메뉴 건너뛰기




Volumn 85, Issue 1, 2016, Pages

Mathematical modeling of population dynamics with Allee effect

Author keywords

Allee effect; Diffusion; Noise; Predator prey model; Spatial pattern

Indexed keywords

CONSERVATION; DIFFUSION; DYNAMICS; POPULATION STATISTICS; PREDATOR PREY SYSTEMS; WAVEFRONTS;

EID: 84959269464     PISSN: 0924090X     EISSN: 1573269X     Source Type: Journal    
DOI: 10.1007/s11071-016-2671-y     Document Type: Review
Times cited : (180)

References (100)
  • 1
    • 34047113508 scopus 로고    scopus 로고
    • Establishing a beachhead: a stochastic population model with an allee effect applied to species invasion
    • Ackleh, A.S., Allen, L.J., Carter, J.: Establishing a beachhead: a stochastic population model with an allee effect applied to species invasion. Theor. Popul. Biol. 71, 290–300 (2007)
    • (2007) Theor. Popul. Biol. , vol.71 , pp. 290-300
    • Ackleh, A.S.1    Allen, L.J.2    Carter, J.3
  • 2
    • 0004255825 scopus 로고
    • University of Chicago Press, Chicago
    • Allee, W.C.: Animal Aggregations. University of Chicago Press, Chicago (1931)
    • (1931) Animal Aggregations
    • Allee, W.C.1
  • 5
    • 84982065090 scopus 로고
    • Studies in animal aggregations: mass protection against colloidal silver among goldfishes
    • Allee, W.C., Bowen, E.: Studies in animal aggregations: mass protection against colloidal silver among goldfishes. J. Exp. Zool. 61, 185–207 (1932)
    • (1932) J. Exp. Zool. , vol.61 , pp. 185-207
    • Allee, W.C.1    Bowen, E.2
  • 7
    • 31944451381 scopus 로고    scopus 로고
    • A numerical model to solve single-species invasion problems with allee effects
    • Almeida, R.C., Delphim, S.A., Costa, M.I.D.S.: A numerical model to solve single-species invasion problems with allee effects. Ecol. Model. 192, 601–617 (2006)
    • (2006) Ecol. Model. , vol.192 , pp. 601-617
    • Almeida, R.C.1    Delphim, S.A.2    Costa, M.I.D.S.3
  • 9
    • 76749134243 scopus 로고    scopus 로고
    • Extinction of metastable stochastic populations
    • Assaf, M., Meerson, B.: Extinction of metastable stochastic populations. Phys. Rev. E 81, 021116 (2010)
    • (2010) Phys. Rev. E , vol.81 , pp. 021116
    • Assaf, M.1    Meerson, B.2
  • 10
    • 84855266299 scopus 로고    scopus 로고
    • Sensitivity analysis of stochastic attractors and noise-induced transitions for population model with allee effect
    • Bashkirtseva, I., Ryashko, L.: Sensitivity analysis of stochastic attractors and noise-induced transitions for population model with allee effect. Chaos 21, 047514 (2011)
    • (2011) Chaos , vol.21 , pp. 047514
    • Bashkirtseva, I.1    Ryashko, L.2
  • 11
    • 33847055875 scopus 로고    scopus 로고
    • Instabilities in spatially extended predator–prey systems: spatio-temporal patterns in the neighborhood of turing–hopf bifurcations
    • Baurmann, M., Gross, T., Feudel, U.: Instabilities in spatially extended predator–prey systems: spatio-temporal patterns in the neighborhood of turing–hopf bifurcations. J. Theor. Biol. 245, 220–229 (2007)
    • (2007) J. Theor. Biol. , vol.245 , pp. 220-229
    • Baurmann, M.1    Gross, T.2    Feudel, U.3
  • 12
    • 33947307582 scopus 로고    scopus 로고
    • Multiple allee effects and population management
    • Berec, L., Angulo, E., Courchamp, F.: Multiple allee effects and population management. Trends Ecol. Evol. 22, 185–191 (2007)
    • (2007) Trends Ecol. Evol. , vol.22 , pp. 185-191
    • Berec, L.1    Angulo, E.2    Courchamp, F.3
  • 14
    • 4444269038 scopus 로고    scopus 로고
    • Allee effects, mating systems and the extinction risk in populations with two sexes
    • Bessa-Gomes, C., Legendre, S., Clobert, J.: Allee effects, mating systems and the extinction risk in populations with two sexes. Ecol. Lett. 7, 802–812 (2004)
    • (2004) Ecol. Lett. , vol.7 , pp. 802-812
    • Bessa-Gomes, C.1    Legendre, S.2    Clobert, J.3
  • 15
    • 0001583654 scopus 로고
    • The effects of habitat and density on breeding success in the common guillemot (uria aalge)
    • Birkhead, T.R.: The effects of habitat and density on breeding success in the common guillemot (uria aalge). J. Anim. Ecol. 46, 751–764 (1977)
    • (1977) J. Anim. Ecol. , vol.46 , pp. 751-764
    • Birkhead, T.R.1
  • 16
    • 34249935507 scopus 로고    scopus 로고
    • How predator functional responses and Allee effects in prey affect the paradox of enrichment and population collapses
    • Boukal, D.S., Sabelis, M.W., Berec, L.: How predator functional responses and Allee effects in prey affect the paradox of enrichment and population collapses. Theor. Popul. Biol. 72, 136–147 (2007)
    • (2007) Theor. Popul. Biol. , vol.72 , pp. 136-147
    • Boukal, D.S.1    Sabelis, M.W.2    Berec, L.3
  • 17
    • 84954271174 scopus 로고    scopus 로고
    • Influences of periodic mechanical deformation on pinned spiral waves
    • Chen, J.-X., Peng, L., Zheng, Q., Zhao, Y.-H., Ying, H.-P.: Influences of periodic mechanical deformation on pinned spiral waves. Chaos 24, 033103 (2014)
    • (2014) Chaos , vol.24 , pp. 033103
    • Chen, J.-X.1    Peng, L.2    Zheng, Q.3    Zhao, Y.-H.4    Ying, H.-P.5
  • 18
    • 84905843006 scopus 로고    scopus 로고
    • Liberation of a pinned spiral wave by a rotating electric pulse
    • Chen, J.-X., Peng, L., Ma, J., Ying, H.-P.: Liberation of a pinned spiral wave by a rotating electric pulse. EPL 107, 38001 (2014)
    • (2014) EPL , vol.107 , pp. 38001
    • Chen, J.-X.1    Peng, L.2    Ma, J.3    Ying, H.-P.4
  • 19
    • 84959766856 scopus 로고
    • Possible effects of schooling on the dynamics of exploited fish populations
    • Clark, C.W.: Possible effects of schooling on the dynamics of exploited fish populations. J. Cons. Int. Explor. Mer 36, 7–14 (1974)
    • (1974) J. Cons. Int. Explor. Mer , vol.36 , pp. 7-14
    • Clark, C.W.1
  • 20
    • 0000582309 scopus 로고    scopus 로고
    • Stochastic foundations of fractional dynamics
    • Compte, A.: Stochastic foundations of fractional dynamics. Phys. Rev. E 53, 4191–4193 (1996)
    • (1996) Phys. Rev. E , vol.53 , pp. 4191-4193
    • Compte, A.1
  • 23
    • 0034503479 scopus 로고    scopus 로고
    • Impact of natural enemies on obligately cooperative breeders
    • Courchamp, F., Grenfell, B.T., Clutton-Brock, T.H.: Impact of natural enemies on obligately cooperative breeders. Oikos 91, 311–322 (2000)
    • (2000) Oikos , vol.91 , pp. 311-322
    • Courchamp, F.1    Grenfell, B.T.2    Clutton-Brock, T.H.3
  • 24
    • 84868305139 scopus 로고    scopus 로고
    • Evolutionary dynamics and strong allee effects
    • Cushing, J., Hudson, J.T.: Evolutionary dynamics and strong allee effects. J. Biol. Dyn. 6, 941–958 (2012)
    • (2012) J. Biol. Dyn. , vol.6 , pp. 941-958
    • Cushing, J.1    Hudson, J.T.2
  • 25
    • 0000604313 scopus 로고
    • Allee-effects: population growth, critical density, and the chance of extinction
    • Dennis, B.: Allee-effects: population growth, critical density, and the chance of extinction. Nat. Res. Model. 3, 481–538 (1989)
    • (1989) Nat. Res. Model. , vol.3 , pp. 481-538
    • Dennis, B.1
  • 26
    • 0036222510 scopus 로고    scopus 로고
    • Allee effects in stochastic populations
    • Dennis, B.: Allee effects in stochastic populations. Oikos 96, 389–401 (2002)
    • (2002) Oikos , vol.96 , pp. 389-401
    • Dennis, B.1
  • 27
    • 0038693574 scopus 로고    scopus 로고
    • Extinction thresholds in host-parasite dynamics
    • Deredec, A., Courchmp, F.: Extinction thresholds in host-parasite dynamics. Ann. Zool. Fenn. 40, 115–130 (2003)
    • (2003) Ann. Zool. Fenn. , vol.40 , pp. 115-130
    • Deredec, A.1    Courchmp, F.2
  • 28
    • 79960499790 scopus 로고    scopus 로고
    • Population models with allee effect: a new model
    • Elaydi, S.N., Sacker, R.J.: Population models with allee effect: a new model. J. Biol. Dyn. 4, 397–408 (2010)
    • (2010) J. Biol. Dyn. , vol.4 , pp. 397-408
    • Elaydi, S.N.1    Sacker, R.J.2
  • 29
    • 84858862001 scopus 로고    scopus 로고
    • Remarks on cannibalism and pattern formation in spatially extended prey–predator systems
    • Fasani, S., Rinaldi, S.: Remarks on cannibalism and pattern formation in spatially extended prey–predator systems. Nonlinear Dyn. 62, 2543–2548 (2012)
    • (2012) Nonlinear Dyn. , vol.62 , pp. 2543-2548
    • Fasani, S.1    Rinaldi, S.2
  • 30
    • 0036350561 scopus 로고    scopus 로고
    • Behavioral stochastic resonance: how the noise from a daphnia swarm enhances individual prey capture by juvenile paddlefish
    • Freund, J., Schimansky-Geier, L., Beisner, B., Neiman, A., Russell, D., Yakusheva, T., Moss, F.: Behavioral stochastic resonance: how the noise from a daphnia swarm enhances individual prey capture by juvenile paddlefish. J. Theor. Biol. 214, 71–83 (2002)
    • (2002) J. Theor. Biol. , vol.214 , pp. 71-83
    • Freund, J.1    Schimansky-Geier, L.2    Beisner, B.3    Neiman, A.4    Russell, D.5    Yakusheva, T.6    Moss, F.7
  • 31
    • 5344241281 scopus 로고    scopus 로고
    • Allee effects driven by predation
    • Gascoigne, J.C., Lipcius, R.N.: Allee effects driven by predation. J. Appl. Ecol. 41, 801–810 (2004)
    • (2004) J. Appl. Ecol. , vol.41 , pp. 801-810
    • Gascoigne, J.C.1    Lipcius, R.N.2
  • 32
    • 44049116564 scopus 로고
    • Fractional diffusion equation for transport phenomena in random media
    • Giona, M., Roman, H.: Fractional diffusion equation for transport phenomena in random media. Phys. A 185, 87–97 (1992)
    • (1992) Phys. A , vol.185 , pp. 87-97
    • Giona, M.1    Roman, H.2
  • 33
    • 15844390604 scopus 로고    scopus 로고
    • A stage structured predator–prey model and its dependence on through-stage delay and death rate
    • Gourley, S., Kuang, Y.: A stage structured predator–prey model and its dependence on through-stage delay and death rate. J. Math. Biol. 49, 188–200 (2004)
    • (2004) J. Math. Biol. , vol.49 , pp. 188-200
    • Gourley, S.1    Kuang, Y.2
  • 34
    • 0031748982 scopus 로고    scopus 로고
    • Allee effects limit population viability of an annual plant
    • Groom, M.: Allee effects limit population viability of an annual plant. Am. Nat. 151, 487–496 (1998)
    • (1998) Am. Nat. , vol.151 , pp. 487-496
    • Groom, M.1
  • 35
    • 0034850846 scopus 로고    scopus 로고
    • Necessary and sufficient conditions for evolutionary suicide
    • Gyllenberg, M., Parvinen, K.: Necessary and sufficient conditions for evolutionary suicide. Bull. Math. Biol. 63, 981–993 (2001)
    • (2001) Bull. Math. Biol. , vol.63 , pp. 981-993
    • Gyllenberg, M.1    Parvinen, K.2
  • 36
    • 0036306866 scopus 로고    scopus 로고
    • Existence of turing instabilities in a two-species fractional reaction–diffusion system
    • Henry, B., Wearne, S.: Existence of turing instabilities in a two-species fractional reaction–diffusion system. SIAM J. Appl. Math. 62, 870–887 (2002)
    • (2002) SIAM J. Appl. Math. , vol.62 , pp. 870-887
    • Henry, B.1    Wearne, S.2
  • 37
    • 0035439412 scopus 로고    scopus 로고
    • An algorithmic introduction to numerical simulation of stochastic differential equations
    • Higham, D.J.: An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev. 43, 525–546 (2001)
    • (2001) SIAM Rev. , vol.43 , pp. 525-546
    • Higham, D.J.1
  • 38
    • 58749105328 scopus 로고    scopus 로고
    • The allee effect and infectious diseases: extinction, multistability, and the (dis-) appearance of oscillations
    • Hilker, F., Langlais, M., Malchow, H.: The allee effect and infectious diseases: extinction, multistability, and the (dis-) appearance of oscillations. Am. Nat. 173, 72–88 (2009)
    • (2009) Am. Nat. , vol.173 , pp. 72-88
    • Hilker, F.1    Langlais, M.2    Malchow, H.3
  • 39
    • 33847279684 scopus 로고    scopus 로고
    • A diffusive SI model with Allee effect and application to FIV
    • Hilker, F.M., Langlais, M., Petrovskii, S.V., Malchow, H.: A diffusive SI model with Allee effect and application to FIV. Math. Biosci. 206, 61–80 (2007)
    • (2007) Math. Biosci. , vol.206 , pp. 61-80
    • Hilker, F.M.1    Langlais, M.2    Petrovskii, S.V.3    Malchow, H.4
  • 40
    • 23944492384 scopus 로고    scopus 로고
    • Pathogens can slow down or reverse invasion fronts of their hosts
    • Hilker, F.M., Lewis, M.A., Seno, H., Langlais, M., Malchow, H.: Pathogens can slow down or reverse invasion fronts of their hosts. Biol. Invasions 7, 817–832 (2005)
    • (2005) Biol. Invasions , vol.7 , pp. 817-832
    • Hilker, F.M.1    Lewis, M.A.2    Seno, H.3    Langlais, M.4    Malchow, H.5
  • 41
    • 78651240331 scopus 로고    scopus 로고
    • Dynamics of an age-structured population with allee effects and harvesting
    • Jang, S.R.J.: Dynamics of an age-structured population with allee effects and harvesting. J. Biol. Dyn. 4, 409–427 (2010)
    • (2010) J. Biol. Dyn. , vol.4 , pp. 409-427
    • Jang, S.R.J.1
  • 42
    • 79956117638 scopus 로고    scopus 로고
    • Expansion or extinction: deterministic and stochastic two-patch models with Allee effects
    • Kang, Y., Lanchier, N.: Expansion or extinction: deterministic and stochastic two-patch models with Allee effects. J. Math. Biol. 62, 925–973 (2011)
    • (2011) J. Math. Biol. , vol.62 , pp. 925-973
    • Kang, Y.1    Lanchier, N.2
  • 43
    • 0037446297 scopus 로고    scopus 로고
    • Consequences for predators of rescue and allee effects on prey
    • Kent, A., Doncaster, C.P., Sluckin, T.: Consequences for predators of rescue and allee effects on prey. Ecol. Model. 162, 233–245 (2003)
    • (2003) Ecol. Model. , vol.162 , pp. 233-245
    • Kent, A.1    Doncaster, C.P.2    Sluckin, T.3
  • 45
    • 0031741955 scopus 로고    scopus 로고
    • Demographic stochasticity and Allee effect on a scale with isotropic noise
    • Lande, R.: Demographic stochasticity and Allee effect on a scale with isotropic noise. Oikos 83, 353–358 (1998)
    • (1998) Oikos , vol.83 , pp. 353-358
    • Lande, R.1
  • 46
    • 79951864384 scopus 로고    scopus 로고
    • Demographic stochasticity, Allee effects, and extinction: the influence of mating system and sex ratio
    • Lee, A.M., Sather, B.E., Engen, S.: Demographic stochasticity, Allee effects, and extinction: the influence of mating system and sex ratio. Am. Nat. 177, 301–313 (2011)
    • (2011) Am. Nat. , vol.177 , pp. 301-313
    • Lee, A.M.1    Sather, B.E.2    Engen, S.3
  • 47
    • 0023115931 scopus 로고
    • Mineral homeostasis in neonates of streptozotocin-induced noninsulin-dependent diabetic rats and in their mothers during pregnancy and lactation
    • Levy, J., Scott, M., Avioli, L.: Mineral homeostasis in neonates of streptozotocin-induced noninsulin-dependent diabetic rats and in their mothers during pregnancy and lactation. Bone 8, 1–6 (1987)
    • (1987) Bone , vol.8 , pp. 1-6
    • Levy, J.1    Scott, M.2    Avioli, L.3
  • 48
    • 0027524391 scopus 로고
    • Allee dynamics and the spread of invading organisms
    • Lewis, M., Kareiva, P.: Allee dynamics and the spread of invading organisms. Theor. Popul. Biol. 43, 141–158 (1993)
    • (1993) Theor. Popul. Biol. , vol.43 , pp. 141-158
    • Lewis, M.1    Kareiva, P.2
  • 49
    • 0034327966 scopus 로고    scopus 로고
    • Modeling and analysis of stochastic invasion processes
    • Lewis, M., Pacala, S.: Modeling and analysis of stochastic invasion processes. J. Math. Biol. 41, 387–429 (2000)
    • (2000) J. Math. Biol. , vol.41 , pp. 387-429
    • Lewis, M.1    Pacala, S.2
  • 50
    • 82255166728 scopus 로고    scopus 로고
    • Impact of noise on pattern formation in a predator–prey model
    • Li, A.-W.: Impact of noise on pattern formation in a predator–prey model. Nonlinear Dyn. 66, 689–694 (2011)
    • (2011) Nonlinear Dyn. , vol.66 , pp. 689-694
    • Li, A.-W.1
  • 51
    • 84855805384 scopus 로고    scopus 로고
    • Pattern dynamics of a spatial predator–prey model with noise
    • Li, L., Jin, Z.: Pattern dynamics of a spatial predator–prey model with noise. Nonlinear Dyn. 67, 1737–1744 (2012)
    • (2012) Nonlinear Dyn. , vol.67 , pp. 1737-1744
    • Li, L.1    Jin, Z.2
  • 52
    • 84861737668 scopus 로고    scopus 로고
    • Spatiotemporal dynamics of a predator–prey model
    • Liu, P.-P., Xue, Y.: Spatiotemporal dynamics of a predator–prey model. Nonlinear Dyn. 69, 71–77 (2012)
    • (2012) Nonlinear Dyn. , vol.69 , pp. 71-77
    • Liu, P.-P.1    Xue, Y.2
  • 53
    • 84892634738 scopus 로고    scopus 로고
    • Force exerted on the spiral tip by the heterogeneity in an excitable medium
    • Liu, T.-B., Ma, J., Zhao, Q., Tang, J.: Force exerted on the spiral tip by the heterogeneity in an excitable medium. EPL 104, 58005 (2013)
    • (2013) EPL , vol.104 , pp. 58005
    • Liu, T.-B.1    Ma, J.2    Zhao, Q.3    Tang, J.4
  • 56
    • 84902545269 scopus 로고    scopus 로고
    • Selection of multi-scroll attractors in Jerk circuits and their verification using Pspice
    • Ma, J., Wu, X., Chu, R., Zhang, L.: Selection of multi-scroll attractors in Jerk circuits and their verification using Pspice. Nonlinear Dyn. 76, 1951–1962 (2014)
    • (2014) Nonlinear Dyn. , vol.76 , pp. 1951-1962
    • Ma, J.1    Wu, X.2    Chu, R.3    Zhang, L.4
  • 57
    • 78650016107 scopus 로고    scopus 로고
    • Transition from spiral wave to target wave and other coherent structures in the networks of Hodgkin–Huxley neurons
    • Ma, J., Wang, C.N., Jin, W.Y., Wu, Y.: Transition from spiral wave to target wave and other coherent structures in the networks of Hodgkin–Huxley neurons. Appl. Math. Comput. 217, 3844–3852 (2010)
    • (2010) Appl. Math. Comput. , vol.217 , pp. 3844-3852
    • Ma, J.1    Wang, C.N.2    Jin, W.Y.3    Wu, Y.4
  • 59
    • 0028159712 scopus 로고
    • Timid consumers: self-extinction due to adaptive change in foraging and anti-predator effort
    • Matsuda, H., Abrams, P.: Timid consumers: self-extinction due to adaptive change in foraging and anti-predator effort. Theor. Popul. Biol. 45, 76–91 (1994)
    • (1994) Theor. Popul. Biol. , vol.45 , pp. 76-91
    • Matsuda, H.1    Abrams, P.2
  • 60
    • 0036733930 scopus 로고    scopus 로고
    • Spatio-temporal complexity of plankton and fish dynamics in simple model ecosystems
    • Medvinsky, A., Petrovskii, S., Tikhonova, I., Malchow, H., Li, B.-L.: Spatio-temporal complexity of plankton and fish dynamics in simple model ecosystems. SIAM Rev. 44, 311–370 (2002)
    • (2002) SIAM Rev. , vol.44 , pp. 311-370
    • Medvinsky, A.1    Petrovskii, S.2    Tikhonova, I.3    Malchow, H.4    Li, B.-L.5
  • 61
    • 79957655081 scopus 로고    scopus 로고
    • Extinction conditions for isolated populations with Allee effect
    • Mendez, V., Sans, C., Llopis, I., Campos, D.: Extinction conditions for isolated populations with Allee effect. Math. Biosci. 232, 78–86 (2011)
    • (2011) Math. Biosci. , vol.232 , pp. 78-86
    • Mendez, V.1    Sans, C.2    Llopis, I.3    Campos, D.4
  • 62
    • 43949160695 scopus 로고
    • Fractional model equation for anomalous diffusion
    • Metzler, R., Glockle, W., Nonnenmacher, T.: Fractional model equation for anomalous diffusion. Phys. A 211, 13–24 (1994)
    • (1994) Phys. A , vol.211 , pp. 13-24
    • Metzler, R.1    Glockle, W.2    Nonnenmacher, T.3
  • 63
    • 84856504736 scopus 로고    scopus 로고
    • Spatiotemporal complexity of biological invasion in a space- and time-discrete predator–prey system with the strong allee effect
    • Mistro, D.C., Rodrigues, L.A.D., Petrovskii, S.: Spatiotemporal complexity of biological invasion in a space- and time-discrete predator–prey system with the strong allee effect. Ecol. Complex. 9, 16–32 (2012)
    • (2012) Ecol. Complex. , vol.9 , pp. 16-32
    • Mistro, D.C.1    Rodrigues, L.A.D.2    Petrovskii, S.3
  • 64
    • 0035135346 scopus 로고    scopus 로고
    • Allee effect, sexual selection and demographic stochasticity
    • Moller, A.P., Legendre, S.: Allee effect, sexual selection and demographic stochasticity. Oikos 92, 27–34 (2001)
    • (2001) Oikos , vol.92 , pp. 27-34
    • Moller, A.P.1    Legendre, S.2
  • 65
    • 34047094522 scopus 로고    scopus 로고
    • On the importance of dimensionality of space in models of space-mediated population persistence
    • Morozov, A., Li, B.: On the importance of dimensionality of space in models of space-mediated population persistence. Theor. Popul. Biol. 71, 278–289 (2007)
    • (2007) Theor. Popul. Biol. , vol.71 , pp. 278-289
    • Morozov, A.1    Li, B.2
  • 66
    • 3042846003 scopus 로고    scopus 로고
    • Bifurcations and chaos in a predator–prey system with the Allee effect
    • Morozov, A., Petrovskii, S., Li, B.: Bifurcations and chaos in a predator–prey system with the Allee effect. Proc. R. Soc. Lond. B 271, 1407–1414 (2004)
    • (2004) Proc. R. Soc. Lond. B , vol.271 , pp. 1407-1414
    • Morozov, A.1    Petrovskii, S.2    Li, B.3
  • 67
    • 28444465570 scopus 로고    scopus 로고
    • Spatiotemporal complexity of patchy invasion in a predator–prey system with the Allee effect
    • Morozov, A., Petrovskii, S., Li, B.: Spatiotemporal complexity of patchy invasion in a predator–prey system with the Allee effect. J. Theor. Biol. 238, 18–35 (2006)
    • (2006) J. Theor. Biol. , vol.238 , pp. 18-35
    • Morozov, A.1    Petrovskii, S.2    Li, B.3
  • 69
    • 77957911001 scopus 로고    scopus 로고
    • Stochastic models of population extinction
    • Ovaskainen, O., Meerson, B.: Stochastic models of population extinction. Trends Ecol. Evol. 11, 643–652 (2010)
    • (2010) Trends Ecol. Evol. , vol.11 , pp. 643-652
    • Ovaskainen, O.1    Meerson, B.2
  • 70
    • 0142053105 scopus 로고    scopus 로고
    • An exactly solvable model of population dynamics with density-dependent migrations and the allee effect
    • Petrovskii, S., Li, B.-L.: An exactly solvable model of population dynamics with density-dependent migrations and the allee effect. Math. Biosci. 186, 79–91 (2003)
    • (2003) Math. Biosci. , vol.186 , pp. 79-91
    • Petrovskii, S.1    Li, B.-L.2
  • 71
    • 23944469183 scopus 로고    scopus 로고
    • An exact solution of a diffusive predator–prey system
    • Petrovskii, S., Malchow, H., Li, B.-L.: An exact solution of a diffusive predator–prey system. Proc. R. Soc. A 461, 1029–1053 (2005a)
    • (2005) Proc. R. Soc. A , vol.461 , pp. 1029-1053
    • Petrovskii, S.1    Malchow, H.2    Li, B.-L.3
  • 72
    • 16344366772 scopus 로고    scopus 로고
    • Regimes of biological invasion in a predator–prey system with the Allee effect
    • Petrovskii, S., Morozov, A., Li, B.: Regimes of biological invasion in a predator–prey system with the Allee effect. Bull. Math. Biol. 67, 637–661 (2005b)
    • (2005) Bull. Math. Biol. , vol.67 , pp. 637-661
    • Petrovskii, S.1    Morozov, A.2    Li, B.3
  • 73
    • 0036113356 scopus 로고    scopus 로고
    • Allee effect makes possible patchy invasion in a predator–prey system
    • Petrovskii, S., Morozov, A., Venturino, E.: Allee effect makes possible patchy invasion in a predator–prey system. Ecol. Lett. 5, 345–352 (2002)
    • (2002) Ecol. Lett. , vol.5 , pp. 345-352
    • Petrovskii, S.1    Morozov, A.2    Venturino, E.3
  • 74
    • 79955117342 scopus 로고    scopus 로고
    • Fractional central pattern generators for bipedal locomotion
    • Pinto, C.M.A., Machado, J.T.A.: Fractional central pattern generators for bipedal locomotion. Nonlinear Dyn. 62, 27–37 (2010)
    • (2010) Nonlinear Dyn. , vol.62 , pp. 27-37
    • Pinto, C.M.A.1    Machado, J.T.A.2
  • 75
    • 0000419742 scopus 로고
    • The kinetics of functional response
    • Real, L.: The kinetics of functional response. Am. Nat. 111, 289–300 (1977)
    • (1977) Am. Nat. , vol.111 , pp. 289-300
    • Real, L.1
  • 76
    • 53149149076 scopus 로고    scopus 로고
    • Dose-dependent infection rates of parasites produce the Allee effect in epidemiology
    • Regoes, R.R., Ebert, D., Bonhoeffer, S.: Dose-dependent infection rates of parasites produce the Allee effect in epidemiology. Proc. R. Soc. Lond. B 269, 271–279 (2002)
    • (2002) Proc. R. Soc. Lond. B , vol.269 , pp. 271-279
    • Regoes, R.R.1    Ebert, D.2    Bonhoeffer, S.3
  • 77
    • 34548305141 scopus 로고    scopus 로고
    • Mobility promotes and jeopardizes biodiversity in rock–paper–scissors games
    • Reichenbach, T., Mobilia, M., Frey, E.: Mobility promotes and jeopardizes biodiversity in rock–paper–scissors games. Nature 448, 1046–1049 (2007a)
    • (2007) Nature , vol.448 , pp. 1046-1049
    • Reichenbach, T.1    Mobilia, M.2    Frey, E.3
  • 78
    • 36849066945 scopus 로고    scopus 로고
    • Noise and correlations in a spatial population model with cyclic competition
    • Reichenbach, T., Mobilia, M., Frey, E.: Noise and correlations in a spatial population model with cyclic competition. Phys. Rev. Lett. 99, 238105 (2007b)
    • (2007) Phys. Rev. Lett. , vol.99 , pp. 238105
    • Reichenbach, T.1    Mobilia, M.2    Frey, E.3
  • 79
    • 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. 52, 807–829 (2006)
    • (2006) J. Math. Biol. , vol.52 , pp. 807-829
    • Shi, J.1    Shivaji, R.2
  • 80
    • 0033215101 scopus 로고    scopus 로고
    • Consequences of the Allee effect for behaviour, ecology and conservation
    • Stephens, P., Sutherland, W.: Consequences of the Allee effect for behaviour, ecology and conservation. Trends Ecol. Evol. 14, 401–405 (1999)
    • (1999) Trends Ecol. Evol. , vol.14 , pp. 401-405
    • Stephens, P.1    Sutherland, W.2
  • 81
    • 64749087718 scopus 로고    scopus 로고
    • The role of noise in a predator–prey model with Allee effect
    • Sun, G.-Q., Jin, Z., Li, L., Liu, Q.-X.: The role of noise in a predator–prey model with Allee effect. J. Biol. Phys. 35, 185–196 (2009)
    • (2009) J. Biol. Phys. , vol.35 , pp. 185-196
    • Sun, G.-Q.1    Jin, Z.2    Li, L.3    Liu, Q.-X.4
  • 82
    • 77249116130 scopus 로고    scopus 로고
    • Rich dynamics in a predator–prey model with both noise and periodic force
    • Sun, G.-Q., Jin, Z., Liu, Q.-X., Li, B.-L.: Rich dynamics in a predator–prey model with both noise and periodic force. BioSystems 100, 14–22 (2010)
    • (2010) BioSystems , vol.100 , pp. 14-22
    • Sun, G.-Q.1    Jin, Z.2    Liu, Q.-X.3    Li, B.-L.4
  • 83
    • 77953360298 scopus 로고    scopus 로고
    • Self-organized wave pattern in a predator–prey model
    • Sun, G.-Q., Jin, Z., Li, L., Li, B.-L.: Self-organized wave pattern in a predator–prey model. Nonlinear Dyn. 60, 265–275 (2010)
    • (2010) Nonlinear Dyn. , vol.60 , pp. 265-275
    • Sun, G.-Q.1    Jin, Z.2    Li, L.3    Li, B.-L.4
  • 84
    • 84940836005 scopus 로고    scopus 로고
    • Influence of isolation degree of spatial patterns on persistence of populations
    • Sun, G.-Q., Wu, Z.-Y., Wang, Z., Jin, Z.: Influence of isolation degree of spatial patterns on persistence of populations. Nonlinear Dyn. 83, 811–819 (2016)
    • (2016) Nonlinear Dyn. , vol.83 , pp. 811-819
    • Sun, G.-Q.1    Wu, Z.-Y.2    Wang, Z.3    Jin, Z.4
  • 85
    • 70349218900 scopus 로고    scopus 로고
    • Predator cannibalism can give rise to regular spatial pattern in a predator–prey system
    • Sun, G.-Q., Zhang, G., Jin, Z.: Predator cannibalism can give rise to regular spatial pattern in a predator–prey system. Nonlinear Dyn. 58, 75–84 (2009)
    • (2009) Nonlinear Dyn , vol.58 , pp. 75-84
    • Sun, G.-Q.1    Zhang, G.2    Jin, Z.3
  • 86
    • 67349154370 scopus 로고    scopus 로고
    • Early warning signals of demographic regime shifts in invading populations
    • Takimoto, G.: Early warning signals of demographic regime shifts in invading populations. Popul. Ecol. 51, 419–426 (2009)
    • (2009) Popul. Ecol. , vol.51 , pp. 419-426
    • Takimoto, G.1
  • 87
    • 77349093588 scopus 로고    scopus 로고
    • Modulation of predator–prey interactions by the Allee effect
    • Verdy, A.: Modulation of predator–prey interactions by the Allee effect. Ecol. Model. 221, 1098–1107 (2010)
    • (2010) Ecol. Model. , vol.221 , pp. 1098-1107
    • Verdy, A.1
  • 88
    • 84859411706 scopus 로고    scopus 로고
    • Invasions in heterogeneous habitats in the presence of advection
    • Vergni, D., Iannaccone, S., Berti, S., Cencini, M.: Invasions in heterogeneous habitats in the presence of advection. J. Theor. Biol. 301, 141–152 (2012)
    • (2012) J. Theor. Biol. , vol.301 , pp. 141-152
    • Vergni, D.1    Iannaccone, S.2    Berti, S.3    Cencini, M.4
  • 89
    • 78049480287 scopus 로고    scopus 로고
    • Analysis of a spatial predator–prey model with delay
    • Wang, B., Wang, A.-L., Liu, Y.-J., Liu, Z.-H.: Analysis of a spatial predator–prey model with delay. Nonlinear Dyn. 62, 601–608 (2010)
    • (2010) Nonlinear Dyn. , vol.62 , pp. 601-608
    • Wang, B.1    Wang, A.-L.2    Liu, Y.-J.3    Liu, Z.-H.4
  • 90
    • 0033552648 scopus 로고    scopus 로고
    • The competitive dynamics of populations subject to an Allee effect
    • Wang, G., Liang, X.-G., Wang, F.-Z.: The competitive dynamics of populations subject to an Allee effect. Ecol. Model. 124, 183–192 (1999)
    • (1999) Ecol. Model. , vol.124 , pp. 183-192
    • Wang, G.1    Liang, X.-G.2    Wang, F.-Z.3
  • 91
    • 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. 62, 291–331 (2011a)
    • (2011) J. Math. Biol. , vol.62 , pp. 291-331
    • Wang, J.1    Shi, J.2    Wei, J.3
  • 92
    • 0035012881 scopus 로고    scopus 로고
    • Speeds of invasion in a model with strong or weak Allee effects
    • Wang, M.-H., Kot, M.: Speeds of invasion in a model with strong or weak Allee effects. Math. Biosci. 171, 83–97 (2001)
    • (2001) Math. Biosci. , vol.171 , pp. 83-97
    • Wang, M.-H.1    Kot, M.2
  • 93
    • 0036483294 scopus 로고    scopus 로고
    • Integrodifference equations, Allee effects, and invasions
    • Wang, M.-H., Kot, M., Neubert, M.G.: Integrodifference equations, Allee effects, and invasions. J. Math. Biol. 44, 150–168 (2002)
    • (2002) J. Math. Biol. , vol.44 , pp. 150-168
    • Wang, M.-H.1    Kot, M.2    Neubert, M.G.3
  • 94
    • 79957800811 scopus 로고    scopus 로고
    • Invasion dynamics of epidemic with the Allee effect
    • Wang, W., Liu, H., Li, Z., Guo, Z., Yang, Y.: Invasion dynamics of epidemic with the Allee effect. BioSystems 105, 25–33 (2011b)
    • (2011) BioSystems , vol.105 , pp. 25-33
    • Wang, W.1    Liu, H.2    Li, Z.3    Guo, Z.4    Yang, Y.5
  • 95
    • 79451472838 scopus 로고    scopus 로고
    • Analysis of a discrete-time predator–prey system with Allee effect
    • Wang, W.-X., Zhang, Y.-B., Liu, C.: Analysis of a discrete-time predator–prey system with Allee effect. Ecol. Complex. 8, 81–85 (2011c)
    • (2011) Ecol. Complex. , vol.8 , pp. 81-85
    • Wang, W.-X.1    Zhang, Y.-B.2    Liu, C.3
  • 96
    • 0036887936 scopus 로고    scopus 로고
    • Chaos, fractional kinetics, and anomalous transport
    • Zaslavsky, G.: Chaos, fractional kinetics, and anomalous transport. Phys. Rep. 371, 461–580 (2002)
    • (2002) Phys. Rep. , vol.371 , pp. 461-580
    • Zaslavsky, G.1
  • 97
    • 84863229302 scopus 로고    scopus 로고
    • Spatial dynamics in a predator–prey model with Beddington–DeAngelis functional response
    • Zhang, X.-Q., Sun, G.-Q., Jin, Z.: Spatial dynamics in a predator–prey model with Beddington–DeAngelis functional response. Phys. Rev. E 85, 021924 (2012)
    • (2012) Phys. Rev. E , vol.85 , pp. 021924
    • Zhang, X.-Q.1    Sun, G.-Q.2    Jin, Z.3
  • 98
    • 11844279070 scopus 로고    scopus 로고
    • The stability of predator–prey systems subject to the Allee effects
    • Zhou, S.-R., Liu, Y.-F., Wang, G.: The stability of predator–prey systems subject to the Allee effects. Theor. Popul. Biol. 67, 23–31 (2005)
    • (2005) Theor. Popul. Biol. , vol.67 , pp. 23-31
    • Zhou, S.-R.1    Liu, Y.-F.2    Wang, G.3
  • 99
    • 1642307509 scopus 로고    scopus 로고
    • Allee-like effects in metapopulation dynamics
    • Zhou, S.-R., Wang, G.: Allee-like effects in metapopulation dynamics. Math. Biosci. 189, 103–113 (2004)
    • (2004) Math. Biosci. , vol.189 , pp. 103-113
    • Zhou, S.-R.1    Wang, G.2
  • 100
    • 70450242711 scopus 로고    scopus 로고
    • The evolution of phenotypic traits in a predator–prey system subject to Allee effect
    • Zu, J., Mimura, M., Wakano, J.-Y.: The evolution of phenotypic traits in a predator–prey system subject to Allee effect. J. Theor. Biol. 262, 528–543 (2010)
    • (2010) J. Theor. Biol. , vol.262 , pp. 528-543
    • Zu, J.1    Mimura, M.2    Wakano, J.-Y.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.