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The Stability of Ecosystems and Paradox of Enrichment via Spatial Prey-Predator Distributions with Active Dispersal


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DOI: https://doi.org/10.15866/irece.v4i3.6866

Abstract


Understanding the transport mechanism is important key to interpret behavioral and physiological responses of organisms or to predict the success by which they find their resources. In this paper, the effect of transport mechanism in the prey-predator populations is investigated. The models suggested are based on classical Lotka-Volterra (LV) and Rosenzweig-MacArthur (RM) systems in which the passive dispersal (diffusion) and active dispersal (directed movement per se or taxis) are considered. The numerical simulation results obtained from this coupling model confirms two important features: 1) Active dispersal playing the convection role and considered as a simple mechanism to stabilize the prey-predator system; and 2) the coupling effect between active and passive dispersals generates heterogeneous distributions of both species of prey or of predator even in the homogenous environment
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Keywords


Prey-Predator Populations; Lotka-Volterra Model; Rosenzweig-MacArthur Model; Reaction-Convection-Diffusion; Active Dispersal; Passive Dispersal; Numerical Simulation

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References


A.J. Lotka, Elements of Physical Biology (Williams and Wilkins, Baltimore, 1925).

V. Volterra, Variazioni e fluttuazionidelnumero d'individui in specie d'animaniconviventi. Mem.AcadLincei, Roma 2: 31-113, 1926.

R.M. May, Models for two interacting populations. Theoretical Ecology (RMMay Edition, 2nd edition, Sianauer, Sunderland, MA, 1981, pp.78-104).

G.F. Gause, The struggle for existence (Williams and Wilkins, Baltimore, Maryland, 1934).

M.L. Rosenzweig and R.H. MacArthur, Graphical representation and stability conditions of predator-prey interactions, American Naturalist, Vol. 97:205-223, 1963.
http://dx.doi.org/10.1086/282272

A.D. Bazykin, Nonlinear dynamics of Interacting populations (World Scientific, Singapore,1998).
http://dx.doi.org/10.1142/2284

L. Arnold, W. Horsthemke and J.W. Stucki, The influence of external real and white noise on the Lotka-Volterra model. Biomed. J., Vol. 21:451-471, 1979.
http://dx.doi.org/10.1002/bimj.4710210507

M.F. Dimentberg, Lotka-Volterra system in a random environment, Physical Review E, Vol. 65 (Issue 3): 03624-03621, 2002.
http://dx.doi.org/10.1103/physreve.65.036204

G.Q. Cai and Y.K. Lin, Stochastic analysis of the Lotka-Volterra model for ecosystems, Physical Review E, Vol. 70(Issue 4), article number: 041910, 2004.
http://dx.doi.org/10.1103/physreve.70.041910

M.L. Rosenzweig, The paradox of enrichment: the destabilization of exploitation ecosystems in ecological time, Science, Vol. 171: 385-387, 1971.
http://dx.doi.org/10.1126/science.171.3969.385

F.M. Hilker and M.A. Lewis, Predator–prey systems in streams and rivers,Theor.Ecol., Vol. 3:175–193, 2010.
http://dx.doi.org/10.1007/s12080-009-0062-4

R.P. Canale, Predator-Prey relationships in a model for the activated process, Biotechnology and Bioengineering, Vol. 11: 887-907, 1969.
http://dx.doi.org/10.1002/bit.260110514

P. Van den Ende, Predator-prey interactions in continuous culture, Science, Vol. 181:562-564, 1973.
http://dx.doi.org/10.1126/science.181.4099.562

C.H. Ratsak, B.W. Kooi and B. Kooijman, Modeling the Individual Growth of Tetrahymena Sp. and its population consequences, J.Euk.Microbiol., Vol. 42( Issue 3):268-276,1995.
http://dx.doi.org/10.1111/j.1550-7408.1995.tb01578.x

T.J. Pedley and J.O. Kessler, Hydrodynamic phenomena in suspensions of swimming micro-organisms, Ann.Rev.Fluid Mech., Vol. 24: 313-358, 1992.
http://dx.doi.org/10.1146/annurev.fl.24.010192.001525

H.N. Comins and D.W.E. Blatt, Prey-Predator Models in Spatially Heterogeneous Environments, J. theor. Biol., Vol.48: 75-83, 1974.
http://dx.doi.org/10.1016/0022-5193(74)90180-5

K.P. Hadeler, U. Van der Heiden and F. Rothe, Nonhomogeneous Spatial Distributions of Population, J. Math. Biol., Vol.1: 165-176, 1974.
http://dx.doi.org/10.1007/bf00275801

R. McMurtrie, Persistence and stability of single-species and prey-predator systems in spatially heterogeneous environments, Math.Biosci. Vol.39: 11-5, 1978.
http://dx.doi.org/10.1016/0025-5564(78)90026-3

A. Okubo, Population dynamics in temporal and spatial domains, in Diffusion and Ecological Problems:Mathematical Models(K. Krickeberg and S. A. Levin, Eds.), Biomathematics (Springer, 1980, pp. 169-223).

J.F. McLaughlin and J. Roughgarden, Pattern and stability in Predator-Prey Communities: How Diffusion in Spatially Variable Environments Affects the Lotka-Volterra Model, Theoretical Population Biology, Vol. 40:148-172, 1991.
http://dx.doi.org/10.1016/0040-5809(91)90051-g

J.F. McLaughlin and J. Roughgarden, Predation across spatial scales in heterogeneous environments, Theoretical Population Biology 41:277-299, 1992.
http://dx.doi.org/10.1016/0040-5809(92)90030-w

F.S. Berezovskaya and G.P. Karev, Bifurcations of travelling waves in population taxis models, Physics - Uspekhi, Russian Academy of Sciences, Vol. 42 (Issue 9): 917-929, 1999.
http://dx.doi.org/10.1070/pu1999v042n09abeh000564

Y. Tyutyunov, A.D. Zagrebneva, F.A. Surkov and A.A.Azovsky, Microscale patchiness of the distribution of Copepods (Harpacticoida) as a result of trophotaxis, Biophysics, Vol. 54 (Issue 3): 508-514, 2009.
http://dx.doi.org/10.1134/s000635090903018x

R. Nallaswamy and J.B.Shukla, Effects of convective and dispersive migration on the linear stability of a two species system with mutualistic interactions and functional response, Bull. Muth.Biol., Vol. 44: 271-282, 1982.
http://dx.doi.org/10.1016/s0092-8240(82)80069-4

T. Nguyen-Quang, T.H. Nguyen, F. Guichard, A.Nicolau, G. Smatzari, G. LePalec, M. Dusser, J. Lafossee, J.L. Bonnet and J. Bohatier, Two dimensional gravitacticbioconvection in a protozoan (Tetrahymenapyriformis) culture,Zoological Science, Vol.26: 54-65, 2009.
http://dx.doi.org/10.2108/zsj.26.54

A. Okubo and S. Levin, Diffusion and Ecological Problems: Modern Perspectives (Springer, 2nd Edition, 2002).
http://dx.doi.org/10.1007/978-1-4757-4978-6

G.Q. Cai and Y.K. Lin, Stochastic analysis of predator-prey ecosystems. Ecological Complexity, Vol. 4: 242-249, 2007.
http://dx.doi.org/10.1016/j.ecocom.2007.06.011

V.P. Shukla, J.B. Shukla and P.C. Das , Environmental effects on the linear stability of a three species food chain model, Math. Biosci., Vol. 57:35-58, 1981.
http://dx.doi.org/10.1016/0025-5564(81)90004-3

R. Nallaswamy, Global stability of a system of two interacting species with convective and dispersive migration. Math.Biosci.Vol. 67:101-111, 1983.
http://dx.doi.org/10.1016/0025-5564(83)90021-4

S.R. Connolly and J. Roughgarden, Theory of marine communities: competition, predation, and recruitment-dependent interaction strength, Ecological Monographs, Vol.69 (Issue 3): 277-296, 1999.
http://dx.doi.org/10.2307/2657158

B. Gaylord andS.D.Gaines , Temperature or transport? Range limits in marine species mediated solely by flow, Am. Nat., Vol. 155:769–789, 2000.
http://dx.doi.org/10.1086/303357

J.E. Byers and J.M. Pringle, Going against the flow: retention, range limits and invasions in advective environments, Mar. Ecol. Prog. Ser. Vol.313: 27–41, 2006.
http://dx.doi.org/10.3354/meps313027

L.T. Takahashi, N.A. Maidana, W.C .Ferreira, P. Pulino, H.M. Yang, Mathematical models for the Aedesaegyptidispersal dynamics: travelling waves by wing and wind, Bull. Math. Biol.Vol.67:509-528, 2005.
http://dx.doi.org/10.1016/j.bulm.2004.08.005

A.B. Potapov and M.A. Lewis, Climate and competition: the effect of moving range boundaries on habitat invisibility, Bull. Math. Biol.Vol.66:975–1008, 2004.
http://dx.doi.org/10.1016/j.bulm.2003.10.010


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