A numerical model to solve single-species invasion problems with Allee effects

Ecological Modelling

Volumn 192, Issue 3-4, 2006, Pages 601-617

  Almeida, Regina C ^a   Delphim, Simone A ^b   Costa, Michel I Da S ^b  

^a LABORATÓRIO NACIONAL DE COMPUTAÇÃO CIENTÍFICA   (Brazil)

^b Laboratorio Nacional de Computacao Cientifica LNCC/MCT   (Brazil)

Author keywords

Biological invasion; Diffusion; Migration and Allee effect; Stabilized finite element

Indexed keywords

BIODIVERSITY; DIFFUSION; NONLINEAR PROGRAMMING; PROBLEM SOLVING;

BIOLOGICAL INVASION; MIGRATION AND ALLEE EFFECT; STABILIZED FINITE ELEMENT;

MATHEMATICAL MODELS;

ALLEE EFFECT; BIOLOGICAL INVASION; NUMERICAL MODEL; POPULATION DYNAMICS;

EID: 31944451381     PISSN: 03043800     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ecolmodel.2005.07.018     Document Type: Article

References (27)

1. D.G. Aronson, and H.F. Weinberger Multidimensional nonlinear diffusion arising in population genetics Adv. Math. 30 1978 33 76
2. K.E. Atkinson An Introduction to Numerical Analysis second ed 1989 John Wiley and Sons
3. H. Banks, P. Kareiva, and L. Zia Analysing field studies of insect dispersal using two-dimensional transport equations Environ. Entomol. 17 1988 815 820
4. P.G. Blackwell Random diffusion models for animal movement Ecol. Model. 100 1997 87 102
5. A.N. Brooks, and T.J.R. Hughes Streamline upwind Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations Comput. Methods Appl. Mech. Eng. 32 1982 199 259
6. C.A.A. Carbonel, and J.L. Valentin Numerical modelling of phytoplankton bloom in the upwelling ecosystem of Cabo Frio Brazil Ecol. Model. 116 1999 135 148
7. J.S. Clark, M. Lewis, and L. Horvath Invasion by extremes: population spread with variation in dispersal and reproduction Am. Nat. 157 2001 537 554
8. H.G. Davis, C.M. Taylor, J.C. Civille, and D.R. Strong An Allee effect at the front of a plant invasion: Spartinain a Pacific estuary J. Ecol. 92 2004 321 327
9. J.W. Demmel Applied Numerical Linear Algebra 1997 SIAM
10. P.C. Fife Lecture Notes in Biomathematics: Mathematical Aspects of Reacting and Diffusing Systems Vol. 28 1979 Springer-Verlag
11. A.C. Galeão, R.C. Almeida, S.M.C. Malta, and A.F.D. Loula Finite element analysis of convection dominated reaction - diffusion problems Appl. Num. Math. 48 2004 205 222
12. B. Gaylord, and S.D. Gaines Temperature or transport? Range limits in marine species mediated solely by flow Am. Nat. 155 6 2000 769 789
13. G. Hauke, and A. García-Olivares Variational subgrid scale formulations for the advection-diffusion-reaction equation Comput. Methods Appl. Mech. Eng. 190 2001 6847 6865
14. C. Hirsch Numerical Computation of Internal and External Flows Vol. 1 1988 John Wiley & Sons
15. T.J.R. Hughes The Finite Element Method - Linear Static and Dynamic Finite Element Analysis 2000 Dover Publications, Inc
16. C. Johnson Numerical Solution of Partial Differential Equations by the Finite Element Method 1990 Cambridge University Press
17. M. Kot, M.A. Lewis, and P. Van Den Driessche Dispersal data and the spread of invading organisms Ecology 77 7 1996 2027 2042
18. M.A. Lewis, and P. Kareiva Allee dynamics and the spread of invading organisms Theor. Popul. Biol. 43 1993 141 158
19. A. Okubo, and S.A. Levin Diffusion and Ecological Problems - Modern Perspectives second ed 2001 Springer
20. S. Petrovskii, and B. Li An exactly solvable model of population dynamics with density-dependent migrations and the Alle effect Math. Biosci. 186 2003 79 91
21. K. Rektorys Variational Methods in Mathematics, Science and Engineering second ed 1980 D. Reidel Publishing Company
22. S.L. Ross Introduction to Ordinary Differential Equations fourth ed 1989 John Wiley and Sons
23. S.J. Schreiber Allee effects, extinctions and chaotic transients in simple population models Theor. Popul. Biol. 64 2003 201 209
24. N. Shigesada, and K. Kawasaki Biological Invasions: Theory and Practice 1997 Oxford University
25. R. Veit, and M. Lewis Dispersal, population growth and the Allee effect: dynamics of the house fish invasion of eastern North America Am. Nat. 148 1996 255 274
26. M. Wang, and M. Kot Speeds of invasion in a model with strong and weak Allee effects Math. Biosci. 171 2001 83 97
27. K. Yamamura, S. Moriya, and K. Tanaka Discrete random walk model to interpret the dispersal parameters of organisms Ecol. Model. 161 2003 151 157