Journal of Mathematical Biology

, Volume 69, Issue 2, pp 267–294 | Cite as

Modeling the presence probability of invasive plant species with nonlocal dispersal

  • Christopher Strickland
  • Gerhard Dangelmayr
  • Patrick D. ShipmanEmail author


Mathematical models for the spread of invading plant organisms typically utilize population growth and dispersal dynamics to predict the time-evolution of a population distribution. In this paper, we revisit a particular class of deterministic contact models obtained from a stochastic birth process for invasive organisms. These models were introduced by Mollison (J R Stat Soc 39(3):283, 1977). We derive the deterministic integro-differential equation of a more general contact model and show that the quantity of interest may be interpreted not as population size, but rather as the probability of species occurrence. We proceed to show how landscape heterogeneity can be included in the model by utilizing the concept of statistical habitat suitability models which condense diverse ecological data into a single statistic. As ecologists often deal with species presence data rather than population size, we argue that a model for probability of occurrence allows for a realistic determination of initial conditions from data. Finally, we present numerical results of our deterministic model and compare them to simulations of the underlying stochastic process.


Invasive species spread Stochastic birth process Integro-differential equation model Ecological niche model Species presence model Heterogeneous landscape model 

Mathematics Subject Classification (2000)

92D25 60G99 92D40 92D30 



We thank Sunil Kumar and Tom Stohlgren of the Colorado State University Natural Resource Ecology Laboratory for the discussions and suggestions that led to this research.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Christopher Strickland
    • 1
  • Gerhard Dangelmayr
    • 1
  • Patrick D. Shipman
    • 1
    Email author
  1. 1.Department of MathematicsColorado State UniversityFort CollinsUSA

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