Dynamics of insect predator and mosquito prey system with mutual interference as a factor for the co-occurrence: Validating through models

Chandrani Mukherjee; Krishna Pada Das; Goutam Panigrahi

doi:10.59400/jam.v1i3.246

Dynamics of insect predator and mosquito prey system with mutual interference as a factor for the co-occurrence: Validating through models

Chandrani Mukherjee Department of Basic Sciences and Humanities, Seacom Engineering College, West Bengal 711302, India
Krishna Pada Das Department of Mathematics, Mahadevananda Mahavidyalaya, West Bengal 700120, India
Goutam Panigrahi Department of Mathematics, NIT Durgapur, West Bengal 713209, India

Ariticle ID: 246

163 Views, 111 PDF Downloads

DOI: https://doi.org/10.59400/jam.v1i3.246

Keywords: functional response; mutual interference; mosquito control; predator-prey interactions; water bugs

Abstract

Several models have been proposed as an extension to the classical Holling’s disc equation to evaluate the predator and prey interactions and their applied aspects in biological control and population regulation of the target organisms. In a one-prey and two-predator dynamic system with mutual interference m as a quadratic parameter of predator density, an evaluation was made of the resultant impact on the prey. A simulation was carried out to see the finite-time extinction of prey and the stability of the system at origin, i.e., when all three species are extinct. We assumed the data obtained was for the interactions between the mosquito and the water bug predators that are common in the freshwater wetlands and involved in population regulation. Despite the benefits to the prey population due to interference and competition, the expected extinction of prey in a finite time is still observed. With varying magnitudes of m, the declining growth curve of the prey population shifted. The equation proposed was also compared with the Crowley-Martin functional response, and considerable differences were observed in selected instances when compared to the growth rate of the predators in a species-specific manner. The stability of the system was deduced from the eigenvalues of the Jacobian matrix at the origin to prove the extinction is stable. Our assessment supports the possible cooccurrence of predators and mosquito prey in the wetlands, with mutual interference being one of the major factors.

References

[1] Murdoch WW, Chesson J, Chesson PL. Biological control in theory and practice. The American Naturalist 1985; 125(3): 344–366. doi: 10.1086/284347

[2] Barbosa PA. In: Barbosa PA (editor). Conservation Biological Control, 1st ed. Academic Press; 1998. 396p.

[3] Murdoch WW. Population regulation in theory and practice. Ecology 1994; 75(2): 271–287. doi: 10.2307/1939533

[4] Saha N, Aditya G, Saha GK. Prey preferences of aquatic insects: Potential implications for the regulation of wetland mosquitoes. Medical and Veterinary Entomology 2013; 28(1): 1–9. doi: 10.1111/mve.12003

[5] Kundu M, Sharma D, Brahma S, et al. Insect predators of mosquitoes of rice fields: Portrayal of indirect interactions with alternative prey. Journal of Entomology and Zoology Studies 2014; 2(5): 97–103.

[6] Bellows TS, Fisher TW, Caltagirone LE, et al. In: Bellows TS, Fisher TW, Caltagirone LE, et al. (editors). Handbook of Biological Control, 1st ed. Academic Press; 1999. 1046p. doi: 10.1016/B978-0-12-257305-7.X5046-2

[7] Finke DL, Denno RF. Spatial refuge from intraguild predation: Implications for prey suppression and trophic cascades. Oecologia 2006; 149(2): 265–275. doi: 10.1007/s00442-006-0443-y

[8] Mogi M, Memah V, Miyagi I, et al. Mosquito (Diptera: Culicidae) and predator abundance in irrigated and rain-fed rice fields in North Sulawesi, Indonesia. Journal of Medical Entomology 1995; 32(3): 361–367. doi: 10.1093/jmedent/32.3.361

[9] Bambaradeniya C, Edirisinghe J, De Silva D, et al. Biodiversity associated with an irrigated rice agro-ecosystem in Sri Lanka. Biodiversity and Conservation 2004; 13: 1715–1753. doi: 10.1023/B:BIOC.0000029331.92656.de

[10] Das PK, Sivagnaname N, Amalraj DD. Population interactions between Culex vishnui mosquitoes and their natural enemies in Pondicherry, India. Journal of Vector Ecology 2006; 31(1): 84–88. doi: 10.3376/1081-1710(2006)31[84:PIBCVM]2.0.CO;2

[11] Fontanarrosa MS, Marinone MC, Fischer S, et al. Effects of flooding and temperature on Aedes albifasciatus development time and larval density in two rain pools at Buenos Aires University City. Memórias do Instituto Oswaldo Cruz 2000; 95(6): 787–793. doi: 10.1590/S0074-02762000000600007

[12] Campos RE, Fernández LA, Sy VE. Study of the insects associated with the floodwater mosquito Ochlerotatus albifasciatus (Diptera: Culicidae) and their possible predators in Buenos Aires Province, Argentina. Hydrobiologia 2004; 524(1): 91–102. doi: 10.1023/B:HYDR.0000036122.10578.d0

[13] Dale PER, Knight JM. Wetlands and mosquitoes: A review. Wetlands Ecology and Management 2008; 16(4): 255–276. doi: 10.1007/s11273-008-9098-2

[14] Wootton JT. The nature and consequences of indirect effects in ecological communities. Annual Review of Ecology and Systematical 1994; 25(1): 443–466. doi: 10.1146/annurev.es.25.110194.002303

[15] Blaustein L, Chase JM. Interactions between mosquito larvae and species that share the same trophic level. Annual Review of Entomology 2007; 52: 489–507. doi: 10.1146/annurev.ento.52.110405

[16] Juliano SA. Species interactions among larval mosquitoes: Context dependence across habitat gradients. Annual Review of Entomology 2009; 54(1): 37–56. doi: 10.1146/annurev.ento.54.110807.090611

[17] Sivagnaname N. Selective and frequency dependent predation of aquatic mosquito predator Diplonychus indicus Venkatesan & Rao (Hemiptera: Belostomatidae) on immature stages of three mosquito species. Entomological Research 2009; 39(6): 356–363. doi: 10.1111/j.1748-5967.2009.00243.x

[18] Brahma S, Aditya G, Sharma D, et al. Influence of density on intraguild predation of aquatic Hemiptera (Heteroptera): Implications in biological control of mosquito. Journal of Entomological and Acarological Research 2014; 46(1): 6–12. doi: 10.4081/jear.2014.1977

[19] Brahma S, Sharma D, Kundu M, et al. Mosquito prey vulnerability in intraguild predation between Ranatra filiformis and Anisops bouvieri: Implications in biological control. Proceedings of the Zoological Society 2015; 68(1): 36–44. doi: 10.1007/s12595-013-0093-0

[20] Brahma S, Sharma D, Kundu M, et al. Intraguild predation in Heteroptera: Effects of density and predator identity on Dipteran prey. Neotropical Entomology 2015; 44(4): 374–384. doi: 10.1007/s13744-015-0286-5

[21] Saha N, Kundu M, Saha GK, Aditya G. Alternative prey influence the predation of mosquito larvae by three water bug species (Heteroptera: Nepidae). Limnological Review 2020; 20(4): 173–184. doi: 10.2478/limre-2020-0017

[22] Elliott J. Interspecific interference and the functional response of four species of carnivorous stoneflies. Freshwater Biology 2003; 48(9): 1527–1539. doi: 10.1046/j.1365-2427.2003.01106.x

[23] Saha N, Aditya G, Bal A, Saha GK. A comparative study of predation of three aquatic heteropteran bugs on Culex quinquefasciatus larvae. Limnology 2007; 8(1): 73–80. doi: 10.1007/s10201-006-0197-6

[24] Saha N, Aditya G, Bal A, Saha GK. Comparative studies on functional response of common heteropteran bugs of East Calcutta Wetlands, Kolkata, India. International Review of Hydrobiology 2007; 92(3): 242–257. doi: 10.1002/iroh.200610939

[25] Holling CS. Some characteristics of simple types of predations and parasitism. The Canadian Entomologist 1959; 91(7): 385–398. doi: 10.4039/Ent91385-7

[26] Antwi-Fordjour K, Parshad RD, Beauregard MA. Dynamics of a predator-prey model with generalized Holling type functional response and mutual interference. Mathmatical Biosciences 2020; 326: 108407. doi: 10.1016/j.mbs.2020.108407

[27] Case TJ. An Illustrated Guide to Theoretical Ecology. Oxford University Press; 2000.

[28] Watt KEF. A mathematical model for the effect of densities of attacked and attacking species on the number attacked. The Canadian Entomologist 1959; 91(3): 129–144. doi: 10.4039/Ent91129-3

[29] Hassell MP, Varley GC. New inductive population model for insect parasites and its bearing on biological control. Nature 1969; 223(5211): 1133–1137. doi: 10.1038/2231133a0

[30] Roger DJ, Hassell MP. General models for insect parasite and predator searching behaviour: Interference. Journal of Animal Ecology 1974; 43(1): 239–253. doi: 10.2307/3170

[31] Beddington JR. Mutual interference between parasites or predators and its effect on searching efficiency. Journal of Animal Ecology 1975; 44(1): 331–340. doi: 10.2307/3866

[32] Hassell MP, Lawton JH, May RM. Patterns of dynamical behaviour in single-species populations. Journal of Animal Ecology 1976; 45(2): 471–486. doi: 10.2307/3886

[33] Santra PK, Mahapatra GS. Dynamical study of discrete-time prey-predator model with constant prey refuge under imprecise biological parameters. Journal of Biological Systems 2020; 28(3): 681–699. doi: 10.1142/S0218339020500114

[34] Mahapatra GS, Santra PK, Bonyah E. Dynamics on effect of prey refuge proportional to predator in discrete-time prey-predator model. New Perspectives in Nonlinear Dynamics of Complex Systems 2021; 2021: 6209908. doi: 10.1155/2021/6209908

[35] Santra PK, Mahapatra GS, Phaijoo GR. Bifurcation analysis and chaos control of discrete prey-predator model incorporating novel prey-refuge concept. Computational and Mathematical Methods 2021; 3(6): e1185. doi: 10.1002/cmm4.1185

[36] Sarwardi S, Mandal PK, Ray S. Analysis of a competitive prey-predator system with a prey refuge. Biosystems 2012; 110(3): 133–148. doi: 10.1016/j.biosystems.2012.08.002

[37] Sarwardi S, Mandal PK, Ray S. Dynamical behaviour of a two-predator model with prey refuge. Journal of Biological Physics 2013; 39(4): 701–722. doi: 10.1007/s10867-013-9327-7

[38] Morin PJ. Community Ecology. John Wiley & Sons; 2011. doi: 10.1002/9781444341966

[39] Hassell MP. Mutual interference between searching insect parasites. Journal of Animal Ecology 1971; 40(2): 473–486. doi: 10.2307/3256

[40] Meer JVD, Ens BJ. Models of interference and their consequences for the spatial distribution of ideal and free predators. Journal of Animal Ecology 1997; 66(6): 846–858. doi: 10.2307/6000

[41] DeLong JP, Vasseur DA. Mutual interference is common and mostly intermediate in magnitude. BMC Ecology 2011; 11: 1. doi: 10.1186/1472-6785-11-1

[42] Mulder C, Hendricks AJ. Half-saturation constants in functional responses. Global Ecology and Conservation 2014; 2: 161–169. doi: 10.1016/j.gecco.2014.09.006

[43] Crowley PH, Martin EK. Functional responses and interference within and between year classes of a dragonfly population. Journal of the North American Benthological Society 1989; 8(3): 211–221. doi: 10.2307/1467324

[44] Skalski GT, Gilliam JF. Functional responses with predator interference: Viable alternatives to the Holling type II model. Ecology 2001; 82(11): 3083–3092. doi: 10.1890/0012-9658(2001)082[3083:FRWPIV]2.0.CO;2

[45] Papanikolaou NE, Dervisoglou S, Fantinou A, et al. Predator size affects the intensity of mutual interference in a predatory mirid. Ecology and Evolution 2021; 11(3): 1342–1351. doi: 10.1002/ece3.7137

[46] Sana N, Aditya G, Bal A, Saha GK. Influence of light and habitat on predation of Culex quinquefasciatus (Diptera: Culicidae) larvae by the waterbugs (Hemiptera: Heteroptera). Insect Science 2008; 15(5): 461–469. doi: 10.1111/j.1744-7917.2008.00234.x

[47] Saha N, Aditya G, Saha GK. Habitat complexity reduces prey vulnerability: An experimental analysis using aquatic insect predators and immature dipteran prey. Journal of Asia-Pacific Entomology 2009; 12(4): 233–239. doi: 10.1016/j.aspen.2009.06.005

[48] Brahma S, Sharma D, Banerjee S, et al. Influence of habitat complexity on the prey mortality in IGP system involving insect predators (Heteroptera) and prey (Diptera): Implications in biological control. PLoS One 2022; 17(3): e0264840. doi: 10.1371/journal.pone.0264840

[49] Soetaert K, Herman PMJ. A Practical Guide to Ecological Modelling: Using R as a Simulation Platform. Springer; 2009. 372p. doi: 10.1007/978-1-4020-8624-3

[50] Stubben C, Milligan B. Estimating and analyzing demographic models using the popbio package in R. Journal of Statistical Software 2007; 22(11): 1–23. doi: 10.18637/jss.v022.i11

[51] Soetaert K, Petzoldt T, Setzer RW. Solving differential equations in R: Package deSolve. Journal of Statistical Software 2010; 33(9): 1–25. doi: 10.18637/jss.v033.i09

[52] ggplot2: Create elegant data visualisations using the grammar of graphics. Available online: https://ggplot2.tidyverse.org/reference/ggplot2-package.html (accessed on 9 November 2023).

[53] Murrell P. Recent changes in grid graphics. R News 2005; 5(1): 12–20.

[54] Sievert C. Interactive Web-Based Data Visualization with R, Plotly, and Shiny, 1st ed. CRC Press; 2020. doi: 10.1201/9780429447273

[55] DeLong JP. The body-size dependence of mutual interference. Biology Letter 2014; 10(6). doi: 10.1098/rsbl.2014.0261

[56] Murdoch WW, Sih A. Age-dependent interference in a predatory insect. Journal of Animal Ecology 1978; 47(2): 581–592. doi: 10.2307/3802

[57] Fox LR, Murdoch WW. Effects of feeding history on short-term and long-term functional responses in Notonecta hoffmanni. Journal of Animal Ecology 1978; 47(3): 945–959. doi: 10.2307/3680

[58] Sih A. Stability, prey density and age/dependent interference in an aquatic insect predator, Notonecta hoffmanni. Journal of Animal Ecology 1981; 50(2): 625–636. doi: 10.2307/4079

[59] Fernando MHJP, Hassell MP. Predator-prey responses in an acarine system. Population Ecology 1980; 22(2): 301–322. doi: 10.1007/BF02530853

[60] Pajunen VI. The effect of age-dependent interference on larval development in Callicorixa producta (Reut.) (Hemiptera, Corixidae). Annales Zoologici Fennici 1982; 19(3): 221–224.

[61] Abrahams MV, Mangel M, Hedges K. Predator-prey interactions and changing environments: Who benefits? Philosophical Transactions of the Royal Society B: Biological Sciences 2007; 362(1487): 2095–2104. doi: 10.1098/rstb.2007.2102

[62] Bertossa RC. Morphology and behaviour: Functional links in development and evolution. Philosophical Transactions of the Royal Society Lond B: Biological Sciences 2011; 366(1574): 2056–2568. doi: 10.1098/rstb.2011.0035

[63] Schmitz O. Predator and prey functional traits: Understanding the adaptive machinery driving predator–prey interactions. F1000 Research 2017; 6: 1767. doi: 10.12688/f1000research.11813.1

Published

2023-10-20

How to Cite

Mukherjee, C., Das, K. P., & Panigrahi, G. (2023). Dynamics of insect predator and mosquito prey system with mutual interference as a factor for the co-occurrence: Validating through models. Journal of AppliedMath, 1(3), 246. https://doi.org/10.59400/jam.v1i3.246

Download Citation

Issue

Vol. 1 No. 3 (2023)

Section

Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

Editor-in-Chief

Assoc. Prof. Ahmad Zeeshan

International Islamic University, Pakistan

eISSN

2972-4805

Publication Frequency

Bi-monthly

About the Publisher

Academic Publishing insists on taking academic exchange and publication as the main line, carrying out comprehensive management based on science and technology, and fully exploring excellent international publishing resources. Within 5 years, it will form a strategic framework and scale with science (S), technology (T), medicine (M), education (E), and humanities and arts (H) as the main publishing fields. Academic Publishing is headquartered in Singapore and based in Malaysia, with the United States and China providing the main scientific and academic resources. At the same time, it has established long-term good cooperative relations with other publishing companies, scientific research communities, and academic organizations in more than a dozen countries and regions. Academic Publishing uses English and Chinese as its main publishing languages, mainly publishing books, journals, and conference papers in print and online. The vast majority of publications follow the international open access policy, providing stable and long-term quality and professional publications. With the joint efforts of the expert team and our professional editorial team, our publications will gradually be indexed by international databases in stages to provide convenient and professional retrieval for various scholars. At the same time, manuscripts we accept will be subject to the peer review principle, and cutting-edge and innovative research articles will be preferentially accepted for peer reference and discussion. All kinds of our publications are welcome for peer to contribute, access, and download.

more

Volume Arrangement

2024

2023

Featured Articles

Octagonal-square tessellation model for masting GSM network: A case study of MTN Kumasi-East, Ghana

Masting in GSM network design is one of the most challenging problems in cell planning. The effect of uniform design pattern has been proven geographically to be hexagonal using uniform cell range. In this paper, we present a new uniform greedy semi-regular tessellation model called the octagonal square tessellation model (OSTM) to address the problem of global minimum overlap difference and area. Data from MTN Kumasi-East Ghana was collected and analyzed using the developed model. The original layout for the 0.6 km cell range accounted for an overlap difference of 937.66 m and a total area of 21.41 km² for 50 GSM mosts whereas the OSTM model accounted for an overlap difference of 1316.95 m with an area of 34.23 km². This is a 59.87% reduction of the original total area. Our solution is shown to be optimal in overlap difference and area for non-uniform cell range.

Computation of topological indices of linear chains of perylene and coronene using M-polynomial

The M-polynomial yields degree based topological indices that anticipate different physical and chemical properties of material being scrutinized. In this work, M- polynomial of linear chains of perylene and coronene are acquired. From M-polynomial, some degree based topological dicriptors are determined. Some topological indices of these compounds are compared by plotting graphs.

H∞ hybrid control and MRD in a steel frame building subjected to excessivevibrations caused by the dynamic action of wind and earthquake

The dynamic loads from earthquakes and winds can destroy lives, cause collapse in civil structures, and interrupt basic services provided to the population. In this scenario, structural designs must be developed to decrease the damage induced by these actions. The objective of this work is to design a hybrid controller based on the H∞ optimization via state feedback and the magneto-rheological damper (MRD) to mitigate the excessive vibrations of a three-story steel frame building, represented through the shear building model, subjected to the simultaneous dynamic action of wind and earthquake. All research is based on computational simulation, experimental research and results will not be addressed. In the numerical analysis, digital computer and MATLAB® software are used, and implemented codes generate the expected results based on the mathematical modeling. With the application of the H∞ control technique via state feedback, the displacements were reduced by 77%. With MRD this reduction was 79%. With the hybrid controller, this reduction was 100%. Thus, the verifications in relation to maximum displacements were met for NBR 15421:2006, NBR 8800:2008 and NBR 6118:2014. From the results, it is concluded that the hybrid controller proved to be more efficient and achieved the proposed objective. The exogenous inputs had zero influence on the behavior of the system output.

Topological analysis of multiple tables

The paper proposes a topological approach in order to explore several data tables simultaneously. These data tables of quantitative and/or qualitative variables measured on different homogeneous themes, collected from the same individuals. This approach, called topological analysis of multiple tables (TAMT), is based on the notion of neighborhood graphs in the context of a joint analysis of several data tables. It allows the simultaneous study of possible links between several thematic tables. The structure of the correlations or associations of the variables in each thematic table is analyzed according to quantitative, qualitative or mixed variables considered. Like the multiple factorial analysis (MFA), the TAMT allows several tables of variables to be analyzed simultaneously, and to obtain results, in particular graphical representations, which make it possible to study the relationship between individuals, variables and tables of data. These can also be tables of temporal data, collected at different times on the same individuals. The proposed TAMT approach is illustrated using real data associated with several and different homogeneous themes. Its results are compared to those from the MFA method.

Development of a stacked hybrid Decision Tree model leveraging the NSL-KDD dataset

Intrusion detection in information technology as well as operational technology networks is highly required in modern day systems due to the increased spate of cyber-attacks in both number and complexity. Anomaly-based intrusion detection systems which have the capacity to detect novel or zero-day attacks are highly employed in this regard. One important component of anomaly-based intrusion detection systems which ensures their behaviour is artificial intelligence in general and machine learning in particular. The burden in modern day cybersecurity research is to investigate and develop models that can outperform existing ones. This paper is aimed at developing a hybrid decision tree model using the stacking ensemble approach. Performances were measured on the basis of recall, precision, accuracy, F1-score, receiver operating characteristics and confusion matrices. The hybrid model presented a precision of 97%, accuracy of 81%, F1-score of 80% and AUC score of 0.96, respectively.