Model description and study area

A detailed description of the Skeeter Buster model has been published [29]. The model can be downloaded directly from http://www.skeeterbuster.net and the source code is available on demand from the authors via this same website. In this section we only provide a summary of the main features of the model. Skeeter Buster is a stochastic model that simulates cohorts of immature mosquitoes in individual water-holding containers, and simulates individual adults in houses. The development of cohorts at each life stage (eggs, larvae, pupae) is described by a temperature-dependent enzyme kinetics model [32] and the intraspecific competition at larval stages is implemented by tracking the amount of nutritional resources in each container, which in turn affects larval growth, survival rates and adult size [33]. Skeeter Buster is a spatial model, where houses are laid out on a rectangular grid. Dispersal is limited to nearest neighbor houses on each day, with a daily dispersal probability of 30% for each adult as found in a previous calibration study [29]. Dispersal direction is chosen at random. Nearest neighbors are the orthogonally-adjacent houses on the grid (von Neumann neighborhood), and houses on the edges have no neighbor beyond the edge. Adult females are assumed to be strictly monogamous [34]. Unmated females mate on the first day that they are located in the same house as one or more adult males. If several males are present in the same house, a mate is chosen with a probability proportional to its size.

For the purpose of evaluating the spread of gene drive elements in a specific natural mosquito population, we chose to simulate the situation of the city of Iquitos, Peru. The distribution of houses in Iquitos is similar to the grid in the model, and the data on Ae. aegypti population dynamics in the city are extensive [30,35,36]. In a previous study, we have described the calibration of Skeeter Buster to the Iquitos case and the ability of the model to reliably simulate this mosquito population [30]. In this study we use the model calibrated in a similar fashion. We simulate a 612-house area within the city, located in the Maynas neighborhood where mosquito population levels and dengue incidence are among the highest in the city. Container distribution in the simulated area is taken directly from data collected in 153 houses (replicated randomly 4 times in the simulations) during entomological surveys carried out in the city [30]. Weather conditions are obtained from NOAA weather collections in the Iquitos station for the period 1999-2003 [37].

Simulating Medea and KR in Skeeter Buster

Many variants of the Medea approach have been explored using general mathematical models [25,27,28]. For our purposes, we use a basic autosomal system with simple, feasible, genetic parameter values that are the focus of the current study. Medea and the linked anti-dengue gene are simulated as a single allele at a locus, where M denotes the Medea/anti-dengue allele and m denotes the wild-type allele. The Medea toxin is at least temporarily present in all embryos and could be associated with an additional fitness cost. We define the fitnesses of genotypes mm, Mm, MM as respectively 1, (1-c_M) and (1-c_M)² where c_M is the value of the cost per construct. This cost is computed as an embryonic cost, i.e. an additional mortality factor applied to newly hatched eggs. Ward et al. [28] explore a wide variety of fitness costs to females, males, and embryos. In this study we consider that the lethality effect of the Medea element (the mortality of non-Medea offspring of a Medea-bearing mother) is 100%, i.e. none of the offspring survives. Although intermediate values of this factor are explored in other models [27,28] the empirical results of Chen et al. [25] indicate that 100% mortality can be achieved. In addition, we consider that the M allele can be associated with an additional, female specific fecundity cost c_F for both heterozygotes and homozygotes. This cost is expected to arise because of the Medea-specific embryonic effects, or because the associated anti-dengue gene is only expected to be expressed in females and is likely to exact a metabolic cost or have off target effects [13]. The simulations presented in the main text all assume c_F=0.1.

For the KR system, K and R are modeled as alleles on unlinked loci, with K and R denoting the killer and rescue transgenic alleles respectively, and k and r denoting their respective wild-type counterparts. We assume that the anti-dengue gene is completely linked to the R allele and thereby is modeled as a component of the R allele. Fitness costs associated with carrying K and/or R transgenes are handled similarly to the Medea case, with c_K and c_R as the respective embryonic fitness costs. No fecundity cost is modeled. Overall fitness of an individual is calculated multiplicatively across loci. Gould et al. [24] explore a number of scenarios for the phenotypic expression of the K and R alleles. Here, for simplicity, we assume that both K and R have dominant effects on killing and rescue, and that the lethality of the K allele and rescue by the R allele are complete. In other words, all individuals carrying at least one copy of the K allele are killed, provided they do not carry a copy of R. Individuals carrying at least one copy of R are insensitive to the lethality conferred by K alleles, whether one or two copies of K are present.

Release scenarios

The main goal of this study is to examine how the spread of an anti-dengue gene will be affected by the specific ecology, movement behavior, and spatial/temporal heterogeneity in density and life stages of the resident and released mosquitoes.

The Skeeter Buster model has previously been used to examine the impacts of a variety of release strategies on the efficacy of a transgenic Ae. aegypti strain with a conditional female-killing gene [31] and the practical rationale for the different release strategies is detailed in that publication. In the current study we consider two possible life stages for release: adults or eggs. The release of adults is simply simulated by uniformly adding cohorts of male (or male and female) adults to all houses on the grid. To simulate the release of eggs, we introduce special containers with cohorts of male and female eggs (in equal numbers) into 10% of the houses. Since there are no practical means of separating male and female eggs, these releases result in both sexes emerging as adults. The released containers have a large initial supply of nutritional resources to guarantee favorable larval development, but they do not receive any additional food during the remainder of the simulation, are not available to female adults for oviposition, and are removed from the simulated area as soon as all released individuals have either died or emerged as adults. This ensures that no additional breeding sites are created in the simulated area. We designate 10% of houses in our simulated area as the release sites because a limited number of households are expected to participate. There is some mortality of eggs and immature stages. Therefore, we assess results of simulations with eggs in terms of the total number of adults expected to be produced over the entire release for each specific number of eggs released per release site. We also present results in terms of how many eggs or adults are released at single sites in a single week.

We can therefore define a number of scenarios based on (1) the spatial pattern of release, (2) the life stage chosen for release, (3) the number of individuals released (and the number of separate releases) and (4) the parameters of the genetic strategy involved (namely the fitness cost values, i.e. c_M and c_F for Medea, c_K and c_R for KR). Because the model has many stochastic processes, 20 simulations were run for each scenario so that information on the variation in outcomes can be examined. Due to space limitations we only present detailed time series plots of allelic frequencies for a small number of simulations. For the most part, we present summaries of the status of the anti-dengue alleles three years after the releases.

We selected the three-year time period as a compromise between two conflicting requirements. On the one hand, a shorter time frame would be favored by public health administrators and citizens of an affected community who would need to consent to the use of the transgenic approach. On the other hand, a sufficiently long evaluation time is required to properly assess the outcome of any particular release scenario. We observed (Figure S1) that shorter time frames would not be appropriate in that regard. A 1-year period (Figure S1A) does not allow Medea elements to significantly increase in frequency under all but the largest release scenarios, and would therefore lead to a significant overestimation of the required release size. A 2-year period (Figure S1B) would mostly correct this overestimation, but remains insufficient in most scenarios for the Medea elements to fully spread in the resident population.

Because the ability of Medea elements to spread throughout populations is of primary interest, we categorize outcomes into classes based on the anti-dengue allele frequency after three years (‘full spread’: freq>0.8; ‘partial spread’: 0.2<freq<0.8; ‘no spread’: 0<freq<0.2; ‘lost’ freq=0). Note that ‘No spread’ indicates only the absence of spread to high frequencies within the timeframe considered in this study, and does not preclude the possibility of the element further increasing in frequency after a longer period.

Single release of homozygous Medea individuals

Because of the selfish spreading ability of Medea genetic constructs, a single uniform release of a sufficient number of transgenic adult males to each house can be enough to obtain high frequencies of the construct 3 years after release, even when a fecundity cost c_F=0.1 is considered (Figure 1). If there is no cost c_M associated with the Medea/anti-dengue construct (Figure 1A), a single release of 16 males per house is sufficient to obtain final frequencies above 0.8 (full spread) in every replicated simulation. Note that with releases of 8 males per house, an increase in frequency of the construct is observed in every simulation; however, the allelic frequency of 0.8 is not always observed after 3 years. If the construct is associated with a fitness cost of c_M=0.1 (Figure 1B), a single release of even 20 males per house is not sufficient for the transgenic element to begin spreading in the population. However, the Medea construct (and the linked anti-pathogen transgene) is not lost from the simulated populations if 6 or more males are released per house. Note that results are qualitatively similar when no fecundity cost c_F is considered (Figure S2), although in this case the construct is much less likely to be lost from the population in cases where it does not spread.

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Figure 1. Single release of homozygous Medea adult males in every house.

Proportion represents the fraction out of 20 simulations that reaches a given outcome 3 years after the first release. Outcomes are defined by the final allelic frequency f of the Medea construct in the population. ‘Spread’: f>0.8; ‘Spreading’: 0.2<f<0.8; ‘No spread’: 0<f<0.2; ‘Lost’: f=0. Both panels: c_F=0.1. Top panel: c_M=0; bottom panel: c_M=0.1.

https://doi.org/10.1371/journal.pone.0083354.g001

When Medea-bearing eggs are released in selected sites into the population, the Medea element attains partial spread in some simulations with a single release of 2000 eggs per site or more (Figure 2A). However, this method is quantitatively much less efficient than the uniform release of adult males (comparing the equivalent total number of adult males needed by each method to attain the same degree of spread). When eggs are the release stage, the Medea construct does not spread into the population in any of our simulations if it is associated with a fitness cost (Figure 2B). The release into only 10% of houses is problematic because it requires the Medea construct to spread spatially as well as temporally. Here again, results are qualitatively similar whether c_F=0.1 (Figure 2) or c_F=0 (Figure S3). The main difference is that, in the presence of a dominant fecundity cost c_F, the construct is more likely to be lost from the population when it is released at low frequencies that do not permit spread. This is likely to be a desirable trait for the strategies examined here, as it may help prevent unwanted spread to non-target populations.

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Figure 2. Single release of homozygous Medea eggs in 10% of houses.

Proportion represents the fraction out of 20 simulations that reaches a given outcome 3 years after the first release. Outcomes are defined by the final allelic frequency f of the Medea construct in the population as in Figure 1. Both panels: c_F=0.1. Top panel: c_M=0; bottom panel: c_M=0.1. The total number of adults produced from released eggs is estimated based on the average adult production of an egg cohort of corresponding size.

https://doi.org/10.1371/journal.pone.0083354.g002

Multiple releases of homozygous Medea individuals

When 10 consecutive weekly releases of homozygous Medea adult males are simulated, the spread of the construct is more efficient (i.e. fewer total males released for the same outcome) than in the single releases (Figure 3). If there is no embryonic fitness cost, high final frequencies are achieved with releases as low as 1 male per house per week (Figure 3A). This type of release represents a total of 6,120 males for the whole release program, a number that does not yield consistent full spread within 3 years when all of the transgenic males are released in a single event (Figure 1A). The difference is more pronounced when the construct is associated with an embryonic fitness cost (Figure 3B). In that case, 10 releases as low as 2 males/house/week, corresponding to a total of 12,240 males, result in consistent full spread within 3 years, whereas the same number in a single release does not result in any spread of the construct (Figure 1B).

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Figure 3. Multiple releases of homozygous Medea adults and eggs.

Proportion represents the fraction out of 20 simulations that reaches a given outcome 3 years after the first release. Outcomes are defined by the final allelic frequency f of the Medea construct in the population as in Figure 1. All scenarios involve 10 weekly releases. All panels: c_F=0.1. Top panels: c_M=0; bottom panels: c_M=0.1. Left column: release of adults in every house. Right column: release of eggs in 10% of houses.

https://doi.org/10.1371/journal.pone.0083354.g003

When eggs are released, multiple releases are also more favorable for the spread of the transgene if it has no embryonic fitness cost (Figure 3C). Partial spread is observed for releases as low as 100 eggs per house per week, whereas spread was not observed at all with single releases of that same total number of eggs (Figure 2A). If there is a fitness cost (Figure 3D), spread is not observed any more than with a single release, although multiple releases still appear somewhat beneficial in that the linked anti-dengue transgene is never lost from the 20 simulated populations (contrary to the single release case, Figure 2B).

Single release of homozygous Medea adults of both sexes

When releasing adults into the resident population, it is generally considered preferable to release only males, since they do not bite and, a fortiori, do not transmit disease. Unfortunately, this imposes a strong limitation on the frequency that a newly introduced genetic element can reach one generation after release. Even under the most favorable assumptions (all females in the resident population are virgin and all mate with released males) the frequency of the transgene cannot exceed 0.50 in the next generation. To overcome this limitation it is necessary to release homozygous transgenic females along with the males. We show that the combined release of males and females substantially improves the fate of a Medea allele in our simulations. When adults are released once in every premise in the simulated area, full spread of the Medea allele is observed in more than 90% of cases when releasing as little as 2 males and 2 females per house (Figure 4A), whereas a male-only release required at least 12 males per house to achieve the same result. The difference is even more striking when the transgene is associated with a cost: whereas male-only releases failed to achieve even partial spread with up to 20 males per house, full spread is observed consistently in our simulations with a single release of 8 males and 8 females per house (Figure 4B).

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Figure 4. Single release of homozygous Medea adult males and females in every house.

Proportion represents the fraction out of 20 simulations that reaches a given outcome 3 years after the first release. Outcomes are defined by the final allelic frequency f of the Medea construct in the population. Categories defined as in Figure 1. Both panels: c_F=0.1. Top panel: c_M=0; bottom panel: c_M=0.1.

https://doi.org/10.1371/journal.pone.0083354.g004

Single release of homozygous KR individuals

A single uniform release of homozygous KR male adults, with numbers as high as 100 males per house (61,200 total males), results only in partial spread of the R allele in the population, with a final frequency remaining below 0.40 (Figure 5A). The final frequency of the R allele increases with the number of males released per house (Figure 6A), but remains at low values. If there is a fitness cost associated with carrying the R allele, the frequency of R does not reach values as high as in the no-cost case, and starts to decrease once the K allele has become rare in the population (Figure 5A). Consequently, with such a fitness cost, the final frequency of the R allele is much lower (Figure 6A).

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Figure 5. Time series of allele frequencies with releases of homozygous KR adult males in every house.

The trajectories represent the change in frequencies of K allele (red, dashed lines) and R allele (green, solid lines) in the population in one simulation of releases of KR males in every house. The model is run for one year without release to establish the resident population, releases then start on day 365. Dark lines: c_K = c_R = 0. Light lines: c_K = c_R = 0.1. Top: single release of 100 males per house. Bottom: 10 weekly releases of 10 males per house each. In both cases, the total number of males released is 61,200.

https://doi.org/10.1371/journal.pone.0083354.g005

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Figure 6. Final R allele frequency with single release of homozygous KR individuals.

For each scenario the final frequency of the R allele in the population is plotted (20 replicates, average ± SD). Top: single release of adult males in every house. Bottom: single release of eggs in 10% of houses. Dark: c_K = c_R = 0. Light: c_K = c_R = 0.1. Note that the Y-axis is different in Figure 6 A and B.

https://doi.org/10.1371/journal.pone.0083354.g006

As in the Medea case, we also consider the case of a release of eggs in 10% of the houses. Similarly to our prior observations, this type of release appears less efficient in the case of a single release (Figure 6B). The final frequency of the R allele does increase with the total number of eggs released. However, at an equal number of adult males produced, the frequency that is reached by releasing eggs is considerably lower than that obtained by releasing adults, whether transgenes are associated with a cost or not.

Multiple releases of homozygous KR individuals

With 10 consecutive weekly releases of KR individuals, the final frequencies of R that can be observed are notably higher. For example, in one simulation with 10 releases of 10 males per week in every house (total number of 61,200 males), the R allele reaches a frequency over 0.90 after three years when there is no cost. When the R allele frequency is above 0.90, the population has less than 1% rr individuals that can transmit disease (see Gould et al. [24]). When there is a fitness cost (Figure 5B) the R allele frequency is still over 0.80 (less than 4% rr individuals). In contrast, with a single release of the same number of adult males, the final R frequencies are below 0.40 and 0.10 respectively (Figure 5A). In each of the simulations in Figure 5, the frequency of the K allele continues to decline throughout the period after release, and as expected, the rate of decline is correlated with the frequency of the rr individuals in the population [24]. The R allele frequency never declines if there is no fitness cost associated with it. In the case with a fitness cost to the R allele and 10 releases (Figure 5B), the R allele does not decline during the 3-year period because the K allele is at a high enough frequency to balance the effect of the fitness cost.

Figure 7A summarizes results of 20 simulations for each of a set of release parameters and shows that an R-bearing construct with no cost can consistently reach frequencies of approximately 0.95 with a total number of released males as low as 40,000 (Figure 7A) provided these releases are conducted over a 10 week period. The final frequencies of the R allele are lower if that construct is associated with a cost (Figure 7B), but frequencies above 0.80 can still be reached and maintained for three years with releases of 60,000 males or higher. This results in less than 4% of the females being capable of dengue virus transmission.

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Figure 7. Final R and K alleles frequencies with multiple releases of homozygous KR adult males in every house.

For each scenario the final frequency of each allele in the population after three years is plotted (20 replicates, average ± SD). Top: c_K = c_R = 0. Bottom: c_K = c_R = 0.1. Dark circles: final frequency of R allele. Light triangles: final frequency of K allele.

https://doi.org/10.1371/journal.pone.0083354.g007