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Avoidance behavior in intraguild predation communities: A cross-diffusion model

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  • A cross-diffusion model of an intraguild predation community in a two-dimensional bounded domain where the intraguild prey employs a fitness based avoidance strategy is examined. The avoidance strategy employed is to increase motility in response to negative local fitness. Global existence of trajectories and the existence of a compact global attractor is proved. It is shown that if the intraguild prey has positive fitness at any point in the habitat when trying to invade, then it will be uniformly persistent in the system if its avoidance tendency is sufficiently strong. This type of movement strategy can lead to coexistence states where the intraguild prey is marginalized to areas with low resource productivity while the intraguild predator maintains high densities in regions with abundant resources, a pattern observed in many real world intraguild predation systems. Additionally, the effects of fitness based avoidance on eigenvalues in more general systems are discussed.
    Mathematics Subject Classification: 35K59, 35B40, 92D40.


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  • [1]

    H. Amann, Dynamic theory of quasilinear parabolic equaitons I: Abstract evolution equaitons, Nonlinear Analysis: Theory, Methods & Applications, 12 (1988), 895-919.doi: 10.1016/0362-546X(88)90073-9.


    H. Amann, Dynamic theory of quasilinear parabolic systems III: Global existence, Mathematische Zeitschrift, 202 (1989), 219-250.doi: 10.1007/BF01215256.


    H. Amann, Dynamic theory of quasilinear parabolic systems II: reaction-diffusion systems, Differential and Integral Equations, 3 (1990), 13-75.


    M. Arim and P. A. Marquet, Intraguild predation: A widespread interaction related to species biology, Ecology Letters, 7 (2004), 557-564.doi: 10.1111/j.1461-0248.2004.00613.x.


    P. Amarasekare, Productivity, dispersal and the coexistence of intraguild predators and prey, Journal of Theoretical Biology, 243 (2006), 121-133.doi: 10.1016/j.jtbi.2006.06.007.


    P. Amarasekare, Spatial dynamics of communities with intraguild predation: The role of dispersal strategies, The American Naturalist, 170 (2007), 819-831.doi: 10.1086/522837.


    J. E. Billotti and J. P. LaSalle, Dissipative periodic processes, Bulletin of the American Mathematical Society, 77 (1971), 1082-1088.doi: 10.1090/S0002-9904-1971-12879-3.


    R. S. Cantrell and C. Cosner, Spatial Ecology via Reaction-Diffusion Equations, Wiley, Chichester, UK, 2003.doi: 10.1002/0470871296.


    S. M. Durant, Living with the enemy: Avoidance of hyenas and lions by cheetahs in the Serengeti, Behavioral Ecology, 11 (2000), 624-632.doi: 10.1093/beheco/11.6.624.


    J. K. Hale and P. Waltman, Persistence in infinite-dimensional systems, SIAM Journal on Mathematical Analysis, 20 (1989), 388-395.doi: 10.1137/0520025.


    D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1983.doi: 10.1007/978-3-642-61798-0.


    R. D. Holt and G. A. Polis, A theoretical framework for intraguild predation, The American Naturalist, 149 (1997), 745-764.doi: 10.1086/286018.


    T. Kimbrell, R. D. Holt and P. Lundberg, The influence of vigilance on intraguild predation, Journal of Theoretical Biology, 249 (2007), 218-234.doi: 10.1016/j.jtbi.2007.07.031.


    D. Le, Cross diffusion systems on n spatial dimensional domains, Indiana University Mathematics Journal, 51 (2002), 625-643.doi: 10.1512/iumj.2002.51.2198.


    G. Lieberman, Second Order Parabolic Equations, World Scientific, Singapore, 1996.doi: 10.1142/3302.


    E. Lucas, D. Coderre and J. Brodeur, Selection of molting and pupation sites by Coleomegilla maculata (Coleoptera: Coccinellidae): avoidance of intraguild predation, Environmental Entomology, 29 (2000), 454-459.doi: 10.1603/0046-225X-29.3.454.


    L. Nirenberg, On elliptic partial differential equations, Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, 13 (1959), 115-162.


    T. Okuyama and R. L. Ruyle, Analysis of adaptive foraging in an intraguild predation system, Web Ecology, 4 (2003), 1-6.doi: 10.5194/we-4-1-2003.


    F. Palomares and P. Ferreras, Spatial relationships between Iberian lynx and other carnivores in an area of southwestern Spain, Journal of Applied Ecology, 33 (1996), 5-13.


    F. Palomares and T. M. Caro, Interspecific killing among mammalian carnivores, The American Naturalist, 153 (1999), 492-508.doi: 10.1086/303189.


    D. Ryan, Fitness Dependent Dispersal in Intraguild Predation Communities, Ph.D thesis, University of Miami, 2011.


    F. Sergio, L. Marchesi and P. Pedrini, Spatial refugia and the coexistence of a diurnal raptor with its intraguild owl predator, Journal of Animal Ecology, 72 (2003), 232-245.doi: 10.1046/j.1365-2656.2003.00693.x.


    F. Sergio, L. Marchesi, P. Pedrini and V. Penteriani, Coexistence of a generalist owl with its intraguild predator: distance-sensitive or habitat-mediated avoidance?, Animal Behaviour, 74 (2007), 1607-1616.doi: 10.1016/j.anbehav.2006.10.022.


    R. Skeel and M. Berzins, A method for the spatial descretization of parabolic equations in one space variable, SIAM Journal on Scientific and Statistical Computing, 11 (1990), 1-32.doi: 10.1137/0911001.


    R. Temam, Infinite Dimensional Dynamical Systems, Springer-Verlag, Berlin, 1997.doi: 10.1007/978-1-4612-0645-3.


    C. M. Thompson and E. M. Gese, Food webs and intraguild predation: Community interactions of a native mesocarnivore, Ecology, 88 (2007), 334-346.

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