Abstract
The mathematical description of poikilothermic organisms’ life cycle, of insects in particular, is a widely discussed argument, above all for its application in decision support systems. The increasing interest among agricultural industries in obtaining products with minor quantities of chemical inputs has led entomologists and model scientists to study in greater depth not only the biology and behaviour of the insects, but also the way to translate these mechanisms into mathematical language. The aim of this work is to provide a new instrument to describe insect pests’ population density. In particular, the study analyses insects’ development through the life stages driven by environmental factors. This has led researchers to consider physiological age, instead of the more widely used chronological age. In addition to mortality and fertility rates, the possibility of improving the simulation by inserting as a boundary condition results from previous field monitoring or the links with diapause models has been considered. The work is validated in the case of the European grapevine moth Lobesia botrana.
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References
Ageno, M.: Le radici della Biologia. Feltrinelli Editore, Milan (1986)
Allen, J.C., Byrd, J.H.: Computer modeling of insect growth and its application to forensic entomology (2000). https://www.ncjrs.gov/pdffiles1/nij/grants/181992.pdf. Accessed 6 Feb 2018
Baumgärtner, J., Gutierrez, A.P., Pesolillo, S., Severini, M.: A model for the overwintering process of European grapevine moth Lobesia botrana (Denis & Schiffermüller) (Lepidoptera, Tortricidae) populations. J. Entomol. Acarol. Res. 44(1), 2 (2012). https://doi.org/10.4081/jear.2012.e2
Briére, J.F., Pracros, P.: Comparison of temperature-dependent growth models with the development of Lobesia botrana (Lepidoptera: Tortricidae). Environ. Entomol. 27(1), 94–101 (1998). https://doi.org/10.1093/ee/27.1.94
Briére, J.F., Pracros, P., Le Roux, A.Y., Pierre, J.S.: A novel rate model of temperature-dependent development for arthropods. Environ. Entomol. 28(1), 22–29 (1999). https://doi.org/10.1093/ee/28.1.22
Brunori, E., Farina, R., Biasi, R.: Sustainable viticulture: the carbon-sink function of the vineyard agro-ecosystem. Agric. Ecosyst. Environ. 223, 10–21 (2016). https://doi.org/10.1016/j.agee.2016.02.012
Castex, V., Beniston, M., Calanca, P., Fleury, D., Moreau, J.: Pest management under climate change: the importance of understanding tritrophic relations. Sci. Total Environ. 616–617, 397–407 (2018). https://doi.org/10.1016/j.scitotenv.2017.11.027
Chou, T., Greenman, C.D.: A hierarchical kinetic theory of birth, death and fission in age-structured interacting populations. J. Stat. Phys. 164, 49–76 (2016). https://doi.org/10.1007/s10955-016-1524-x
Cocco, A., Deliperi, S., Lentini, A., Mannu, R., Delrio, G.: Seasonal phenology of Tuta absoluta (Lepidoptera: Gelechiidae) in protected and open-field crops under Mediterranean climatic conditions. Phytoparasitica 43(5), 713–724 (2015). https://doi.org/10.1007/s12600-015-0486-x
Damos, P., Savopoulou-Soultani, M.: Temperature-driven models for insect development and vital thermal requirements. Psyche (2012). https://doi.org/10.1155/2012/123405
Delbac, L., Thiéry, D.: Lobesia botrana (Lepidoptera: Tortricidae) larval population assessment by damage to grape flowers: could empty larval nests monitoring be useful? IOBC-WPRS Bull. 128, 37–44 (2017)
Diekmann, O., Lauwerier, H.A., Aldenberg, T., Metz, J.A.J.: Growth, fission and the stable size distribution. J. Math. Biol. 18(2), 135–148 (1983). https://doi.org/10.1007/BF00280662
Feldman, R.M., Curry, G.L.: A PDE formulation and numerical solution for a boll weevil–cotton crop model. Comput. Math. Appl. 9(3), 393–402 (1983). https://doi.org/10.1016/0898-1221(83)90054-8
Fraga, H., Santos, J.A., Moutinho-Pereira, J., Carlos, C., Silvestre, J., Eiras-Dias, J., Mota, T., Malheiro, A.C.: Statistical modelling of grapevine phenology in Portuguese wine regions: observed trends and climate change projections. J. Agric. Sci. 154(5), 795–811 (2016). https://doi.org/10.1017/S0021859615000933
Gillanders, S.W., Saunders, D.S.: A coupled pacemaker-slave model for the insect photoperiodic clock: interpretation of ovarian diapause data in Drosophila melanogaster. Biol. Cybern. 49, 149–154 (1984). https://doi.org/10.1371/journal.pone.0046143
Ikemoto, T., Kiritani, K.: Novel method of specifying low and high threshold temperatures using thermodynamic SSI model of insect development. Environ. Entomol. 48(3), 479–488 (2019). https://doi.org/10.1093/ee/nvz031
Iltis, C., Martel, G., Thiéry, D., Moreau, J., Louâpre, P.: When warmer means weaker: high temperatures reduce behavioural and immune defences of the larvae of a major grapevine pest. J. Pest Sci. 91(4), 1315–1326 (2018). https://doi.org/10.1007/s10340-018-0992-y
Logan, J.A., Wollkind, D.J., Hoyt, S.C., Tanigoshi, L.K.: An analytic model for description of temperature dependent rate phenomena in arthropods. Environ. Entomol. 5(6), 1133–1140 (1976). https://doi.org/10.1093/ee/5.6.1133
Lucchi, A., Scaramozzino, P.L., Michl, G., Loni, A., Hoffmann, C.: The first record in italy of Trichogramma cordubense Vargas & Cabello 1985 (Hymenoptera Trichogrammatidae) emerging from the eggs of Lobesia botrana (Denis & Schiffermüller, 1775) (Lepidoptera Tortricidae). VITIS-J. Grapevine Res. 55(4), 161–164 (2016). https://doi.org/10.5073/vitis.2016.55.161-164
McKendrick, A.G.: Applications of mathematics to medical problems. Edimburgh Math. Soc. (1926). https://doi.org/10.1017/S0013091500034428
Meisner, M.H., Harmon, J.P., Ives, A.R.: Temperature effects on long-term population dynamics in a parasitoid-host system. Ecol. Monogr. 84(3), 457–476 (2014). https://doi.org/10.1890/13-1933.1
Mirhosseini, M.A., Fathipour, Y., Reddy, G.V.P.: Arthropod development’s response to temperature: a review and new software for modeling. Ann. Entomol. Soc. Am. 110(6), 507–520 (2017). https://doi.org/10.1093/aesa/sax071
Moshtaghi Maleki, F., Iranipour, S., Hejazi, M.J., Saber, M.: Temperature-dependent age-specific demography of grapevine moth (Lobesia botrana) (Lepidoptera: Tortricidae): jackknife vs. bootstrap techniques. Arch. Phytopathol. Plant Prot. 49(11–12), 263–280 (2016). https://doi.org/10.1080/03235408.2016.1140566
Nemani, R.R., White, M.A., Cayan, D.R., Jones, G.V., Running, S.W., Coughlan, J.C., Peterson, D.L.: Asymmetric warming over coastal California and its impact on the premium wine industry. Clim. Res. 19(1), 25–34 (2001). https://doi.org/10.3354/cr019025
Pavan, F., Floreani, C., Barro, P., Zandigiacomo, P., Dalla Montà, L.: Occurrence of two different development patterns in Lobesia botrana (Lepidoptera: Tortricidae) larvae during the second generation. Agric. For. Entomol. 15(4), 398–406 (2013). https://doi.org/10.1111/afe.12027
Pennington, T., Reiff, J.M., Theiss, K., Entling, M.H., Hoffmann, C.: Reduced fungicide applications improve insect pest control in grapevine. BioControl 63(5), 687–695 (2018). https://doi.org/10.1007/s10526-018-9896-2
Preto, C.R., Bellamy, D.E., Walse, S.S., Zalom, F.G.: Predicting larval stage distribution of Lobesia botrana (Lepidoptera: Tortricidae) at three constant temperatures. J. Econ. Entomol. 112(2), 585–590 (2019). https://doi.org/10.1093/jee/toy374
Rojano, F., Ibarra-Juárez, L.A., Lira-Noriega, A., Escobar-Sarria, F., González-Tokman, D.: Application of a modified McKendrick-Von Foerster equation to predict beetle population dynamics (Xyleborus affinis) under artificial medium in growth chambers. In: AgEng Conference, 1–8 July (2018)
Rossini, L., Contarini, M., Severini, M., Talano, D., Speranza, S.: A modelling approach to describe the Anthonomus eugenii (Coleoptera: Curculionidae) life cycle in plant protection: a priori and a posteriori analysis. Fla. Entomol. (2020) (in press)
Rossini, L., Severini, M., Contarini, M., Speranza, S.: A novel modelling approach to describe an insect life cycle vis-à-vis plant protection: description and application in the case study of Tuta absoluta. Ecol. Model. 409(July), 108778 (2019). https://doi.org/10.1016/j.ecolmodel.2019.108778
Rossini, L., Severini, M., Contarini, M., Speranza, S.: Use of ROOT to build a software optimized for parameter estimation and simulations with Distributed Delay Model. Ecol. Inform. 50(January), 184–190 (2019). https://doi.org/10.1016/j.ecoinf.2019.02.002
Rossini, L., Severini, M., Contarini, M., Speranza, S.: EntoSim, a ROOT-based simulator to forecast insects’ life cycle: description and application in the case of Lobesia botrana. Crop Prot. 129, 105024 (2020). https://doi.org/10.1016/j.cropro.2019.105024
Rupnik, R., Kukar, M., Vračar, P., Košir, D., Pevec, D., Bosnić, Z.: AgroDSS: a decision support system for agriculture and farming. Comput. Electron. Agric. 161(November 2017), 260–271 (2019). https://doi.org/10.1016/j.compag.2018.04.001
Saunders, D.S.: Insect photoperiodism: effects of temperature on the induction of insect diapause and diverse roles for the circadian system in the photoperiodic response. Entomol. Sci. 17(1), 25–40 (2014). https://doi.org/10.1111/ens.12059
Schoolfield, R.M., Sharpe, P.J., Magnuson, C.E.: Non-linear regression of biological temperature-dependent rate models based on absolute reaction-rate theory. J. Theor. Biol. 88(4), 719–31 (1981). https://doi.org/10.1016/0022-5193(81)90246-0
Speranza, S., Colonnelli, E., Garonna, A.P., Laudonia, S.: First record of Anthonomus eugenii (Coleoptera: Curculionidae) in Italy. Fla. Entomol. 97(2), 844–845 (2014). https://doi.org/10.1653/024.097.0275
Speranza, S., Sannino, L.: The current status of Tuta absoluta in Italy. EPPO Bull. 42(2), 328–332 (2012). https://doi.org/10.1111/epp.2579
Tauber, E., Kyriacou, B.P.: Insect photoperiodism and circadian clocks: models and mechanisms. J. Biol. Rhythm. 16(4), 381–390 (2001). https://doi.org/10.1177/074873001129002088
Thiéry, D., Monceau, K., Moreau, J.: Larval intraspecific competition for food in the European grapevine moth Lobesia botrana. Bull. Entomol. Res. 104(4), 517–524 (2014). https://doi.org/10.1017/S0007485314000273
Tonnang, H.E.Z., Mohamed, S.F., Khamis, F., Ekesi, S.: Identification and risk assessment for worldwide invasion and spread of Tuta absoluta with a focus on Sub-Saharan Africa: implications for phytosanitary measures and management. PloS One 10(8), 1–19 (2015). https://doi.org/10.1371/journal.pone.0135283
Trucco, E.: Mathematical models for cellular systems: the Von Foerster equation. Part I. Bull. Math. Biophys. 27(3), 449–471 (1965). https://doi.org/10.1007/BF02476849
Trucco, E.: Mathematical models for cellular systems: the Von Foerster equation. Part II. Bull. Math. Biophys. 27, 449–471 (1965)
Varela, L.G., Smith, R.J., Cooper, M.L., Hoenisch, R.W.: European grapevine moth, Lobesia botrana, in Napa Valley vineyards. Practical Winery & Vineyard, 1–5 March/April (2010)
Vassiliou, V.A.: Effectiveness of insecticides in controlling the first and second generations of the Lobesia botrana (Lepidoptera: Tortricidae) in table grapes. J. Econ. Entomol. 104(2), 580–585 (2011). https://doi.org/10.1603/EC10343
Verpy, A., Gil, F., Mary, S., Delbac, L., Thiéry, D.: Temporal differences in Lobesia botrana’s lifecycle at local scale, the example of the Saint Emilion vineyard. IOBC-WPRS Bull. 105, 197–204 (2014)
Von Foerster, H.: Some remarks on changing populations. In: Stohlman Jr., F. (ed.) The Kinetics of Cellular Proliferation, pp. 382–407. Grune and Stratton, New York (1959)
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The authors are grateful to the anonymous reviewers for their comments and suggestions, which have been greatly helpful for the improvement of this manuscript. The research was carried out in the framework of the MIUR (Ministry for Education, University and Research) initiative “Department of Excellence” (Law 232/2016).
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Rossini, L., Contarini, M. & Speranza, S. A novel version of the Von Foerster equation to describe poikilothermic organisms including physiological age and reproduction rate. Ricerche mat 70, 489–503 (2021). https://doi.org/10.1007/s11587-020-00489-6
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DOI: https://doi.org/10.1007/s11587-020-00489-6