Drive characteristics and two-species models

We previously modelled highly efficient homing suppression drives in spatially continuous models, finding that with sufficient efficiency, successful and rapid suppression was usually possible (Champer et al., 2022; Champer, Kim, et al., 2021; Champer, Oakes, et al., 2021; Liu & Champer, 2022). In this study, we focus on a less efficient drive. Specifically, our default drive has a drive conversion efficiency of 80%, a 10% germline resistance allele formation rate, a 10% embryo resistance allele formation rate (caused by maternally deposited Cas9 and gRNA in the progeny of drive females), a 10% somatic fitness costs in females, and a 5% direct fitness cost in drive homozygotes (with multiplicative costs per allele). Such an imperfect suppression drive would be expected to reach a high equilibrium frequency in the population, potentially eliminating it if enough females are sterile at this point.

The same drive, in our discrete generation panmictic population model, would still be able to suppress the population (Figure S1). Despite having a genetic load of 0.85 (the fractional reduction in reproductive capacity compared to an equivalent wild-type population) at the drive's high equilibrium frequency, this drive would not be able to suppress an infinite population with our default low-density growth rate of 10 (for which a genetic load of 0.9 would be necessary). However, stochastic effects would still allow the drive to successfully suppress the population in all cases, though this often takes an extended period of time (Figure S1). In any given region of a spatial population, stochastic effects would be exaggerated due to smaller local population, theoretically allowing suppression to occur even more quickly. Note that in our mosquito model, population suppression never occurs under these conditions (Figure S1), despite the same low-density growth rate. These mosquito populations are more robust due to differences in the population dynamics caused by the weekly time steps and viability-based competition. Specifically, the larger number of larva initially created tends to reduce stochasticity in this model compared to the discrete generation model.

In our previous discrete-generation spatial models, however, a drive with these default performance parameters would always fail to suppress the population and instead result in long-term ‘chasing’ dynamics (Champer, Kim, et al., 2021). During chasing, the drive suppresses the population in a local area, but then the area is recolonized by a few wild-type individuals that escape the drive from adjacent areas. Due to low competition, these individuals can reproduce very quickly. The drive is still present and will reinvade the region, but complete suppression over the entire space is often never achieved. Even releases of better drives with a genetic load higher than 0.9 (sufficient to eliminate deterministic panmictic populations) often lead to this outcome, which is even more common in the mosquito model (Champer et al., 2022), though sufficiently high-drive efficiency will produce more successful outcomes (Champer et al., 2022; Champer, Kim, et al., 2021).

Nevertheless, drives with higher efficiencies (or at least lower fitness costs) may be difficult to construct. Successful gene drive-induced suppression may still be possible with our default drive, however, if a second species can also put pressure on the target species. Here, we examine three different two-species scenarios. In the first, two species coexist in the same region (Figure 1a). They have different ecological niches and thus compete with each other to a limited degree. In the second scenario, we divide the arena into two regions, and each species is specialized to one of these regions (Figure 1b). Normally, each species would be mostly confined to their own region, with migration resulting in some limited overlap at equilibrium. In the third scenario, we model separate predator and prey species (Figure 1c), where the prey suffers in the presence of predators, and the predators require the presence of prey to reproduce at a normal rate.

Competing species promote population suppression

To assess the potential influence of a competing species on suppression drive outcomes (Figure 1a), we first implemented two different species in our discrete-generation model. The two species share the same habitat but occupy different ecological niches, so there will be some resource competition between them. In this model, we simplify the competition and life cycle characteristics of the two species, adjusting fecundity based on total competition from nearby individuals. Competition is determined by the number of individuals around the target species, which is separated into intraspecies competition and interspecies competition. Our model uses a competition factor variable to represent the relative interspecies competition strength between two species (0 = no competition, 1 = interspecies competition is as strong as intraspecies competition, an inherently unstable situation). When the target species is suppressed, the competing species tends to somewhat increase in population in the areas where the target species is no longer present. This can make it more difficult for chasing to occur since the target species could still experience substantial competition in areas cleared by the drive that it recolonizes.

We first assumed that the competition factor is equal for both species (symmetrical competition), varying the population size of the competing species and the competition factor (Figure 2). Because our drive had modest efficiency, lack of competition invariably results in long-term chasing dynamics, with the drive still chasing after 1000 generations, similar to our previous results (Champer, Kim, et al., 2021). With an increasing number of competing species and higher competition factor, it's easier to suppress the target species, with the competition factor having a substantially larger effect in our parameter range. As the competition factor increases, there is a small region of suppression after a period of chasing (Figure 2), though by the time the competition factor reaches about 0.5, the dominant outcome is usually suppression without chasing. For simulations where chasing occurred before suppression, the period of chasing was usually short, but when competing species size and competition factor are low, chasing could last for several hundred generations (Figure 2). Though chasing can make drives more vulnerable to complete failure by functional resistance allele formation (Champer, Kim, et al., 2021; Liu & Champer, 2022), the existence of this phenomenon does not prevent potentially substantial benefits from being achieved, depending on the specific drive application. Specifically, reductions in female reproductive capacity could reduce the fertile female population compared to its initial state (Figure 2). During short chases, patchy suppression tends to result in a higher number of average fertile females, but for more important longer chases, conditions that increase the drive's efficiency or other factors that put pressure on the population such as high competition tend to reduce the average number of fertile females.

Another mode of suppression drive failure involves stochastic loss of the drive allele. This is because gene drive individuals may struggle to find a potential mate in a limited distance after the population is sufficiently suppressed, removing the gene drive form the population while clusters of wild-type individuals still remain (at which point they could quickly repopulate the arena). This outcome is usually rare in one-species models for suppression drives targeting female fertility genes (Champer, Kim, et al., 2021; Liu & Champer, 2022). However, drive loss is substantially more common in our model of competing species (Figure 2). Though never the dominant outcome, it represents a substantial fraction for the entire parameter range except when competition between the species is very low (when long-term chasing outcomes dominate).

Another potentially important scenario is asymmetric competition, where species affect each other differently. We found that the competition on the target species from the competing species accounts for most of the observed effect, and the effect of competition of the target species on the competing species has only a small effect on ultimate outcomes (see Supplemental Results text and Figure S2).

We previously developed a mosquito-specific model, which indicated that successful suppression would be substantially more difficult than in our discrete-generation model (Champer et al., 2022). Because most mosquito vectors have broadly similar lifecycles, we used a simplified model in which the two species have the same reproduction rules, and we assumed symmetric competition. As in the discrete-generation competition model, suppression without chasing was the most common outcome when competition factor and competing species population were high, shifting to suppression after chasing and eventually long-term chasing (Figure 3). However, compared to the discrete-generation model, long-term chasing occupied a much greater fraction of the parameter range. Furthermore, drive loss becomes a major outcome, more common than suppression after chasing in the intermediate parameter range. This is unexpected because, in previous studies with one species, drive loss was less common in the mosquito model than in the discrete-generation model (Champer et al., 2022). When the competition factor was low, chasing could last for a long time with a high average population of adult fertile females, despite the lower initial population compared to the discrete-generation model (Figure S3).

Regional specialists

For many competing species, instead of being specialized to particular ecological niches within a region, they are specialized to certain regions themselves in a variety of ways. We modelled this situation by dividing our arena into two equal halves, representing different environments (Figure 1b). Each of the two competing species is specialized to one of these environments. In their preferred environment, the species compete normally, but their competition factor is reduced for interspecies competition when in their non-preferred environment. In this scenario, the migration rate is also important because it will determine the initial degree of population overlap between the two species, together with the competition factor. As expected, higher migration results in more suppression outcomes, while low migration results in more drive loss outcomes (Figure S4), consistent with previous results (Champer et al., 2022; Champer, Kim, et al., 2021; Liu & Champer, 2022). Competition also had similar effects in this environment, with a modest level of competition allowing suppression without chasing in most cases or shorter chases, as long as migration was not very low.

In our mosquito model of two regional specialists, we found that the general pattern compared to the discrete-generation model was mostly the same (Figure 4; Figure S5), though higher levels of competition and migration were required to avoid long-term chasing results. Similar results were seen in scenarios when larvae had an advantage in their preferred region (Figure 4) and when females had a higher chance of reproduction in their preferred region (Figure S6). This latter phenomenon could be caused by different mosquito species being specialized to target humans or other animals and thus having different reproductive success in natural environments and those with high human populations.

Predator–prey model

Predator–prey relationships between species are also common, and this asymmetric scenario could be expected to affect gene drive outcomes differently depending on whether the predator or the prey is targeted. We modelled predator–prey relationships by assuming that predators provide competition to prey depending on the predation intensity, which could allow a predator to provide more ‘competition’ to a prey than a member of the same species. Predators compete with each other and are also influenced by the predator resource fraction (representing the importance of the prey in the predators' diet). Predators received a reproductive penalty when few prey individuals were nearby and a bonus if prey were plentiful.

As expected, high predation intensity values had a similar effect as a competing species (Figure S7), with even modest values being sufficient to allow for suppression without chasing (though still with some risk of drive loss). However, when the predator resource fraction was high, the population of predators tended to decrease after the suppression drive reduced the prey population. This could substantially reduce predation levels of the prey, allowing them to more effectively avoid the suppression drive in these cases. Even with high predation intensity, high predator resource fractions could effectively prevent suppression. When the gene drive targeted the predator species, the drive had a harder time suppressing the population due to the increased reproduction of predators at low densities due to higher prey densities (see Supplemental Results text; Figure S8).

Mosquitoes are often prey of many species, so to create a simple model, we implemented a generic mosquito predator that preys on the common larval stage. The predation intensity here has to be scaled upward compared to the discrete-generation for the predators to provide roughly the same relative competition compared to intraspecies competition (e.g. a predation intensity of 1.25 means that predators provide as much average competition as intraspecies competition in the discrete generation model, but the corresponding predation intensity for larvae in the mosquito model is 6.96). Overall, we find a broadly similar pattern to the panmictic model (Figure 5), though with substantially higher predation intensity required for successful suppression to be possible, and even then, drive loss outcomes are often more common. Even moderately high predator resource fractions can fix the outcome at long-term chasing when predation intensity is high. However, while predators can certainly impact mosquito populations (Onen et al., 2021; Russell et al., 2022), it remains unclear if any target mosquito species actually represents a substantial portion of the diet of any predator (Bonds et al., 2022; Collins et al., 2019; Onen et al., 2021), so lower values of this variable are likely more realistic.

Effect of seasonality on the mosquito model

In many environments, mosquitoes (particularly Anopheles malaria mosquitoes) experience major population fluctuations based on the climate (Eckhoff et al., 2017; Lambert et al., 2018; Niaz Arifin et al., 2014; North et al., 2019; Wu et al., 2021). During the wet season, populations are high. Such populations can be greatly reduced or even locally eliminated during the dry season. These fluctuations could add a degree of stochasticity, potentially aiding gene drive-based suppression. However, at the beginning of a wet season, the pressure from competing species could be removed, allowing the target species to achieve high growth rates, which may increase the frequency of chasing. Without a competing species, seasonality had only a modest effect on outcomes (see Supplemental Results text; Figures S9 and S10).

In a competing species model, we set the population of the competing species as equal to the target species while allowing the competition factor and seasonality intensity to vary. In this situation, seasonality could allow the target species to be partly released from competition during the beginning of the wet season. Unlike the single-species model, increased seasonality intensity was usually harmful to the drive over most of its parameter range. When the competition was high enough to potentially enable suppression, higher seasonality with sharp seasonal transitions reduced the rate of suppression without chasing, with these results generally converted into suppression after chasing (Figure 6). Drive loss outcomes were also similarly changed. However, these periods of chasing tended to be short (albeit with a high average number of fertile females), so the overall effect of seasonality was not substantial. These effects were also seen to an even lesser degree with the sinusoidal seasonal model with softer seasonal transitions (Figure S11).