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Gene drive through a landscape: Reaction–diffusion models of population suppression and elimination by a sex ratio distorter

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  • Beaghton, Andrea
  • Beaghton, Pantelis John
  • Burt, Austin

Abstract

Some genes or gene complexes are transmitted from parents to offspring at a greater-than-Mendelian rate, and can spread and persist in populations even if they cause some harm to the individuals carrying them. Such genes may be useful for controlling populations or species that are harmful. Driving-Y chromosomes may be particularly potent in this regard, as they produce a male-biased sex ratio that, if sufficiently extreme, can lead to population elimination. To better understand the potential of such genes to spread over a landscape, we have developed a series of reaction–diffusion models of a driving-Y chromosome in 1-D and radially-symmetric 2-D unbounded domains. The wild-type system at carrying capacity is found to be unstable to the introduction of driving-Y males for all models investigated. Numerical solutions exhibit travelling wave pulses and fronts, and analytical and semi-analytical solutions for the asymptotic wave speed under bounded initial conditions are derived. The driving-Y male invades the wild-type equilibrium state at the front of the wave and completely replaces the wild-type males, leaving behind, at the tail of the wave, a reduced- or zero-population state of females and driving-Y males only. In our simplest model of a population with one life stage and density-dependent mortality, wave speed depends on the strength of drive and the diffusion rate of Y-drive males, and is independent of the population dynamic consequences (suppression or elimination). Incorporating an immobile juvenile stage of fixed duration into the model reduces wave speed approximately in proportion to the relative time spent as a juvenile. If females mate just once in their life, storing sperm for subsequent reproduction, then wave speed depends on the movement of mated females as well as Y-drive males, and may be faster or slower than in the multiple-mating model, depending on the relative duration of juvenile and adult life stages. Numerical solutions are shown for parameter values that may in part be representative for Anopheles gambiae, the primary vector of malaria in sub-Saharan Africa.

Suggested Citation

  • Beaghton, Andrea & Beaghton, Pantelis John & Burt, Austin, 2016. "Gene drive through a landscape: Reaction–diffusion models of population suppression and elimination by a sex ratio distorter," Theoretical Population Biology, Elsevier, vol. 108(C), pages 51-69.
  • Handle: RePEc:eee:thpobi:v:108:y:2016:i:c:p:51-69
    DOI: 10.1016/j.tpb.2015.11.005
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    References listed on IDEAS

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    1. Bellen, Alfredo & Zennaro, Marino, 2003. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780198506546.
    2. Roberto Galizi & Lindsey A. Doyle & Miriam Menichelli & Federica Bernardini & Anne Deredec & Austin Burt & Barry L. Stoddard & Nikolai Windbichler & Andrea Crisanti, 2014. "A synthetic sex ratio distortion system for the control of the human malaria mosquito," Nature Communications, Nature, vol. 5(1), pages 1-8, September.
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    Cited by:

    1. Silvia Grilli & Roberto Galizi & Chrysanthi Taxiarchi, 2021. "Genetic Technologies for Sustainable Management of Insect Pests and Disease Vectors," Sustainability, MDPI, vol. 13(10), pages 1-19, May.
    2. Beaghton, P.J. & Burt, Austin, 2022. "Gene drives and population persistence vs elimination: The impact of spatial structure and inbreeding at low density," Theoretical Population Biology, Elsevier, vol. 145(C), pages 109-125.

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