Bulletin of Mathematical Biology

, Volume 78, Issue 4, pp 695–712 | Cite as

Mate Finding, Sexual Spore Production, and the Spread of Fungal Plant Parasites

  • Frédéric M. Hamelin
  • François Castella
  • Valentin Doli
  • Benoît Marçais
  • Virginie Ravigné
  • Mark A. Lewis
Original Article


Sexual reproduction and dispersal are often coupled in organisms mixing sexual and asexual reproduction, such as fungi. The aim of this study is to evaluate the impact of mate limitation on the spreading speed of fungal plant parasites. Starting from a simple model with two coupled partial differential equations, we take advantage of the fact that we are interested in the dynamics over large spatial and temporal scales to reduce the model to a single equation. We obtain a simple expression for speed of spread, accounting for both sexual and asexual reproduction. Taking Black Sigatoka disease of banana plants as a case study, the model prediction is in close agreement with the actual spreading speed (100 km per year), whereas a similar model without mate limitation predicts a wave speed one order of magnitude greater. We discuss the implications of these results to control parasites in which sexual reproduction and dispersal are intrinsically coupled.


Allee effect Density-dependent dispersal Facultative parthenogenesis Pushed wave Spore-producing pathogens 

Mathematics Subject Classification

92D25 92D30 35Q92 



MAL gratefully acknowledges a Canada Research Chair, a Killam Fellowship, and NSERC Discovery and Accelerator awards. VR benefited from funds from project BIOFIS (reference 1001-001) of the Agropolis Fondation (Montpellier, France). FMH acknowledges funding from the French National Research Agency (ANR) as part of the ‘Blanc 2013’ programme (ANR-13-BSV7-0011, FunFit project) and from the French National Institute for Agricultural Research (INRA) ‘Plant Health and the Environment’ Division. FMH thanks Thomas Hillen for early mathematical feedback and Isaline Aubert and Antoine Ollivier for their contributions to this work through short internship periods. We thank the two anonymous reviewers for their helpful comments.


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Copyright information

© Society for Mathematical Biology 2016

Authors and Affiliations

  1. 1.AGROCAMPUS OUEST, UMR1349 IGEPPRennesFrance
  2. 2.Université de Rennes 1, UMR 6625 IRMARRennesFrance
  3. 3.CIRAD, UMR BGPIMontpellierFrance
  4. 4.CIRAD, UMR PVBMTSaint PierreFrance
  5. 5.INRA, UMR 1136 IAMChampenouxFrance
  6. 6.University of AlbertaEdmontonCanada

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