Abstract
Necessity to understand the role of additional food as a tool in biological control programs is being increasingly felt, particularly due to its eco-friendly nature. A thorough mathematical analysis in this direction revealed the vital role of quality and quantity of the additional food in the controllability of the predator–prey systems. In this article controllability of the additional food—provided predator–prey system is studied from perspectives of pest eradication and biological conservation. Time optimal paths have been constructed to drive the state of the system to a desired terminal state by choosing quantity of the additional food as control variable. The theory developed in this article has been illustrated by solving problems related to pest eradication and biological conservation.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Azzouz, H., Giordanengo, P., Wäckers, F. L., & Kaiser, L. (2004). Effects of feeding frequency and sugar concentration on behavior and longevity of the adult aphid parasitoid: Aphidius ervi (Haliday) (Hymenoptera: Braconidae). Biol. Control, 31, 445–452.
Beach, J. P., Williams, L. III, Hendrix, D. L., & Price, L. D. (2003). Different food sources affect the gustatory response of Anaphes iole, an egg parasitoid of Lugus spp. J. Chem. Ecol., 29, 1203–1222.
Berndt, L. A., Wratten, S. D., & Hassan, P. (2002). Effects of buckwheat flowers on leafroller (Lepidoptera: Tortricidae) parasitoids in a New Zealand vineyard. Agric. For. Entomol., 4, 39–45.
Bilde, T., & Toft, S. (1998). Quantifying food limitation of arthropod predators in the field. Oecologia, 115, 54–58.
Buttermore, R. E., Turner, E., & Morrice, M. G. (1994). The introduced northern Pacific seastar Asterias amurensis in Tasmania. Mem. Qld. Mus., 36, 21–25.
Cesari, L. (1983). Applications of mathematics series: Vol. 17. Optimization—theory and applications: problems with ordinary differential equations. New York: Springer.
Clark, C. W. (2005). Mathematical bioeconomics—the optimal management of renewable resoruces. New Jersey: Wiley.
Coll, M., & Guershon, M. (2002). Omnivory in terrestrial arthropods: mixing plant and prey diets. Annu. Rev. Entomol., 47, 267–297.
Davis, S. E., Nager, R. G., & Furness, R. W. (2005). Food availability affects adult survival as well as breeding success of Parasitic Jaegers. Ecology, 86(4), 1047–1056.
DeBach, P., & Rosen, D. (1974). Biological control by natural enemies. London: Cambridge University Press.
De Clercq, P. (2008). Culture and natural enemies on factitious foods and artificial diets. In J. L. Capinera (Ed.), Encyclopedia of entomology (Vol. I, pp. 1133–1136). Dordrecht: Springer.
Fadamiro, H. Y., & Heimpel, G. E. (2001). Effects of partial sugar deprivation on lifespan and carbohydrate mobilization in the parasitoid Macrocentrus grandii (Hymenopters: Braconidae). Ann. Entomol. Soc. Am., 94, 909–916.
Gurr, G. M., & Wratten, S. D. (1999). Integrated biological control: a proposal for enhancing success in biological control. Int. J. Pest Manag., 45(2), 81–84.
Harmon, J. P. (2003), Indirect interactions among a generalist predator and its multiple foods. Ph.D. thesis, St. Paul, MN, University of Minnesota.
Harwood, J. D., Sunderland, K. D., & Symondson, W. O. C. (2004). Prey selection by linyphiid spiders: molecular tracking of the effects of alternative prey on rates of aphid consumption in the field. Mol. Ecol., 13, 3549–3560.
Harwood, J. D., Sunderland, K. D., & Symondson, W. O. C. (2005). Monoclonal antibodies reveal the potential of the tetragnathids spider Pachygnatha degeeri (Araneae: Tetragnathidae) as an aphid predator. Bull. Entomol. Res., 95, 161–167.
Harwood, J. D., & Obrycki, J. J. (2005). The role of alternative prey in sustaining predator populations. In M. S. Hoddle (Ed.), Proc. second int. symp. biol. control of arthropods (Vol. II, pp. 453–462).
Hendrix, D., Wei, Y., & Leggett, J. E. (1992). Homopteran honeydew sugar composition is determined by both the insect and plant species. Comp. Biochem. Physiol. B, 101, 23–27.
Holling, C. S. (1959). Some characteristics of simple types of predation and parasitism. Can. Entomol., 91, 385–398.
Jervis, M. A. (1998). Functional and evolutionary aspects of mouthpart structure in parasitoid wasps. Biol. J. Linn. Soc., 63, 461–493.
Kot, M. (2001). Elements of mathematical ecology. Cambridge: Cambridge University Press.
Lafferty, K. D., & Kuris, A. M. (1994). Potential uses for biological control of alien marine species. In D. Cottingham (Ed.), Proc. conf. and workshop on nonindigenous estuarine and marine organisms, U.S. Department of Commerce, NOAA Office of the Chief Scientist. Washington: U.S. Gov. Printing Office.
Lafferty, K. D., & Kuris, A. M. (1996). Biological control of marine pests. Ecology, 77(7), 1989–2000.
Landis, D. A., Wratten, S. D., & Gurr, G. M. (2000). Habitat management to conserve natural enemies of arthropod pests in agriculture. Annu. Rev. Entomol., 45, 175–201.
Margaritopoulos, J. T., Tsitsipis, J. A., & Perdikis, D. C. (2003). Biological characteristics of the mirids Macrolophus costalis and Macroplophus pygmaeus preying on the tobacco form of Myzus persicae (Hemiptera: Aphididae). Bull. Entomol. Res., 93, 39–45.
McDougall, S. J., & Mills, N. J. (1997). The influence of hosts, temperature and food sources on the longevity of Trichogramma platneri. Entomol. Exp. Appl., 83, 195–203.
Miller, R. F. (1985). Sea urchin pathogen: a possible tool for biological control. Mar. Ecol. Prog. Ser., 21, 169–174.
Moyle, P. B. (1991). Ballast water introductions. Fishereis, 16, 4–6.
Murdoch, W. W., Chesson, J., & Chesson, P. L. (1985). Biological control in theory and practice. Am. Nat., 125(3), 344–366.
Perdikis, D., & Lykouressis, D. (2000). Effects of various items, host plants, and temperature on the development and survival of Macrolophus pygmaeus Rambur (Hemiptera: Miridae). Biol. Control, 17, 55–60.
Perdikis, D., & Lykouressis, D. (2004). Macrolophus pygmaeus (Hemiptera: Miridae) population parameters and biological characteristics when feeding on eggplant and tomato without prey. J. Econ. Entomol., 97, 1291–1298.
Perdikis, D., Lykouressis, D., & Economou, L. (1999). The influence of temperature, photoperiod and plant type on the predation rate of Macrolophus pygmaeus on Myzus persicae. BioControl, 44, 281–289.
Sabelis, M. W., & van Rijn, P. C. J. (2005). When does alternative food promote biological pest control. In M. S. Hoddle (Ed.), Proc. second int. symp. biol. control of arthropods (Vol. II, pp. 428–437).
Shannon, P. S., Chrzanowski, T. H., & Grover, J. P. (2007). Prey food quality affects flagellate ingestion rates. Microb. Ecol., 53, 66–73.
Siekmann, G., Tenhumberg, B., & Keller, M. A. (2001). Feeding and survival in parasitic wasps: sugar concentration and timing matter. Oikos, 95(3), 425–430.
Srinivasu, P. D. N., Prasad, B. S. R. V., & Venkatesulu, M. (2007). Biological control through provision of additional food to predators: a theoretical study. Theor. Popul. Biol., 72, 111–120. doi:10.1016/j.tpb.2007.03.011.
Srinivasu, P. D. N., & Prasad, B. S. R. V. (2010). Time optimal control of an additional food provided predator–prey system with applications to pest management and biological conservation. J. Math. Biol., 60, 591–613. doi:10.1007/s00285-009-0279-2.
Toft, S. (2005). The quality of aphids as food for generalist predators: implications for natural control of aphids. Eur. J. Entomol., 102(3), 371–383.
van Baalen, M., Křivan, V., van Rijn, P. C. J., & Sabelis, M. W. (2001). Alternative food, switching predators, and the persistence of predator–prey systems. Am. Nat., 157(5), 512–524.
van Rijn, P. C. J., van Houten, Y. M., & Sabelis, M. W. (2002). How plants benefit from providing food to predators even when it is also edible to herbivores. Ecology, 83, 2664–2679.
Vandekerkhove, B., & De Clercq, P. (2010). Pollen as an alternative or supplementary food for the mirid predator. Macrolophus pygmaeus. Biol. Control, 53, 238–242.
Wäckers, F. L. (2004). Assessing the suitability of flowering herbs as parasitoid food soruces: flower attractiveness and nectar accessibility. Biol. Control, 29, 307–314.
Wäckers, F. L. (2005). Suitability of (extra-) floral nectar, pollen, and honeydew as insect food sources. In F. L. Wäckers, P. C. J. van Rijn, & L. Bruin (Eds.), Plant-provided food for carnivorous insects, a protective mutualism and its applications (pp. 17–74). London: Cambridge University Press.
Wade, M. R., Zalucki, M. P., Wrateen, S. D., & Robinson, K. A. (2008). Conservation biological control of arthropods using artificial food sprays: current status and future challenges. Biol. Control, 45, 185–199.
Wootton, J. T. (1994). The nature and consequences of indirect effects in ecological communities. Ann. Rev. Ecol. Syst., 25, 443–466.
Wratten, S., Berndt, L., Gurr, G., Tylianakis, J., Fernando, P., & Didham, R. (2002). Adding floral diversity to enhance parasitoid fitness and efficacy. In R. G. Van Driesche (Ed.), Proc. first int. symp. biol. control of arthropods (pp. 211–214).
Wu, H., Meng, L., & Li, B. (2008). Effects of feeding frequency and sugar concentrations on lifetime reproductive success of Meteorus pulchricornis (Hymenoptera: Braconidae). Biol. Control, 45, 353–359.
Zhao, B., Qiu, J. W., & Qian, P. Y. (2003). Effects of food availability on larval development in the slipper limpet Crepidula onyx (Sowerby). J. Exp. Mar. Biol. Ecol., 294, 219–223.
Author information
Authors and Affiliations
Corresponding author
Additional information
This work is supported by CSIR, Govt. of India—sanction no. 25(0159)/08/EMR-II.
Rights and permissions
About this article
Cite this article
Srinivasu, P.D.N., Prasad, B.S.R.V. Role of Quantity of Additional Food to Predators as a Control in Predator–Prey Systems with Relevance to Pest Management and Biological Conservation. Bull Math Biol 73, 2249–2276 (2011). https://doi.org/10.1007/s11538-010-9601-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11538-010-9601-9