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Two Interacting Populations

  • Frithjof Lutscher
Chapter
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 49)

Abstract

Most biological populations do not exist in isolation but interact with other species in many ways that may increase or decrease their reproductive ability, affect their survival, or alter their dispersal behavior. Species interactions can lead to phenomena such as sustained population oscillations or competitive exclusion. In this chapter, we present some of the spatial aspects of population interaction in the context of IDEs. We begin with a brief background on nonspatial models before we move to study critical patch-sizes for predator and prey systems. Some of the most surprising and beautiful results in this section relate to dispersal-induced pattern formation in these systems. Spatial invasion dynamics of predator and prey show rich and complex behavior. We then present the phenomenon of anomalous spreading speeds in mutualism systems. Finally, we consider several aspects of persistence and invasion of competing species.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Frithjof Lutscher
    • 1
  1. 1.Mathematics and StatisticsUniversity of OttawaOttawaCanada

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