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Volumn 11, Issue , 2012, Pages 12-27

Bifurcation analysis of a ratio-dependent prey-predator model with the Allee effect

Author keywords

Allee effect; Paradox of enrichment; Population persistence; Predator prey model; Ratio dependent functional response

Indexed keywords


EID: 84864301019     PISSN: 1476945X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ecocom.2012.01.002     Document Type: Article
Times cited : (181)

References (64)
  • 1
    • 0027954761 scopus 로고
    • The fallacies of " ratio-dependent" predation
    • Abrams P.A. The fallacies of " ratio-dependent" predation. Ecology 1994, 75:1842-1850.
    • (1994) Ecology , vol.75 , pp. 1842-1850
    • Abrams, P.A.1
  • 2
    • 0034255819 scopus 로고    scopus 로고
    • The nature of predation: prey dependent, ratio dependent, or neither?
    • Abrams P.A., Ginzburg L. The nature of predation: prey dependent, ratio dependent, or neither?. Trends Ecol. Evol. 2000, 15(8):337-341.
    • (2000) Trends Ecol. Evol. , vol.15 , Issue.8 , pp. 337-341
    • Abrams, P.A.1    Ginzburg, L.2
  • 4
    • 4944258042 scopus 로고
    • Coupling in predator-prey dynamics: ratio-dependence
    • Arditi R., Ginzburg L.R. Coupling in predator-prey dynamics: ratio-dependence. J. Theor. Biol. 1989, 139:311-326.
    • (1989) J. Theor. Biol. , vol.139 , pp. 311-326
    • Arditi, R.1    Ginzburg, L.R.2
  • 5
    • 0000542895 scopus 로고
    • Variation in plankton densities among lakes: a case for ratio-dependent models
    • Arditi R., Ginzburg L.R., Akcakaya H.R. Variation in plankton densities among lakes: a case for ratio-dependent models. Am. Nat. 1991, 138:1287-1296.
    • (1991) Am. Nat. , vol.138 , pp. 1287-1296
    • Arditi, R.1    Ginzburg, L.R.2    Akcakaya, H.R.3
  • 6
    • 0001884135 scopus 로고
    • The biological control paradox
    • Arditi R., Berryman A.A. The biological control paradox. TREE 1991, 6:32.
    • (1991) TREE , vol.6 , pp. 32
    • Arditi, R.1    Berryman, A.A.2
  • 7
    • 0027100815 scopus 로고
    • Empirical evidence of the role of heterogeneity in ratio-dependent consumption
    • Arditi R., Saiah H. Empirical evidence of the role of heterogeneity in ratio-dependent consumption. Ecology 1992, 73:1544-1551.
    • (1992) Ecology , vol.73 , pp. 1544-1551
    • Arditi, R.1    Saiah, H.2
  • 8
    • 0034162515 scopus 로고    scopus 로고
    • Aggregation and emergence in ecological modelling: integration of ecological levels
    • Auger P., Charles S., Viala M., Poggiale J.C. Aggregation and emergence in ecological modelling: integration of ecological levels. Ecol. Model. 2000, 127:11-20.
    • (2000) Ecol. Model. , vol.127 , pp. 11-20
    • Auger, P.1    Charles, S.2    Viala, M.3    Poggiale, J.C.4
  • 9
    • 85028093389 scopus 로고    scopus 로고
    • Self-organised spatial patterns and chaos in a ratio-dependent predator-prey system
    • Banerjee M., Petrovskii S. Self-organised spatial patterns and chaos in a ratio-dependent predator-prey system. Theor. Ecol. 2011, 4:37-53.
    • (2011) Theor. Ecol. , vol.4 , pp. 37-53
    • Banerjee, M.1    Petrovskii, S.2
  • 11
    • 0000076167 scopus 로고
    • Mutual interference between parasites or predators and its effect on searching efficiency
    • Beddington J.R. Mutual interference between parasites or predators and its effect on searching efficiency. J. Anim. Ecol. 1975, 44:331-340.
    • (1975) J. Anim. Ecol. , vol.44 , pp. 331-340
    • Beddington, J.R.1
  • 12
    • 33947307582 scopus 로고    scopus 로고
    • Multiple Allee effects and population management
    • Berec L., Angulo E., Courchamp F. Multiple Allee effects and population management. TREE 2007, 22:185-191.
    • (2007) TREE , vol.22 , pp. 185-191
    • Berec, L.1    Angulo, E.2    Courchamp, F.3
  • 13
    • 0035460669 scopus 로고    scopus 로고
    • Parametric analysis of the ratio-dependent predator-prey model
    • Berezovskaya F., Karev G., Arditi R. Parametric analysis of the ratio-dependent predator-prey model. J. Math. Biol. 2001, 43:221-246.
    • (2001) J. Math. Biol. , vol.43 , pp. 221-246
    • Berezovskaya, F.1    Karev, G.2    Arditi, R.3
  • 14
    • 33748922626 scopus 로고    scopus 로고
    • Ratio-dependent response of a temperate Australian estuarine system to sustained nitrogen loading
    • Bishop M.J., Kelaher B.P., Smith M., York P.H., Booth D.J. Ratio-dependent response of a temperate Australian estuarine system to sustained nitrogen loading. Oecologia 2006, 149:701-708.
    • (2006) Oecologia , vol.149 , pp. 701-708
    • Bishop, M.J.1    Kelaher, B.P.2    Smith, M.3    York, P.H.4    Booth, D.J.5
  • 16
    • 0022766987 scopus 로고
    • Global analysis of a system of predator-prey equations
    • Conway E.D., Smoller J.A. Global analysis of a system of predator-prey equations. SIAM J. Appl. Math. 1986, 46:630-642.
    • (1986) SIAM J. Appl. Math. , vol.46 , pp. 630-642
    • Conway, E.D.1    Smoller, J.A.2
  • 17
    • 0033180314 scopus 로고    scopus 로고
    • Effects of spatial grouping on the functional response of predators
    • Cosner C., DeAngelis D.L., Ault J.S., Olson D.B. Effects of spatial grouping on the functional response of predators. Theor. Pop. Biol. 1999, 56:65-75.
    • (1999) Theor. Pop. Biol. , vol.56 , pp. 65-75
    • Cosner, C.1    DeAngelis, D.L.2    Ault, J.S.3    Olson, D.B.4
  • 18
    • 0033214426 scopus 로고    scopus 로고
    • Inverse density dependence and the Allee effect
    • Courchamp F., Clutton-Brock T., Grenfell B. Inverse density dependence and the Allee effect. TREE 1999, 14:405-410.
    • (1999) TREE , vol.14 , pp. 405-410
    • Courchamp, F.1    Clutton-Brock, T.2    Grenfell, B.3
  • 21
    • 0000604313 scopus 로고
    • Allee effect: population growth, critical density, and chance of extinction
    • Dennis B. Allee effect: population growth, critical density, and chance of extinction. Nat. Resour. Model. 1989, 3:481-538.
    • (1989) Nat. Resour. Model. , vol.3 , pp. 481-538
    • Dennis, B.1
  • 22
    • 41849111281 scopus 로고    scopus 로고
    • Scaling up the functional response for spatially heterogeneous systems
    • Englund G., Leonardsson K. Scaling up the functional response for spatially heterogeneous systems. Ecol. Lett. 2008, 11:440-449.
    • (2008) Ecol. Lett. , vol.11 , pp. 440-449
    • Englund, G.1    Leonardsson, K.2
  • 23
    • 0027098565 scopus 로고
    • Consequences of ratio-dependent predation for steady state properties of ecosystems
    • Ginzburg L.R., Akcakaya H.R. Consequences of ratio-dependent predation for steady state properties of ecosystems. Ecology 1992, 73:1536-1543.
    • (1992) Ecology , vol.73 , pp. 1536-1543
    • Ginzburg, L.R.1    Akcakaya, H.R.2
  • 24
    • 37049248026 scopus 로고
    • Enriched predator-prey systems: theoretical stability
    • Gilpin M.E. Enriched predator-prey systems: theoretical stability. Science 1972, 177:902-904.
    • (1972) Science , vol.177 , pp. 902-904
    • Gilpin, M.E.1
  • 25
    • 77955713687 scopus 로고    scopus 로고
    • Dynamical complexities in the Leslie-Gower predator-prey model as consequences of the Allee effect on prey
    • González-Olivares E., Mena-Lorca J., Rojas-Palma A., Flores J.D. Dynamical complexities in the Leslie-Gower predator-prey model as consequences of the Allee effect on prey. Appl. Math. Model. 2011, 35:366-381.
    • (2011) Appl. Math. Model. , vol.35 , pp. 366-381
    • González-Olivares, E.1    Mena-Lorca, J.2    Rojas-Palma, A.3    Flores, J.D.4
  • 26
    • 0001397558 scopus 로고
    • The functional response of predators: worries about scale
    • Hanski I. The functional response of predators: worries about scale. TREE 1991, 6:141-142.
    • (1991) TREE , vol.6 , pp. 141-142
    • Hanski, I.1
  • 27
    • 58349121665 scopus 로고    scopus 로고
    • Ratio-dependent predator-prey models of interacting populations
    • Haque M. Ratio-dependent predator-prey models of interacting populations. Bull. Math. Biol. 2009, 71(2):430-452.
    • (2009) Bull. Math. Biol. , vol.71 , Issue.2 , pp. 430-452
    • Haque, M.1
  • 29
    • 78651247833 scopus 로고    scopus 로고
    • Population collapse to extinction: the catastrophic combination of parasitism and Allee effect
    • Hilker F.M. Population collapse to extinction: the catastrophic combination of parasitism and Allee effect. J. Biol. Dyn. 2010, 4:86-101.
    • (2010) J. Biol. Dyn. , vol.4 , pp. 86-101
    • Hilker, F.M.1
  • 30
    • 58749105328 scopus 로고    scopus 로고
    • The Allee effect and infectious diseases: extinction, multistability, and the (dis-)appearance of oscillations
    • Hilker F.M., Langlais M., Malchow H. The Allee effect and infectious diseases: extinction, multistability, and the (dis-)appearance of oscillations. Am. Nat. 2009, 173:72-88.
    • (2009) Am. Nat. , vol.173 , pp. 72-88
    • Hilker, F.M.1    Langlais, M.2    Malchow, H.3
  • 31
    • 0002188006 scopus 로고
    • The role of the Allee effect in species packing
    • Hopf.F.A., Hopf.F.W. The role of the Allee effect in species packing. Theor. Pop. Biol. 1985, 27:25-50.
    • (1985) Theor. Pop. Biol. , vol.27 , pp. 25-50
    • Hopf, F.A.1    Hopf, F.W.2
  • 32
    • 0035376255 scopus 로고    scopus 로고
    • Global analysis of the Michaelis-Menten type ratio-dependent predator-prey system
    • Hsu S.B., Hwang T.W., Kuang Y. Global analysis of the Michaelis-Menten type ratio-dependent predator-prey system. J. Math. Biol. 2001, 42:489-506.
    • (2001) J. Math. Biol. , vol.42 , pp. 489-506
    • Hsu, S.B.1    Hwang, T.W.2    Kuang, Y.3
  • 33
    • 0000809487 scopus 로고
    • Experimental studies on predation: dispersion factors and predator-prey oscillations
    • Huffaker C.B. Experimental studies on predation: dispersion factors and predator-prey oscillations. Hilgardia 1958, 27:343-383.
    • (1958) Hilgardia , vol.27 , pp. 343-383
    • Huffaker, C.B.1
  • 34
    • 0033061694 scopus 로고    scopus 로고
    • About deterministic extinction in ratio-dependent predator-prey model
    • Jost C., Arino O., Arditi R. About deterministic extinction in ratio-dependent predator-prey model. Bull. Math. Biol. 1999, 61:19-32.
    • (1999) Bull. Math. Biol. , vol.61 , pp. 19-32
    • Jost, C.1    Arino, O.2    Arditi, R.3
  • 35
    • 0025526270 scopus 로고
    • Population dynamics in spatially complex environments: theory and data
    • Kareiva P. Population dynamics in spatially complex environments: theory and data. Phil. Trans. R. Soc. Lond. B 1990, 330:175-190.
    • (1990) Phil. Trans. R. Soc. Lond. B , vol.330 , pp. 175-190
    • Kareiva, P.1
  • 36
    • 0000941262 scopus 로고    scopus 로고
    • Rich Dynamics of Gause-type ratio-dependent predator-prey systems
    • Kuang Y. Rich Dynamics of Gause-type ratio-dependent predator-prey systems. Fields Inst. Commun. 1999, 21:325-337.
    • (1999) Fields Inst. Commun. , vol.21 , pp. 325-337
    • Kuang, Y.1
  • 37
    • 0000252357 scopus 로고    scopus 로고
    • Global qualitative analysis of a ratio-dependent predator-prey system
    • Kuang Y., Beretta E. Global qualitative analysis of a ratio-dependent predator-prey system. J. Math. Biol. 1998, 36:389-406.
    • (1998) J. Math. Biol. , vol.36 , pp. 389-406
    • Kuang, Y.1    Beretta, E.2
  • 39
    • 0027101175 scopus 로고
    • The problem of pattern and scale in ecology: the Robert H. MacArthur Award. Lecture
    • Levin S.A. The problem of pattern and scale in ecology: the Robert H. MacArthur Award. Lecture. Ecology 1992, 73:1943-1967.
    • (1992) Ecology , vol.73 , pp. 1943-1967
    • Levin, S.A.1
  • 40
    • 0027524391 scopus 로고
    • Allee dynamics and the spread of invading organisms
    • Lewis M.A., Kareiva P. Allee dynamics and the spread of invading organisms. Theor. Popul. Biol. 1993, 43:141-158.
    • (1993) Theor. Popul. Biol. , vol.43 , pp. 141-158
    • Lewis, M.A.1    Kareiva, P.2
  • 41
    • 35349008509 scopus 로고    scopus 로고
    • Heteroclinic bifurcation in the Michaelis-Menten type ratio-dependent predator-prey system
    • Li B., Kuang Y. Heteroclinic bifurcation in the Michaelis-Menten type ratio-dependent predator-prey system. SIAM J. Appl. Math. 2007, 67:1453-1464.
    • (2007) SIAM J. Appl. Math. , vol.67 , pp. 1453-1464
    • Li, B.1    Kuang, Y.2
  • 42
    • 0025251336 scopus 로고
    • Evaluation of natural enemies for biological control: a behavioral approach
    • Luck R.F. Evaluation of natural enemies for biological control: a behavioral approach. TREE 1990, 5:196-199.
    • (1990) TREE , vol.5 , pp. 196-199
    • Luck, R.F.1
  • 43
    • 0000386086 scopus 로고
    • Coexistence in laboratory populations of Paramecium aurelia and its predator Didinium nasutum
    • Luckinbill L.S. Coexistence in laboratory populations of Paramecium aurelia and its predator Didinium nasutum. Ecology 1973, 54:1320-1327.
    • (1973) Ecology , vol.54 , pp. 1320-1327
    • Luckinbill, L.S.1
  • 44
    • 77953684545 scopus 로고    scopus 로고
    • Emergence of Holling type III zooplankton functional response: bringing together field evidence and mathematical modelling
    • Morozov A.Yu. Emergence of Holling type III zooplankton functional response: bringing together field evidence and mathematical modelling. J. Theor. Biol. 2010, 265:45-54.
    • (2010) J. Theor. Biol. , vol.265 , pp. 45-54
    • Morozov, A.1
  • 45
    • 28444465570 scopus 로고    scopus 로고
    • Spatiotemporal complexity of patchy invasion in a predator-prey system with the Allee effect
    • Morozov A.Y., Petrovoskii S., Li B.L. Spatiotemporal complexity of patchy invasion in a predator-prey system with the Allee effect. J. Theor. Biol. 2006, 238:18-35.
    • (2006) J. Theor. Biol. , vol.238 , pp. 18-35
    • Morozov, A.Y.1    Petrovoskii, S.2    Li, B.L.3
  • 46
    • 70549093325 scopus 로고    scopus 로고
    • Patterns of zooplankton functional response in communities with vertical heterogeneity: a model study
    • Morozov A.Y., Arashkevich A.G. Patterns of zooplankton functional response in communities with vertical heterogeneity: a model study. Math. Modelling Nat. Phenom. 2008, 3:131-148.
    • (2008) Math. Modelling Nat. Phenom. , vol.3 , pp. 131-148
    • Morozov, A.Y.1    Arashkevich, A.G.2
  • 48
    • 0034895545 scopus 로고    scopus 로고
    • How predation can slow, stop or reverse a prey invasion
    • Owen M.R., Lewis M.A. How predation can slow, stop or reverse a prey invasion. Bull. Math. Biol. 2001, 63:655-684.
    • (2001) Bull. Math. Biol. , vol.63 , pp. 655-684
    • Owen, M.R.1    Lewis, M.A.2
  • 49
    • 44949242883 scopus 로고    scopus 로고
    • Computational ecology: from the complex to the simple and back
    • (electronic)
    • Pascual M. Computational ecology: from the complex to the simple and back. PLoS Comput. Biol. 2005, 1:2. (electronic).
    • (2005) PLoS Comput. Biol. , vol.1 , pp. 2
    • Pascual, M.1
  • 51
    • 16344366772 scopus 로고    scopus 로고
    • Regimes of biological invasion in a predator-prey system with the Allee effect
    • Petrovskii S.V., Morozov A.Y., Li B.-L. Regimes of biological invasion in a predator-prey system with the Allee effect. Bull. Math. Biol. 2005, 67:637-661.
    • (2005) Bull. Math. Biol. , vol.67 , pp. 637-661
    • Petrovskii, S.V.1    Morozov, A.Y.2    Li, B.-L.3
  • 52
    • 0031742563 scopus 로고    scopus 로고
    • Emergence of donor control in patchy predator-prey systems
    • Poggiale J.C., Michalski J., Arditi R. Emergence of donor control in patchy predator-prey systems. Bull. Math. Biol. 1998, 60:1149-1166.
    • (1998) Bull. Math. Biol. , vol.60 , pp. 1149-1166
    • Poggiale, J.C.1    Michalski, J.2    Arditi, R.3
  • 53
    • 0030986552 scopus 로고    scopus 로고
    • Predation and bark beetle dynamics
    • Reeve J.D. Predation and bark beetle dynamics. Oecologia 1997, 112:48-54.
    • (1997) Oecologia , vol.112 , pp. 48-54
    • Reeve, J.D.1
  • 54
    • 0025226663 scopus 로고
    • The importance of scale to predator-prey spatial correlations: an example of Atlantic fishes
    • Rose G.A., Leggett W.C. The importance of scale to predator-prey spatial correlations: an example of Atlantic fishes. Ecology 1990, 71:33-43.
    • (1990) Ecology , vol.71 , pp. 33-43
    • Rose, G.A.1    Leggett, W.C.2
  • 55
    • 0015243940 scopus 로고
    • Paradox of enrichment: destabilization of exploitation systems in ecological time
    • Rosenzweig M.L. Paradox of enrichment: destabilization of exploitation systems in ecological time. Science 1971, 171:385-387.
    • (1971) Science , vol.171 , pp. 385-387
    • Rosenzweig, M.L.1
  • 56
    • 34248173835 scopus 로고    scopus 로고
    • The stability of ecosystems: a brief overview of the paradox of enrichment
    • Roy S., Chattopadhyay J. The stability of ecosystems: a brief overview of the paradox of enrichment. J. Biosci. 2007, 32:421-428.
    • (2007) J. Biosci. , vol.32 , pp. 421-428
    • Roy, S.1    Chattopadhyay, J.2
  • 57
    • 54549114355 scopus 로고    scopus 로고
    • Type III functional response in Daphnia
    • Sarnelle O., Wilson A.E. Type III functional response in Daphnia. Ecology 2008, 89:1723-1732.
    • (2008) Ecology , vol.89 , pp. 1723-1732
    • Sarnelle, O.1    Wilson, A.E.2
  • 58
    • 33646715121 scopus 로고    scopus 로고
    • Persistence in reaction-diffusion models with weak Allee effect
    • Shi J., Shivaji R. Persistence in reaction-diffusion models with weak Allee effect. J. Math. Biol. 2006, 52:807-829.
    • (2006) J. Math. Biol. , vol.52 , pp. 807-829
    • Shi, J.1    Shivaji, R.2
  • 59
    • 0033215101 scopus 로고    scopus 로고
    • Consequences of the Allee effect for behaviour, ecology and conservation
    • Stephens P.A., Sutherland W.J. Consequences of the Allee effect for behaviour, ecology and conservation. TREE 1999, 14:401-405.
    • (1999) TREE , vol.14 , pp. 401-405
    • Stephens, P.A.1    Sutherland, W.J.2
  • 60
    • 34548565990 scopus 로고    scopus 로고
    • Heteroclinic orbits indicate overexploitation in predator-prey systems with a strong Allee effect
    • van Voorn G.A.K., Hemerik L., Boer M.P., Kooi B.W. Heteroclinic orbits indicate overexploitation in predator-prey systems with a strong Allee effect. Math. Biosci. 2007, 209:451-469.
    • (2007) Math. Biosci. , vol.209 , pp. 451-469
    • van Voorn, G.A.K.1    Hemerik, L.2    Boer, M.P.3    Kooi, B.W.4
  • 61
    • 0035012881 scopus 로고    scopus 로고
    • Speeds of invasion in a model with strong or weak Allee effects
    • Wang M.E., Kot M. Speeds of invasion in a model with strong or weak Allee effects. Math. Biosci. 2001, 171:83-97.
    • (2001) Math. Biosci. , vol.171 , pp. 83-97
    • Wang, M.E.1    Kot, M.2
  • 62
    • 79951508642 scopus 로고    scopus 로고
    • Predator-prey system with strong Allee effect in prey
    • Wang J., Shi J., Wei J. Predator-prey system with strong Allee effect in prey. J. Math. Biol. 2011, 62:291-331.
    • (2011) J. Math. Biol. , vol.62 , pp. 291-331
    • Wang, J.1    Shi, J.2    Wei, J.3
  • 63
    • 0035464834 scopus 로고    scopus 로고
    • Global dynamics of a ratio-dependent predator-prey system
    • Xiao D., Ruan S. Global dynamics of a ratio-dependent predator-prey system. J. Math. Biol. 2001, 43:268-290.
    • (2001) J. Math. Biol. , vol.43 , pp. 268-290
    • Xiao, D.1    Ruan, S.2
  • 64
    • 11844279070 scopus 로고    scopus 로고
    • The stability of predator-prey systems subject to the Allee effects
    • Zhou S., Liu Y., Wang G. The stability of predator-prey systems subject to the Allee effects. Theor. Pop. Biol. 2005, 67:23-31.
    • (2005) Theor. Pop. Biol. , vol.67 , pp. 23-31
    • Zhou, S.1    Liu, Y.2    Wang, G.3


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