested honey bee colonies,” Journal of Animal Ecology 73 (2004) 51. DOI: https://doi.org/10.1111/j.1365-2656.2004.00776.x
M. H. Haydak, “Age of nurse bees and brood rearing”, Journal of Apicultural Research 2 (1963) 101. DOI: https://doi.org/10.1080/00218839.1963.11100067
N. W. Calderone, “Insect pollinated crops, insect pollinators and agriculture: trend analysis of aggregate data for the period 1992–2009”, Plos ONE 7 (2012) e37235. DOI: https://doi.org/10.1371/journal.pone.0037235
S. N. Sushil, J. Stanley, N. K. Hedau & J. C. Bhatt, “Enhancing seed production of three Brassica vegetables by honey bee pollination in northwestern Himalayas of India”, Universal Journal of Agricultural Research 1 (2013) 49. DOI: https://doi.org/10.13189/ujar.2013.010301
A. Mishra, O. Afik, M. L. Cabrera, K. S. Delaplane & J. E. Mowrer, “Inorganic nitrogen derived from foraging honey bees could have adaptive benefits for the plants they visit”, PLoS ONE 8 (2013) e70591. DOI: https://doi.org/10.1371/journal.pone.0070591
B. Yucel & I. Duman, “E ects of foraging activity of honeybees (Apis mellifera L.) on onion (Allium cepa) seed production and quality”, Pakistan Journal of Biological Sciences 8 (2005) 123. DOI: https://doi.org/10.3923/pjbs.2005.123.126
J. D. Ellis, J. D. Evans & J. Pettis, “Colony losses, managed colony population decline, and colony collapse disorder in the United States”, Journal of Apicultural Research 49 (2010) 134. DOI: https://doi.org/10.3896/IBRA.22.214.171.124
F. L. W. Ratnieks & N. L. Carreck, “Clarity on honey bee collapse?”, Science 327 (2010) 152. https://www.science.org/lookup/doi/10.1126/science.1185563 DOI: https://doi.org/10.1126/science.1185563
K. Watson & J. A. Stallins, “Honey Bees and Colony Collapse Disorder: A Pluralistic Reframing”, Geography Compass 10 (2016) 222. https://doi.org/10.1111/gec3.12266 DOI: https://doi.org/10.1111/gec3.12266
E. Varol & B. Yucel, “The E ects of Environmental Problems on Honey Bees in view of Sustainable Life”, Mellifera 19 (2019) 23.
M. Henry, M. Beguin, F. Requier, O. Rollin, J. F. Odoux, P. Aupinel, J. Aptel, S. Tchamitchian & A. Decourtye, “A common pesticide decreases foraging success and survival in honey bees” Science 336 (2012) 348. DOI: https://doi.org/10.1126/science.1215039
C. Ko, Y. Chen & Y. Nai, “Evaluating the E ect of Environmental Chemicals on Honey Bee Development from the Individual to Colony Level”, Journal of Visualized Experiments 122 (2017) 1. DOI: https://doi.org/10.3791/55296
D. Naug, “Nutritional stress due to habitat loss may explain recent honeybee colony collapses”, Biological Conservation 142 (2009) 2369. DOI: https://doi.org/10.1016/j.biocon.2009.04.007
H. N. Scofield & H. R. Mattila, “Honey bee workers that are pollen stressed as larvae become poor foragers and waggle dancers as adults”, Plos One 10 (2015) e0121731. DOI: https://doi.org/10.1371/journal.pone.0121731
Y. Le Conte & M. Navajas, “Climate change: impact on honey bee populations and diseases”, Revue Scientifique Et Technique-Of fice International Des Epizooties 27 (2008) 499. DOI: https://doi.org/10.20506/rst.27.2.1819
R. D. Girling, I. Lusebrink, E. Farthing, T. A. Newman & G. M. Poppy, “Diesel exhaust rapidly degrades floral odours used by honeybees”, Scientific Reports 3 (2013) 499. DOI: https://doi.org/10.1038/srep02779
A. Core, C. Runckel, J. Ivers, C. Quock, T. Siapno, S. DeNault, B. Brown, J. DeRisi, C. D. Smith & J. Hafernik, “A new threat to honey bees, the parasitic phorid fly Apocephalus borealis”, Plos ONE 7 (2012) e29639. DOI: https://doi.org/10.1371/journal.pone.0029639
T. E. Ferrari, “Magnets, magneticfield fluctuations and geomagnetic disturbances impair the homing ability of honey bees (Apis mellifera )”, Journal of Apicultural Research 49 (2014) 134. DOI: https://doi.org/10.3896/IBRA.126.96.36.199
G. DeGrandi-Ho man, S. A. Roth, G. L. Loper & E. H. Erickson, “BEEPOP: A Honeybee population dynamics simulation model”, Ecological Modelling 45 (1989) 133. DOI: https://doi.org/10.1016/0304-3800(89)90088-4
T. Schmickl & K. Crailsheim, “HoPoMo: A model of honeybee intracolonial population dynamics and resource management”, Ecological Modelling 204 (2007) 219. DOI: https://doi.org/10.1016/j.ecolmodel.2007.01.001
P. Magal, G. F. Webb & Y. Wu, “An Environmental Model of Honey Bee Colony Collapse Due to Pesticide Contamination”, Bulletin of Mathematical Biology 81 (2019) 4908. https://doi.org/10.1007/s11538-019-00662-5 DOI: https://doi.org/10.1007/s11538-019-00662-5
A. Petric, E. Guzman-Novoa & H. J. Eberl, “A mathematical model for the interplay of Nosema infection and forager losses in honey bee colonies”, Journal of Biological Dynamics 11 (2017) 348. https://doi.org/10.1080/17513758.2016.1237682 DOI: https://doi.org/10.1080/17513758.2016.1237682
A. D´enes & M. A. Ibrahim, “Global dynamics of a mathematical model for a honeybee colony infested by virus-carrying Varroa mites”, Journal of Applied Mathematics and Computing 61 (2019) 349. DOI: https://doi.org/10.1007/s12190-019-01250-5
D. J. Torres & N. A. Torres, “Modeling the Influence of Mites on Honey Bee Populations”, Veterinary sciences 7 (2020) 1. https://doi.org/10.3390/vetsci7030139 DOI: https://doi.org/10.3390/vetsci7030139
J. R. Comper & H. J. Eberl, “Mathematical modelling of population and food storage dynamics in a honey bee colony infected with Nosema ceranae”, Heliyon 6 (2020) e04599. https://doi.org/10.1016/j.heliyon.2020.e04599 DOI: https://doi.org/10.1016/j.heliyon.2020.e04599
D. S. Khoury, M. R. Myerscough & A. B. Barron, “Quantitative Model of Honey Bee Colony Population Dynamics”, PLoS ONE 6 (2011) 1. https://doi.org/10.1371/journal.pone.0018491 DOI: https://doi.org/10.1371/journal.pone.0018491
D. S. Khoury, A. B. Barron & M. R. Myerscough, “Modelling Food and Population Dynamics in Honey Bee Colonies”, PLoS ONE 8 (2013) 1. https://doi.org/10.1371/journal.pone.0059084 DOI: https://doi.org/10.1371/journal.pone.0059084
N. Danner, A. Keller, S. Ha` Ertel & I. Ste an-Dewenter, “Honey bee foraging ecology: Season but not landscape diversity shapes the amount and diversity of collected pollen”, PLoS ONE 12 (2017) e0183716. https://doi.org/10.1371/journal.pone.0183716 DOI: https://doi.org/10.1371/journal.pone.0183716
F. Requier, J. F. Odoux, T. Tamic, N. Moreau, M. Henry & A. Decourtye, “Honey bee diet in intensive farmland habitats reveals an unexpectedly high flower richness and a major role of weeds”, Ecological Applications
A. M. Stuart & A. R. Humphries, Dynamical Systems and Numerical Analysis, Cambridge University Press, 1998.
V. Lakshmikantham, S. Leela & A. A. Martynyuk, Stability Analysis of Non-linear Systems, Marcel Dekker, Inc., New York and Basel, 1989. DOI: https://doi.org/10.1142/1192
N. Bradbear, Bees and their role in forest livelihoods, FAO, Viale delle di Caracalla, 00153 Rome, Italy, 2009.
S. Marino, I. B. Hogue, C. J. Ray, & D. E. Kirschner, “A methodology for performing global uncertainty and sensitivity analysis in systems biology”, Journal of Theoretical Biology 254 (2008) 178. https://doi.org/10.1016/j.jtbi.2008.04.011 DOI: https://doi.org/10.1016/j.jtbi.2008.04.011
A. S. Hassan & J. M. W. Munganga, “Mathematical global dynamics and control strategies on Echinococcus multilocularis infection”, Computational and mathematical methods in medicine, 2019, (2019) 1. DOI: https://doi.org/10.1155/2019/3569528
M. O. Adeniyi, M. I. Ekum, C. Iluno, A. S. Ogunsanya, J. A. Akinyemi, I. O. Segun & M. B. Matadi, “Dynamic model of COVID-19 disease with exploratory data analysis”, Scientific African 000 (2020) e00477. DOI: https://doi.org/10.1016/j.sciaf.2020.e00477
D. J. Schulz, Z. Y. Huang & G. E. Robinson, “E ects of colony food shortage on behavioral development in honey bees”, Behav. Ecol. Sociobiol. 42 (1998) 295. DOI: https://doi.org/10.1007/s002650050442
How to Cite
Copyright (c) 2021 Journal of the Nigerian Society of Physical Sciences
This work is licensed under a Creative Commons Attribution 4.0 International License.
The Journal of the Nigerian Society of Physical Sciences (JNSPS) is published under the Creative Commons Attribution 4.0 (CC BY-NC) license. This license was developed to facilitate open access, namely, it allows articles to be freely downloaded and to be re-used and re-distributed without restriction, as long as the original work is correctly cited. More specifically, anyone may copy, distribute or reuse these articles, create extracts, abstracts, and other revised versions, adaptations or derivative works of or from an article, mine the article even for commercial purposes, as long as they credit the author(s).
Most read articles by the same author(s)
- Adamu Shitu Hassan, Nafiu Hussaini, Analysis of an HIV - HCV simultaneous infection model with time delay , Journal of the Nigerian Society of Physical Sciences: Volume 3, Issue 1, February 2021