Mathematical Treatment of Biological Diffusion

  • Akira Okubo
  • Daniel Grünbaum
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 14)


In the lifetime of most animals there occurs a time when the site of inhabitation is abandoned in favor of migration. Thus, in an environment changing through space and time, the most probable strategy for a new individual to adapt to survive and reproduce may not necessarily consist of remaining to compete with its parents or congeners, but may rather consist of migrating elsewhere to find an empty niche to inhabit (Taylor and Taylor, 1977; see also Lidicker and Caldwell, 1982). As a result the spread of population, i.e., dispersal, takes place. Such animal movement includes nomadism, whereby animals wander with no particular direction in search of sustenance, in a manner that resembles the random walk; and migration, which may be either periodic as animals move from one habitat to another in a repetitive cycle, or nonperiodic, implying a certain degree of permanence to the move. In addition, animals may display a restricted movement as they carry on their daily activities within a given domain of their habitat (home range).


Random Walk Mathematical Treatment Animal Motion Random Walk Model Telegraph Equation 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Akira Okubo
  • Daniel Grünbaum

There are no affiliations available

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