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Spatiotemporal Variation of Mistletoes: a Dynamic Modeling Approach

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Abstract

Mistletoes are common aerial stem-parasites and their seeds are dispersed by fruit-eating birds. In the mutually beneficial relationships between mistletoes and bird species that disperse mistletoes’ seeds, the preference of birds for infected trees influences the spread of mistletoes and the spatiotemporal pattern formation of mistletoes. We formulate a deterministic model to describe the dynamics of mistletoes in an isolated patch containing an arbitrary number of trees. We establish concrete criterions, expressed in terms of the model parameters, for mistletoes establishing in this area. We conduct numerical simulations based on a field study to reinforce and expand our results.

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Authors and Affiliations

  1. Department of Mathematics and Department of Zoology and Physiology, University of Wyoming, Laramie, WY, 82071, USA

    Rongsong Liu

  2. Department of Zoology and Physiology, University of Wyoming, Laramie, WY, 82071, USA

    Carlos Martinez del Rio

  3. Centre for Disease Modeling and Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada

    Jianhong Wu

Authors
  1. Rongsong Liu
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  2. Carlos Martinez del Rio
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  3. Jianhong Wu
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Correspondence to Rongsong Liu.

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Liu, R., del Rio, C.M. & Wu, J. Spatiotemporal Variation of Mistletoes: a Dynamic Modeling Approach. Bull Math Biol 73, 1794–1811 (2011). https://doi.org/10.1007/s11538-010-9592-6

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  • DOI: https://doi.org/10.1007/s11538-010-9592-6

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