Biological Invasion into Periodically Fragmented Environments: A Diffusion-Reaction Model

  • Nanako Shigesada
  • Noriko Kinezaki
  • Kohkichi Kawasaki
  • Fugo Takasu


Range expansions of invading species in homogeneous environments have been extensively studied since the pioneering work of Fisher 1937 and Skellam 1951 [1, 4, 5, 7, 8, 10]. Here we focus on range expansion of a species in a two-dimensional heterogeneous environment that is generated by segmenting an original favorable habitat into a regularly striped or criss-cross pattern as shown in Fig. 18.1:
  1. (a)

    Striped fragmentation — an environment is segmented into belts in such a way that favorable and unfavorable habitats with widths l 1 and l 2 respectively, are arranged alternately [6].

  2. (b)

    Criss-cross fragmentation — an environment is segmented in both horizontal and vertical axes in such a way that square-shaped favorable habitats with a side l 1 are regularly distributed to leave the criss-cross unfavorable belt with width l 2 in the background.



Unit Structure Biological Invasion Range Expansion Intrinsic Growth Rate Favorable Habitat 
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Copyright information

© Springer Japan 2003

Authors and Affiliations

  • Nanako Shigesada
    • 1
  • Noriko Kinezaki
    • 1
  • Kohkichi Kawasaki
    • 2
  • Fugo Takasu
    • 1
  1. 1.Department of Information and Computer SciencesNara Women’s UniversityKita-Uoya Nishimachi, NaraJapan
  2. 2.Department of Knowledge Engineering and Computer SciencesDoshisha UniversityKyotanabeJapan

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