Modeling the Dynamics of Banana Weevil, Cosmopolites Sordidus (Germar), by Trapping with Holling Type II Response Function
DOI:
https://doi.org/10.26713/jims.v12i3.1387Keywords:
Asymptotic stability, Banana weevil, Holling type 2 functional response, Logistic growth model, Pseudostem traps, Saddle node bifurcationAbstract
A harvested logistic growth model that incorporates trapping of the adult banana weevils is formulated and solved both analytically and numerically. Key in the analysis of the model is the derivation of the critical trapping rate, that is, the threshold above which extinction of the banana weevils is a possibility. The existence of the saddle-node bifurcation is investigated. It is established that the stability of the equilibria is dependent on the relative sizes of the intrinsic growth rate and the carrying capacity. It is also found out that when the trapping rate exceeds the critical value, the model displays chaotic behavior and the trapping of the adult banana weevils in isolation can only provide short term relief. Thus a management package that targets all developmental stages of the banana weevils would be more effective. Numerical simulations are performed and agree with the analytical results.
Downloads
References
A. M. Abera-Kalibata, C. S. Gold, R. G. Van Driesche, and P. E. Ragama, Composition, distribution, and relative abundance of ants in banana farming systems in Uganda, Biological Control 40(2) (2007), 168 – 178, DOI: 10.1016/j.biocontrol.2006.11.006.
R. Bakyalire and M. W. Ogenga-Latigo, Aspects of the life cycle and behavior of the banana weevil, Cosmopolites Sordidus Germar (Coleoptera: Curculionidae), in Recent Contribution to Banana Entomology in Uganda (1990-1992), M. W. Ogenga-Latigo (ed.), Department of Crop Sciences, Makerere University, Uganda (1992).
R. Bakyalire, A study of the life cycle and behavior of the banana weevil Cosmopolites Sordidus Germar in Uganda, 118pp, Masters Thesis, Makerere University, Kampala, Uganda (1992).
F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer (2000), URL: https://link.springer.com/book/10.1007/978-1-4614-1686-9.
F. Brauer and D. A. Sanchez, Constant rate population harvesting: equilibrium and stability, Theoretical Population Biology 8(1975), 12 – 30, DOI: 10.1016/0040-5809(75)90036-2.
W. J. Budenberg, I. O. Ndiege and F. W. Karago, Evidence for volatile male-produced pheromone in banana weevil Cosmopolites sordidus, Journal of Chemical Ecology 19 (1993), 1905 – 1916, DOI: 10.1007/BF00983795.
FAOSTAT, Banana and Plantain Surface and Production in 2013, available at http//faostat.fao.org/site/339/default.aspx (2014).
C. S. Gold and M. I. Bagabe, Banana weevil, Cosmopolites Germar (Coleoptera, Curculionidae) infestation of cooking and beer bananas in adjacent stands in Uganda, African Entomology 5(1) (1997), 103 – 108, URL: https://www.ingentaconnect.com/content/sabinet/ento/1997/00000005/00000001/art00017.
C. S. Gold, J. E. Pena and E. B. Karamura, Biology and integrated pest management for the banana weevil Cosmopolites Sordidus (Germar) (Coleoptera Curculionidae), Integrated Pest Management Reviews 6(2001), 75 – 155, DOI: 10.1023/a:1023330900707.
C. S. Gold,G. H. Kagezi, G. Night and P. E. Ragama, The effects of banana weevil, Cosmopolites Sordidus (Germar) damage on highland banana growth, yield and stand duration in Uganda, Annals of Applied Biology 145(3)(2004), 263 – 269, DOI: 10.1111/j.1744-7348.2004.tb00382.x.
D. J. Greathead, Opportunities for control of insect pests in tropical Africa, Review of Zoology Africa (Revue de Zoologie Africaine) 100(1) (1986), 85 – 96, URL: https://www.cabi.org/isc/abstract/19870546138.
C. S. Holling, Some characteristics of simple types of predation and parasitism, The Canadian Entomologist 91(1959), 385 – 398, DOI: 10.4039/Ent91385-7.
E. B. Karamura and C. S. Gold, The elusive banana weevil, Cosmopolites sordidus Germar, in I International Symposium on Banana: I International Conference on Banana and Plantain for Africa 540 (1996), 471 – 485, DOI: 10.17660/ActaHortic.2000.540.53.
A. Kiggundu, W. Tushemereirwe and K. Kunert, Enhancing banana weevil resistance by plant genetic modification: a perspective. African Journal of Biotechnology 2(12)(2003), 563 – 569, DOI: 10.5897/AJB2003.000-1109.
A. M. Koppenhofer, K. V. Senshu-Reddy, G. Madel and M. C. Lubega, Predators of banana weevil Cosmopolites Sordidus, (Germar) (Col., Curculionidae), in western Kenya, Journal of Applied Entomology 114(1992), 530 – 533, DOI: 10.1111/j.1439-0418.1992.tb01161.x.
A. M. Koppenhofer, K. V. Seshu-Reddy and R. A. Sikora, Reduction of banana weevil populations with pseudostem traps, International Journal of Pest Management 40 (1994), 300 – 304, DOI: 10.1080/09670879409371903.
D. Ludwig, D. D. Jones and C. S. Holling, Qualitative analysis of the insect outbreak systems: The spruce budworm and the forest, The Journal of Animal Ecology 47(1) (1978), 315 – 332, DOI: 10.2307/3939.
M. Masanza, Effect of crop sanitation on banana weevil Cosmopolites Sordidus populations and associated damage, PhD. Thesis, Wageningen University, The Netherlands (2003).
I. O. Ndiege, S. Jarayama, A. C. Oehlschlager, L. Gonzalez, G. Alpizar and M. Fallas, Convenient synthesis and field activity of a male-produced aggregation pheromone of Cosmopolites Sordidus, Naturwissenschafften 83(6) (1996), 280 – 282, DOI: 10.1007/BF01149603.
I. Perfecto, Ants (Hymenoptera: Formicidae) as natural control agents of pests in irrigated maize in Nicaragua, Journal of Economic Entomology 84(1) (1991), 65 – 70, DOI: 10.1093/jee/84.1.65.
E. R. Pianka, On r-and K-selection, The American Naturalist 104(940) (1970), 592 – 597, URL: https://www.journals.uchicago.edu/doi/pdfplus/10.1086/282697.
R. Roche and S. Abreu, Control of the banana weevil Cosmopolites Sordidus by the ant Tetramorium guineense, Ciencias de la Agricultura 17(1983), 41 – 49, URL: https://www.cabdirect.org/cabdirect/abstract/19850524533.
P. M. Room, The relative abundance of ant species in Ghana's cocoa farms, The Journal of Animal Ecology 40 (1971), 735 – 751, DOI: 10.2307/3447.
N. D. T. M. Rukazambuga, C. S. Gold and S. R. Gowen, Yield loss in East African highland banana (Musa spp., AAA-EA group) caused by the banana weevil, Cosmopolites Sordidus Germar, Crop Protection 17(7) (1998), 581 – 589, DOI: 10.1016/S0261-2194(98)00056-8.
R. A. Sikora, N. D. Bafokuzara, A. S. S. Mbwana, G. W. Oloo, B. Uronu and K. S. Reddy, Interrelationship between banana weevil, root lesion nematode and agronomic practices, and their importance for banana decline in the United Republic of Tanzania, FAO Plant Protection Bulletin 37(4) (1989), 151 – 157, URL: https://www.cabdirect.org/cabdirect/abstract/19911179818.
D. F. Waterhouse, Biological control of Insect pests: South East Asia Prospects, ACIAR Monograph No. 51, Canberra, Australia (1998), URL: https://swfrec.ifas.ufl.edu/hlb/database/pdf/00000382.pdf.
E. C. Zeeman, Catastrophe theory, Scientific American 234(4) (1976), 65 – 83, DOI: 10.1038/scientificamerican0476-65.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
