Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 114, Issue 32, Pages 8452-8457Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1705868114
Keywords
gene drive; Fisher wave; bistable wave
Categories
Funding
- National Science Foundation [DMR1608501, MCB1344191, DMS1614907]
- Harvard Materials Science Research and Engineering Center [DMR1435999]
- Division Of Materials Research
- Direct For Mathematical & Physical Scien [1608501] Funding Source: National Science Foundation
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Gene drives have the potential to rapidly replace a harmful wildtype allele with a gene drive allele engineered to have desired functionalities. However, an accidental or premature release of a gene drive construct to the natural environment could damage an ecosystem irreversibly. Thus, it is important to understand the spatiotemporal consequences of the super-Mendelian population genetics before potential applications. Here, we use a reaction-diffusion model for sexually reproducing diploid organisms to study how a locally introduced gene drive allele spreads to replace the wild-type allele, although it possesses a selective disadvantage s > 0. Using methods developed by Barton and collaborators, we show that socially responsible gene drives require 0.5 < s < 0.697, a rather narrow range. In this pushed wave regime, the spatial spreading of gene drives will be initiated only when the initial frequency distribution is above a threshold profile called critical propagule, which acts as a safeguard against accidental release. We also study how the spatial spread of the pushed wave can be stopped by making gene drives uniquely vulnerable (sensitizing drive) in a way that is harmless for a wildtype allele. Finally, we show that appropriately sensitized drives in two dimensions can be stopped, even by imperfect barriers perforated by a series of gaps.
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