royalsocietypublishing.org/journal/rspb

ResearchCite this article: Holman L. 2019Evolutionary simulations of Z-linked

suppression gene drives. Proc. R. Soc. B 286:20191070.

http://dx.doi.org/10.1098/rspb.2019.1070

Received: 9 May 2019

Accepted: 16 September 2019

Subject Category:Evolution

Subject Areas:bioengineering, evolution, theoretical biology

Keywords:sex chromosomes, gene drives, population

control, schistosomiasis, selfish genes

Author for correspondence:Luke Holman

e-mail: luke.holman@unimelb.edu.au

One contribution to the Special Feature

‘Natural and synthetic gene drive systems’.

Guest edited by Nina Wedell, Anna Lindholm

and Tom Price.

Electronic supplementary material is available

online at https://doi.org/10.6084/m9.figshare.

c.4687277.

© 2019 The Author(s) Published by the Royal Society. All rights reserved.

Evolutionary simulations of Z-linkedsuppression gene drives

Luke Holman

School of BioSciences, The University of Melbourne, Melbourne, Victoria 3010, Australia

LH, 0000-0002-7268-2173

Synthetic gene drives may soon be used to suppress or eliminate populationsof disease vectors, pathogens, invasive species, and agricultural pests. Recentproposals have focused on using Z-linked gene drives to control species withZW sex determination, which include Lepidopteran pests, parasitic tre-matodes, and cane toads. These proposals include Z-linked ‘W-shredders’,which would suppress populations by cleaving the W chromosome andcausing females to produce only sons, as well as Z-linked female-sterilizinggene drives. Here, I use eco-evolutionary simulations to evaluate the potentialof some proposed Z-linked gene drives, and to produce recommendationsregarding their design and use. The simulations show that W-shredders arelikely to be highly effective at eradicating populations provided that resistanceto W-shredding cannot evolve. However, W-shredder alleles can invadepopulations from very low frequencies, making it difficult to eliminate specificpopulations while leaving nearby populations untouched; this issue mayrestrict their possible uses.

1. IntroductionDevelopments in genetic engineeringwill soonmake it feasible to alter or eliminatepopulations of disease vectors, pathogens, agricultural pests, and invasive speciesusing ‘gene drives’ [1–6]. Gene drives cause particular alleles (usually transgenes)to propagate through populations via a range of mechanisms, including geneconversion, poison-antidote systems, segregation distortion, and genetic incom-patibility [7–9]. For example, CRISPR-Cas9 gene editing can be used to create atransgene that will be transmitted to almost 100% of the offspring of heterozygousindividuals instead of the usual 50%; this type of gene drive functions by inducinga double-stranded DNA break at the homologous wild-type locus, which is thenrepaired using the transgene as a template. Gene drives are often categorizedinto two types: replacement drives, which aim to spread a human-beneficialallele throughout a population (e.g. amosquito allele that interfereswith the trans-mission of malaria [1,10]), and suppression drives, which reduce the size of apopulation (potentially to extinction). Suppression drives typically work byusing non-Mendelian inheritance to spread alleles that cause lethality or sterility[2,5,11], or skew the offspring sex ratio—typically towards males [12–16].

Recent theoretical papers have investigated the feasibility, efficacy, and poten-tial negative consequences of various types of gene drives. For example, Nobleet al. [6] showed that the basic version of a CRISPR-Cas9 gene drive might behighly invasive and could rapidly spread to fixation across whole species,which is often an undesirable outcome. Conversely, othermodels have concludedthat gene drives are likely to fail if populations can evolve resistance to their effects[17,18]. The issue of resistance is compounded because the standard imple-mentation of a CRISPR-Cas9 gene drive (but perhaps not updated versions;[4,5,18,19]) tends to create its own resistance alleles, e.g. when the double-stranded break induced byCas9 is repaired using an alternativeDNA repair path-way (non-homologous end joining; NHEJ) instead of homology-directed repair[1–3,18,20]. Given the potential safety, ethical, and sociopolitical concerns sur-rounding gene drives, some models have focused on gene drives that would go

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Figure 1. Some hypothetical Z-linked suppression drives considered in this study. Panel (a) illustrates normal inheritance of sex chromosomes in a wild-type ZWfemale (assumed to be mated to a wild-type ZZ male; not shown): the offspring sex ratio is even. (b) The female carries a W-shredder allele (Z*) that kills gametesor offspring early enough that missing daughters are replaced with more Z*-bearing sons. (c) The lost daughters are not replaced, though their absence increases thesurvival probability of the sons somewhat (shown by their larger size), causing super-Mendelian inheritance of the Z* allele. Lastly, panel (d ) shows a Z-linkedfemale-sterilizing allele (e.g. an allele that cleaves the W chromosome or a female-essential gene in somatic cells); since it is strongly disadvantageous in females,such an allele would go extinct unless it benefits from gene drive in heterozygous males. (Online version in colour.)

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extinct after a time [15,21,22], would stay confined to particularpopulations [11,22], and/or could be reversed once they havespread [23].

This paper focuses on the evolutionary dynamics ofZ-linked suppression gene drives. The simulation is inspiredby proposals for various types of Z-linked gene drives byKevin Esvelt and colleagues, as well as ongoing efforts todevelop these Z drives (see www.sculptingevolution.org; atthe time of writing, these ideas have not been published else-where). Various Z-linked suppression drives proposed byEsvelt and colleagues are shown schematically in figure 1.Depending on its design, mode of action, and the biology ofthe target species, Z chromosomes carrying the drive allele(denoted Z*) might enjoy a transmission advantage in Z*Wfemales (figure 1b, and perhaps also 1c), and optionally alsoin Z*Z males. Esvelt et al. focus on using Z drives to controlthe Schistosoma trematodes responsible for schistosomiasis,though Z drives could theoretically be used to control anyorganism with female-heterogametic sex determination, suchas Lepidopteran agricultural pests, invasive populations ofcane toads Bufo marinus [24], or even invasive birds.

A Z-linked gene drive could suppress populations by bias-ing gametogenesis in females, for example, by inducingdouble-stranded DNA breaks in the W chromosome in orderto inactivate it; such a gene drive would be a ‘W-shredder’,analogous to the X- and Y-shredders under development forXY species [12,13,15,16,25,26]. Females carrying the genedrive would thus produce relatively few viable W-bearingeggs, and therefore produce mainly drive-carrying sons.Esvelt et al. point out that the evolutionary dynamics of thedrive will depend on the fitness of drive carriers relative towild types, the timing of W-shredding (e.g. in germ cells,ova, or zygotes), and the ecology of the target species.For example, some W-shredder designs might allow drivefemales to produce roughly the same number of (mostlymale) offspring as a wild-type female provided that the

W chromosome is destroyed early enough in oogenesis/development that the lost daughters can be replaced by sons(figure 1b). Alternatively, drive-carrying females might pro-duce half the number of offspring (or fewer), e.g. if the driveworks bydestroying all ova or offspring that carry aW chromo-some, and this loss is not compensated by reduced competitionon the surviving offspring. Esvelt et al. also proposed that onecould suppress populations using a Z-linked locus that causedsterility or lethality in females, either by shredding the Win somatic tissues, or by spreading some other allele thatharms females but not males. If this female-harming allelewere capable of gene drive in males, it could perhaps reachhigh enough frequencies to suppress the population. TheW-shredder could be designed to also cause gene drive inmales. Male gene drive could be accomplished using ‘standard’CRISPR-Cas9 gene conversion, whereby the driving Z allelewould convert thewild-type locus using homing endonucleaseactivity followed by homology-directed repair, causing hetero-zygous males to produce mostly drive-carrying sperm. Esveltet al. note that male gene drive might not be necessary, since aZ-linked locus that prevents transmission of theWmay alreadyenjoy a transmission advantage (figure 1b,c).

Here, I present an evolutionary simulation that canaccommodate all of these proposed Z-linked drives. I aimedto test which properties of the gene drive and the ecologyof the target species are critical to determining the likelihoodand speed of extinction. For example, the gene drive will pre-sumably spread faster if it can bias transmission in both sexes,but perhaps a simpler female-only drive would be adequate.Also, since the population will become more male-biased asthe gene drive invades, eco–evo feedback might affect theoutcome of the drive release in non-intuitive ways. Forexample, alleles that prevent W-shredding might have anespecially large fitness advantage relative to resistance allelesagainst ‘standard’ CRISPR drives [17,18], since the formerrestore a normal sex ratio as well as defusing the harmful

Table 1. List of variables, and their corresponding parameter(s) in the model, which were varied in order to study their effects on extinction.

variable parameter(s)

strength of gene drive in females (e.g. W-shredding) pshredstrength of gene drive in males (e.g. gene conversion) pconvcost of gene drive allele to female fecundity cfcost of gene drive allele to male mating success cmfrequency of W-linked resistance mutations μWfrequency of Z-linked resistance mutations and NHEJ μZ and pnhejfrequency of autosomal resistance alleles μA and μBpatchiness of the population k

dispersal rate of males and females xm and xfglobal versus local density-dependence of female fecundity ψ

contribution of males relative to females in density-dependence δ

number of gene drive carrier males released nreleaserelease strategy: all in one patch, or global —

fecundity of females at low population densities r

shape of density dependence α

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effect of the driver on individual fitness. Moreover, thechange in sex ratio could affect the ecology and evolutionof the population, particularly if males and females contrib-ute differentially to density-dependent population growth[27,28], or have different dispersal rates [29]. The modelincorporates the possibility that Z-linked resistant-to-drivealleles are sometimes created by NHEJ in heterozygotemales, to test whether resistance is just as problematic asfor autosomal drives [1–3,18,20].

2. MethodsA full description of the simulation is provided as electronicsupplementary material. In brief, I simulate a finite population ofdioecious diploids with ZW sex determination that inhabits k dis-crete habitat patches arranged linearly in a ring. The aim of thesimulation is to identify properties of the gene drive and the ecol-ogy of the target species that influence the outcome of a singlerelease of nrelease homozygote males carrying a Z-linked genedrive allele, Z*. The drive allele causes biased inheritance and/orreduced fecundity in females, and optionally also causes biasedinheritance in heterozygous males (e.g. via gene conversion).Each generation proceeds in discrete steps: birth, dispersal betweenpatches, breeding within patches, and death of the parental gener-ation. The equilibrium population size was roughly 10 000 in allsimulations upon release of the gene drive, and the main outcomesof interest are the likelihood and speed of extinction. The simulationwas written in R v. 3.4.0 and run on the Spartan cluster at the Uni-versity of Melbourne; table 1 lists the simulation parameters thatwere manipulated to study their effects.

Eachmale carries two diploid autosomal loci (termedA/a andB/b) and one diploid Z-linked locus, while females carry bothautosomal loci, a single allele at the Z-linked locus, plus a Wchromosome. There are three possible Z-linked alleles: the driveallele (Z*), a wild-type allele (Z+) that is vulnerable to gene drivein Z*Z+ males, and a resistant allele (Zr) that is immune to genedrive in Z*Zr males. Similarly, there are two types of W chromo-some: a wild-type W that is vulnerable to shredding by the Z*allele (W+), and an immune variant (Wr). The autosomal allelesA and B are dominant ‘trans-acting’ resistance alleles that confer

immunity to W-shredding and gene conversion, respectively.The Z* allele imposes a cost cf on the fecundity of female carriers,and a cost cm on the mating success of male carriers. The resistancealleles Wr, Zr, A, and B are assumed to be cost-free. Setting cf = 1allows simulation of a female-sterilizingZ-linked drive (figure 1d).

Females carrying Z* (and no A or Wr alleles) produce12 (1þ pshred) Z-bearing gametes and 1

2 (1� pshred) W-bearinggametes, and thus produce >50% sons when pshred > 0. Secondly,Z*Z+ males produce 1

2 (1þ pconv � pconvpnhej) gametes carryingthe Z* allele, 1

2 (1� pconv) gametes carrying the Z+ allele, and12 (pconvpnhej) gametes carrying the Zr allele. Thus, gene conversionoccurs in males if pconv > 0, meaning that the Z* allele is over-represented in the gametes of these three male genotypes. Theparameter pnhej represents the creation of resistance alleles viaNHEJ.

Female fecundity depends on the local and/or global densityand fitness of other females, and the density ofmales, via functionsinvolving five parameters that control the carrying capacity (K),maximum possible fecundity (r), the shape of the density-dependence function (α), the relative effect of males and femaleson density (δ), and the scale of density-dependence (local orglobal; ψ). These parameters allow the model to capture a rangeof possible life histories suitable for different organisms thatcould be suppressed with W-shredders. For example, maximumfecundity r is lower for birds than for cane toads, and δ might belower in Lepidoptera than trematodes, since male trematodesconsume space/resources inside the host (and males are muchlarger than females), while male Lepidoptera do not consumeone of the main limited resources that females need (i.e. hostplants on which to lay their eggs). Female and male offspring dis-perse to other patches with probabilities xf and xm, respectively,allowing for variable and sex-specific gene flow between patches.Dispersal was either local or global (i.e. to a neighbouring patch ora random patch).

3. Results(a) Three illustrative simulation runsFigure 2 shows three contrasting simulation runs. In figure 2a,the release of Z*Z* males at generation 50 caused the Z* alleleto invade and fix, causing rapid extinction due to a lack of

Z* invades and causes extinction Z* invades but fails to cause extinction

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Figure 2. Three illustrative runs of the simulation, showing evolution in response to the release of males carrying a W-shredder at generation 50 (dotted line). (a)The driving Z* allele fixed very quickly, causing population extinction through a shortage of females. (b) The Z* allele fixed but did not cause extinction, becausecarrier females continued to produce some daughters due to incomplete W-shredding. (c) The Z* allele invaded, which selected for the W-shredding resistance alleleA, causing Z* to go extinct by removing its transmission advantage. The population size N is shown as a fraction of its maximum value of 10 000. Electronicsupplementary material, table S1 lists the parameter spaces used for these three runs. (Online version in colour.)

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females. The simulation run in figure 2a assumed thatZ* causesnear-complete W-shredding, Z* benefits from gene drive inmales, that Z* has moderate fitness costs to carriers, and thereis no resistance to W-shredding (electronic supplementarymaterial, table S1).

In figure 2b,Z*went to fixation but failed to cause extinction,due to incomplete W-shredding by the Z* allele. In this run,pshred = 0.84 (electronic supplementarymaterial, table S1),mean-ing that 8% of the offspring of Z*W+ mothers are female. Theinvasion of Z* altered the population sex ratio, but did notcause extinction (or even a decline in population size).

Lastly, figure 2c shows a case where the invasion of Z* wasreversed by the evolution of autosomal resistance alleles.Following the release of theZ* allele, the initially rare autosomalresistance allele A (which prevents W-shredding) rapidlyincreased in frequency, disarming the effects of Z* in femalesand returning the population-level sex ratio to 50 : 50, eventhough the Z* allele reached fixation. Incidentally, the resistantallele A was favoured over a because the male-biased popu-lation sex ratio created by Z* favours the production ofdaughters, and AA and Aa females produce more daughtersthan aa females in populations where Z* is present.

(b) Effects of each parameter on the evolution of aW-shredder

Figure 3 shows the effects of each parameter for simulationsof a Z-linked W-shredder allele that also potentially causesgene drive in Z*Z males. Figure 3 assumes completeW-shredding (pshred = 1), because initial trials revealed thatextinction almost never occurred if pshred < 0.95 (electronicsupplementary material, figure S1). This result confirmsthat a W-shredder needs to effectively prevent female carriersfrom producing daughters in order to reliably cause extinc-tion. Otherwise, all the parameters were allowed to varywithin pre-specified limits using Latin hypercube sampling.Thus, the relationships in figure 3 show the expected effectof the focal parameter on extinction probability, while the

other parameters vary independently within the rangesshown on the x-axis of figure 3. Figure 4 is similar to figure3, except that it plots the average time until extinction (forthe subset of runs in which extinction actually occurred).

(i) Gene drive parametersExtinction probability declined sharply as the costs of the genedrive to female fecundity (cf ) and male mating success (cm)increased, suggesting that one should work to minimize suchcosts when developing a W-shredder. Consistent with thisconclusion, time until extinction increased monotonicallywith the cost of male mating success cm, but interestingly,the relationship between cf and the speed of extinction washump-shaped. W-shredders with no costs in females causedextinction quickly due to their more rapid spread, whileW-shredders that carried a sufficiently high cost to femalesactually resulted in faster extinction (though note that extinc-tion rarely occurred when cf was high), since femalefecundity is critical to population growth. On balance, themodel suggests that W-shredders should be designed to haveminimal impact of the fitness of carriers, though reassuringly(from a design standpoint), extinction still occurred frequentlyeven if carriers were 10–20% less fit than wild types.

Another very important parameter was the presence/absence of autosomal resistance alleles that prevent W-shredding from occurring: extinction almost never happenedwhen such alleles were present. Perhaps surprisingly, when Iallowed wild-type W+ chromosomes to mutate to a resistanttype, ensuring the population almost always contained asmall number of resistant Wr chromosomes, the probabilityof extinction was essentially unaffected. The difference in out-come relative to the A allele may have to do with the reducedpopulation size of the W chromosome, which is limited tofemales, whose population size drops very rapidly once theZ* allele invades (figure 2).

Extinction was substantially more likely when the W-shredderwas also capable of genedrive inZ*Zmales. Although

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Z-linked resistance (µZ) shape of density dependence (a) release size (number Z*Z* males) initial freq. allele B

dispersal typemale effect on density (d )importance of local density (y)male dispersal frequency (xm)

number of patches (k) gene drive in males (pconv) maximum fecundity (r) female dispersal frequency (xf)

Figure 3. The plot shows the effect of each model parameter on the percentage of simulation runs in which the population went extinct, for simulations of aZ-linked W-shredder that completely prevents the production of daughters by females (pshred = 1; see also electronic supplementary material, figure S1). The plotwas generated by sampling evenly from the complete parameter space 721 587 times using Latin hypercube sampling, such that each plot shows the marginal effectof one parameter while the other parameters vary independently across their possible ranges (shown by the relevant x-axis scale). Continuous parameters weregrouped into 51 bins (each containing approx. 14 400 runs, 2% of the total), and the lines were fitted using LOESS (locally estimated scatterplot smoothing). Notethat the y-axis scales to the range of the data, and the panels are ordered by this range (showing the approximate relative importance of each parameter). (Onlineversion in colour.)

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male gene drive was non-essential for theW-shredder to causeextinction, efficient male-acting drive greatly reduced thenumber of generations required for extinction to occur (seeinset of figure 4). Similarly, resistance to the male-acting com-ponent of the gene drive reduced the extinction probability(and increased the time until extinction), especially when resist-ance alleles were created byNHEJ rather than arising randomlyby mutation (presumably because the latter causes the resist-ance alleles to appear in the same patches as the drive allele,where they immediately enjoy a selective advantage).

The number of Z*Z* males released into the populationhad little effect on extinction probability: releasing 20 individ-uals was almost as likely to cause extinction as releasing 100.This result reflects the classic population genetics result thatthe fixation probability of a strongly selected allele (such asa gene drive) does not depend on its frequency (only on selec-tion and population structure; reviewed in [30]). Additionally,releasing the drive-carrying males throughout the meta-population was equally likely to cause extinction as releasingthem all in one patch. As well as suggesting that multi-site

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Figure 4. The main plot shows the average number of generations until extinction, among the subset of runs in which extinction occurred. The density plot in thelower right shows the distribution of the response variable across all the parameter spaces in which the Z* allele was costly (defined as cf > 0.05 and/or cm > 0.05)or not costly (cf < 0.05 and cm < 0.05), and in which the Z* allele benefitted from strong gene drive in males (pconv > 0.95) or not (pconv < 0.95). Other details arethe same as for figure 3. (Online version in colour.)

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release programmes might not be strictly necessary, thisresult implies that Z-linked gene drives are very likely tospread between populations connected by gene flow, aspreviously found for autosomal drives [6].

(ii) Ecological drive parametersThe most important ecological parameter was the number ofpatches intowhich the populationwas divided. Spatially struc-tured populations were harder to drive extinct, presumablybecause the population can persist in habitat patches wherethe drive allele is absent, and because migrants can recolonize

patches where local extinction has occurred. Since patches con-taining the gene drive will produce fewer migrants (due totheir imbalanced sex ratio), migrants that recolonize emptypatches are more likely to carry wild-type or drive-resistantalleles. The time until extinction increased with the patchinessof the population, with diminishing returns.

Interestingly, the migration rate had a sex-specificrelationship with extinction probability. Extinction becameincreasingly likely as the male migration rate (xm) increased,since the drive allele is primarily carried by males due toits effect on the sex ratio. Conversely, the effect of thefemale migration rate (xf ) was U-shaped. With very high

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female migration rates, population structure is much reduced,ensuring that the drive allele quickly reaches any patch thatlacks it. With low female migration rates, the gene drivecauses local extinctions faster than patches can be recolonizedby dispersal. Intermediate rates of female dispersal allow forthe creation of long-lasting refugia from the drive allele, andalso allow for some recolonization, resulting in a reducedprobability of extinction.

Unsurprisingly, extinction was more likely when the maxi-mum possible fecundity of each female (r) was lower.However, the decline was not linear, and the results suggestthatW-shredders are capable of eliminating even those speciesin which a handful of surviving females can rapidly repopu-late. The results also suggest that extinction was slightlymore probablewhen female fecunditywas determined primar-ily by local rather than global density (ψ). This is because localdensity can remain high (and thus, per-female fecundity canremain low) even in meta-populations that are declining dueto the spread of the Z* allele in some of their sub-populations.

Theparameter δ,which represents sexdifferences in ecologi-cal niche use and behaviour, had a hump-shaped relationshipwith extinction probability. Low δ indicates that female fecund-ity is only weakly affected by the density of males, and thisscenario was associated with lower extinction probabilities.This is because the gene drive creates male-biased populations,boosting female fecundity for any given population size, andhelping to stave off extinction. Conversely when δ is high,male density has a stronger negative effect on female fecundity,which slightly reduced the probability of extinction (perhapsbecause patches containing many drive alleles are male-biased, and thus send out comparatively few drive-carryingmigrants when δ is high). Extinction was most likely for inter-mediate values of δ. By contrast, the time until extinctiondeclined monotonically with δ, since high values of δ meanthat male-biased populations produce even fewer offspring.

Finally, the parameter α, which controls the shape of therelationship between female fecundity and population den-sity, had a weak negative effect on the likelihood or speedof extinction. Setting α < 1 means that female fecunditydeclines at a decelerating rate as population density increases,such that per-female fecundity only approaches its maximumpossible value once the population is heavily depleted,making extinction more likely.

(c) Well-designed W-shredders cause rapid extinctionThe inset of figure 4 shows the frequency distribution for timeuntil extinction. With a well-designedW-shredder and favour-able ecological conditions, the Z* allele caused extinction in asfew as nine generations. When considering only those simu-lations in which pshred = 1 (i.e. drive females produce nodaughters) and the fitness of drive carriers was within 5% ofthe wild type, extinction occurred within 20 generations forthe majority of the parameter space shown in figures 3 and 4,illustrating that a well-designed W-shredder is likely tosucceed in controlling species with very different ecologies.

(d) Female-sterilizing Z-linked gene driveFor runs inwhich theZ* allele caused females to become sterilerather than biasing the offspring sex ratio (i.e. cf = 1), extinctionnever occurred (in 1 559 817 simulation runs). This was trueeven when all other parameters besides cf took values thatmake extinction more likely, e.g. when the Z* allele was

transmitted to 100% of the offspring of male heterozygotes,and when Z* did not harm male fitness. The reason for thisresult is that the fitness gains from gene drive in males werenot compensated by a complete loss of fitness in females, atleast for the ecological conditions considered here. I hypoth-esize that a female-sterilizing Z* allele might be capable ofcausing extinction if Z* males were continuously releasedinto the population, but this possibility is outside the scopeof the model implemented here.

4. DiscussionThemodel shows thatW-shredders are, in principle, very effec-tive at eliminating populations, particularly if they fullyprevent females from producing daughters (pshred≈ 1) and ifresistance to W-shredding cannot evolve. The results haveimplications for the design of Z-linked W-shredders andfemale-sterilizing suppression drives, and help to identify eco-logical parameters that are (and are not) important to theoutcome of a gene drive release.

A major design consideration is whether to engineerW-shredders that are also capable of gene drive in males,e.g. by including guide RNAs that target the Z as well as theW chromosome, to allow gene conversion in male heterozy-gotes. Foregoing male drive could simplify the design ofW-shredders since they would only need to target the Wchromosome (and not also the Z), particularly becausemale-acting gene conversion drives seem more challengingto develop than female-acting ones in some taxa (due to sexdifferences in DNA repair; [31]). In the model, W-shreddersvery often caused extinction even without male gene drive(i.e. when pconv≈ 0), provided that individuals carrying theW-shredder had comparable fitness to wild types, and thatcarrier females produce very few daughters (as in figure 1b).Conversely, if W-shredder females had low fecundity(around half that of a wild type, or below; figure 1c) or pro-duced some daughters, male gene drive tended to beessential for extinction to occur, or at least for extinction tooccur rapidly enough to be useful. Although male genedrivewas not always needed for extinction to occur, it did sub-stantially reduce the number of generations until extinction.Therefore, I conclude that it would almost certainly beworth the effort to incorporate a male-acting componentwhen developing a W-shredder, especially in species withlonger generation times.

Another aim when designing W-shredders should be toensure that female carriers produce as few daughters as poss-ible (ideally none; represented in the model as pshred = 1),while producing a large number of drive-carrying sons (ideallyas many as the total offspring produced by non-carriers; cf = 0).This implies that one should aim to design a construct thatcleaves theW chromosome early in gametogenesis or offspringdevelopment, to increase the chance that the number of surviv-ing progeny produced by each female is unaffected. Expressionof Cas9 and cleavage of the W should also be restricted to thetissues where it is needed (e.g. the germline), to minimize fit-ness losses due to the loss of the W in somatic cells, ordetrimental effects of Cas9. For some species, this may be assimple as placing theW-shredder under the control of a promo-ter such as nanos [32,33], assuming that females are able toreplace lost W-bearing oocytes before they are provisionedwith limiting resources. Even if the lost daughters are notreplaced with additional sons, the Z* allele might still exhibit

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super-Mendelian inheritance across generations, becauseZ*-bearing males will experience reduced competition due tothe deaths of their sisters (somewhat like the selfish geneticelement Medea; [34]). In Lepidoptera, juvenile density is oftenstrongly negatively correlated with survival, and there are var-ious maternally transmitted endosymbionts that drive throughpopulations by killing males to lessen competition on theirinfected sisters (e.g. [35,36]); these observations suggest thatW-shredder alleles might drive through Lepidopteran popu-lations even if Z*W females produced half as many viableeggs, though male gene drive would certainly help the inva-sion. The model also highlighted that strong fitness costs tomales (cm) hinder the spread of the drive allele, though itseems unlikely that a W-shredder allele would have majorcosts in males.

TheW-shredding mechanism should also be designed in away that makes it difficult for W-linked or trans-acting resist-ance to shredding to evolve. One way to do this would be touse a single-guide RNA that targets W-specific sequencesthat are present in multiple copies, or to use multiple guideRNAs that target multiple W-linked sequences [32,37]; theformer is similar to the X-shredder developed for Anophelesmosquitos, which cleaves repetitive, X-linked ribosomalgenes [13]. By designing gene drives with multiple targets,the reference sequencemust evolvemultiple changes to acquireresistance to cleavage, which is relatively unlikely. To ensurethat the targets of cleavage do not become resistant as aresult of indels induced by NHEJ, one can ensure that theguide RNA’s target lies within an essential gene where anindel would be selectively disadvantageous, preventing resist-ant alleles from accumulating in the population [32,37]. Thismay not be necessary if the W-shredder targets manyW-linked loci, but it is an important design consideration forthe male gene drive component of the W-shredder, becausethe evolution of Z-linked resistance completely nullified theusefulness of male gene drive in the simulation (echoing[18]). Recent work demonstrated the feasibility of arrays con-taining many guide RNAs separated by spacers [38],suggesting itmay soon be easier to create gene driveswithmul-tiple guide RNAs. A final way of developing resistance is to‘disarm’ the endonuclease responsible for W-shredding andgene conversion, for example, by producing a protein that inhi-bits Cas9, or through evolution of gene regulatory processesthat cause the Cas9 to no longer be expressed at the righttime. There appears to be little data on whether this type ofresistance is possible or likely, though models such as the pre-sent one indicate that they could certainly impede populationsuppression efforts.

The model also indicated that extinction does notrequire the release of large numbers of individuals: releasingjust 20 Z* males was often enough to eliminate a spatiallystructured metapopulation of 10 000 individuals in a fewgenerations. On the one hand, this is advantageous becauseW-shredders would be cheap and easy to deploy once theyare developed, and they are likely to extirpate whole meta-populations even if gene flow between sites is quite weak.However, such high invasiveness is not always desirable,because it makes the gene drive very difficult to restrict to aparticular area. This could limit the usefulness of W-shreddersto control species like Lepidoptera and birds, where one maywish to eradicate only invasive or agriculturally damagingpopulations, while leaving other populations untouched.Modifications to gene drive design—such as the self-limiting

‘daisy drive’ system—might someday address this importantconcern [21,22].

The model found several ecological variables that affectthe likelihood of extinction, but reassuringly the effects onextinction probability were somewhat minor, and I found noecological parameter values that made extinction impossible.Populations in which females can produce many offspring(high r) were harder to drive extinct, though the effect of rreached an asymptote around r = 250, such that even extremelyfecund organisms could be controlled usingW-shredders: thisis because fecundity does not matter if the population is all-male. Patchy populations were harder to drive extinct,though this could probably be mitigated by releasing genedrive individuals in larger numbers, over a greater range,over multiple releases. Dispersal was a double-edged sword:weak gene flow meant that the gene drive spread moreslowly through the metapopulation, while high dispersalrates allow for re-colonization of patches in which the genedrive had caused extinction. Demographic parameters suchas the scale of competition (ψ) and the shape of density-dependence (α) mattered little. Perhaps surprisingly, the rela-tive importance of male density to population growth (δ) hadonly a weak effect: extinction was a little more likely whenthe presence of males suppresses female fecundity just asmuch (or more so) as the presence of other females. However,extinction still occurred when female fecundity depended onlyweakly on male density (again, probably because femalefecundity becomes unimportant as females begin to disappearfrom the population).

Finally, I note that W-shredders might in general be easierto develop than X-shredders. Efforts to develop an X-shredderin Anopheles mosquitos were initially hindered, because the I-PpoI protein used to cleave the X was paternally transmittedto the embryo inside sperm, causing all of the drive male’s off-spring to die (not just the daughters) due to cleavage of thematernally inherited X in the male’s sons. Although this tech-nical issue was later addressed [13], such intergenerationaleffects would not hinder a W-shredder since the W chromo-some is unique to females (provided that the W-shreddingprotein was not expressed in males, or at least was absentfrom their sperm). Additionally, W-shredders might some-times be easier to develop than gene drives that work bydeleting genes that are essential to female (but notmale) fitness(e.g. [15]). This is because one could design a prototypeW-shredder based only on sequence data from the sex chromo-somes, while identifying genes with female-specific fitnesseffects requires more detailed data (e.g. expression profilingor knockout studies) that are unavailable for most taxa.

Data accessibility. A website presenting all R scripts used to the run thesimulation and analyse the data can be found at https://lukeholman.github.io/W_shredder/.

Competing interests. I declare I have no conflict of interests.Funding. This project was stimulated by an ESEB Progress Meetings inEvolutionary Biology meeting, funded by grants from ESEB (Euro-pean Society for Evolutionary Biology) and from the SwissNational Science Foundation.

Acknowledgements. I thank the organizers (Anna Lindholm and TomPrice), funding bodies (European Society for Evolutionary Biology;Swiss National Science Foundation), and attendees of the 2018ESEB Progress Meetings in Evolutionary Biology, which provided theimpetus for this paper. I also thank Kevin Esvelt and colleagues fordescribing their ongoing research on a personal webpage; theirideas were instrumental to this paper.

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