caa a22 4500 469060751 CHVBK 20180323132856.0 cr unu---uuuuu 170328e19920601xx s 000 0 eng 10.1007/BF01200565 doi (NATIONALLICENCE)springer-10.1007/BF01200565 Prey dispersal and predator persistence [Elektronische Daten] [V. Jansen, M. Sabelis] To understand how patchiness influences population dynamics of a tri-trophic interaction, a tractable model is formulated in terms of differential equations. Motivated by the structure of systems such as plants, phytophagous mites and predatory mites, the model takes dispersal into account at the middle trophic level. The effect of dispersal for the middle level in a tri-trophic system could be either stabilising or destabilising since the middle level acts both as prey and as predator. First a simple model with logistic growth for the lowest level is formulated. A model with logistic growth for the lowest level and instantaneous dispersal has a globally stable three-species equilibrium, if this equilibrium exists. Addition of a middle level dispersal phase of non-negligible duration influences equilibrium stability. In the absence of the top trophic level a limit cycle can occur, caused by the delay that exists in the reaction of the middle level to the changes in the lowest level. With low predator efficiency, it is also possible to have an unstable three-species equilibrium. So addition of a middle level dispersal phase of non-negligible duration can work destabilising. Next the persistence of the third trophic level is studied. Even when the three-species equilibrium exists, the third trophic level need not be persistent. A two-species limit cycle can keep its stability when a three-species equilibrium exists; the system is then bistable. It is argued that such a bistability can offer an alternative explanation for pesticide-induced outbreaks of spider mites and failure of predator introduction. Elsevier Science Publishers B.V., 1992 Jansen V. Institute of Theoretical Biology, University of Leiden, P.O. Box 9516, 2300 RA, Leiden, Netherlands aut Sabelis M. Department of Pure and Applied Ecology, University of Amsterdam, Amsterdam, Netherlands aut Experimental & Applied Acarology Kluwer Academic Publishers 14/3-4(1992-06-01), 215-231 0168-8162 14:3-4<215 1992 14 10493 https://doi.org/10.1007/BF01200565 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01200565 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jansen V. Institute of Theoretical Biology, University of Leiden, P.O. Box 9516, 2300 RA, Leiden, Netherlands aut NATIONALLICENCE 700 1- Sabelis M. Department of Pure and Applied Ecology, University of Amsterdam, Amsterdam, Netherlands aut NATIONALLICENCE 773 0- Experimental & Applied Acarology Kluwer Academic Publishers 14/3-4(1992-06-01), 215-231 0168-8162 14:3-4<215 1992 14 10493 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer