Spreading to a limit: some preliminary results

Mark Williamson, Jon Pitchford, Calvin Dytham

Research output: Chapter in Book/Report/Conference proceedingConference contribution


The spread of any alien species in a given area will eventually come to a limit. The aim of this study is to model this process and compare empirical data with the model results. The folded family of transformations, y = p(t) - q(t) (0 >= p >= 1, q = 1 - p), an extension of the power family of transformations y = x(t), is useful for data limited at zero and at a known maximum. Members of both families are familiar to biologists, if not under those names. Analytical models and both deterministic and stochastic simulations of spreading to a limit were studied. Data were on plants in the Czech Republic and on Sciurus and Impatiens in Britain and some other sets not reported here. In models, the pattern of spread depends on the starting point in relation to the limit, the limit may be reached suddenly or asymptotically and the pattern of spread depends on the relation of the dispersal kernel to the total area. Some model results are linear on folded square root (froot) or on folded logarithmic (logit) plots but some are not linear throughout, or at all, on either. In real data, linearization by froots seems quite common, linearization by logits seems rarer but does occur. To understand fully the spread of invasions, models and analyses of the whole process are needed. This paper is a first step in a process that will help managers and inform policy.

Original languageEnglish
Title of host publicationBiological Invasions toward a synthesis Neobiota 8
EditorsPetr Pysek, Jan Pergl
Number of pages9
ISBN (Electronic)1314-2488
Publication statusPublished - 2009


  • analytical models
  • Czech Republic plants
  • deterministic simulations
  • folded transformations
  • Impatiens
  • Sciurus
  • stochastic simulations

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