Bulletin of Mathematical Biology

, Volume 71, Issue 1, pp 107–129 | Cite as

First Passage Time Analysis of Animal Movement and Insights into the Functional Response

  • Hannah W. McKenzie
  • Mark A. Lewis
  • Evelyn H. Merrill
Original Article


Movement plays a role in structuring the interactions between individuals, their environment, and other species. Although movement models coupled with empirical data are widely used to study animal distribution, they have seldom been used to study search time. This paper proposes first passage time as a novel approach for understanding the effect of the landscape on animal movement and search time. In the context of animal movement, first passage time is the time taken for an animal to reach a specified site for the first time. We synthesize current first passage time theory and derive a general first passage time equation for animal movement. This equation is related to the Fokker–Planck equation, which is used to describe the distribution of animals in the landscape. We illustrate the first passage time method by analyzing the effect of territorial behavior on the time required for a red fox to locate prey throughout its home range. Using first passage time to compute search times, we consider the effect of two different searching modes on a functional response. We show that random searching leads to a Holling type III functional response. First passage time analysis provides a new tool for studying how animal movement may influence ecological processes.


First passage time Animal movement Search time Predation 


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Copyright information

© Society for Mathematical Biology 2008

Authors and Affiliations

  • Hannah W. McKenzie
    • 1
    • 2
  • Mark A. Lewis
    • 1
    • 2
  • Evelyn H. Merrill
    • 2
  1. 1.Centre for Mathematical Biology, Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada
  2. 2.Department of Biological SciencesUniversity of AlbertaEdmontonCanada

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