Skip to main content
Download PDF

Modelling spatiotemporal trends in the frequency of genetic mutations conferring insecticide target-site resistance in African mosquito malaria vector species

BMC Biology volume 20, Article number: 46 (2022) Cite this article

Abstract

Background

Resistance in malaria vectors to pyrethroids, the most widely used class of insecticides for malaria vector control, threatens the continued efficacy of vector control tools. Target-site resistance is an important genetic resistance mechanism caused by mutations in the voltage-gated sodium channel (Vgsc) gene that encodes the pyrethroid target-site. Understanding the geographic distribution of target-site resistance, and temporal trends across different vector species, can inform strategic deployment of vector control tools.

Results

We develop a Bayesian statistical spatiotemporal model to interpret species-specific trends in the frequency of the most common resistance mutations, Vgsc-995S and Vgsc-995F, in three major malaria vector species Anopheles gambiae, An. coluzzii, and An. arabiensis over the period 2005–2017. The models are informed by 2418 observations of the frequency of each mutation in field sampled mosquitoes collected from 27 countries spanning western and eastern regions of Africa. For nine selected countries, we develop annual predictive maps which reveal geographically structured patterns of spread of each mutation at regional and continental scales. The results show associations, as well as stark differences, in spread dynamics of the two mutations across the three vector species. The coverage of ITNs was an influential predictor of Vgsc allele frequencies, with modelled relationships between ITN coverage and allele frequencies varying across species and geographic regions. We found that our mapped Vgsc allele frequencies are a significant partial predictor of phenotypic resistance to the pyrethroid deltamethrin in An. gambiae complex populations.

Conclusions

Our predictive maps show how spatiotemporal trends in insecticide target-site resistance mechanisms in African An. gambiae vary across individual vector species and geographic regions. Molecular surveillance of resistance mechanisms will help to predict resistance phenotypes and track their spread.

Background

A major challenge in malaria control involves managing the threat that insecticide resistance in mosquitoes poses to the efficacy of vector control technologies. Insecticide-based vector control techniques, including indoor residual spraying (IRS) and insecticide-treated bed nets (ITNs), are pivotal to malaria prevention, with ITNs in particular being responsible for a large portion of the reductions in malaria cases achieved over the period 2000–2015 [1]. ITNs rely on pyrethroid insecticides, which are used in the treatment of all ITNs pre-approved by the WHO and in many indoor residual sprays still used today [2,3,4]. Pyrethroid resistance in malaria vectors has spread extensively throughout Sub-Saharan Africa [5], and in 2017, the mosquito sample mortality following exposure to a pyrethroid as measured by a WHO standard susceptibility test had dropped to less than 50% in at least 34 malaria endemic countries (compared to less than 2% of susceptibility tests recording mortalities of less than 50% prior to 2006 [5]).

The prevalence of insecticide resistance phenotypes in African malaria vector species is highly heterogeneous across geographic space [5], and underpinned by variation in genetic resistance mechanisms [6], which have the potential for rapid long range spread [7]. Geographically comprehensive insecticide resistance monitoring and surveillance is therefore essential to track changes in resistance, interpret trends and anticipate upcoming threats. Unfortunately, despite the recommendations of the WHO Global Plan for Insecticide Resistance Management (GPRIM) [8] for the instigation of comprehensive and routine insecticide resistance monitoring, the available surveillance data is sparse throughout Sub-Saharan Africa, with 89% of administrative districts having no recorded measurements in the period 2015–2017 [9]. Standard susceptibility bioassays to measure phenotypic resistance are labour intensive and difficult to scale up. Moreover, where morphologically cryptic vectors are present, susceptibility bioassays are rarely used to measure resistance at the level of individual species and do not provide information about mechanisms of resistance. Results can also be sensitive to environmental testing conditions, which are often difficult to standardise in the field [10, 11]. Genetic, and in due course genomic, surveillance to track the frequency of variants that are associated with phenotypic resistance is more scalable, insensitive to collection and environmental conditions, and can distinguish between different resistance mechanisms across different vector species.

A major challenge for genetic surveillance lies in identifying variants, or genomic regions, that are important determinants of different types of phenotypic resistance [12]. Target-site resistance is an important pyrethroid resistance mechanism in Anopheles gambiae complex mosquitoes [6, 7] and is the most widely monitored genetic mechanism in field malaria vector populations. It is caused by mutations within the Vgsc gene that encodes the voltage-gated sodium channel, which is the physiological target of pyrethroid insecticides. Three single point mutations (SNPs) within the Vgsc gene are known to confer pyrethroid resistance; these include two substitutions on the 995 codon, L995F (originally named L1014 F[13];) and L995S (originally named L1014S [14];), and a third substitution N1570Y (originally named N1575Y [15];). The L995F and L995S mutations occur in the same codon and they cannot co-occur on a single chromosome, while the N1570Y mutation occurs in a different codon and has been found to increase resistance in association with L995F [15]. Genome sequencing has recently identified numerous other non-synonymous SNPs within the Vgsc gene, some apparently subject to recent positive selection, indicating that target-site resistance has a complex molecular basis, likely increasingly so over time [7].

The extent to which phenotypic resistance in field malaria vector populations depends on these multifaceted genetic mechanisms remains uncertain [12]. Genotype-phenotype association studies are complicated by the polygenic nature of insecticide resistance and the complex population structure of African Anopheles gambiae mosquitoes [16, 17]. The Anopheles gambiae complex is made up of at least eight individual vector species, five of which are major malaria vectors: An. gambiae, An. coluzzii, An. arabiensis, An. melus, and An. merus [18,19,20]. The distribution of the different vector species is geographically heterogeneous, with gradients in species composition occurring across regional and continental scales [21]. Mechanisms of insecticide resistance differ across these three species [22]. The evolutionary trajectories of resistance depend on the specific ecology of individual species, the selection pressures present in the environment, and patterns of dispersal, migration and introgression across different populations [16, 23,24,25].

Spatial modelling analysis is required to interpret spatial and temporal trends in insecticide resistance surveillance data that monitor the prevalence of different types of resistance in vector species [5]. This is because sampling locations are heterogeneously distributed across Africa and variable across sampling times and across the different types of resistance phenotypes and/or genetic mechanisms that were tested in the sample. Geospatial models can quantify geographically explicit temporal trends in resistance [5]. The ability of geospatial models to extrapolate predictions across unsampled locations can help compensate for sparsity in surveillance data and allow anticipation of contemporary resistance levels before new surveillance results become available [9]. Further, geospatial models offer a flexible framework for combining different datasets that describe separate but related aspects of resistance. They can incorporate measures of resistance across different vector species, as well as genetic and phenotypic measures of resistance, within the same modelling framework [26]. The ability of spatial models to predict resistance can benefit greatly from incorporating information about environmental characteristics such as climate, vegetation, and land use; importantly, variables describing the distribution of insecticide-based vector control interventions across the landscape can be included as potential predictors [5].

Here, we develop a Bayesian statistical spatiotemporal model ensemble to interpret species-specific trends in the frequency of two target-site resistance mutations in the Vgsc gene, 995S and 995F, in three vector species An. gambiae, An. coluzzii, and An. arabiensis over the period 2005–2017, which encompasses the period of major scaling up of ITN distributions. The models are informed by 2418 observations of the frequency of each mutation in field sampled mosquitoes collected from 27 countries spanning western and eastern regions of Africa. For nine focal countries, we develop a series of fine resolution annual predictive maps. These models reveal the geographically structured patterns of spread of each mutation at both regional and continental scales. We use our geospatial predictions of Vgsc allele frequencies to address two questions of importance to malaria vector control. Firstly, we analyse associations between the Vgsc allele frequencies and phenotypic resistance to pyrethroids seen in field vector populations. Secondly, we explore the sensitivity of the predicted Vgsc allele frequencies to differences in the coverage of ITNs.

Results

Predictive accuracy of the spatiotemporal model ensemble

Our spatiotemporal model ensemble, based on field-sampled Vgsc resistance allele frequencies in mosquito species from the African An. gambiae complex, confirmed our ability to interpolate allele frequencies. Predictive accuracy was assessed by testing the ability of the model ensemble to predict withheld data (using 10-fold out-of-sample cross-validation; see the “Methods” section), which showed a mean absolute prediction error (MAE; the average absolute difference between model predictions and observations) of less than 10% (MAE = 0.083) across all observed Vgsc allele frequencies (with a root mean square error (RMSE) of 0.137; Additional File 1: Figure S1 and Table S1).

Spatiotemporal trends in the frequency of target-site resistance mutations

The nine mapped countries were chosen based on their number and spatial coverage of sampled Vgsc allele frequencies (see the “Methods” section and Additional File 1: Figures S2-S5). In western Africa, we developed maps of the predicted frequency of the Vgsc-995F mutation for Burkina Faso, Benin, Cameroon, and Equatorial Guinea. In 2005, the earliest year in the data set, our maps show substantial geographic variation in the Vgsc-995F frequency, within each country and between countries. The marker frequency also varied markedly across the three vector species (Fig. 1). In all four countries, the marker frequency in 2005 was highest in An. gambiae and lowest in An. arabiensis, with frequencies in An. coluzzii also being low in large parts of each country. In Burkina Faso, Benin, and Cameroon, the marker frequency in 2005 is higher in southern compared to northern areas. We note that in these three countries the relative abundance of An. arabiensis declines southwards with decreasing latitude, with An. gambiae and An. coluzzii becoming more dominant (see Additional File 1: Figure S7). It is possible that there is a greater selection pressure for the development of insecticide resistance acting on An. gambiae and An. coluzzii populations, because these two species have a stronger tendency towards indoor human biting than An. arabiensis and are therefore more likely to encounter insecticide-treated surfaces (see the “Discussion” section).

Fig. 1
figure 1

Predicted frequencies of the Vgsc-995F allele in malaria vector species for four countries in west Africa: Burkina Faso (top row), Benin (second row), Cameroon (third row), Equatorial Guinea (bottom row). Allele frequency maps for the first and final year are shown: the year 2005 is shown on the left (columns 1, 2, and 3) and the year 2017 is shown on the right (columns 4, 5, and 6). Columns 1 and 4 show maps for An. gambiae, columns 2 and 5 show maps for An. coluzzii, and columns 3 and 6 show maps for An. arabiensis

Full size image

In all three vector species and all four countries, Vgsc-995F increased markedly between 2005 and 2017, with frequencies in An. gambiae and An. coluzzii in 2017 exceeding 0.5 in over 80% of the spatial area of each country (Fig. 1). A lesser increase occurred in An. arabiensis, with the strongest rise occurring in southern Cameroon. We did not map the Vgsc-995S frequency for the countries in western Africa, owing to its general scarcity (full reasons for exclusion of countries from each part of the modelling analyses are provided in Additional File 1: Table S2).

In eastern Africa, we developed maps of the predicted frequencies of Vgsc-995S and Vgsc-995F for four countries: Sudan, Ethiopia, Kenya, and Uganda (Additional File 1: Table S2). For Sudan, we mapped only a region in the west of the country (see the “Methods” section). The frequency of the Vgsc-995S allele in the four eastern African countries shows a dichotomous pattern across species, with much higher frequencies in An. gambiae than in An. arabiensis (Fig. 2). In 2005, the frequency was low in An. arabiensis and very heterogeneous in An. gambiae. The frequency increased markedly in An. gambiae over 2005–2017, reaching very high levels in the north-west part of our mapped region in Sudan, south-east Ethiopia, west Kenya, and most of Uganda. The Vgsc-995S frequency also increased in An. arabiensis, but to a much lesser extent, with the highest frequencies occurring in southern Uganda in the final year of the modelled time period.

Fig. 2
figure 2

Predicted frequencies of the Vgsc-995S allele in malaria vector species for four countries in east Africa: Sudan (top row; the mapped area is confined to a region in the west (see the “Methods” section)), Ethiopia (second row), Kenya (third row), and Uganda (bottom row). Allele frequency maps for the first and final year are shown: the year 2005 is shown on the left (columns 1 and 2) and the year 2017 is shown on the right (columns 3 and 4). Columns 1 and 3 show maps for An. gambiae, and columns 2 and 4 show maps for An. arabiensis

Full size image

It is important to note that, in these four eastern African countries, the abundance of An. arabiensis relative to that of An. gambiae is typically much higher than in western Africa (Additional File 1: Figure S7), and An. coluzzii is very rarely reported. In Ethiopia and Sudan, the species composition is almost entirely dominated by An. arabiensis. In general, the temporal dynamics of Vgsc-995F in An. arabiensis in these four countries followed a similar pattern to those in western Africa, with the frequency in 2005 being lower than that in An. gambiae, and then increasing in some areas to reach moderate to high frequencies in 2017 (Fig. 3).

Fig. 3
figure 3

Predicted frequencies of the Vgsc-995F allele in malaria vector species for four countries in east Africa: Sudan (top row; the mapped area is confined to a region in the west (see the “Methods” section)), Ethiopia (second row), Kenya (third row), and Uganda (bottom row). Allele frequency maps for the first and final year are shown: the year 2005 is shown on the left (columns 1 and 2) and the year 2017 is shown on the right (columns 3 and 4). Columns 1 and 3 show maps for An. gambiae, and columns 2 and 4 show maps for An. arabiensis

Full size image

In Ethiopia, Kenya, and Uganda, the frequency of Vgsc-995F in An. gambiae was typically lower in 2005 compared to the western countries, and there was a lesser increase in the frequency over 2005-2017 (Fig. 3). In 2017, there was still substantial spatial heterogeneity in the Vgsc-995F frequency, with regions of high frequency in northwest Ethiopia, northwest Kenya, and northern Uganda and low frequencies elsewhere. In An. gambiae, the historical presence of Vgsc-995S at moderate to high frequencies (Fig. 2) is likely to slow the spread of Vgsc-995F in this species (see the “Discussion” section). In the south and west of our mapped region in Sudan, however, the Vgsc-995F frequency in An. gambiae was already high in 2005. Frequencies increased from 2005 to 2017, particularly in the north-western part of the region. For all four countries, there is a high degree of spatial overlap in the areas of relatively high Vgsc-995F frequency between An. gambiae and An. arabiensis (Fig. 3).

For the DRC, we developed maps of the frequency of Vgsc-995F in An. gambiae only (Additional File 1: Table S2). In the DRC, the spatiotemporal trends in Vgsc-995F in An. gambiae are more similar to the western countries, with a moderate to a high initial frequency in 2005, followed by a widespread increase to high frequencies in 2017 (Fig. 4).

Fig. 4
figure 4

Predicted frequencies of the Vgsc-995F allele in An. gambiae in the Democratic Republic of the Congo (DRC). Allele frequency maps for the first and final year are shown: 2005 (left) and 2017 (right)

Full size image

Associations amongst the allele frequencies in the three vector species

The spatial patterns in the increases in Vgsc-995F frequencies in An. gambiae and An. coluzzii in the western countries over 2005–2017 were closely associated with each other, with the increase in An. coluzzii lagging behind that in An. gambiae (Fig. 5 and Additional File 1: Figure S11). This is consistent with the results of genomic studies that show introgression of target-site resistance from An. gambiae to An. coluzzii [16]. We found significant but less strong associations between the spatial patterns in Vgsc-995F frequency in An. arabiensis and both An. gambiae and An. coluzzii in the western countries over the years 2005–2017 (Additional File 1: Figure S8). Moreover, in the eastern countries (Ethiopia, Kenya, Uganda, and Sudan), spatial increases in both the Vgsc-995F and Vgsc-995S frequencies were significantly associated across An. gambiae and An. arabiensis (Additional File 1: Figures S9 & S10).

Fig. 5
figure 5

Associations between the predicted frequency of the Vgsc-995F allele in An. gambiae and An. coluzzii. Bagplots show the distribution across all mapped pixels within four countries in west Africa: Burkina Faso, Benin, Cameroon, and Equatorial Guinea. The red asterisk shows the median, the dark blue shaded area contains 50% of all data points, and the light blue shaded area contains all data points. Plots for four years are shown (from left to right): 2006, 2010, 2014, and 2017

Full size image

Associations between resistance allele frequencies and the prevalence of resistance phenotypes

We investigated whether the variation in our mapped Vgsc mutation frequencies could explain variation in phenotypic resistance to pyrethroids in field malaria vector populations. Specifically, we analysed associations between predicted frequencies of the Vsgc-995F mutation in the mosquito samples and phenotypic resistance to deltamethrin, the most commonly used insecticide in malaria vector control during the period studied. Measures of mosquito mortality following exposure to deltamethrin were derived from standardised insecticide susceptibility tests (see the “Methods” section). We excluded Equatorial Guinea, Uganda, Kenya, and the DRC from this analysis (Additional File 1: Table S2). We do not consider associations between Vsgc-995S frequencies and the prevalence of deltamethrin resistance because Vsgc-995S frequencies are low in the majority of our selected countries and strongly segregated across the An. gambiae complex species (Fig. 2 and see the “Discussion” section).

For three countries in western Africa (Burkina Faso, Benin, and Cameroon) and two countries in eastern Africa (Ethiopia and Sudan), the mortality to deltamethrin is consistently high when the Vgsc-995F frequency is close to zero, and there is a trend of decreasing mean mortality to deltamethrin with increasing Vgsc-995F frequency (Fig. 6A, B). For each country, we fitted ordinary least-squares (OLS) linear regression models to the mean mortality values using the predicted Vgsc-995F frequency as a covariate (see the “Methods” section). The relationship with the Vgsc-995F covariate was significant for all countries except Sudan, in which case the 95% credible interval (CI) had a borderline overlap with zero (Table 1).

Fig. 6
figure 6

The mean mortality to deltamethrin and the frequency of the Vgsc-995F allele in Gambiae Complex mosquitoes at sampled locations in countries in west Africa (A) and east Africa (B). In the west (A), results for three countries are shown: Burkina Faso (green dots; n = 159), Benin (purple triangles; n = 297), and Cameroon (brown diamonds; n = 184). In the east (B), results for two countries are shown: Ethiopia (blue squares; n = 134) and Sudan (dark red diamonds; n = 256)

Full size image
Table 1 OLS regression model results for each country. The model is fitted to mean mortality to deltamethrin across sets of bioassay sampling locations using the frequency of the Vgsc-995F allele in the Gambiae Complex as a covariate. The asterisk denotes statistical significance assessed by the 95% credible interval (CI)
Full size table

Despite the uncertainty associated with estimating frequencies of both phenotypic resistance and Vgsc alleles across multiple mosquito species in field populations, the interpolated Vgsc-995F allele frequency is able to partially explain the variation in mortality to deltamethrin. The level of explained variation varies across countries; adjusted R2 values were close to 0.3 for Burkina Faso, Cameroon, and Ethiopia, but less than 0.1 for Benin and Sudan (Table 1). Moreover, the form of the relationship varies across countries. In Benin, many mortality values remain high across increasing Vgsc-995F frequencies (Fig. 6), consistent with the poor explanatory value of the model, despite a significant negative slope (Table 1).

Relationships with predictor variables

Our model ensemble included 99 predictor variables describing environmental and biological processes that could potentially drive selection for insecticide resistance (see the “Methods” section). We analysed which of these variables were the most influential predictors of Vgsc allele frequencies using variable importance measures, which describe the influence of each variable in terms of its impact on model predictions, relative to all other predictor variables (see the “Methods” scetion). Our model ensemble included three constituent models: an extreme gradient boosting model (XGB), a random forest model (RF), and a neural network model (NN). For each model, we obtained a ranking of the most influential variables using a variable importance measure that was chosen based on the type of model (see the “Methods” section).

For all three models, the highest-ranked predictor variable was related to climate, with solar radiation ranking highest for the XGB and RF models and relative humidity ranking highest for the NN model (Table 2). These two variables may be influential because they segregate dry arid areas and wetter tropical regions (see the “Discussion” section). The coverage of insecticide-treated bed nets (ITNs) was strongly influential in the XGB and RF models, with variables describing ITN coverage at different time lags ranking second, fifth, and ninth in both models (Table 2). In the NN model, the coverage of evergreen broadleaf forest was highly influential, with different time lags of this variable ranking second, fourth, and eighth. In general, with the exception of ITN coverage, the highest-ranked variables for the XGB and RF models are related to climate and elevation, and the highest ranked variables for the NN model include variables relating to land cover, climate, and elevation.

Table 2 The top ten highest ranked variables, as determined by variable importance measures, for the three machine learning models included in the model ensemble. Variable name suffixes (-1), (-2), and (-3) denote time lags of 1, 2, and 3 years, respectively. One, two, and three asterisks denote the first, second, and third principal component, respectively, for variables available on a monthly time step (see the “Methods” section)
Full size table

Impacts of increasing ITN coverage on predicted Vgsc mutation frequencies

Relationships between ITN coverage and the development of insecticide resistance have significant implications for malaria vector control (see the “Discussion” section). We further examined the relationship between ITN coverage and the interpolated frequencies of the Vgsc-995F allele by calculating the independent conditional expectation (ICE) of the predicted frequency under changing ITN coverage [27, 28]. The ICE can be calculated for any of the locations (pixels) of our predictive maps, and we selected a single location in each country to evaluate the ICE (see the “Methods” section). We chose to analyse these relationships for the year 2005, because up until this time the resistance allele frequencies were unlikely to be affected by widespread ITN usage (the reported ITN coverage in this year and the 3 years prior is very close to zero). We varied the ITN coverage in the years 2002-2005 from zero to 0.9, or 0–90% of people slept under an ITN the preceding night, in increments of 0.1 (because the predictor variables include three annual time lags; see the “Methods” section). It is important to note that this variation in ITN coverage that we simulate was never actually observed in the period 2002–2005. We did not analyse relationships between ITN coverage and the Vgsc-995S allele frequency because Vgsc-995S shows low frequencies for all years in most of the countries included in our model.

For the four countries in western Africa, increasing the ITN coverage causes the model to predict increasing Vgsc-995F frequencies in 2005 in all three mosquito species (Fig. 7A). The impact of increasing ITN coverage varies geographically across countries and also between mosquito species. In An. gambiae, the Vgsc-995F frequency at the selected location was already high (> 0.4) in 2005 for all countries except Benin. Increasing the ITN coverage from zero to 0.9 resulted in further increases in frequencies to very high values, with the largest increases occurring when the frequency at zero ITN coverage was lower (Fig. 7A). In An. coluzzii, Vgsc-995F frequencies in 2005 were relatively low at zero ITN coverage, and predicted frequencies increased strongly as ITN coverage increased to high values. An. arabiensis showed the lowest Vgsc-995F frequencies in 2005 under zero ITN coverage, and the impact of increasing ITN coverage on predicted frequencies was much less than in An. gambiae and An. coluzzii. This behaviour is consistent with the trends in Vgsc-995F in An. arabiensis over the years 2005–2017 (Fig. 1), with frequencies remaining relatively low while the coverage of ITNs increased from 2005 onwards in all four countries to reach moderate to high values (Additional File 1: Figures S12-S14).

Fig. 7
figure 7

The variation in the model-predicted Vgsc-995F frequency in malaria vector species for the year 2005 as the coverage of insecticide treated bed nets (ITNs) is increased. Within each country, the predicted frequency for a single point location is shown (see text). Solid circles represent the predicted frequency corresponding to an ITN coverage of zero over the years 2002–2005, which is close to the recorded ITN coverage over this period. Solid lines show the range of variation in the predicted frequency at these locations for the year 2005 as the ITN coverage is increased from 0 to 0.9. Results for four countries in west Africa (A) and five countries in central and east Africa (B) are shown. Black, blue, and green lines and circles represent predicted frequencies in An. gambiae, An. coluzzii, and An. arabiensis, respectively

Full size image

For the four countries in eastern Africa, the impact of increasing ITN coverage on the model predictions of Vgsc-995F frequencies is relatively small (Fig. 7B), reflecting the differences in malaria vector species composition, and the different types of insecticide resistance mechanisms present, between the eastern and western regions of Africa (see the “Discussion” section). In Ethiopia and Sudan, the species composition consists mostly of An. arabiensis (see Additional File 1: Figure S7); the Vgsc-995F frequencies in An. arabiensis were low in 2005 and increasing ITN coverage resulted in only a small increase in frequencies. In Kenya and Uganda, the predicted Vgsc-995F frequencies were almost unchanged by increasing ITN coverage. This is consistent with the trends in Vgsc-995F frequencies in both An. arabiensis and An. gambiae in eastern Africa from 2005 to 2017 (Fig. 3), with Vgsc-995F frequencies increasing by a small amount in some areas and not increasing at all in other areas, although ITN coverage did increase in these countries over the period (Additional File 1: Figures S12-S14). In An. gambiae, the earlier increases in the frequencies of Vgsc-995S may have reduced the selection pressures driving the spread of the Vgsc-995F allele (see the “Discussion” section). In the DRC, the variation in predicted Vgsc-995F frequencies with increasing ITN coverage shows a similar pattern to the western countries, with predicted frequencies in An. gambiae in 2005 increasing from an intermediate value at zero ITN coverage to a very high value with increasing ITN coverage (Fig. 7B).

Discussion

Our annual maps of the frequencies of target-site insecticide resistance mutations in the three dominant malaria vector species of the African An. gambiae complex have characterised the species-specific spread dynamics of target-site resistance, showing how these dynamics have varied geographically, across national and continental scales. Our geospatial machine learning model ensemble brings together data sets describing multiple, multifaceted processes affecting insecticide resistance in field vector populations. Relationships between mutation frequencies and the prevalence of resistance phenotypes can be explored, as well as relationships with the coverage of vector control interventions such as ITNs. In this study, we have used these models to investigate questions of importance to malaria vector control.

Firstly, we found significant relationships between frequencies of the target-site resistance mutation Vgsc-995F and phenotypic resistance to the pyrethroid deltamethrin in field samples. This demonstrates explanatory power of target-site resistance for phenotypic variation in field An. gambiae complex populations, supporting the relationships between target-site and phenotypic resistance shown by functional [14, 29] and genomic [6, 7] studies. Our maps show substantial spatial heterogeneity in Vgsc allele frequencies in recent years, with frequencies in 2017 varying both across vector species and geographic regions. Continued surveillance of these target-site markers is therefore important to track current and future regional temporal trends in resistance.

A substantial amount of phenotypic variation was unexplained by the Vgsc-995F frequencies, however, which is in part due to the fact that the sample mortality is often not disaggregated by the individual species within the An. gambiae complex. Our maps show how target-site resistance frequencies differ across these species depending on geographic region, with dichotomous differences in some regions. This highlights that species-specific trends in phenotypic resistance cannot be fully understood using susceptibility test mortality values at the An. gambiae complex level. According to our Vgsc allele frequency maps, in Kenya and Uganda, there is a close coupling between vector species and which type of target-site resistance mechanism is more prevalent (995F or 995S); therefore, errors due to aggregating across species will be particularly high in these countries. For this reason, we were unable to assess associations between phenotypic pyrethroid resistance and frequencies of the Vgsc-995S mutation, which has a high frequency in these two countries and relatively low frequencies in our other focal countries.

We modelled the association between the frequency of Vgsc-995F and the mortality to deltamethrin using a linear relationship, but in wild mosquito populations, the relationship is unlikely to be straightforward. The frequencies of different Vgsc genotypes are not available for most of the samples in our database, and so our models cannot capture differences in phenotypes associated with heterozygous and homozygous genotypes. An experimental study that used gene editing to investigate the functional relationship between Vgsc-995F and mortality to pyrethroids found significant resistance to permethrin and a-cypermethrin only in homozygosity [29], as measured by WHO standard susceptibility tests. The molecular basis of target site resistance to pyrethroids is, however, likely to depend on other mutations in the Vgsc gene, as shown by whole genome analyses that identified three clusters of novel non-synonymous variants within the Vgsc gene showing signals of recent positive selection [7]. Thus, the two target site resistance alleles considered in this study do not act in isolation in influencing resistance phenotypes.

In addition to target-site resistance, geospatial analysis of the distribution of metabolic resistance mechanisms could greatly improve our ability to understand spatiotemporal trends in resistance. Metabolic resistance, the insect’s increased ability to metabolise insecticide, is another important mechanism that can generate high levels of pyrethroid resistance in An. gambiae [30, 31], and especially Anopheles funestus, which lacks resistance-associated Vgsc mutations [32]. Metabolic resistance occurs through the upregulation of metabolic genes that encode detoxification enzymes. Many metabolic genes have shown associations with pyrethroid resistance, with genomic studies of the An. gambiae complex finding strong signals of positive selection around gene clusters implicated in insecticide metabolism [6, 33]. Amplicon sequencing panels, which screen a panel of markers of interest across many loci [34, 35], can incorporate target-site as well as metabolic resistance markers, including known mutations in the Gtse2 and Cyp6p gene clusters [6]. The anticipated increased use of amplicon sequencing panels in genetic surveillance of vector populations in the coming years will lead to exciting opportunities to better quantify the polygenic nature of resistance.

Secondly, our models indicate that the coverage of ITNs is influential in predicting Vgsc allele frequencies, but that the strength of this influence varies both geographically and across vector species. These relationships between ITN coverage and Vgsc allele frequencies produced by our models need to be interpreted with caution, because the machine learning approaches that we have applied do not allow causal inferences to be made, and correlations amongst predictor variables can make relationships with any given variable difficult to identify. Nonetheless, our results are consistent with evidence from field studies showing changes in Vgsc allele frequencies following the implementation of ITN interventions. Our results showed that ITN coverage had the greatest influence on Vgsc-995F frequencies in the western African countries in An. gambiae and An. coluzzii. Field studies have also shown increases in Vgsc-995F frequencies in these two species following the scale-up of ITNs in Cameroon [36], Ghana [37], and Mali [38]. In Kenya and Uganda, we found no influence of ITN coverage on predicted Vgsc-995F frequencies in An. gambiae, which reflects the more limited spread of the 995F mutation in eastern An. gambiae populations. It is possible that the spread of Vgsc-995F in An. gambiae in eastern Africa was inhibited by the presence of the Vgsc-995S mutation, which is known to have been present in Kenyan An. gambiae populations since 1986 [14]. Resistance conferred by Vgsc-995S could lead to reduced selection for Vgsc-995F, and it is also possible that the strength of selection could have been reduced if other mechanisms, such as metabolic resistance, were already present.

The influence of ITN coverage on predicted allele frequencies is consistently lower in An. arabiensis across all nine countries compared to the other two species, which reflects the more limited spread of both Vgsc alleles in An. arabiensis across the western and eastern countries. An. arabiensis have a greater tendency towards biting outdoors than An. gambiae and An. coluzzii, and their peak biting times occur earlier in the evening while the other two species bite most commonly in the middle of the night [39,40,41]. An. arabiensis also has a lower human blood index than An. gambiae and An. coluzzii, indicating a relatively high proportion of bites taken on animals rather than humans [42]. It is therefore plausible that An. arabiensis has lower exposure to ITNs, and thus ITN coverage has a lesser impact on selection for resistance in this species. Observed shifts in vector species composition towards higher proportions of An. arabiensis following the scaling up of ITN interventions supports this hypothesis [21, 40]. The evolutionary pathway of resistance differs across the three vector species, however, and we expect greater divergence in the case of An. arabiensis which has lower rates of hybridisation with the other two species [43], with higher rates of hybridisation occurring between An. gambiae and An. coluzzii [44]. For example, hybridisation led to the introgression of target-site resistance from An. gambiae to An. coluzzii [16, 38], accelerating the development and spread of target-site resistance in An. coluzzii.

Variables describing solar radiation and humidity were the highest ranking in terms of their impact on predicted allele frequencies. While we cannot identify a mechanistic explanation for this result, we note that these climate variables provide a broadscale spatial separation of areas that are arid from those that are wet and tropical. They may, therefore, represent unmeasured differences in mosquito population structure and genetics that give rise to regional differences in resistance patterns. We also found, however, that the most influential variables were different across the different machine learning models, with the neural network model showing less commonality with the two regression tree-based models (extreme gradient boosting and random forest). Lucas et al. [28] found that variable importance measures for neural network models are not replicable, with different variable importance rankings being produced each time the model is fitted to the same data set. This emphasises that models fitted by machine learning algorithms do not represent a single unique optimal solution, and there may be many different ways that a machine learning model can combine the predictor variables to produce similarly accurate results, as measured by out-of-sample testing [45]. The machine learning models do not specify any mechanistic interactions between predictor variables and the target outcome and are based on learning a series of high dimensional predictive relationships that do not distinguish between mechanistic processes and non-causal associations.

Conclusions

Our geospatial analyses illustrate how insecticide target-site resistance dynamics in African malaria vectors vary across species and geographic regions, emphasising that resistance management strategies need to be based on local information about resistance genetics and vector species composition, as well as phenotype surveillance. Our results demonstrate that genetic surveillance of resistance can help to predict resistance phenotypes in field vector populations and understand their mechanistic drivers. This capacity would be improved by surveillance of resistance phenotypes at the level of individual vector species. In addition to target-site resistance, surveillance of other genetic resistance mechanisms, such as metabolic resistance, is needed to understand, predict and manage the spread of resistance.

Methods

Summary

We analysed trends in the frequencies of target-site insecticide resistance mutations across space and time in three African malaria vector species: An. gambiae, An. coluzzii, and An. arabiensis. We use spatiotemporal modelling approaches that apply both Bayesian statistics and machine learning methods in order to predict mutation frequencies jointly across the three species over a spatial grid of approximately 5 km resolution. Our model predictions are based on surveillance data that records observed frequencies in mosquitoes sampled widely throughout west and northeast Africa. The machine learning methods predict the proportions of each allele in each mosquito sample, and they are informed by 99 potential predictor variables that represent environmental and biological processes which may influence selection for resistance. A Bayesian multinomial metamodel then combines predictions across the multiple machine learning models in order to make more accurate and robust predictions (a methodology known as stacked generalisation [46]). Using the metamodel, we predict the frequencies of each mutation in all grid cells within our nine selected countries for all years in the period 2005–2017.

Vgsc allele frequency data

Our models are informed by a database containing frequencies of Vgsc mutations in mosquito samples belonging to the Anopheles gambiae species complex collected from within western and eastern Africa over the period 2005–2017 (Additional File 1: Figures S2-S6). This database is an updated version of a publicly available data set containing Vgsc allele frequencies [47] and collates data sets from multiple contributors, including published and unpublished sources. The database records the number of mosquitoes tested in each sample, together with the frequencies of the Vgsc-995 L, Vgsc-995F, and Vgsc-995S alleles in the sample. Some, but not all, data sets in the database record the Vgsc genotype of the sampled mosquitoes. The database also records information about the mosquito species tested, the molecular screening methods used for species identification and Vgsc allele identification, and the geographic coordinates of the sample collection location. We only included samples that are representative of the An. gambiae population sampled at each place and time (i.e. randomly sampled from the population). We also only included samples that contained five or more mosquitoes. The final data set included 2418 samples distributed across 27 countries.

We developed predictive maps of Vgsc allele frequencies for a focal selection of countries which had the highest number of samples, excluding those countries for which the spatial distribution of samples was strongly clustered (Additional File 1: Figures S2 and S3). In selecting countries for inclusion in our mapping analysis, we subdivided the African continent into western and eastern regions, with Cameroon and countries further west of Cameroon falling within our western region and countries that lie east of the Central African Republic falling within our eastern region. Within the western region, we selected the five countries with the greatest number of samples (Additional File 1: Figure S4), excluding Senegal because of a tight clustering of sampling locations around the border with The Gambia (Additional File 1: Figure S2). In the eastern region, we selected all countries that had samples that were included in our modelling analysis (Additional File 1: Figure S5), excluding Tanzania due to a strong spatial clustering of the sampling observations (Additional File 1: Figure S3). Sudan is the most data-rich country included in our study (Additional File 1: Figure S5), but it covers a large spatial area and the sampling locations are all located in a region in the eastern part (Additional File 1: Figure S3). Therefore, we developed predictive maps only for a region in the east of Sudan that does not extend further west than a longitude of 29.5° E or further north of 17° N. In the case of Ethiopia, we excluded the region east of a longitude of 44° E because we have no samples located in this region.

We included one central African country, the Democratic Republic of Congo (DRC), in our mapping analysis. Although the Vgsc allele frequency data is sparse throughout the country (Additional File 1: Figures S2, S3 and S5), we included the DRC because it covers a region that is rarely studied. In the case of the DRC, our modelling analysis is restricted to predicting the frequency of the Vsgc-995F mutation only, and we do not predict Vsgc-995S frequencies (see below). We excluded the data on Vsgc-995S frequencies from the DRC analysis because most studies from the DRC only perform an assay capable of detecting L995F, which can lead to erroneous genotypes when both resistant alleles are present, which appears typical in DRC (Loonen 2020 [48], Lynd et al. 2018).

Potential predictor variables

Our set of predictors is similar to that described in Hancock et al. [5, 9] and includes 99 variables describing environmental characteristics that could potentially be related to the development and spread of insecticide resistance in populations of Anopheles gambiae complex mosquito species. These variables describe the coverage of insecticide-based vector control interventions, agricultural land use [49, 50], and the environmental fate of agricultural insecticides [51], other types of land use [49, 52,53,54], climate [49, 55, 56], and relative species abundance. A detailed description of this set of predictor variables is provided in Additional File 1: Table S3. Our vector control intervention data includes a variable estimating ITN coverage in terms of the proportion of people who slept under a net the preceding night, at each ~ 5 km pixel location for each year [57, 58]. Relative species abundance is represented by a variable estimating the abundance of An. arabiensis relative to the abundance of An. gambiae and An. coluzzii [21]. For all variables, we obtained spatially explicit data on a grid with a 2.5 arc-minute resolution (which is approximately 5 km at the equator) covering sub-Saharan Africa. For variables for which temporal data were available at an annual resolution, we included time-lagged representations with lags of 0, 1, 2, and 3 years.

Stacked generalization ensemble modelling approach

We used stacked generalization to develop a model ensemble that combines the predictions generated by multiple machine learning models [46, 59]. Stacked generalization uses a meta-model, or “generalizer”, that learns a weighted combination of the predictions across each model in the ensemble, where the predictions of each model are the out-of-sample predictions derived from K-fold cross validation. The predictions produced by the generalizer correct for the biases of each model and are expected to have improved prediction accuracy relative to any of the individual models included in the ensemble [46, 59, 60].

Machine learning models

Our model ensemble included three different machine learning models that predicted the frequencies of the Vgsc-995 L, Vgsc-995F, and Vgsc-995S at each pixel within our mapped countries for each year within the period 2005–2017. The three machine learning models were an extreme gradient boosting (XGB) model, a random forest (RF) model, and a neural network (NN) model. These models were chosen due to their demonstrated high predictive performance [60, 61], which derives from their ability to represent non-linear relationships and high-level interactions across the model features [5, 60]. The XGB model was implemented using the R package xgboost [62], and the RF and NN models were implemented using the sklearn [63] and keras packages [64] in Python. The label for these models was a categorical variable corresponding to whether the Vgsc-995 L, Vgsc-995F, or Vsgc-995S mutation was detected across all the alleles screened in each sample. All Vgsc allele frequency observations from the 27 countries in our data set were used to inform the model (see above). The models predict the expected frequencies of each allele at each mapped pixel. The features used in the models included the 99 environmental predictor variables together with the 1-, 2-, and 3-year lags for those variables that vary on a yearly time step. A factor variable representing the mosquito species (An. gambiae, An. coluzzii, An. arabiensis, or An. gambiae s.l) was also included as a feature, where the An. gambiae s.l. category describes individuals within samples for which species within the Anopheles gambiae complex were not identified. Finally, the year in which the bioassay and allele frequency samples were collected was also included as a feature. For each machine learning model, parameter tuning was performed using out-of-sample validation by subdividing the data into training, validation, and test subsets (see Additional File 1).

We developed an additional model ensemble that predicted only the frequency of Vsgc-995F, which we used to develop predictive maps of the Vsgc-995F frequency for the DRC. This model ensemble included the three machine learning models as described above, and the label was a categorical variable corresponding to whether the Vsgc-995F mutation was detected across all the alleles screened in the sample. The label included the full data set containing the Vsgc-995F frequencies in the 2418 samples. The features used were the same as those used in the above models, and parameter tuning was performed as described above.

Model stacking and multinomial logistic regression

We use a Bayesian multinomial logit regression model as our meta-model to combine the out-of-sample predictions obtained from performing K-fold cross-validation on each of the three machine learning models in the model ensemble [65,66,67] (see www.r-inla.org). The multinomial logit model represents observations where the sampling unit corresponds to one of a set of mutually exclusive alternatives j ∈ {1, …, J}; in our case J = 3, with the alternatives being the Vgsc-995 L, Vgsc-995F, or Vgsc-995S marker (we do not account for diploid genotypes in our model). Our observations yij are the numbers of Vgsc-995 L alleles (j = 1), Vsgc-995F alleles (j = 2), and Vsgc-995S alleles (j = 3) in sample i, with i = 1,….,N samples in total. Our model has three covariates which are the out-of-sample predictions of the frequencies of each allele in each sample given by the three machine learning models, transformed using the empirical logit transform to avoid discontinuities at 0 and 1. We store these covariates in the matrices X1, X2, and X3, which have dimension N × J, with each matrix containing the predictions of frequencies of the three alleles for one of the three machine learning models. Our multinomial logit model uses the following linear predictor:

$${V}_{ij}={\beta}_j^1{X}_{ij}^1+{\beta}_j^2{X}_{ij}^2+{\beta}_j^3{X}_{ij}^3$$

where there are three sets of three coefficients \({\beta}_j^1\), \({\beta}_j^2\)and \({\beta}_j^3\) (j = 1,2,3); we combine these into the vector Β. For each observation i, the expected probabilities of each alternative are:

$${p}_{ij}=\frac{g_{ij}\left(\mathrm{B}\right)}{G_i\left(\mathrm{B}\right)}$$

where gij(Β) =  exp (Vij) and \({G}_i=\sum_{j=1}^J{g}_{ij}\left(\mathrm{B}\right)\) (see Croissant [66] and www.r-inla.org). We use the multinomial-Poisson transformation [67], which gives the following expression for the Poisson likelihood [67]:

$$L\left({y}_{ij}|\mathrm{B},\phi \right)=\prod_i\prod_{j=1}^J{\left({g}_{ij}\left(\mathrm{B}\right)\mathit{\exp}\left({\phi}_i\right)\right)}^{y_{ij}}\mathit{\exp}\left(-{g}_{ij}\left(\mathrm{B}\right)\mathit{\exp}\left({\phi}_i\right)\right)$$

where ϕi are N additional parameters that need to be estimated in order to use the multinomial-Poisson transformation. Posterior distributions of the parameters Β and ϕi are obtained by fitting the model using the R-INLA package [65] (see www.r-inla.org), with the coefficients Β as fixed effects and the intercepts ϕi as an independent (iid) random effect. Our implementation constrains each of the nine coefficients to be positive \(\left({\beta}_j^q\ge 0,\forall j,q,q=1,2,3\right)\) [60]. Once the parameter estimation has been performed, the final set of predictions given by the model ensemble are obtained by replacing the elements of X1, X2, and X3 with the in-sample predictions of the machine learning models obtained by fitting each of these models to all the data (all the labels and the corresponding sets of features). For our second model ensemble for predicting only Vsgc-995F frequencies, the formulation of the meta-model is the same as described above, with J = 2.

Posterior validation

To assess the ability of our model to accurately represent the data, we performed posterior validation of our model ensemble using 10-fold out-of-sample cross-validation. Specifically, the data were divided into 10 subsets (or “test” sets, using random sampling without replacement), and 10 successive model fits were performed, each withholding a different test set. The test sets were withheld from each of the three machine learning models included in the ensemble, as well as from the multinomial logit metamodel. The root mean squared error (RMSE) across all (withheld) Vgsc allele frequency observations confirmed that the model ensemble delivered higher prediction accuracy than each of the three machine learning model constituents (Additional File 1: Table S1).

Insecticide resistance bioassay data

To analyse relationships between our predicted resistance allele frequencies and resistance phenotypes observed in field vector populations, we utilised a database of insecticide resistance bioassay data [5] including samples tested over the period 2005–2017. All species included in the samples are from the Anopheles gambiae complex and the composition of sibling species is unknown for the majority of samples. The data record the number of mosquitoes in the sample and the proportional sample mortality resulting from the bioassay, as well as variables describing the mosquitoes tested, the sample collection site, and the bioassay conditions and protocol. We selected the bioassay results for standard diagnostic dose WHO susceptibility tests performed using deltamethrin for all samples collected within the five countries included in our analysis (see the “Results” section), resulting in 159 results for Burkina Faso, 297 results for Benin, 184 results for Cameroon, 134 results for Ethiopia– and 256 results for Sudan. The bioassay data set included only two bioassay results for Equatorial Guinea and 22 bioassay results for Uganda, so we excluded these countries from our analysis of associations between our mapped Vgsc allele frequencies and the prevalence of insecticide resistance phenotypes. Susceptibility tests have a high measurement error; Hancock et al. [5] estimated that the measurement error associated with the sample proportional mortality had a standard deviation (sd) = 0.25 for bioassays performed using deltamethrin. Therefore, we used the predicted mean mortality to deltamethrin for Anopheles gambiae complex mosquitoes obtained from a series of annual predictive maps [5], using the predicted value for each sample collection location and year in our analysis.

Regression models of associations between resistance allele frequencies and mortality following exposure to deltamethrin

We assessed associations between the predicted mean mortality following exposure to deltamethrin and the predicted frequency of the Vsgc-995F allele. Mean mortality measurements represent the entire Anopheles gambiae complex, so we combined our species-specific predictions of Vsgc-995F frequencies across An. gambiae, An. coluzzii, and An. arabiensis to estimate the Vsgc-995F frequency in the An. gambiae complex for each sample collection location and year, fC, i:

$${f}_{C,i}={R}_{a,i}{f}_{a,i}+\left(1-{R}_{a,i}\right)\left({f}_{g,i}+{f}_{z,i}\right)/2$$
(1)

where Ra,i is the abundance of An. arabiensis at location i relative to the combined abundance of An. gambiae and An. coluzzii, and fa, i, fg, i, and fz, i are the predicted frequencies of the Vsgc-995F allele in An. arabiensis, An. gambiae, and An. coluzzii at location i, respectively. Values of the relative abundance of An. arabiensis at each geographic location were obtained from the maps developed by [21]. We do not have spatially explicit estimates of the relative abundances of An. gambiae and An. coluzzii, so we used the mean frequency across these two species in our calculation. We excluded Kenya from our regression analysis because frequencies of Vsgc-995F are low at our sampled locations (observed Vsgc-995F frequencies are less than 0.07 across 90% of samples). We tested the accuracy of our estimated Vgsc-995F frequencies for the An. gambiae complex (Eq. 1) against 797 of the observed Vgsc-995F sample frequencies in our data set that were representative of the An. gambiae complex [47] and found a good level of accuracy (Additional File 1: Figure S15).

We fitted OLS linear regression models to predict mean mortality to deltamethrin using fC, i as a covariate. Before model fitting, we applied the empirical logit transformation to both the independent variable and the covariate. To allow for serial autocorrelation in the data, we calculated Newey-West robust standard errors [68,69,70], using the sandwich package in R [70,71,72], specifying automated calculation of the bandwidth parameter.

Importance of potential explanatory variables

In order to identify which of our potential predictor variables were having the most impact on our modelled Vgsc allele frequencies, we calculated measures of the importance of each predictor variable for each of the machine-learning models used in our model ensemble. It is important to note that variable importance measures cannot be used to infer causality, and they can be difficult to interpret when predictor variables are correlated. For XGB, we used the gain measure calculated for each variable using the xgboost package [62], which is the fractional total reduction in the training error gained across all of that variable’s splits. For RF, we use the Gini importance, which is calculated using the sklearn package [63]. The Gini importance measures the influence of a variable in discriminating between classes in a classification algorithm [73]. For NN, we use the permutation importance, again calculated using the sklearn package. The permutation importance of a variable is obtained by randomly shuffling the values of the variable across all observations and recalculating the model score, which in our case is the prediction error across all data points.

Independent conditional expectation (ICE) analysis across varying ITN coverage

We studied how variation in ITN coverage impacted our model-predicted resistance allele frequencies using ICE analysis. For a single chosen location in each country, we calculated the ICE [27] of the model predicted Vsgc-995F frequency with varying ITN coverage for the year 2005. The ICE simply calculates the predicted response value from the model across a range of a focal predictor variable, keeping all other predictor variables fixed at their original values. This can be used to explore how the focal covariate influences the model predictions, by examining the shape and magnitude of the relationship. It is important to be aware, however, that the variation in the focal covariate is artificial and does not represent the actual variation in that particular covariate over space or time. Our ICE calculations represent variation in the model predictions for a single location and year only. The selected location within each country was chosen at random from the Vgsc allele frequency sampling locations for that country (the coordinates of each location are shown in Additional File 1: Table S4). We used our model ensemble to calculated predicted Vsgc-995F frequencies across values of the ITN coverage in the year 2005 from zero to one in intervals of 0.1.

Availability of data and materials

The data on Vgsc allele frequencies used in this study, together with the full series of annual predictive map for each Vgsc allele and species, are available on Figshare at https://figshare.com/articles/dataset/Vgsc_allele_frequencies_in_African_malaria_vector_species_field_data_and_predictive_map_data_grids/19082429 [74].

The computer code for fitting the geospatial statistical models is available on Github https://github.com/pahanc/mapping-vgsc-allele-frequencies [75].

References

  1. Bhatt S, Weiss DJ, Cameron E, Bisanzio D, Mappin B, Dalrymple U, et al. The effect of malaria control on Plasmodium falciparum in Africa between 2000 and 2015. Nature. 2015;526(7572):207–2011.

    Article  CAS  Google Scholar 

  2. Moyes CL, Lees RS, Yunta C, Walker KJ, Hemmings K, Oladepo F, et al. Assessing cross-resistance within the pyrethroids in terms of their interactions with key cytochrome P450 enzymes and resistance in vector populations. Parasites Vectors. 2021;14(1). https://doi.org/10.1186/s13071-021-04609-5.

  3. Tangena J-A, Hendricks CJM, Devine M, Tammaro M, Trett AE, de Pina A, et al. Indoor residual spraying for malaria control in Sub-Saharan Africa 1997 to 2017: an adjusted retrospective analysis. 2019:Available at SSRN: https://ssrn.com/abstract=tbc.

  4. World Health Organization. Prequalified products list. https://www.who.int/pq-vector-control/prequalified-lists/en/; 2020.

  5. Hancock PA, Hendriks CJM, Tangena JA, Gibson H, Hemingway J, Coleman M, et al. Mapping trends in insecticide resistance phenotypes in African malaria vectors. PLoS Biol. 2020;18(6). https://doi.org/10.1371/journal.pbio.3000633.

  6. Miles A, Harding NJ, Botta G, Clarkson CS, Antao T, Kozak K, et al. Genetic diversity of the African malaria vector Anopheles gambiae. Nature. 2017;552(7683):96.

  7. Clarkson CS, Miles A, Harding NJ, O'Reilly AO, Weetman D, Kwiatkowski D, et al. The genetic architecture of target-site resistance to pyrethroid insecticides in the African malaria vectors Anopheles gambiae and Anopheles coluzzii. Molecular Ecology. 2021;5303-17.

  8. World Health Organization. Global plan for insecticide resistance management in malaria vectors. Geneva: World Health Organization; 2012.

    Google Scholar 

  9. Moyes CL, Athinya DK, Seethaler T, Battle KE, Sinka M, Hadi MP, et al. Evaluating insecticide resistance across African districts to aid malaria control decisions. PNAS. 2020;117(36):22042–50.

    Article  CAS  Google Scholar 

  10. Ismail BA, Kafy HT, Sulieman JE, Subramaniam K, Thomas B, Mnzava A, et al. Temporal and spatial trends in insecticide resistance in Anopheles arabiensis in Sudan: outcomes from an evaluation of implications of insecticide resistance for malaria vector control. Parasit Vectors. 2018;11. https://doi.org/10.1186/s13071-018-2732-9.

  11. Weetman D, Wilding CS, Neafsey DE, Muller P, Ochomo E, Isaacs AT, et al. Candidate-gene based GWAS identifies reproducible DNA markers for metabolic pyrethroid resistance from standing genetic variation in East African Anopheles gambiae. Sci Rep. 2018;8. https://doi.org/10.1038/s41598-018-21265-5.

  12. Donnelly MJ, Isaacs AT, Weetman D. Identification, validation, and application of molecular diagnostics for insecticide resistance in malaria vectors. Trends Parasitology. 2016;32(3):197–206.

    Article  CAS  Google Scholar 

  13. Martinez-Torres D, Chandre F, Williamson MS, Darriet F, Berge JB, Devonshire AL, et al. Molecular characterization of pyrethroid knockdown resistance (kdr) in the major malaria vector Anopheles gambiae S.S. Insect Mol Biol. 1998;7(2):179–84.

    Article  CAS  Google Scholar 

  14. Ranson H, Jensen B, Vulule JM, Wang X, Hemingway J, Collins FH. Identification of a point mutation in the voltage-gated sodium channel gene of Kenyan Anopheles gambiae associated with resistance to DDT and pyrethroids. Insect Mol Biol. 2000;9(5):491–7.

    Article  CAS  Google Scholar 

  15. Jones CM, Liyanapathirana M, Agossa FR, Weetman D, Ranson H, Donnelly MJ, et al. Footprints of positive selection associated with a mutation (N1575Y) in the voltage-gated sodium channel of Anopheles gambiae. PNAS. 2012;109(17):6614–9.

    Article  CAS  Google Scholar 

  16. Clarkson CS, Weetman D, Essandoh J, Yawson AE, Maslen G, Manske M, et al. Adaptive introgression between Anopheles sibling species eliminates a major genomic island but not reproductive isolation. Nat Commun. 2014;5. https://doi.org/10.1038/ncomms5248.

  17. Miles A, Clarkson C, Donnelly M, Kwiatkowski D. The emergence and spread of insecticide resistance mutations in Anopheles gambiae and An-coluzzii: Insights from deep whole-genome sequencing of natural populations. Am J Trop Med Hyg. 2017;95(5):581.

  18. Barron M, Paupy C, Rahola N, Akone-Ella O, Ngangue MF, Wilson-Bahun T, et al. A new species in the major malaria vector complex sheds light on reticulated species evolution. Sci Rep. 2019;9. https://doi.org/10.1038/s41598-019-49065-5.

  19. Charlwood JD. The ecology of malaria vectors. Taylor and Francis: CRC Press; 2019.

    Book  Google Scholar 

  20. Wiebe A, Longbottom J, Gleave K, Shearer FM, Sinka ME, Massey NC, et al. Geographical distributions of African malaria vector sibling species and evidence for insecticide resistance. Malaria J. 2017;16:85.

    Article  Google Scholar 

  21. Sinka ME, Golding N, Massey NC, Wiebe A, Huang Z, Hay SI, et al. Modelling the relative abundance of the primary African vectors of malaria before and after the implementation of indoor, insecticide-based vector control. Malaria J. 2016;15. https://doi.org/10.1186/s12936-016-1187-8.

  22. Ranson H, N'Guessan R, Lines J, Moiroux N, Nkuni Z, Corbel V. Pyrethroid resistance in African anopheline mosquitoes: what are the implications for malaria control? Trends Parasitol. 2011;27(2):91–8.

    Article  CAS  Google Scholar 

  23. Pombi M, Kengne P, Gimonneau G, Tene-Fossog B, Ayala D, Kamdem C, et al. Dissecting functional components of reproductive isolation among closely related sympatric species of the Anopheles gambiae complex. Evolutionary Applications. 2017;10(10):1102–20.

    Article  Google Scholar 

  24. Simard F, Ayala D, Kamdem GC, Pombi M, Etouna J, Ose K, et al. Ecological niche partitioning between Anopheles gambiae molecular forms in Cameroon: the ecological side of speciation. BMC Ecology. 2009;9. https://doi.org/10.1186/1472-6785-9-17.

  25. Fontaine MC, et al. Extensive introgression in a malaria vector species complex revealed by phylogenomics. Science (New York, N.Y.). 2015;347:1258524. https://doi.org/10.1126/science.1258524.

  26. Hancock PA, Wiebe A, Gleave KA, Bhatt S, Cameron E, Trett A, et al. Associated patterns of insecticide resistance in field populations of malaria vectors across Africa. PNAS. 2018;115(23):5938–43.

    Article  CAS  Google Scholar 

  27. Goldstein A, Kapelner A, Bleich J, Pitkin E. Peeking inside the black box: visualizing statistical learning with plots of individual conditional expectation. J Computational Graphical Statistics. 2015;24(1):44–65.

    Article  Google Scholar 

  28. Lucas TCD. A translucent box: interpretable machine learning in ecology. Ecol Monogr. 2020;90(4). https://doi.org/10.1002/ecm.1422.

  29. Grigoraki L, Cowlishaw R, Nolan T, Donnelly M, Lycett G, Ranson H. CRISPR/Cas9 modified An. gambiae carrying kdr mutation L1014F functionally validate its contribution in insecticide resistance and combined effect with metabolic enzymes. Plos Genetics. 2021:doi.org/10.1371/journal.pgen.1009556.

  30. Mitchell SN, Rigden DJ, Dowd AJ, Lu F, Wilding CS, Weetman D, et al. Metabolic and target-site mechanisms combine to confer strong DDT resistance in Anopheles gambiae. Plos One. 2014;9(3). https://doi.org/10.1371/journal.pone.0092662.

  31. Edi CV, Djogbenou L, Jenkins AM, Regna K, Muskavitch MAT, Poupardin R, et al. CYP6 P450 enzymes and ACE-1 duplication produce extreme and multiple insecticide resistance in the malaria mosquito Anopheles gambiae. Plos Genetics. 2014;10(3). https://doi.org/10.1371/journal.pgen.1004236.

  32. Riveron JM, Huijben S, Tchapga W, Tchouakui M, Wondji MJ, Tchoupo M, et al. Escalation of pyrethroid resistance in the malaria vector anopheles funestus induces a loss of efficacy of piperonyl butoxide-based insecticide-treated nets in Mozambique. Journal of Infectious Diseases. 2019;220(3):467–75.

    Article  CAS  Google Scholar 

  33. Njoroge H, van’t Hof A, Oruni A, Pipini D, Nagi SC, Lynd A, et al. Identification of a rapidly-spreading triple mutant for high-level metabolic insecticide resistance in Anopheles gambiae provides a real-time molecular diagnostic for anti-malarial intervention deployment. bioRxiv. 2021. https://doi.org/10.1101/2021.02.11.429702.

  34. Lucas ER, Rockett KA, Lynd A, Essandoh J, Grisales N, Kemei B, et al. A high throughput multi-locus insecticide resistance marker panel for tracking resistance emergence and spread in Anopheles gambiae. Sci Rep. 2019;9. https://doi.org/10.1038/s41598-019-49892-6.

  35. Makunin A, Korlevic P, Park N, Goodwin S, Waterhouse RM, von Wyschetzki K, et al. A targeted amplicon sequencing panel to simultaneously identify mosquito species and Plasmodium presence across the entire Anopheles genus. Mol Ecol Resour. 2021;22(1):28-44.

  36. Mandeng SE, Awono-Ambene HP, Bigoga JD, Ekoko WE, Binyang J, Piameu M, et al. Spatial and temporal development of deltamethrin resistance in malaria vectors of the Anopheles gambiae complex from North Cameroon. Plos One. 2019;14(2). https://doi.org/10.1371/journal.pone.0212024.

  37. Lynd A, Weetman D, Barbosa S, Yawson AE, Mitchell S, Pinto J, et al. Field, genetic, and modeling approaches show strong positive selection acting upon an insecticide resistance mutation in Anopheles gambiae s.s. Mol Biol Evol. 2010;27(5):1117–25.

    Article  CAS  Google Scholar 

  38. Norris LC, Main BJ, Lee Y, Collier TC, Fofana A, Cornel AJ, et al. Adaptive introgression in an African malaria mosquito coincident with the increased usage of insecticide-treated bed nets. PNAS. 2015;112(3):815–20.

    Article  CAS  Google Scholar 

  39. Fornadel CM, Norris LC, Glass GE, Norris DE. Analysis of Anopheles arabiensis blood feeding behavior in southern Zambia during the two years after introduction of insecticide-treated bed nets. Am J Trop Med Hyg. 2010;83(4):848–53.

    Article  Google Scholar 

  40. Russell TL, Govella NJ, Azizi S, Drakeley CJ, Kachur SP, Killeen GF. Increased proportions of outdoor feeding among residual malaria vector populations following increased use of insecticide-treated nets in rural Tanzania. Malaria J. 2011;10. https://doi.org/10.1186/1475-2875-10-80.

  41. Sinka ME, Bangs MJ, Manguin S, Coetzee M, Mbogo CM, Hemingway J, et al. The dominant Anopheles vectors of human malaria in Africa, Europe and the Middle East: occurrence data, distribution maps and bionomic precis. Parasit Vectors. 2010;3. https://doi.org/10.1186/1756-3305-3-117.

  42. Mayagaya VS, Nkwengulila G, Lyimo IN, Kihonda J, Mtambala H, Ngonyani H, et al. The impact of livestock on the abundance, resting behaviour and sporozoite rate of malaria vectors in southern Tanzania. Malaria J. 2015;14. https://doi.org/10.1186/s12936-014-0536-8.

  43. Weetman D, Wilding CS, Steen K, Pinto J, Donnelly MJ. Gene flow-dependent genomic divergence between Anopheles gambiae M and S forms. Mol Biol Evol. 2012;29(1):279–91.

    Article  CAS  Google Scholar 

  44. Vicente JL, Clarkson CS, Caputo B, Gomes B, Pombi M, Sousa CA, et al. Massive introgression drives species radiation at the range limit of Anopheles gambiae. Sci Rep. 2017;7. https://doi.org/10.1038/srep46451.

  45. Hastie T, Tibshirani R, Friedman J. The elements of statistical learning. 2nd ed. doi:https://doi.org/10.1007/978-0-387-84858-7: Springer; 2009.

  46. Wolpert DH. Stacked generalization. Neural Networks. 1992;5(2):241–59.

    Article  Google Scholar 

  47. Moyes CL, Wiebe A, Gleave K, Trett A, Hancock PA, Padonou GG, et al. Analysis-ready datasets for insecticide resistance phenotype and genotype frequency in African malaria vectors. Scientific Data. 2019;6(1):121.

    Article  Google Scholar 

  48. Loonen JACM, Dery DB, Musaka BZ, Bandibabone JB, Bousema T, van Lenthe M, Pop-Stefanija B, Fesselet JF, Koenraadt CJM. Identification of main malaria vectors and their insecticide resistance profile in internally displaced and indigenous communities in Eastern Democratic Republic of the Congo (DRC). Malar J. 2020;19(1):425. https://doi.org/10.1186/s12936-020-03497-x.

  49. Friedl M, Sulla-Menashe D. MCD12Q1 MODIS/Terra+Aqua Land Cover Type Yearly L3 Global 500m SIN Grid V006. NASA EOSDIS Land Processes DAAC; 2015.

  50. You L, Wood-Sichra U, Fritz S, Guo Z, See L, Koo J. Spatial production allocation model (SPAM) 2005 v2.0: mapspam.info; [Available from: mapspam.info.

  51. Hendriks CJM, Gibson H, Trett A, Python A, Weiss DJ, Vrieling A, et al. Mapping geospatial processes affecting the environmental fate of agricultural pesticides in Africa. Int J Environ Res Public Health. 2019;16(3523):https://doi.org/10.3390/ijerph16193523.

  52. Tatem AJ. WorldPop, open data for spatial demography. Scientific Data. 2017;4.

  53. Esch T, Heldens W, Hirner A, Keil M, Marconcini M, Roth A, et al. Breaking new ground in mapping human settlements from space - The Global Urban Footprint. ISPRS J Photogrammetry Remote Sensing. 2017;134:30–42.

    Article  Google Scholar 

  54. Sulla-Menashe D, Gray JM, Abercrombie SP, Friedl MA. Hierarchical mapping of annual global land cover 2001 to present: The MODIS Collection 6 Land Cover product. Remote Sensing Environm. 2019;222:183–94.

    Article  Google Scholar 

  55. Funk C, Peterson P, Landsfeld DP, Verdin J, Shukla S, Husak G, et al. The climate hazards infrared precipitation with stations - a new environmental record for monitoring extremes. Scientific Data. 2015;2. https://doi.org/10.1038/sdata.2015.66.

  56. Trabucco A, Zomer RJ. Global Aridity Index (Global-Aridity) and Global Potential Evapo-Transpiration (Global-PET) Geospatial Database. CGIAR-CSI GeoPortal; 2009. https://doi.org/10.7554/eLife.09672.

  57. Bhatt S, Weiss DJ, Mappin B, Dalrymple U, Cameron E, Bisanzio D, et al. Coverage and system efficiencies of insecticide-treated nets in Africa from 2000 to 2017. ELife. 2015;4.

  58. Weiss DJ, Lucas TCD, Nguyen M, Nandi A, Bisanzio D, Battle KE, et al. Mapping the global prevalence, incidence, and mortality of Plasmodium falciparum, 2000-17: a spatial and temporal modelling study. Lancet. 2019;394(10195):322–31.

    Article  Google Scholar 

  59. Ting KM, Witten IH. Stacked generalization: when does it work? In: Pollack ME, editor. Ijcai-97 - Proceedings of the Fifteenth International Joint Conference on Artificial Intelligence, Vols 1 and 2. International Joint Conference on Artificial Intelligence1997. p. 866-871. https://doi.org/10.1098/rsif.2017.0520.

  60. Bhatt S, Cameron E, Flaxman SR, Weiss DJ, Smith DL, Gething PW. Improved prediction accuracy for disease risk mapping using Gaussian process stacked generalization. J R Soc Interface. 2017;14(134).

  61. Crisci C, Ghattas B, Perera G. A review of supervised machine learning algorithms and their applications to ecological data. Ecological Modelling. 2012;240:113–22.

    Article  Google Scholar 

  62. Chen T, Guestrin C. XGBoost: A scalable tree boosting system. Proceedings of the 22nd ACM SIGDD International Conference on Knowledge Discovery and Data Mining. KDD ‘16. New York: ACM; 2016. p. 785-94.

  63. Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, et al. Scikit-learn: machine learning in Python. J Machine Learn Res. 2011;12:2825–30.

    Google Scholar 

  64. Chollet F, others. 2015 [Available from: https://keras.io.

  65. Rue H, Martino S, Chopin N. Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. J Royal Stat Soc Series B-Stat Methodol. 2009;71:319–92.

    Article  Google Scholar 

  66. Croissant Y, editor Estimation of multinomial logit models in R : The mlogit Package2010.

  67. Baker SG. The Multinomial-Poisson transformation. Statistician. 1994;43(4):495–504.

    Article  Google Scholar 

  68. Cameron AC, Miller DL. A practitioner’s guide to cluster-robust inference. J Human Resources. 2015;50(2):317–72.

    Article  Google Scholar 

  69. Conley TG. GMM estimation with cross sectional dependence. J Econometrics. 1999;92(1):1–45.

    Article  Google Scholar 

  70. Newey WK, West KD. A simple, positive semidefinite, heteroskedasticity and autocorrelation consistent covariance-matrix. Econometrica. 1987;55(3):703–8.

    Article  Google Scholar 

  71. Zeileis A, Köll S, Graham N. Various versatile variances: an object-oriented implementation of clustered covariances in R. J Stat Software. 2020;95:1–36.

    Article  Google Scholar 

  72. Zeileis A. Econometric computing with HC and HAC covariance matrix estimators. J Stat Software. 2004;11:1–17.

    Article  Google Scholar 

  73. Breiman L. Random forests. Machine Learn. 2001;45(1):5–32.

    Article  Google Scholar 

  74. Hancock PA, Lynd A, Wiebe A, Devine M, Essandoh J, Wat’senga F, et al. Vgsc allele frequencies in African malaria vector species: field data and predictive map data grids. figshare https://doi.org/10.6084/m9.figshare.19082429.v1 2022.

  75. Hancock PA. pahanc/mapping-vgsc-allele-frequencies. 10.5281/zenodo.5905730 2022.

Download references

Acknowledgements

We are grateful to Chantal Hendriks and Harry Gibson for their help in interpreting the predictor variables that informed our models. We thank Joseph Chabi, Edi Constant, Samuel Dadzie, Luc Djogbenou, Alex Egyir Yawson, Xavier Grau Bove, Seth Irish, Bilali Kabula, Eric Lucas, Daniel McDermott, Sanje Nagi, Eric Ochomo, and Sean Tomlinson for discussions that helped in developing this work.

Funding

This work was funded by the National Institute of Health (NIH grant R01-AI116811) and the Wellcome Trust Grant 108440/Z/15/Z (awarded to CLM)

Author information

Authors and Affiliations

  1. Big Data Institute, University of Oxford, Oxford, OX3 7LF, UK

    Penelope A. Hancock, Antoinette Wiebe, Maria Devine & Catherine L. Moyes

  2. Department of Vector Biology, Liverpool School of Tropical Medicine, Liverpool, L35QA, UK

    Amy Lynd, John Essandoh, Martin J. Donnelly & David Weetman

  3. Institut National de Recherche Biomédicale, PO Box 1192, Kinshasa, Democratic Republic of Congo

    Francis Wat’senga & Emile Z. Manzambi

  4. USAID President’s Malaria Initiative, VectorLink Project, Abt Associates, 6130 Executive Blvd 16, Rockville, MD, 20852, USA

    Fiacre Agossa

Authors
  1. Penelope A. Hancock
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Amy Lynd
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Antoinette Wiebe
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Maria Devine
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. John Essandoh
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Francis Wat’senga
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Emile Z. Manzambi
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Fiacre Agossa
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Martin J. Donnelly
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. David Weetman
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Catherine L. Moyes
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

PAH designed the study, conducted the spatiotemporal modelling analysis, and wrote the paper; AL, AW, MD, and JE contributed Vgsc allele frequency data and commented on manuscript drafts; FW, EZM, and FA contributed Vgsc allele frequency data; MJD and DW contributed Vgsc allele data, assisted with the study design, and contributed to writing the paper; and CLM processed and analysed Vgsc allele frequency data, assisted with the study design, and contributed to writing the paper. The authors read and approved the final manuscript.

Corresponding author

Correspondence to Penelope A. Hancock.

Ethics declarations

Ethics approval and consent to participate

Not applicable

Consent for publication

Not applicable

Competing interests

The authors declare that they have no competing interests.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Additional file 1:

Additional results and information to support this manuscript, including: Figure S1. Results of 10-fold out-of-sample posterior validation for the spatiotemporal model ensemble. Figures S2 & S3. Sampling locations of the observed frequencies of the Vgsc-995F and Vgsc-995S markers in Africa that were included in our modelling analysis. Figures S4 & S5. The number of samples of the frequencies of the Vgsc-995F and Vgsc-995S markers included in our data set for each country. Figure S6. The total number of Vgsc allele frequency observations that were used to inform the spatiotemporal model ensemble by each year and each vector species. Figure S7. The abundance of An. arabiensis relative to the combined abundance of An. gambiae and An. coluzzii in the nine mapped countries. Figures S8, S9, S10 & S11. Associations between predicted frequencies of Vgsc mutations across species. Figures S12, S13 & S14. The ITN coverage across the nine mapped countries in years 2005, 2011 and 2017. Figure S15. The predicted L1014F frequency in the An. gambiae complex derived from combining species-specific frequencies (eq 1) vs observed frequencies. Table S1. The root mean square error (RMSE) and the mean absolute error (MAE) across the out-of-sample predictions of all Vgsc allele frequency observations, obtained using 10-fold cross validation. Table S2. Countries that were included in (i) each type of mapping analysis, and (ii) in the analysis of relationships between deltamethrin resistance phenotype and Vgsc mutation frequencies. Table S3. Descriptions of each potential explanatory variable used in the ensemble model.

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hancock, P.A., Lynd, A., Wiebe, A. et al. Modelling spatiotemporal trends in the frequency of genetic mutations conferring insecticide target-site resistance in African mosquito malaria vector species. BMC Biol 20, 46 (2022). https://doi.org/10.1186/s12915-022-01242-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1186/s12915-022-01242-1

Keywords

  • Insecticide target-site resistance
  • Resistance surveillance
  • Malaria vector control
  • Genetic resistance markers
  • Geostatistical model
  • Anopheles
  • spatiotemporal model
  • Mapping resistance
  • Multinomial model

BMC Biology

ISSN: 1741-7007

Contact us