Modelling Lippia spread down flooding river systems.

Abstract

Lippia (Phyla canescens) is an invasive, non-native plant prevalent in the Australian Murray--Darling river system that is considered detrimental in terms of lost agricultural production and environmental damage. This weed predominantly spreads as clonal fragments during floods and its growth rate is strongly related to soil moisture content. We use stage structured integro-difference equations to model the dispersal of reproductive units (clonal fragments and seeds) and explore the effects of flood length and height on spatial spread rates of the weed. References

• J. Earl, The distribution and impact of Lippia (Phyla canescens) in the Murray Darling system. Agricultural Information and Monitoring Services report for the Lippia Working Group, 2003. http://www.cotton.crc.org.au/Publicat/Weeds/index.htm
• K. Hennessy, K. McInnes, D. Abbs, R. Jones, J. Bathols, R. Suppiah, J. Ricketts, T. Rafter, D. Collins, D. Jones, Climate change in New South Wales, Part 2: Projected changes in climate extremes, CSIRO Consultancy Report for NSW Greenhouse Office, 2004.
• R. Suppiah, K. J. Hennessy, Trends in total rainfall, heavy rain events and number of dry days in Australia, 1910--1990. International Journal of Climatology, 18, 1141--1164, 1998. doi:0.1002/(SICI)1097-0088(199808)18:10<1141::AID-JOC286>3.0.CO;2-P
• A-M. Truscott, C. Soulsby, C. F. Palmer, L. Newell, P. E. Hulme, The dispersal characteristics of the invasive plant Mimulus guttatus and the ecological significance of increased occurrence of high-flow events. J. Ecology, 94, 1080--1091, 2006. doi:10.1111/j.1365-2745.2006.01171.x
• 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, Elements of Mathematical Ecology, Cambridge University Press, 2001.
• R. Hickson, S. I. Barry, K. Stokes, Comparison of weed spread models, ANZIAM J(E), 49, C324--C340, 2008; in Proceedings of the 8th Biennial Engineering Mathematics and Applications Conference, EMAC-2007, Eds. Geoffry N. Mercer and A. J. Roberts. http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/339
• T. Riis, K. Sand-Jensen, Dispersal of plant fragments in small streams, Freshwater Biology, 51, 274--286, 2005. doi:10.1111/j.1365-2427.2005.01496.x
• M. Macdonald, W. Whalley, B. Sindel, M. Julien, J. Duggin, Flood induced recruitment of Lippia. In: B. Hackney, K. Bailes, J. Pilz, H. Burns (Eds) Proceedings of the 21st Annual Conference of The Grassland Society of NSW, Wagga Wagga, NSW, 135--136, 2006.
• M. Macdonald, The ecology of Lippia (Phyla canescens). PhD Thesis, The University of New England, Armidale, NSW, Australia, 2007.
• C. W. P. M. Blom, Adaptations to flooding stress: from plant community to molecule. Plant Biology, 1, 261--273, 1999. doi:10.1055/s-2007-978515
• R. McCosker, Lippia (Phyla nodiflora): An invasive plant of floodplain ecosystems in the Murray--Darling Basin. A report on the distribution and ecology of Lippia in the lower Gwydir Valley and the Murray Darling Basin prepared for the Gingham Watercourse Landcare Group. University of New England, Australia, 1994.
• A. Hobson, Invasive weeds: a threat to wetland ecosystems. Honours Thesis, University of New England, Armidale, NSW, Australia, 1999.
• B. Taylor, G. C. Ganf, Comparative ecology of two co-occurring floodplain plants: the native Sporobolus mitchellii and the exotic Phyla canescens. Marine and Freshwater Research, 56, 431--440., 2005 doi:10.1071/MF04196
• M. A. Lewis, S. Pacala, {Modelling and analysis of stochastic invasion processes}, J. Math. Biology, 41, 387--429, 2000. doi:10.1007/s002850000050
• F. Lutscher, A short note on short dispersal events, Bull. Math. Biology, 69, 1615--1630, 2007. doi:10.1007/s11538-006-9182-9