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A mathematical analysis of factors affecting the rate of spread of patches of annual weeds in an arable field

Published online by Cambridge University Press:  20 January 2017

Jodie L. Woolcock  and
Roger Cousens
Jodie L. Woolcock
Affiliation:
Department of Agricultural Sciences, La Trobe University, Bundoora, Victoria 3083, Australia
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Abstract

A model is presented of the spread of a weed from a point source, with dispersal being both unaided and aided by a combine harvester. Four “type” weeds were modeled, chosen to represent species of differing population and dispersal ecologies and based broadly on Avena spp. (wild oats), Raphanus raphanistrum (wild radish), Bromus spp. (bromegrass), and Fumaria spp. (fumitory). Wind-adapted species were excluded. The greatest rate of spread was predicted to be for R. raphanistrum and the least for Fumaria, regardless of whether dispersal by combine harvester was included. Rate of spread was more sensitive to dispersal parameters than to demographic parameters and increased up to 16-fold as soon as any seeds were dispersed by the harvester. Given that uptake by the harvester is a function of phenology of seed production and dispersal, better data on such processes is required for weeds. Because rate of spread is more dependent on dispersal than on demographic factors, greater attention needs to be given to describing dispersal frequency distributions and especially to analysis of their shapes.

Keywords

Bromus spp., bromegrassRaphanus raphanistrum L. RAPRA, wild radishAvena spp., wild oats; Fumaria spp., fumitorySeed dispersalmanagementmodelpopulation growthpatchesspatial dynamicsRAPRA
Type
Research Article
Information
Weed Science , Volume 48 , Issue 1 , February 2000 , pp. 27 - 34
Copyright
Copyright © Weed Science Society of America 

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References

Literature Cited

Allen, E. J. and Allen, L.J.S. 1996. Dispersal and competition models for plants. J. Math. Biol. 34:455–481.Google Scholar
Allen, L.J.S., Allen, E. J., and Ponweera, S. 1996. A mathematical model for weed dispersal and control. Bull. Math. Biol. 58:815–834.Google Scholar
Andersen, M. 1991. Mechanistic models for the seed shadows of winddispersed plants. Am. Nat. 137:476–497.Google Scholar
Audsley, E. 1993. Operational research analysis of patch spraying. Crop Prot. 12:111–119.Google Scholar
Auld, B. A. 1988. Dynamics of pasture invasion by three weeds, Avena fatua L., Carduus tenuiflorus Curt. and Onopordum acanthium L. Aust. J. Agric. Res. 39:589–596.Google Scholar
Auld, B. A. and Coote, B. G. 1990. INVADE: towards the simulation of plant spread. Agric. Ecosyst. Environ. 30:121–128.Google Scholar
Ballaré, C. L., Scopel, A. L., Ghersa, C. M., and Sánchez, R. A. 1987a. The population ecology of Datura ferox in soybean crops. A simulation approach incorporating seed dispersal. Agric. Ecosyst. Environ. 19:177–188.Google Scholar
Ballaré, C. L., Scopel, A. L., Ghersa, C. M., and Sánchez, R. A. 1987b. The demography of Datura ferox in soybean crops. Weed Res. 27:91–102.CrossRefGoogle Scholar
Benoit, D. L., Derksen, D. A., and Panneton, B. 1992. Innovative approaches to seedbank studies. Weed Sci. 40:660–669.Google Scholar
Bergelson, J., Newman, J. A., and Floresroux, E. M. 1993. Rates of spread in spatially heterogeneous environments. Ecology 74:999–1011.Google Scholar
Chancellor, R. J. 1976. Changes in the weeds of Upper Begbroke field (1961–76). Pages 227–234 In V Colloque International sur l’Écologie et la Biologie des Mauvaises Herbes. Dijon: Columa.Google Scholar
Chancellor, R. J. 1985a. Changes in the weed flora of an arable field cultivated for 20 years. J. Appl. Ecol. 22:491–501.Google Scholar
Chancellor, R. J. 1985b. Maps of the Changes in the Weeds of Boddington Barn Field over Twenty Years (1961–1981). Yarnton, Oxfordshire: Technical Report of the Agricultural and Food Research Council Weed Research Organization 84, pp. 1–38.Google Scholar
Chancellor, R. J. 1986. Decline of arable weed seeds during 20 years in soil under grass and the periodicity of seedling emergence after cultivation. J. Appl. Ecol. 23:631–637.Google Scholar
Cheam, A. H. and Code, G. R. 1995. The biology of Australian weeds. 24. Raphanus raphanistrum L. Plant Prot. Q. 10:2–13.Google Scholar
Collingham, Y. C., Hill, M. O., and Huntley, B. 1996. The migration of sessile organisms: a simulation model with measurable parameters. J. Veg. Sci. 7:831–846.Google Scholar
Cousens, R. and Mortimer, M. 1995. Dynamics of Weed Populations. Cambridge: Cambridge University Press. 332 p.Google Scholar
Cousens, R. D. and Woolcock, J. L. 1997. Spatial dynamics of weeds: an overview. Pages 613–618 In Proceedings of the Brighton Crop Protection Conference—Weeds. Farnham: Brighton Crop Protection Conference.Google Scholar
Cousens, R., Doyle, C. J., Wilson, B. J., and Cussans, G. W. 1986. Modelling the economics of controlling Avena fatua in winter wheat. Pestic. Sci. 17:1–12.CrossRefGoogle Scholar
Firbank, L. G., Manlove, R. J., Mortimer, A. M., and Putwain, P. D. 1984. The management of grass weeds in cereal crops, a population biology approach. Pages 375–384 in Proceedings of the 7th International Symposium of Weed Biology, Ecology and Systematics, Paris: Columa.Google Scholar
Forcella, F. 1985. Final distribution is related to rate of spread in alien weeds. Weed Res. 25:181–191.CrossRefGoogle Scholar
Froud-Williams, R. J., Chancellor, R. J., and Drennan, D.S.H. 1984. The effects of seed burial and soil disturbance on emergence and survival of arable weeds in relation to minimal cultivation. J. Appl. Ecol. 21:629–641.Google Scholar
Gerhards, R., Wyse-Pester, D. Y., Mortensen, D., and Johnson, G. A. 1997. Characterizing spatial stability of weed populations using interpolated maps. Weed Sci. 45:108–119.Google Scholar
González-Andujar, J. L. and Perry, J. N. 1995. Models for the herbicidal control of the seed bank of Avena sterilis: the effects of spatial and temporal heterogeneity and of dispersal. J. Appl. Ecol. 32:578–587.CrossRefGoogle Scholar
Harradine, A. R. 1985. Dispersal and establishment of slender thistle, Carduus pynocephalus L., as affected by ground cover. Aust. J. Agric. Res. 36:791–797.CrossRefGoogle Scholar
Heisel, T., Andreasen, C., and Ersbøll, A. K. 1996. Annual weed distributions can be mapped with kriging. Weed Res. 36:325–337.Google Scholar
Howard, C. L. 1990. Comparative ecology of four brome grasses. , University of Liverpool. 210 p.Google Scholar
Howard, C. L., Mortimer, A. M., Gould, P., Putwain, P. D., Cousens, R., and Cussans, G. W. 1991. The dispersal of weeds—seed movement in arable agriculture. Pages 664–673 In Proceedings of the Brighton Crop Protection Conference—Weeds. Farnham: Brighton Crop Protection Conference.Google Scholar
Kot, M. 1992. Discrete-time travelling waves: ecological examples. J. Math. Biol. 30:413–435.Google Scholar
Kot, M., Lewis, M. A., and van den Driessche, P. 1996. Dispersal data and the spread of invading organisms. Ecology 77:2027–2042.Google Scholar
Lapham, J. 1985. Unrestricted growth, tuber formation and spread of Cyperus esculentus L. in Zimbabwe. Weed Res. 25:323–329.Google Scholar
Martin, R. J. and Felton, W. L. 1990. Effect of crop rotation, tillage practice and herbicide use on the population dynamics of wild oats. Pages 20–23 In Proceedings of the 9th Australian Weeds Conference. Adelaide: Crop Science Society of South Australia.Google Scholar
Maxwell, B. D. and Colliver, C. T. 1995. Expanding economic thresholds by including spatial and temporal weed dynamics. Pages 1069–1076 In Proceedings of the Brighton Crop Protection Conference—Weeds. Farnham: Brighton Crop Protection Conference.Google Scholar
Maxwell, B. D. and Ghersa, C. 1992. The influence of weed seed dispersion versus the effect of competition on crop yield. Weed Technol. 6:196–204.Google Scholar
Mortimer, A. M., Latore, J., and Gould, P. 1996. From weed populations to weed communities: patch size and patch composition. Pages 35–40 In Proceedings of the Second International Weed Control Congress. Copenhagen: Department of Weed Control and Pesticide Ecology.Google Scholar
Moss, S. R. 1990. The seed cycle of Alopecurus myosuroides in winter cereals: a quantitative analysis. Pages 27–36 In Proceedings of the European Weed Research Society Symposium. Integrated Weed Management in Cereals. Wageningen: European Weed Research Society.Google Scholar
Nietschke, B. S. 1996. Cultural weed management of wild oats. Plant Prot. Q. 11:187–189.Google Scholar
Okubo, A. 1980. Diffusion and Ecological Problems: Mathematical Models. Berlin: Springer-Verlag. 254 p.Google Scholar
Paice, M.E.R., Miller, P.C.H., and Day, W. 1996. Control requirements for spatially selective herbicide sprayers. Comput. Electron. Agric. 14:163–177.Google Scholar
Paice, M.E.R., Day, W., Rew, L. J., and Howard, A. 1998. A stochastic simulation model for evaluating the concept of patch spraying. Weed Res. 38:373–388.Google Scholar
Perry, J. N. and González-Andujar, J. L. 1993. Dispersal in a metapopulation neighbourhood model of an annual plant with a seedbank. J. Ecol. 81:453–463.Google Scholar
Petzold, K. 1956. Combine-harvesting and weeds. J. Agric. Eng. Res. 1:178–181.Google Scholar
Piqueras, J., Klimes, L., and Redbo-Torstensson, P. 1999. Modelling the morphological response to nutrient availability in the clonal plant Trientalis europaea L. Plant Ecol. 141:117–127.Google Scholar
Portnoy, S. and Willson, M. F. 1993. Seed dispersal curves: behavior of the tail of the distribution. Evol. Ecol. 7:25–44.Google Scholar
Rew, L. J. and Cussans, G. W. 1995. Patch ecology—how much do we know? Pages 1059–1068 in Proceedings of the Brighton Crop Protection Conference—Weeds. Farnham: Brighton Crop Protection Conference.Google Scholar
Rew, L. J. and Cussans, G. W. 1997. Horizontal movement of seeds following tine and plough cultivation: implications for spatial dynamics of weed infestations. Weed Res. 37:247–256.Google Scholar
Rew, L. J., Froud-Williams, R. J., and Boatman, N. D. 1996. Dispersal of Bromus sterilis and Anthriscus sylvestris seed within arable field margins. Agric. Ecosyst. Environ. 59:107–114.Google Scholar
Schippers, P., Ter Borg, S. J., Van Groenendael, J. M., and Habekotte, B. 1993. What makes Cyperus esculentus (yellow nutsedge) an invasive species?—A spatial model approach. Pages 495–504 In Proceedings of the Brighton Crop Protection Conference—Weeds. Farnham: Brighton Crop Protection Conference.Google Scholar
Shaw, M. W. 1995. Simulation of population expansion and spatial pattern when individual dispersal distributions do not decline exponentially with distance. Proc. Royal Soc. Lond. Ser. B 259:243–248.Google Scholar
Sheldon, J. C. and Burrows, F. M. 1973. The dispersal effectiveness of the achene-pappus units of selected compositae in steady winds with convection. New Phytol. 72:665–675.Google Scholar
Shigesada, N. and Kawasaki, K. 1997. Biological Invasions: Theory and Practice. Oxford: Oxford University Press, pp. 64–65.Google Scholar
Wallinga, J. 1995. The role of space in plant population dynamics: annual weeds as an example. Oikos 74:377–383.Google Scholar
Willson, M. F. 1993. Dispersal mode, seed shadows, and colonization patterns. Vegetatio 107/108:261–280.Google Scholar
Wilson, B. J. and Brain, P. 1991. Long-term stability of distribution of Alopecurus myosuroides Huds. within cereal fields. Weed Res. 31:367–373.Google Scholar
Wilson, B. J., Cousens, R., and Cussans, G. W. 1984. Exercises in modelling populations of Avena fatua L. to aid strategic planning for the long term control of this weed in cereals. Pages 287–294 In Proceedings of the 7th International Symposium on Weed Biology, Ecology and Systematics. Paris: Columa.Google Scholar