Numerous models of weed spread and growth exist in ecology. We compare four common models: reaction diffusion, integro-difference, `scatter' model, and an `occupation' model. We discuss their similarities, strengths and limitations. After verifying the equivalence of the integro-difference model, with a Gaussian kernel, against the reaction diffusion model, we show how to equate parameters of the different models. We also investigate the effect of the occupation model parameters on spread behaviour. References H. Caswell. Matrix population models: construction, analysis and interpretation. USA: Sinauer Associates, Inc. 2nd edition, 2001. R. A. Fisher. The wave of advance of advantageous genes. Annals of Eugenics, 7, 353--369, 1937. http://digital.library.adelaide.edu.au/dspace/bitstream/2440/15125/1/152.pdf A. Hastings. Models of spatial spread: is the theory complete? Ecology, 77(6), 1675--1679, 1996. http://www.jstor.org/view/00129658/di986021/98p0171i/0 S. I. Higgins, D. M. Richardson. A review of models of alien plant spread. Ecological Modelling, 87, 249--265, 1996. doi:0304-3800(95)00022-4 M. Kot, M. A. Lewis, P. van den Driessche. Dispersal data and the spread of invading organisms. Ecology, 77(7), 2027--2042, 1996. http://www.jstor.org/view/00129658/di986022/98p0217b/0 M. Kot. Elements of mathematical ecology. UK: Cambridge University Press, 2001. M. A. Lewis, M. G. Neubert, H. Caswell, J. S. Clark, K. Shea. A guide to calculating discrete-time invasion rates from data. Conceptual ecology and invasion biology, 1, 169--192, 2006. http://www.math.ualberta.ca/ mlewis/publications/Cadotte.pdf M. A. Lewis, S. Pacala. Modeling and analysis of stochastic invasion processes. Journal of Mathematical Biology, 41, 387--429, 2000. doi:10.1007/s002850000050 R. Lui. A nonlinear integral operator arising from a model in population genetics. I. monotone initial data. SIAM Journal of Mathematical Analysis, 13(6), 913--937, 1982. doi:10.1137/0513064 M. G. Neubert, H. Caswell. Demography and dispersal: calculation and sensitivity analysis of invasion spread for structured populations. Ecology, 81(6), 1613--1628, 2000. http://www.jstor.org/view/00129658/ap010022/01a00120/0 K. A. Andow, P. M. Kareiva, S. A. Levin and A. Okubo. Spread of invading organisms. Landscape Ecology, 4(2/3), 177--188, 1990. doi:10.1007/BF00132860 M. G. Neubert, I. M. Parker. Projecting rates of spread for invasive species. Risk Analysis, 24(4), 817--831, 2004. doi:10.1111/j.0272-4332.2004.00481.x A. Okubo. Diffusion and ecological problems: mathematical models. New York: Springer--Verlag, 1980. M. Rees, Q. Paynter. Biological control of Scotch Broom: modelling the determinants of abundance and the potential impact of introduced insect herbivores. Journal of Applied Ecology, 34, 1203--1221, 1997. http://www.jstor.org/view/00218901/di996085/99p0309w/0 J. G. Skellam. Random dispersal in theoretical populations. Biometrika, 8, 196--218, 1951. doi:10.1007/BF02464427 H. F. Weinberger. Asymptotic behavior of a model in population genetics. In: J. M. Chadam (ed) Lecture Notes in Mathematics No. 648: Nonlinear partial differential equations and applications, 47--96. Proceedings Indiana 1967--1977 (1978). H. F. Weinberger. Long-time behaviour of a class of biological models. SIAM journal on Mathematical Analysis, 13(3), 323--352, 1982. doi:10.1137/0513028 B. Baeumer, M. Kovacs, M. M. Meerschaert. Fractional reaction-diffusion equation for species growth and dispersal. To appear in Journal of Mathematical Biology, 2007. http://www.maths.otago.ac.nz/ mcubed/JMBseed.pdf S. I. Barry, R. I. Hickson, K. Stokes. Modelling Lippia spread down flooding river systems. To appear in ANZIAM J. (E), 2007. F. van den Bosch, J. A. J. Metz, O. Diekmann. The velocity of spatial population expansion. Journal of Mathematical Biology, 28, 529--565, 1990. doi:10.1007/BF00164162
@article{339,
title = {Comparison of weed spread models},
journal = {ANZIAM Journal},
volume = {48},
year = {2008},
doi = {10.21914/anziamj.v49i0.339},
language = {EN},
url = {http://dml.mathdoc.fr/item/339}
}
Hickson, Roslyn; Barry, Steven; Stokes, Kate. Comparison of weed spread models. ANZIAM Journal, Tome 48 (2008) . doi : 10.21914/anziamj.v49i0.339. http://gdmltest.u-ga.fr/item/339/