Skip to main content
SpringerLink
Log in

Analyzing maps of dispersal around a single focus

  • Published:
Environmental and Ecological Statistics Aims and scope Submit manuscript

Abstract

The spatial pattern of organisms may be used to characterize their dispersal, quantify spread or estimate the point of introduction of an alien species. Their distribution may be represented by maps of individuals, or by counts or by presence/absence at known positions within a sampled area. The problems and relative merits of these different forms of data for spatial inference are discussed. Three datasets concerning dispersal from a single focus are analyzed: counts of aphids, Rhopalosiphum padi and Sitobion avenae, on barley plants, Hordeum vulgare, grown in experi- mental trays; mapped locations of couch grass, Elymus repens, tillers within plots of a field experiment; locations of sightings of the lupin aphid, Macrosiphum albifrons, as it invaded Great Britain between 1981 and 1984. A method for generating maps from counts is proposed to overcome problems caused by recording imprecision. Several statistics are used to quantify dispersal and spatial pattern in the experimental data and together provide a clear picture of the spatial pattern observed; they enabled several effects of the experimental treatments to be identified. The value of the statistics are compared. Estimates of the source of the lupin aphid invasion are obtained using the backtracking methods of Perry (1995b) and do not contradict previous suggestions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Agassiz, D.J.L., Nash, D.R., Godfray, H.C.J. and Lawton, J.H. (1994) Estimating the spread of small invading organisms using public information. Global Ecology and Biogeography Letters, 4, 1–8.

    Google Scholar 

  • Alston, R. (1994) Statistical analysis of animal populations. Ph.D. thesis, University of Kent.

  • Augustin, N.H., Mugglestone, M.A. and Buckland, S.T. (1996) An autologistic model for the spatial distribution of wildlife. Journal of Applied Ecology, 33, 339–47.

    Google Scholar 

  • Baddeley, A.J., Moyeed, R.A., Howard, C.V. and Boyde, A. (1993) Analysis of a three-dimensional point pattern with replication. Applied Statistics, 42, 641–68.

    Google Scholar 

  • Banks, P.M., Kareiva, P.M. and Zia, L. (1988) Analyzing field studies of insect dispersal using two-dimensional transport equations. Environmental Entomology, 17, 815–20.

    Google Scholar 

  • Bartlett, P.W. (1993) Essig's lupin aphid (Macrosiphum albifrons Homoptera: Aphididae), introduction and spread in Europe. In Plant health and the European single market, D.L. Ebbels (ed), British Crop Protection Monograph no. 54, Farnham, Surrey. pp. 361–6.

  • Bergelson, J., Newman, J.A. and Floresroux, E.M. (1993) Rates of weed spread in spatially heterogeneous environments. Ecology, 74, 999–1011.

    Google Scholar 

  • Bliss, C.I. (1941) Statistical problems in estimating populations of Japanese beetle larvae. Journal of Economic Entomology, 34, 221–32.

    Google Scholar 

  • Boag, B., Neilson, R., Palmer, L.F. and Jones, H.D. (1994) A further record of the New Zealand flatworm Artioposthia triangulata (Dendy) in England. Plant Pathology, 43, 220–2.

    Google Scholar 

  • Camann, M.A., Culbreath, A.K., Pickering, J., Todd, J.W. and Denski, J.W. (1995) Spatial and temporal patterns of spotted wilt epidemics in peanut. Phytopathology, 85, 879–85.

    Google Scholar 

  • Clark, S.J., Perry, J.N. and Marshall, E.J.P. (1996) Estimating Taylor's power law parameters for weeds and the effect of spatial scale. Weed Research, 36, 405–17.

    Google Scholar 

  • Diggle, P.J. (1983) Statistical Analysis of Spatial Point Patterns. Academic Press, London.

    Google Scholar 

  • Diggle, P.J., Lange, N. and Beneš, F.M. (1991) Analysis of variance for replicated spatial point patterns in clinical neuroanatomy. Journal of the American Statistical Association, 86, 618–25.

    Google Scholar 

  • Dobzhansky, T.H. and Wright, S. (1943) Genetics of natural populations. Dispersal rates in Drosophila pseudobscura, Genetics, 28, 304–40.

    Google Scholar 

  • Fisher, N.I, Lewis, T. and Embleton, B.J.J. (1987) Statistical Analysis of Spherical Data, Cambridge University Press, Cambridge.

    Google Scholar 

  • Fleming, W.E. and Baker, F.E. (1936) A method for estimating populations of larvae of the Japanese beetle in the field. Journal of Agricultural Research, 53, 319–31.

    Google Scholar 

  • Freeman, G.H. (1977) A model relating numbers of dispersing insects to distance and time. Journal of Applied Ecology, 14, 477–87.

    Google Scholar 

  • Greig-Smith, P. (1952) The use of random and contiguous quadrats in the study of plant communities. Annals of Botany, 16, 293–316.

    Google Scholar 

  • Killion, M.J. and Grant, W.E. (1995) A colony-growth model for the imported fire ant-potential geographic range of an invading species. Ecological Modelling, 77, 73–84.

    Google Scholar 

  • Leakey, R.R.B., Chancellor, R.J. and Vince-Prue, D. (1978) Regeneration from rhizome fragments of Agropyron repens (L.) Beauv. III. Effects of nitrogen and temperature on the development of dominance amongst shoots on multi-node fragments. Annals of Botany, 42, 197–204.

    Google Scholar 

  • Lonsdale, W.M. (1993) Rates of spread of an invading species-Mimosa pigra in northern Australia. Journal of Ecology, 81, 513–21.

    Google Scholar 

  • Mack, R.N. (1985) Invading Plants: Their Potential Contribution to Population Biology. Studies on Plant Demography: A Festschrift for John L. Harper, J. White (ed), Academic Press, London. pp. 127–42.

    Google Scholar 

  • Marshall, E.J.P. (1988) Field-scale estimates of grass weed populations in arable land. Weed Research, 28, 191–8.

    Google Scholar 

  • Marshall, E.J.P. (1990) Interference between sown grasses and the growth of rhizome of Elymus repens (couch grass). Agriculture, Ecosystems and Environment, 33, 11–22.

    Google Scholar 

  • Mortimer, A.M. and McMahon, D.J. (1982) Time, space and the growth of couch grass. Proceedings British Crop Protection Conference-Weeds (1982), British Crop Protection Council. pp. 771–8.

  • Mugglestone, M.A. (1996) The role of tessellation methods in the analysis of three-dimensional spatial point patterns. Journal of Agricultural, Biological and Environmental Statistics, 1, 141–53.

    Google Scholar 

  • Nash, D.R., Agassiz, D.J.L., Godfray, H.C.J. and Lawton, J.H. (1995) The pattern of spread of invading species: two leaf-mining moths colonizing Great Britain. Journal of Applied Ecology, 64, 225–33.

    Google Scholar 

  • Nelson, S.C. (1996) A simple analysis of disease foci. Phytopathology, 86, 332–9.

    Google Scholar 

  • Nelson, S.C. and Campbell, C.L. (1993) Comparative spatial analysis of foliar epidemics in white clover caused by viruses, fungi and a bacterium. Phytopathology, 83, 288–301.

    Google Scholar 

  • Perry, J.N. (1995a) Spatial aspects of animal and plant distribution in patchy farmland habitats. In Ecology and Integrated Arable Farming Systems, D. Glen, M. Greaves and H.M. Anderson (eds), Wiley, Chichester. pp. 221–42.

  • Perry, J.N. (1995b) Spatial analysis by distance indices. Journal of Animal Ecology, 64, 303–14.

    Google Scholar 

  • Perry, J.N., Bell, E.D., Smith, R.H. and Woiwod, I.P. (1996) SADIE: software to measure and model spatial pattern. Aspects of Applied Biology, 46, 95–102.

    Google Scholar 

  • Perry, J.N. and Hewitt, M. (1991) A new index of aggregation for animal counts. Biometrics, 47, 1505–18.

    Google Scholar 

  • Piron, P.G.M. (1987) The advance of the American lupin aphid (Macrosiphum albifrons Essig) (Homoptera: Aphididae) in Europe. Journal of Applied Entomology, 103, 111–2.

    Google Scholar 

  • Richardson, W.G. and Parker, C. (1976) The activity and post-emergence selectivity of some recently developed herbicides: HOE 22870, HOE 23408, flamprop-methyl, metamitron and cyperquat. Technical Report Agricultural Research Council Weed Research Organization No. 39, 59 pp.

  • Ripley, B.D. (1988) Statistical Inference for Spatial Processes, Cambridge University Press, Cambridge.

    Google Scholar 

  • Sharov, A.A., Liebhold, A.M. and Roberts, E.A. (1997) Methods for monitoring the spread of gypsy moth (Lepidoptera: Lymantriidae) populations in the Appalachian mountains. Journal of Economic Entomology, 90, 1259–66.

    Google Scholar 

  • Sharov, A.A., Roberts, E.A. and Liebhold, A.M. (1996) Spread of gypsy moth (Lepidoptera, Lymantriidae) in the central Appalachians: comparison of population boundaries obtained from male moth capture, egg mass counts, and defoliation records. Environmental Entomology, 25, 783–92.

    Google Scholar 

  • Sharov, A.A., Roberts, E.A., Liebhold, A.M. and Ravlin, F.W. (1995) Gypsy moth (Lepidoptera, Lymantriidae) spread in the central Appalachians: three methods for species boundary estimation. Environmental Entomology, 24, 1529–38.

    Google Scholar 

  • Shigesada, N. and Kawasaki, K. (1997) Biological Invasions: Theory and Practice, Oxford University Press, Oxford.

    Google Scholar 

  • Silander, J.A. Jr and Pacala, S.W. (1985) Neighbourhood predictors of plant performance. Oecologia, 66, 256–63.

    Google Scholar 

  • Skellam, J.G. (1952) Studies in statistical ecology I. Spatial pattern. Biometrika 39, 346–62.

    Google Scholar 

  • Soderstrom, L. and Jonsson, B.G. (1989) Spatial pattern in the leafy hepatic Ptilidium pulcherrimum. Journal of Bryology, 15, 793–802.

    Google Scholar 

  • Stewart, V.I. and Blackshaw, R.P. (1993) Genetic variation in populations of the terrestrial planarian Artioposthia triangulata (Dendy) and evidence for passive dispersal in Northern Ireland. Annals of Applied Biology, 123, 459–68.

    Google Scholar 

  • Stroyan, H.L.G. (1981) A North American lupin aphid found in Britain. Plant Pathology, 30, 253.

    Google Scholar 

  • Taylor, L.R. (1961) Aggregation, variance and the mean. Nature, 189, 732–5.

    Google Scholar 

  • Taylor, L.R. (1986) Synoptic dynamics, migration and the Rothamsted Insect Survey. Journal of Animal Ecology, 55, 1–38.

    Google Scholar 

  • Taylor, L.R., Woiwod, I.P. and Perry, J.N. (1978) The density-dependence of spatial behaviour and the rarity of randomness. Journal of Animal Ecology, 47, 383–406.

    Google Scholar 

  • Taylor, R.A.J. (1978) The relationship between density and distance of dispersing insects. Ecological Entomology, 3, 63–70.

    Google Scholar 

  • Tower, W.L. (1906) An investigation of evolution in Chrysomelid beetles of the genus, Leptinotarsa, Carnegie Institute, Washington D.C., 320pp.

    Google Scholar 

  • Trewhella, W.J. and Harris, S. (1988) A simulation-model of the pattern of dispersal in urban fox (Vulpes vulpes) populations and its application for rabies control. Journal of Applied Ecology, 25, 435–50.

    Google Scholar 

  • Williamson, M.H. (1996) Biological Invasions, Chapman and Hall, London.

    Google Scholar 

  • Wilson, B.J. and Brain, P. (1991) Long-term stability of distribution of Alopecurus myosuroides Huds. within cereal fields. Weed Research, 31, 367–73.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Statistics Department, IACR-Rothamsted, Harpenden, Herts, AL5 2JQ, United Kingdom

    S. Korie, S.J Clark & M. A. Mugglestone

  2. Entomology and Nematology Department, IACR-Rothamsted, Harpenden, Herts, AL5 2JQ, United Kingdom

    J.N Perry

  3. MAFF Central Science Laboratory, Plant Health Group, Sand Hutton, York, YO4 1LZ, United Kingdom

    P .W. Bartlett

  4. Crop and Environmental Sciences Department, IACR-Long Ashton Research Station, Department of Agricultural Sciences, University of Bristol, Long Ashton, Bristol, BS18 9AF, United Kingdom

    E. J . P. Marshall

  5. ICER, IACR-Rothamsted, Harpenden, Herts, AL5 2JQ, United Kingdom

    J. A. Mann

Authors
  1. S. Korie
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S.J Clark
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J.N Perry
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. A. Mugglestone
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. P .W. Bartlett
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. E. J . P. Marshall
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. J. A. Mann
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Korie, S., Clark, S., Perry, J. et al. Analyzing maps of dispersal around a single focus. Environmental and Ecological Statistics 5, 317–344 (1998). https://doi.org/10.1023/A:1009603804998

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1009603804998

Search

Navigation