Philippa Kaur

The “consumer first” pattern of spatial self-organization is the minority pattern
We first determined which of the two patterns of spatial self-organization (i.e., the “producer first” or “consumer first” pattern (Fig. 1B, C)) is the minority pattern. We reasoned that the minority pattern is the one likely to be caused by genetic or nongenetic variants. When we performed range expansion experiments using equivalent initial cell densities of the producer and consumer (i.e., initial producer and consumer proportions of 0.5), the “consumer first” pattern was clearly the minority pattern (Fig. 1B). Among nine independent replicates, we observed mean numbers of 64 “producer first” patterns (SD = 9, n = 9) and 20 “consumer first” patterns per range expansion (SD = 4, n = 9), and the mean number of “producer first” patterns was significantly greater than the mean number of “consumer first“ patters (two-sample two-sided t test; P = 1 × 10−6, n = 9). Overall, “consumer first” patterns accounted for 24% (SD = 4%, n = 9) of the total number of patterns per range expansion. We therefore conclude that the “consumer first” pattern is indeed the minority pattern, and thus the pattern likely to be caused by genetic or phenotypic variants.
The number of “consumer first” patterns depends on initial cell densities
If the “consumer first” pattern were caused by genetic variants, then the number of “consumer first” patterns that emerge per range expansion should depend on the initial cell densities of the producer or consumer. For example, if a genetic variant of the consumer causes the emergence of the “consumer first” pattern, then increasing the initial cell density of the consumer should increase the number of the causative variants of the consumer, and thus promote the emergence of more “consumer first” patterns.
To test this, we varied the initial producer proportion while holding the total initial cell density of the producer and consumer constant, thus allowing us to avoid potential confounding effects that may result from modifying the total initial cell density. We then quantified the mean number of “consumer first” patterns that emerged per range expansion as a function of the initial producer proportion. When we tested an initial producer proportion of 0.5 (i.e., an initial consumer proportion of 0.5), we observed the characteristic emergence of the two different patterns, where the “consumer first” pattern was the minority pattern (Fig. 2B). When we tested an initial producer proportion of 0.98 (i.e., an initial consumer proportion of 0.02), the “consumer first” pattern completely disappeared while the “producer first” pattern occupied the entire expansion area (Fig. 2A). In contrast, when we tested an initial producer proportion of 0.001 (i.e., an initial consumer proportion of 0.999), the “producer first” pattern completely disappeared while the “consumer first” pattern occupied the entire expansion area (Fig. 2C). We then repeated the experiment across a range of initial producer proportions and observed a decreasing monotonic relationship between the mean number of “consumer first” patterns that emerged per range expansion and the initial producer proportion (Fig. 3). We could model the decreasing relationship with a Poisson regression using the natural logarithm as the link function (intercept = 3.76, slope = −4.15, P for both parameters = 2 × 10−16, n = 9) (black line; Fig. 3). Thus, the number of “consumer first” patterns that emerge per range expansion does indeed depend on the initial cell densities of the producer and consumer.
Fig. 2: Effect of the initial producer proportion on the number of “consumer first” patterns that emerge per range expansion after 4 weeks.

The producer expressed the cyan fluorescent protein-encoding ecfp gene (blue) while the consumer expressed the green fluorescent protein-encoding egfp gene (green). Initial producer proportions include (A) 0.98, (B) 0.5, and (C) 0.001. The total initial cell densities of producer and consumer were identical across all of the tested initial producer proportions.

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Fig. 3: Effect of the initial producer proportion on the number of “consumer first” patterns that emerge per range expansion after 4 weeks.

Each data point is the number of “consumer first” patterns that emerged for an independent range expansion. The black line is the fit of a Poisson regression model to the data. The gray area is the 95% confidence interval of Poisson distributions with λ = predicted value of the Poisson regression fit. The green line is the expected relationship between the number of “consumer first” patterns and the initial producer proportion if the “consumer first” pattern were caused by genetic variants of the consumer. The blue line is the expected relationship between the number of “consumer first” patterns and the initial producer proportion if the “consumer first” pattern were caused by genetic variants of the producer. The total initial cell densities of producer and consumer were identical across all of the tested initial proportions.

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Genetic variants as a cause of the observed pattern diversification
While we found that the number of “consumer first” patterns that emerge per range expansion depends on the initial cell densities of the producer and consumer (Fig. 3), the log-linear form of the decreasing relationship is inconsistent with the “consumer first” pattern being caused by genetic variants. Consider initial producer proportions of 0.02. 0.05, or 0.1 (i.e., initial consumer proportions of 0.98, 0.95, or 0.9). At these initial producer proportions, the initial cell density of the consumer is approximately twofold greater (1.96-, 1.90-, and 1.8-fold, respectively) than that for an initial producer proportion of 0.5 (i.e., an initial consumer proportion of 0.5). If genetic variants of the consumer cause the emergence of the “consumer first” pattern, we would therefore expect approximately twofold more “consumer first” patterns to emerge per range expansion. More generally, we would expect the number of “consumer first” patterns that emerge per range expansion to decrease linearly as the initial producer proportion increases (i.e., as the initial consumer proportion decreases) (Fig. 3, green line) (see the Supplementary Text for the formulation of this expectation). We did not observe either of these expectations. First, at initial producer proportions of 0.02, 0.05, or 0.1 (i.e., initial consumer proportions of 0.98, 0.95, or 0.9), the number of “consumer first” patterns was not approximately twofold greater than at an initial producer proportion of 0.5 (i.e., an initial consumer proportion of 0.5). Instead, it was three to fivefold greater (Fig. 3) (one-sample two-sided t test; P = 6 × 10−5, n = 3). Second, we experimentally observed a decreasing log-linear relationship (black line; Fig. 3) rather than the expected decreasing linear relationship (green line; Fig. 3) between the number of “consumer first” patterns that emerged per range expansion and the initial producer proportion. Thus, we conclude that genetic variants of the consumer are unlikely to cause the emergence of the two patterns of spatial self-organization.
Our analysis above assumes that the “consumer first” pattern is caused by genetic variants of the consumer. However, it is plausible that the “consumer first” pattern is instead caused by genetic variants of the producer. The form of the relationship between the number of “consumer first” patterns that emerged per range expansion and the initial cell densities of the producer and consumer, however, is again inconsistent with this hypothesis (Fig. 3). If genetic variants of the producer cause the emergence of the “consumer first” pattern, then we would expect the number of “consumer first” patterns that emerge per range expansion to increase as the initial producer proportion increases (blue line; Fig. 3). Stated alternatively, increasing the initial producer proportion will increase the abundance of the causative variants of the producer, and thus increase the number of “consumer first” patterns that emerge. However, we observed the opposite outcome, where the number of “consumer first” patterns that emerged per range expansion decreased as the initial producer proportion increased (black line; Fig. 3). Thus, we conclude that genetic variants of the producer are also unlikely to cause the emergence of the two different patterns of spatial self-organization.
While the above analyses provide circumstantial evidence that genetic variants do not cause the simultaneous emergence of the two different patterns of spatial self-organization, we sought to provide more conclusive evidence of this by testing whether the “consumer first” pattern is heritable. To achieve this, we obtained a collection of isolates purified from prior “consumer first” patterns. We then mixed the isolates together (one producer with one consumer; initial producer and consumer proportions of 0.5) and repeated the range expansion experiment. Finally, we counted the numbers of “consumer first” patterns that emerged during the second range expansion and compared the numbers to those for pairs of the ancestral strains (producer and consumer). If the emergence of the “consumer first” pattern were heritable, we would expect more “consumer first” patterns when using pairs of isolates purified from prior “consumer first” patterns.
We found that pairs of isolates (producer and consumer) purified from prior “consumer first” patterns do not behave differently when compared to pairs of the ancestral strains (producer and consumer). Among ten independent range expansions for a pair of isolates (producer and consumer) purified from a prior “consumer first” pattern, we found that the “consumer first” pattern completely covered the expansion area for one of the ten replicates (Supplementary Fig. S3a). However, among ten independent range expansions for the pair of ancestral strains (producer and consumer), we found that the “consumer first” pattern also completely covered the expansion area for one of the ten replicates (Supplementary Fig. S3b). Overall, among the remaining nine independent range expansions, we did not detect more “consumer first” patterns per range expansion for the pair of isolates (producer and consumer) purified from a prior “consumer first” pattern than for the pair of ancestral strains (producer and consumer) (two-sample two-sided t test; P = 0.27, n = 9). Moreover, we sequenced the genomes of four producer isolates and four consumer isolates purified from prior “consumer first” patterns and found only one putative genetic difference in a single consumer isolate when compared to their respective ancestors (Supplementary Text and Supplementary Table S3). Thus, the “consumer first” pattern is not heritable, and its emergence is therefore not caused by genetic variants.
Neighborhood effects as a cause for the observed pattern diversification
If the simultaneous emergence of the two different patterns of spatial self-organization is not caused by genetic variants, what then could be the cause? We argue that one plausible cause is neighborhood effects that emerge due to local differences in the initial spatial positionings of otherwise identical individuals. Consider random initial distributions of producer and consumer cells across a surface (initial producer and consumer proportions of 0.5; Fig. 4B). At some spatial locations, producer cells may initially lie sufficiently close to the expansion frontier such that the consumer cells do not physically impede their expansion (white arrow; Fig. 4B). The producer cells would then expand first while the consumer cells would expand afterwards, giving rise to the “producer first” pattern (white arrow; Fig. 4B). However, at other spatial locations, producer cells may initially lie behind a cluster of consumer cells such that the consumer cells physically impede the expansion of the producer cells (green arrow; Fig. 4B). Indeed, we observed this experimentally at an intermediate timepoint of expansion (Supplementary Fig. S4). These clusters of consumer cells can occur purely as a consequence of the random initial spatial positionings of those cells, a process known as Poisson clumping [55]. The producer cells would then shove the consumer cells forward as they expand, giving rise to the “consumer first” pattern (green arrow; Fig. 4B). This hypothesis assumes that cell shoving is the dominant form of cell movement in the densely packed expanding microbial colonies produced by our synthetic microbial community, which is an assumption supported by numerous experimental and theoretical investigations [17, 53, 56,57,58,59,60].
Fig. 4: Conceptual model for how local differences in the initial spatial positionings of individual cells could promote diversification in patterns of spatial self-organization.

The producer is blue while the consumer is green. The initial producer proportion is (A) approximating to 1, (B) 0.5, or (C) approximating to 0. White arrows indicate “producer first” patterns and green arrows indicate “consumer first” patterns. The horizontal panels from left to right depict pattern formation over time.

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Importantly, this hypothesis is qualitatively consistent with our experimentally observed relationship between the number of “consumer first” patterns that emerge per range expansion and the initial proportions of the producer and consumer (Fig. 3). If producer cells initially far outnumber consumer cells, then the “consumer first” pattern should become less numerous (Fig. 4A). This is because there are fewer consumer cells present to create the necessary cell clusters that physically impede the expansion of the producer cells, and the producer cells can therefore expand immediately giving rise to the “producer first” pattern (Fig. 4A). In contrast, if the consumer cells initially far outnumber producer cells, then the “consumer first” pattern should become more numerous (Fig. 4C). This is because there are more consumer cells present to create the necessary cell clusters that physically impede the expansion of the producer cells, and the producer cells must therefore shove the consumer cells forward giving rise to the “consumer first” pattern (Fig. 4C).
This hypothesis is also consistent with quantitative features of our experimentally observed relationship between the number of “consumer first” patterns that emerge per range expansion and the initial proportions of the producer and consumer (Fig. 3). The initial spatial distributions of producer and consumer cells can be thought of as realizations of a Poisson point process. Such a process by chance produces clusters of consumer cells whose occurrence is described by a Poisson distribution with mean and variance λ. The mean number of consumer clusters and variance depend on the initial proportion of the consumer in a log-linear manner. As the initial proportion of the consumer increases, the probability for a consumer cluster to occur also increases. This, in turn, increases the probability that a “consumer first” pattern will form and increases the variance in the expected number of “consumer first” patterns. We found that this Poisson process accurately captures key features of our experimental data. First, the relationship between the number of “consumer first” patterns and the initial consumer proportion is modeled very well by a Poisson regression (Fig. 3). Second, the variance in the number of “consumer first” patterns increases as the experimentally observed number of “consumer first” patterns increases (Fig. 3). Third, the 95% confidence intervals of the Poisson distributions with λ equal to the predicted value of the Poisson regression matches the spread of the experimentally observed number of “consumer first” patterns (Fig. 3). In summary, the log-linear shape and the increasing variance of the data are thus consistent with our hypothesis that Poisson clumping due to the random initial spatial positionings of individuals causes the ‘consumer first’ pattern and promotes the observed diversification in patterns of spatial self-organization.
To provide further evidence that neighborhood effects due to local differences in the initial spatial positionings of individuals can promote diversification in patterns of spatial self-organization, we performed mathematical simulations with an individual-based model that accounts for cell shoving during range expansion. The original model and its adaptions to range expansion are described in detail elsewhere [17, 53]. We further adapted the model to simulate the emergence of spatial self-organization during expansion of our own synthetic microbial community [20]. In this study, we applied the model for two purposes. First, we asked whether the model could simulate the simultaneous emergence of the two different patterns of spatial self-organization in the absence of spatial heterogeneity in the initial abiotic environment. Second, we varied the initial producer proportion and evaluated the consequences on the number of “consumer first” patterns that emerge during range expansion. Note that our implementation of the model does not incorporate genetic or stochastic phenotypic heterogeneity or demographic effects. However, our implementation does account for heterogeneity in the initial spatial positionings of individuals, as we randomly distributed individuals of the producer and consumer across the inoculation area prior to the onset of community expansion.
Our simulations revealed three important outcomes. First, when we tested an initial producer proportion of 0.98 (i.e., an initial consumer proportion of 0.02), we found rare localized spatial areas where consumer cells were pushed forward by producer cells (Fig. 5A and Supplementary Movie S1). These cells maintained a spatial position at the expansion frontier for a prolonged period of time and formed a characteristic “consumer first” pattern (Fig. 5A and Supplementary Movie S1). Second, at this initial producer proportion, both “producer first” and “consumer first” patterns emerged simultaneously, from the very origin of expansion, and at the same length scale, even though the initial abiotic environment was spatially homogeneous and all individuals were subject the same deterministic rules (Fig. 5A and Supplementary Movie S1). Finally, when we decreased the initial producer proportion to 0.02 (i.e., an initial consumer proportion of 0.98), the number of consumer cells that maintained a position at the expansion frontier increased, thus indicating the formation of more “consumer first” patterns (Fig. 5B and Supplementary Movie S2). All three of these observations are consistent with our experimental observations and, importantly, did not require the consideration of heterogeneity in the initial abiotic environment, genetic or stochastic phenotypic heterogeneity within populations, or demographic effects. Thus, neighborhood effects due to local differences in the initial spatial positionings of individuals are sufficient alone to promote pattern diversification and result in the emergence of two different patterns of spatial self-organization.
Fig. 5: Individual-based modeling simulations of the effect of the initial producer proportion on the number of “consumer first” patterns that emerge per range expansion.

The producer is blue while the consumer is green. Initial producer proportions are (A) 0.98 (see Supplementary Movie S1) and (B) 0.02 (see Supplementary Movie S2). The initial abiotic environment was spatially homogeneous and genetic heterogeneity, stochastic phenotypic heterogeneity, and demographic effects were not incorporated into the model. Producer and consumer cells were distributed randomly around the center prior to the onset of expansion and the total initial cell densities of producer and consumer were identical across all of the simulations. The white arrows indicate “producer first” patterns and the green arrow indicates a “consumer first” pattern.

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The different patterns of spatial self-organization have different community properties
We finally asked whether the different patterns of spatial self-organization have different community-level properties. More specifically, we tested whether the different patterns have different expansion speeds. Two features of our previous experimental observations already point towards this being the case. First, the “consumer first” patterns (green arrows; Fig. 1C) extend further in the radial direction of expansion than do the “producer first” patterns (white arrows; Fig. 1C). This is readily observed at the expansion frontier, where the “consumer first” patterns tend to protrude outwards in the radial direction (Fig. 1C). Second, the “consumer first” patterns increase in width in the direction of expansion (green arrows; Fig. 1C). Both of these features are consistent with faster expansion speeds [61, 62].
To further test this, we varied the initial producer proportion, and thus varied the ratio of “consumer first” to “producer first” patterns (Fig. 3), and quantified the expansion radii over time. We found that the initial expansion speeds were significantly faster for an initial producer proportion of 0.001 (i.e., an initial consumer proportion of 0.999) than for 0.98 (i.e., an initial consumer proportion of 0.02) (F-test; P = 1 × 10−5) (Fig. 6A). Thus, smaller initial producer proportions that promote the emergence of more ‘consumer first’ patterns result in faster expansion speeds. Moreover, when we varied the initial producer proportion between 0.02 and 0.98 (i.e., initial consumer proportions between 0.98 and 0.02), we found a decreasing relationship between the final expansion radius and the initial producer proportion (linear model: final expansion radius ~ initial producer proportion; slope = −263, R2 = 0.42, P = 2 × 10−4, n = 9) (Fig. 6B). Thus, smaller initial producer proportions that promote the emergence of more “consumer first” patterns result in a greater extent of community expansion over the time-course of the experiment. Together, our data demonstrate that the different patterns of spatial self-organization do indeed have different expansion speeds.
Fig. 6: Effect of the initial producer proportion on expansion properties.

A Effect on the initial expansion speed. B Effect on the final expansion radius. Each data point is the expansion radius for an independent range expansion. The lines are linear models and the gray areas are the 95% confidence intervals. The total initial cell densities of producer and consumer were identical across all of the tested initial producer proportions. The final expansion radii were measured after 4 weeks of incubation.

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This research presents HD-ClvR, which is a combination of three gene drives: homing, cleave-and-rescue and daisyfield. Our modelling indicates that HD-ClvR overcomes an important trade-off in current homing gene drive designs: the trade-off between resistance allele formation and gene drive efficiency. This strategy benefits from the efficiency of a homing gene drive and the evolutionary stability of cleave-and-rescue gene drive. Due to the inclusion of a daisyfield system, HD-ClvR is self-limiting and can be controlled by supplementation of gene drive animals.
HD-ClvR compared to other gene drives
Over recent years, many different gene drives have been published and developments have been geared towards both efficiency and safety38. An ongoing issue has been the development of resistance alleles. For CRISPR-based homing gene drive there are two fundamental approaches to combat resistance allele formation: careful gRNA targeting and gRNA multiplexing. When a gRNA targets a conserved sequence in a gene, resistance alleles are likely to disrupt gene function through NHEJ repair and will therefore reduce fitness39. Recently, population suppression was already shown to work with a carefully targeted homing gene drive in contained mosquito populations39, however, current data suggests that homing might be less efficient in mammals than in insects14. A recent paper has proposed the concept of ‘tethered homing gene drive’, which combines a threshold-dependent underdominance gene drive with a homing gene drive for improved suppression capabilities40. We use this concept in a different manner in HD-ClvR, by relying on a daisyfield rather than threshold-dependence for self-limitation. Very recently, two new papers have proposed a gene drive similar to HD-ClvR, but intented for population modification instead of suppression41,42. These studies also combine homing and cleave-and-rescue principles to combat resistance alleles and their modifications are able to persist stably in cage experiments, which is promising for HD-ClvR.
In addition to targeting conserved sequences, when gRNA multiplexing, resistant allele allele formation is reduced because multiple sites are targeted simultaneously. For homing gene drives, multiplexing has been shown to reduce homing efficiency when more than two gRNAs are used28. In contrast, cleave-and-rescue gene drives do not have this problem, as they do not use homing and can therefore multiplex gRNAs without any efficiency costs. HD-ClvR separates the elimination of resistance alleles and homing efficiency, and therefore gRNAs can be optimised for both goals separately.
To date, most gene drive research has focused on improving the efficiency, however, equally important is the development of strategies that allow for containment, or even reversibility, of the gene drives29,43. For contained gene drives, density dependence is often used, which requires large numbers of gene drive individuals to be released into a target population to spread44. Therefore, non-target populations are unlikely to be affected by this type of gene drive. However, a large single release of gene drive individuals can put significant pressure on the local ecosystem, and if a population is already at carrying capacity, it may lead to starvation or mass migration of the population. In contrast, HD-ClvR uses ongoing input in the form of gene drive animals to control the extent of population suppression and contain spread, while the total amount of gene drive animals necessary for release is similar to threshold-dependent gene drives. Therefore, the use of HD-ClvR seems more feasible than threshold-dependent gene drives. Although self-limitation comes with increased cost and labour relative to unlimited gene drives, we believe this is justified by the control and safety of HD-ClvR.
As stated above, the initial introduction frequency for a standard cleave-and-rescue gene drive in our randomly mating model was increased 10-fold over the other homing-based strategies. This increase is necessary due to the significant cost to the reproduction rate that is incurred when using a standard cleave-and-rescue gene drive. On average, cleave-and-rescue animals will produce 50% less offspring than wild-type animals21,24. This significantly slows the spread of the gene drive and due to density dependent dynamics, requires large initial releases of cleave-and-rescue animals for population suppression. With a homing-cleave-and-rescue drive, more offspring inherit the drive and there is less cost to the reproduction rate. Effectively, for homing-cleave-and-rescue, the reproduction rate of gene drive individuals is equal to the homing efficiency (plus half of the homing failure rate, where the gene drive is inherited by chance), which so far has been shown to range from 0.7 to 1 in different organisms14,39,45.
Supplementation
As animal supplementation is a critical component of HD-ClvR, our modelling investigated how daisyfield size and the level and placement of supplemented HD-ClvR animals effects efficiency and safety of population suppression. Optimisation of these parameters can significantly reduce cost and labour, as well as reduce the risk of unwanted impacts on non-target populations. We modelled our supplementation as a percentage of the total population size, therefore the number of individuals needed for supplementation increases linearly with population size. We also want to minimise the risk of non-target populations being impacted by the gene drive, and therefore, there is a trade-off between safety (size of the daisyfield) and cost and labour (level of supplementation required).
The least number of daisy elements that can suppress the population with a realistic level of supplementation, but does not cause any serious issues in non-target populations, should be objectively established through an in-depth risk assessment process. In a larger population however, the spread is slower than in a small one. Therefore, for improved safety and efficiency, gene drives are best applied in small sub-populations separately. The impact of a single introduction, such as a rogue deployment or migration, depends on the population size. The smaller the population, the bigger the impact. This it is a concern when the target population is much larger than the non-target population, but this is not the case for invasive UK grey squirrels and many other invasive species.
The appropriate daisyfield size also depends on the rate of NHEJ ((P_n)) of the gene drive system; the higher the ((P_n)), the more embryonic lethal offspring will arise and the sooner daisyfield burns out. To choose a safe number of daisy elements, we also need an estimate of how many animals a rogue party could obtain, potential breed and add into a non-target population for their own benefit. Overall, each target population and prospective gene drive strategy needs to be considered on a case-by-case basis and include an in-depth multidisciplinary risk assessment process.
When we consider the spatial aspects of a HD-ClvR supplementation programme, the picture becomes more complex. A key factor is the supplementation location of individuals. Obviously, supplementing individuals in a location where the population has already been suppressed will be ineffective. Therefore, different placement strategies can be adopted to keep placing individuals in a relevant area. A monitoring system where not only the size of the population is known, but also the location can significantly help HD-ClvR continue spreading and suppress a targeted population.
In this study, we modelled HD-ClvR using five different supplementation placement strategies in grey squirrel. These were: supplementation at the mean of population location, the mode of population location, randomly, randomly in 10 groups, and in a moving front (Fig. 6a). With supplementation at the mean of the population location, supplementation started in the middle of the population. After a few generations, a gap appears in the middle due to local suppression. The mean of the populations location still lies in the middle, as can be seen in Fig. 6c at 20 generations. Therefore, supplementation is not effective until the population is also suppressed in another location, thereby shifting the mean. Additionally, when there is a single large patch of the population left and additional smaller clusters, supplementation in the middle of the large patch allows the smaller clusters to recover, as can be seen in Fig. 6c after 64 generations.
With supplementation at the mode of the population location, we supplement in a location where there are many individuals. This placement strategy avoids the problem of supplementing in a location without individuals, either in a doughnut-like spatial population structure or in a multi-patch population. However, this placement strategy still allows small patches to form and recover. Supplementation at a random location theoretically means that supplementation happens uniformly, but in reality, this is not the case. Initially HD-ClvR spreads in multiple locations, but after the population is suppressed in certain regions, supplementation in those regions becomes ineffective. Therefore, at a later stage of population suppression this placement scheme becomes increasingly ineffective.
Supplementation at random locations is more effective when they are broken up into multiple groups (ten in our model). The gene drive spreads in many locations initially like the random single location placement scheme. After significant suppression of the population some but not all of the 10 groups supplemented are at ineffective locations. The groups that are placed at relevant locations are enough to keep the gene drive spreading. In our model supplementation in groups at random locations gets close to the speed at which a gene drive spreads in a non-spatial model.
The moving front placement scheme is very effective initially, as the gene drive spreads uniformly across the front. In this case, supplementation keeps ahead of where the populations is being suppressed. This placement strategy allows the population to recover behind the moving front after effective initial spread and near-complete suppression. To improve efficiency of the moving front strategy, it may be beneficial to include random supplementation behind the moving front to prevent animals from re-establishing.
Finally, in our spatial model, it was evident that there is more uncertainty in levels of population suppression than a randomly mating model leads us to believe. As can be seen in Fig. 6b, the 95% quantiles are broader than the quantiles in Fig. 3. Therefore, we conclude that to tailor the amount of supplementation, it is vital to closely monitor a population where a gene drive is used.
Assumptions and future work
Our model works under the following six assumptions. First, our model excludes some complexities of the optimal number of gRNAs for homing. Although our model suggests that multiplexing gRNAs for both the homing and cleave-and-rescue gene drives is most effective, a recent study using a more complex model and in vivo data shows that the optimal number of gRNAs to use for homing in Drosphilia melanogaster is two. They report a decrease in homing efficiency with more than two gRNAs due to reduced homology and Cas nuclease saturation28. Therefore, our gene drive with four gRNAs for both homing and cleave-and-rescue will likely be less efficient in such a complex model. We suggest using two homing gRNAs and four cleave- and-rescue gRNAs is likely most efficient, while still eliminating all resistance alleles28. It would be prudent to analyse our gene drive in this complex model as well to get a definitive estimate, as Cas saturation is thought to have an influence on gene drive efficiency when multiplexing is used28.
Second, we assumed there was no embryonic Cas-gRNA expression. Embryonic Cas-gRNA expression might be problematic as it leads to resistance allele formation and can interfere with the cleave-and-rescue mechanism by cleaving alleles from the wildtype parent. As our gene drive eliminates resistance alleles, embryonic Cas-gRNA expression may not inhibit spread, depending on the rate. Additionally, if the embryonic Cas-gRNA expression turns out to be more common in grey squirrel or other species, the cleave-and-rescue part of the gene drive can be harnessed with a double rescue mechanism to overcome this issue, as reported by Champer et al.24.
Third, we did not take other types of resistance alleles into account such as mutations rendering the CRISPR-Cas non-functional. As this is a universal assumption in gene drive research, we will have to await multigenerational studies to see if this is problematic.
Fourth, HD-ClvR has not been tested in vivo, which is our next step. The two recent papers testing a gene drive similar to HD-ClvR for population modification have performed in vivo tests in Drosophila melanogaster which showed very efficient conversion rates41. Proof-of-concept testing of HD-ClvR would likely initially occur in D. melanogaster and mouse models before progressing to squirrel studies. Recent reports have shown that the VASA promoter for Cas expression in homing gene drives is not optimal and further investigation to identify a meiosis-specific germline promoter is needed15. Furthermore, the integration of many daisies in a squirrel genome will be a molecular challenge and is a feat which has not yet been reported on in any species. This task could be achieved using either a random integration strategy, such as lentiviruses46 or a targeted integration strategy that exploits neutral repetitive sequences in the genome as target sites32. Also, non-model species might be difficult to genetically engineer, although grey squirrel embryology will likely follow the extensive knowledge on rodent and farmed animal embryology, and similar reagents and equipment could be used. An important consideration when engineering gene drive is that the modified animals maintain enough wild vigour to survive and breed in a wild population. Promising technologies for generating gene drive harbouring mammals with as little intervention as possible include in situ delivery of CRISPR reagents to the oviduct47.
Fifth, for our spatial modelling, we assumed that an estimation of population size could be made every year, although there is a significant amount of room for error in this estimate. Additionally, for some of our placement schemes, we assumed an accurate estimate of population location. As the random placement in groups scheme turned out most effective, this is not a problem so much as further potential for improvement. Another direction for future spatial work is the modelling of real landscapes, which are more complex than what we modelled in this study48. In complex landscapes, it might be that gene drive spread is slower or even regionally confined in some situations. Additionally, there might be spatial dynamics to gene drives in general such as ’chasing’, which is the perpetual escaping and chasing of wildtype and gene drive animals34. Further efforts are necessary to create a more realistic spatial model before we can consider using a gene drive.
A final consideration is that the ecological services the grey squirrel and other invasive species provide are largely unchartered. Ecologists need to investigate the ecological services that an invasive species performs and how an abrupt suppression of this invasive population might impact the ecosystem as a whole. We need to consider other restorative measures such as reintroducing native species to fragmented habitats, amongst other ecological interventions49. From a regulatory perspective, there is no tested legislative framework for the release of gene drive organisms; and with regard to our test animal it is currently illegal to breed grey squirrels in the UK. Developing these legislative frameworks alongside gene drive research is important. More importantly, the UK needs to continue to broaden public engagement and see whether the public is receptive to the deployment of gene drive technology in parallel to a financial overview of how much it would cost to apply gene drives reflecting our predicted need for supplementation.
Summary
HD-ClvR offers an efficient, self-limiting, and controllable gene drive strategy. We show that in the spatial model, complete population suppression is achieved approximately 5 years later than in the randomly mating population model. We then explored how the placement of supplemented animals could impact population suppression. Our results show that spatial dynamics of supplementation placement are not prohibitive to the spread of the gene drive, but that in fact, with an optimised strategy, spread at a rate equal to randomly mating population can be achieved. In our models, we have shown that grey squirrels have a spatial life history which facilitates the spread of a gene drive. Therefore, gene drives could be a valuable tool in the conservation toolbox. More

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Phenology
Ceratina nigrolabiata excavate new nests mainly in May and June, however, some newly excavated nests were also recorded later in the season (Figs. 1, 2). Active brood nests (Table 1) occurred from half of June and appeared in high proportion through whole July. First full brood nests first occurred at the end of June, but the main peak of full brood nests was in July. Full brood nests were also frequent in August. Full-mature and mature brood nests occurred from the end of July, and they were very frequent through August. Other types of nests occurred mainly in the beginning and at the end of season. At the beginning of the season occurred mainly old hibernacula or adults of C. nigrolabiata visiting nests of other Ceratina. In the late phases of season occurred abandoned nests with only parasites and newly excavated burrows for hibernation.
Figure 1

Nesting cycle of C. nigrolabiata. (a) newly excavated nests—burrow which contains only adult(s) and sometimes fillings. (b) discarded nest—burrow where previous nest was discarded, and there are pollen remnants on the walls (c) active brood nest—nest in phase brood cell provisioning (d) large active brood nest, where egg is present at the top, but young adults already developed at the bottom of nest (f) guarded full brood nest—mother guards this nest (f) plugged full brood nest—nest is unguarded and closed by a thick filling plug (g) orphaned full brood nest—last brood cell partition is thin and above it is commonly pollen from incompletely provisioned brood cell (h) full-mature brood nest—this nest contains juveniles, young adults, and sometimes mother (i) mature brood nest—this nest contains young adults and sometimes mother. All these figures are hypothetical examples, they are not based on concrete dissected nests.

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Figure 2

Phenology of C. nigrolabiata through nesting season.

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Table 1 Criteria for classification of nest stages.
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Type of nest founding
We found two types of newly founded nests. Newly excavated nests, which were built by excavating pith from a twig. Discarded nests are the other type. These nests were built from previous nest of Ceratina (probably other C. nigrolabiata in most cases) by discarding a part of or all original offspring (Figs. S1 and S2). We observed nests of C. nigrolabiata, where nest partitions were destroyed and pollen from brood cells was placed on side of the nest. We suppose that original offspring were discarded out of the nest (and on several occasions, we observed discarding of offspring out of the nest). Pollen provisions of the previous nest owner were usually moved to the sides of the nest (Fig. S1). From newly founded nests, 82.69% (86/104) were newly excavated and 17.30% (18/104) were discarded nests. When we counted only nests founded after half of June, the proportion of discarded nests was 22.78% (18/79). From active brood nests, 4.66% (29/622) had apparent relics of usurpation and discarding.
Presence of parents
Newly excavated nests
In newly founded nests, only male was present in 53.48% of nests (46/86, Table 2), only female was present in 10.46% of nests (9/86) and male and female together were present in 36.04% (31/86) nests. Newly founded nests were on average 5.47 cm long (SD = 4.68, range 1–22.1, N = 86). Nests with only male were on average 3.82 cm long (SD = 3.26, range 1.2–16.7, N = 46), nests with only female were on average 5.73 cm long (SD = 4.72, range 1–14.1, N = 9), nests with both male and female were on average 7.85 cm long (SD = 5.49, range 1.9–22.1, N = 31). Nests with both parents were significantly longer than nests with only a male (Tukey HSD test on logarithmic data, difference = 0.6743, p = 0.0003), but not significantly longer than nests with only a female (Tukey HSD test on logarithmic data, difference 0.4427 p = 0.2256).
Table 2 Presence of individuals of parental generation in different nest stages.
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Discarded nests
In 72.22% (13/18) of discarded nests one male and one female were present. Female and two males were present in two nests, only a male was present in one nest, only a female was present in one nest and no adult was found in one nest.
Active brood nests
We found male–female pair in 84.72% of nests (527/622), female and two males were found in 1.29% of nests (8/622), female and three males were found in 0.16% (1/622) of nests, no adult was present in 1.76% (11/622) of nests, only male was in 5.6% (35/622) and only female in 6.43% (40/622) of nests.
Full brood nests
Most of full brood nests (73.51%, 493/672) were not guarded by any parent (Table 2). When a full brood nest was guarded, then usually by a female (15.18%, 102/672). Only male was present in 4.31% (29/672) and male and female were present in 7.14% (48/672). Males were significantly more often present in nests, where female was also present, than in nests without a female (Chi-square test, Chi = 81.06, df = 1, p  More