Gene drives have the potential to rapidly replace a harmful wild-type 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 prior to potential applications. Here, we employ a reaction-di↵usion model for sexually reproducing diploid organisms to study how a locally introduced gene drive allele spreads to replace the wild-type allele, even though it posses a selective disadvantage s > 0. Using methods developed by N. 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 wild-type allele. Finally, we show that appropriately sensitized drives in two dimensions can be stopped even by imperfect barriers perforated by a series of gaps.. CC-BY-NC 4.0 International license peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/126722 doi: bioRxiv preprint first posted online Apr. 11, 2017; 2 The development of the CRISPR/Cas9 system [1][2][3][4], derived from an adaptive immune system in prokaryotes [5], has received much recent attention, in part due to its exceptional versatility as a gene editor in sexually-reproducing organisms, compared to similar exploitations of homologous recombination such as zinc-finger nucleases (ZFNs) and the TALENS system [4,6]. Part of the appeal is the potential for introducing a novel gene into a population, allowing control of highly pesticide-resistant crop pests and disease vectors such as mosquitoes [7][8][9][10]. Although the genetic modifications typically introduce a fitness cost or a "selective disadvantage", the non-Mendelian population genetics embodied in CRISPR/Cas9 gene drives nevertheless allows edited genes to spread, even when the fitness cost of the inserted gene is large. The idea of using constructs that bias gene transmission rates to rapidly introduce novel genes into ecosystems has been discussed for many decades [11][12][13][14][15][16]. Similar "homing endonuclease genes" (in the case of CRISPR/Cas9, the homing ability is provided by a guide RNA) were considered earlier by ecologists in the context of control of malaria in Africa [17,18].As a hypothetical example of a gene drive applied to a pathogen vector requiring both a vertebrate and insect host, consider plasmodium, carried by mosquitoes and injected with its saliva into humans. Femal...