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Mathematical modelling of spatial sorting and evolution in a host-parasite system.

Matthew H Chan1, Richard Shine2, Gregory P Brown2

  • 1School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia.

Journal of Theoretical Biology
|June 30, 2015
PubMed
Summary

Mathematical modeling reveals how cane toads (Rhinella marina) and their lungworm parasites spatially self-structure traits. Spatial sorting influences range expansion, with host-parasite dynamics critical for understanding this process.

Keywords:
Evolutionary dynamicsPopulation dynamicsSpatial structure

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Evolutionary Biology

Background:

  • Spatial self-structuring of traits, or spatial sorting, is well-studied in cane toads (Rhinella marina) in Australia using empirical and agent-based models.
  • Few mathematical modeling studies have investigated spatial sorting, particularly concerning co-evolving host-parasite populations.

Purpose of the Study:

  • To mathematically model the spatial self-structuring of traits in cane toads and their lungworm parasites.
  • To examine the evolution of dispersal ability in cane toads and prepatent period and larval size in lungworm parasites.

Main Methods:

  • Formulation of a reaction-diffusion based partial-integro-differential equation model.
  • Adaptation of an existing model by Bouin et al. (2012) to incorporate host-parasite co-evolutionary dynamics.

Main Results:

  • Confirmed observations from empirical and agent-based studies, including a lag between host and parasite populations dependent on parasite functional response.
  • Demonstrated that older populations exhibit reduced dispersal speeds.
  • Showed that spatial sorting can occur even with reproductive or survival disadvantages for more motile individuals.

Conclusions:

  • A significant disadvantage in reproduction or survival for more motile individuals is unlikely if spatial sorting is to notably impact the rate of range expansion.
  • The findings support the observed rate of cane toad range expansion in northern Australia over the past 60 years.