메뉴 건너뛰기




Volumn 70, Issue 1, 2006, Pages 26-42

A master equation for a spatial population model with pair interactions

Author keywords

Clustering; Competition kernel; Diffusion reaction; Individual based model; Logistic equation; Master equation; Pattern formation; Population dynamics; Reproductive pair correlations; Spatial dynamics

Indexed keywords

BROWNIAN MOTION; COMPUTER SIMULATION; EQUATION; POPULATION DYNAMICS; POPULATION MODELING; SPATIAL DISTRIBUTION;

EID: 33744531622     PISSN: 00405809     EISSN: 10960325     Source Type: Journal    
DOI: 10.1016/j.tpb.2005.11.007     Document Type: Article
Times cited : (51)

References (29)
  • 1
    • 33744548394 scopus 로고    scopus 로고
    • Adler, R., 1997. Superprocesses and plankton dynamics. In: Monte Carlo Simulation in Oceanography. Proceedings of the 'Aha Huliko'a Hawaiian Winter Workshop, University of Hawaii at Manoa.
  • 2
    • 0031408804 scopus 로고    scopus 로고
    • Using moment equations to understand stochastically driven spatial pattern formation in ecological systems
    • Bolker B.M., and Pacala S.W. Using moment equations to understand stochastically driven spatial pattern formation in ecological systems. Theor. Popul. Biol. 52 (1997) 179-197
    • (1997) Theor. Popul. Biol. , vol.52 , pp. 179-197
    • Bolker, B.M.1    Pacala, S.W.2
  • 3
    • 0032783836 scopus 로고    scopus 로고
    • Spatial moment equations for plant competition: understanding spatial strategies and the advantages of short dispersal
    • Bolker B.M., and Pacala S.W. Spatial moment equations for plant competition: understanding spatial strategies and the advantages of short dispersal. Am. Nat. 153 (1999) 575-602
    • (1999) Am. Nat. , vol.153 , pp. 575-602
    • Bolker, B.M.1    Pacala, S.W.2
  • 4
    • 33744532522 scopus 로고    scopus 로고
    • Dieckmann, U., Law, R., Metz, J.A.J., 2000. The Geometry of Ecological Interactions: Simplifying Spatial Complexity. Cambridge University Press, Cambridge, UK, 564+xiv pp.
  • 5
    • 21844433698 scopus 로고    scopus 로고
    • Extinction times for birth-death processes: exact results continuum asymptotics and the failure of the Fokker-Planck approximation
    • Doering C.R., Sargsyan K.V., and Sanders L.M. Extinction times for birth-death processes: exact results continuum asymptotics and the failure of the Fokker-Planck approximation. SIAM J. Multiscale Modeling Simulation 3 (2005) 283-299
    • (2005) SIAM J. Multiscale Modeling Simulation , vol.3 , pp. 283-299
    • Doering, C.R.1    Sargsyan, K.V.2    Sanders, L.M.3
  • 6
    • 36149049574 scopus 로고
    • Second quantization representation for classical many-particle system
    • Doi M. Second quantization representation for classical many-particle system. J. Phys. A 9 (1976) 1465-1477
    • (1976) J. Phys. A , vol.9 , pp. 1465-1477
    • Doi, M.1
  • 7
    • 0001199360 scopus 로고
    • Stochastic theory of diffusion-controlled reaction
    • Doi M. Stochastic theory of diffusion-controlled reaction. J. Phys. A 9 (1976) 1479-1495
    • (1976) J. Phys. A , vol.9 , pp. 1479-1495
    • Doi, M.1
  • 8
    • 33744519030 scopus 로고    scopus 로고
    • Etheridge, A.M., 2000. An Introduction to Superprocesses. University Lecture Series, vol. 20. American Mathematical Society, Providence, RI, 187+xii pp.
  • 9
    • 33744539753 scopus 로고    scopus 로고
    • Feller, W., 1968. An Introduction to Probability Theory and its Applications, third ed., vol. I. Wiley, New York, 509+xviii pp.
  • 10
    • 0000672594 scopus 로고
    • A pain in the torus: some difficulties with models of isolation by distance
    • Felsenstein J. A pain in the torus: some difficulties with models of isolation by distance. Am. Nat. 109 (1975) 359-368
    • (1975) Am. Nat. , vol.109 , pp. 359-368
    • Felsenstein, J.1
  • 11
    • 0000268135 scopus 로고
    • The wave of advance of advantageous genes
    • Fisher R.A. The wave of advance of advantageous genes. Ann. Eugen. 7 (1937) 355-369
    • (1937) Ann. Eugen. , vol.7 , pp. 355-369
    • Fisher, R.A.1
  • 12
    • 0642285276 scopus 로고    scopus 로고
    • Nonlocal interaction effects on pattern formation in population dynamics
    • Fuentes M.A., Kuperman M.N., and Kenkre V.M. Nonlocal interaction effects on pattern formation in population dynamics. Phys. Rev. Lett. 91 (2004) 158104
    • (2004) Phys. Rev. Lett. , vol.91 , pp. 158104
    • Fuentes, M.A.1    Kuperman, M.N.2    Kenkre, V.M.3
  • 13
    • 45849155761 scopus 로고    scopus 로고
    • Clustering, advection and patterns in a model of population dynamics with neighborhood-dependent rates
    • Hernández-García E., and López C. Clustering, advection and patterns in a model of population dynamics with neighborhood-dependent rates. Phys. Rev. E 70 (2004) 016216
    • (2004) Phys. Rev. E , vol.70 , pp. 016216
    • Hernández-García, E.1    López, C.2
  • 14
    • 28544448516 scopus 로고    scopus 로고
    • Hernández-García, E., López, C., 2005. Birth, death and diffusion of interacting particles. J. Phys.: Condens. Matter 17, S4263-S4274.
  • 17
    • 33744506040 scopus 로고    scopus 로고
    • Kolmogorov, A., Petrovsky, I., Piscunov, H., 1937. Study of the diffusion equation with growth of the quantity of matter and its application to a biology problem. In: Pelcé, P. (Ed.), Originally published in Bulletin de l'Université d'état à Moscou Série Internationale, Section A, 1, 1937. For an English translation see: Dynamics of Curved Fronts, 1988. Academic Press, San Diego, 514+xv pp.
  • 18
    • 0041313947 scopus 로고    scopus 로고
    • Population growth in space and time: spatial logistic equations
    • Law R., Murrel D.J., and Dieckmann U. Population growth in space and time: spatial logistic equations. Ecology 84 (2003) 252-262
    • (2003) Ecology , vol.84 , pp. 252-262
    • Law, R.1    Murrel, D.J.2    Dieckmann, U.3
  • 19
    • 4143075038 scopus 로고    scopus 로고
    • A Malthusian curb on spatial structure in microorganism populations
    • Martin A.P. A Malthusian curb on spatial structure in microorganism populations. J. Theor. Biol. 230 (2004) 343-349
    • (2004) J. Theor. Biol. , vol.230 , pp. 343-349
    • Martin, A.P.1
  • 20
    • 33744525587 scopus 로고    scopus 로고
    • Maruvka, Y.E., Shnerb, N.M., 2005. Nonlocal competition and logistic growth: patterns, defects and fronts. arXiv:nlin.PS/0506046.
  • 21
    • 0000197082 scopus 로고    scopus 로고
    • Clustering of independently diffusing individuals by birth and death process
    • Meyer M., Havlin S., and Bunde A. Clustering of independently diffusing individuals by birth and death process. Phys. Rev. E 54 (1996) 5567
    • (1996) Phys. Rev. E , vol.54 , pp. 5567
    • Meyer, M.1    Havlin, S.2    Bunde, A.3
  • 22
    • 33744549961 scopus 로고    scopus 로고
    • Rapaport, D.C., 1995. The Art of Molecular Dynamics Simulation. Cambridge University Press, Cambridge, 549+xiii pp.
  • 23
    • 33744546761 scopus 로고    scopus 로고
    • Renshaw, E., 1991. Modelling Biological Populations in Space and Time. Cambridge University Press, Cambridge, 403+xvii pp.
  • 24
    • 45849154793 scopus 로고    scopus 로고
    • Pattern formation and nonlocal logistic growth
    • Shnerb N.M. Pattern formation and nonlocal logistic growth. Phys. Rev. E 69 (2004) 061917
    • (2004) Phys. Rev. E , vol.69 , pp. 061917
    • Shnerb, N.M.1
  • 25
    • 0009636209 scopus 로고
    • Random dispersion in theoretical populations
    • Skellam J.G. Random dispersion in theoretical populations. Biometrika 38 (1951) 196-218
    • (1951) Biometrika , vol.38 , pp. 196-218
    • Skellam, J.G.1
  • 26
    • 0012799777 scopus 로고    scopus 로고
    • Scaling limits and super-Brownian motion
    • Slade G. Scaling limits and super-Brownian motion. Not. Am. Math. Soc. 49 (2002) 1056-1067
    • (2002) Not. Am. Math. Soc. , vol.49 , pp. 1056-1067
    • Slade, G.1
  • 27
    • 33744549458 scopus 로고    scopus 로고
    • van Kampen, N.G., 1997. Stochastic Processes in Physics and Chemistry, second ed. North-Holland, Amsterdam, 465+xiv pp.
  • 28
    • 0035913371 scopus 로고    scopus 로고
    • Reproductive pair correlations and the clustering of organisms
    • Young W.R., Roberts A.J., and Stuhne G. Reproductive pair correlations and the clustering of organisms. Nature 412 (2001) 328-331
    • (2001) Nature , vol.412 , pp. 328-331
    • Young, W.R.1    Roberts, A.J.2    Stuhne, G.3
  • 29


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.