Abstract:
:Population management using artificial gene drives (alleles biasing inheritance, increasing their own transmission to offspring) is becoming a realistic possibility with the development of CRISPR-Cas genetic engineering. A gene drive may, however, have to be stopped. "Antidotes" (brakes) have been suggested, but have been so far only studied in well-mixed populations. Here, we consider a reaction-diffusion system modeling the release of a gene drive (of fitness [Formula: see text]) and a brake (fitness [Formula: see text], [Formula: see text]) in a wild-type population (fitness 1). We prove that whenever the drive fitness is at most 1/2 while the brake fitness is close to 1, coextinction of the brake and the drive occurs in the long run. On the contrary, if the drive fitness is greater than 1/2, then coextinction is impossible: the drive and the brake keep spreading spatially, leaving in the invasion wake a complicated spatiotemporally heterogeneous genetic pattern. Based on numerical experiments, we argue in favor of a global coextinction conjecture provided the drive fitness is at most 1/2, irrespective of the brake fitness. The proof relies upon the study of a related predator-prey system with strong Allee effect on the prey. Our results indicate that some drives may be unstoppable and that if gene drives are ever deployed in nature, threshold drives, that only spread if introduced in high enough frequencies, should be preferred.
journal_name
Bull Math Bioljournal_title
Bulletin of mathematical biologyauthors
Girardin L,Calvez V,Débarre Fdoi
10.1007/s11538-019-00668-zsubject
Has Abstractpub_date
2019-12-01 00:00:00pages
5054-5088issue
12eissn
0092-8240issn
1522-9602pii
10.1007/s11538-019-00668-zjournal_volume
81pub_type
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