Philippa Kaur

The following section assesses our main results in terms of the growth in fenced areas over time relative to 1) types of protection, 2) administrative boundaries, and 3) other fences.Fencing relative to land governanceAcross the Greater Mara, a general growth in fenced areas can be observed throughout the 00 s but in particular over the last decade (Fig. 1). Based on satellite images, 35,067 ha were fenced in 1985, corresponding to c. 5%. In the following 25 years there was only an insignificant increase in fenced plots. However, from 2010, the number of fences suddenly grew rapidly, and in the following period (2015–2020) the fenced area increased even more radically, in an exponential manner (Fig. 2). For example, in 2015 there was 63,112 ha of fenced land; in 2016 this number rose to c. 75,176 ha, corresponding to a c. 20% annual increase. From 2010 to 2020, the ha fenced area increased by 170%. This corresponds to a roughly four times increase in the area enclosed by fences during the study period (1985–2020).Figure 2Conservative estimate of the fenced area of the entire Greater Mara, Kenya (1985–2020) expressed in hectares.Full size imageIn almost all regions, the number of fences continued to increase in 2019–20 (Fig. 2). The result is a total of 130,277 ha of fenced land in 2020, corresponding to 19% of the Greater Mara.Hence, there appears to be a building momentum in the expansion of fences in the Greater Mara: those regions that had many fences in 2016 ( > 1,000 ha) continue to experience an increase in the area enclosed by fences, with fences spreading almost everywhere in 2020 in particular. Those regions with the fewest fences in 2016 ( More

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Testing H1 and H2 at community composition levelAs noted above, the simple fact that fungi grow more slowly than bacteria is the basis of the hypotheses that (H1) fungal communities should be more resistant than bacterial communities to drought stress, and (H2) that fungal communities should be less resilient than bacterial communities when the stress is relieved by rewetting18. In addition to growth rate, these two hypotheses may be related to differences in the form of growth between fungi and bacteria. For example, multicellular hyphal growth versus unicellular division or the greater thickness of fungal cell walls as compared to those of bacteria47,48. We tested H1 and H2 at the community composition level by blending the fungal and bacterial datasets generated from the same leaf, root, rhizosphere and soil samples collected from field-grown sorghum that had been either irrigated as a control, or subjected to preflowering drought followed by regular wetting beginning at flowering10,11.We followed the approach of Shade et al.17 to detect resistance and resilience, which had been developed for univariate variables, e.g., richness. For multivariate data, e.g., community composition, we modified it by calculating pairwise community dissimilarity for two groups: within-group (control-control pairs, drought-drought pairs, or rewetting-rewetting pairs), and between-group (control-drought pairs, or control-rewetting pairs). Ecological resistance to drought stress is detected by comparing compositional dissimilarity of between-group pairs (control-drought pairs) against within-group pairs (control-control pairs and drought-drought pairs) for each of the droughted weeks (weeks 3–8). Ecological resilience to rewetting is detected by assessing, from before to after rewetting, the change in the difference of compositional dissimilarity between within-group pairs and between-group pairs. Here, the point just before rewetting was week 8 and the points after rewetting were weeks 9–17. A t-test was used to assess the statistical significance of the differences in resistance or resilience between bacterial and fungal communities at each time point for each compartment.To account for the different resolutions of ITS and 16 S, we compared bacterial 16 S OTUs against both fungal ITS, species-level OTUs as well the fungal family level (Supplementary Fig. 1). The results of analyses using either fungal families or OTUs are consistent. Out of 36 comparisons (15 roots, 15 rhizospheres and 6 soils), different family and OTUs results were detected in four instances. In two of these, significances detected by OTUs were not detected by family (root, weeks 4 and 17) and, in the other two cases, significances detected by family were not detected by OTUs (rhizosphere, weeks 7 and 8). (Fig. 1). We report only results that are consistent at both the species and family levels (Fig. 1).In line with our first hypothesis, H1, we found that the resistance to drought stress for fungal mycobiomes was consistently stronger than that for bacterial microbiomes for weeks 5 in root, weeks 4–6 in rhizosphere, and weeks 4 and 6–8 in soil (Fig. 1, Supplementary Fig. 1 and Supplementary Table 2). In support of our second hypothesis, H2, when the stress of pre-flowering drought was relieved by rewetting, we found that the resilience of the bacterial communities was consistently higher than that for the fungi in weeks 9–16 in root, and weeks 11–17 in rhizosphere (Fig. 1, Supplementary Fig. 1 and Supplementary Table 2).Surprisingly, we found that resilience was stronger for fungal than bacterial communities in the first week (week 9) of rewetting in the rhizosphere (Fig. 1, Supplementary Fig. 1 and Supplementary Table 2). This high resilience of fungi may be associated with the quick growth of sorghum roots when rewetted. The rhizosphere zone around these newly formed roots may be quickly colonized by soil fungi, a community that was weakly affected by drought. This result suggests that re-assembly of the rhizosphere microbial community is more complex than previously expected.The finding that fungal community composition in the soil is not shaped by drought prevented us from further detecting resilience (Fig. 1). Note fungal community in early leaves was excluded from analysis due to the high proportion of non-fungal reads in sequencing11.Testing H1 and H2 at all-correlation levelNext, we moved from the comparison of whole communities to correlation among individual bacterial and fungal taxa to test the hypotheses about resistance, H1, and resilience, H2. As noted above, previous research provided the foundation for the stress gradient hypothesis, which predicts an increase in positive associations in stress32,33,34,35,36,37. Further, ecological modeling predicts that negative associations promote stability40. Concerning specific associations, studies of Arabidopsis and associated microbes reported that positive associations are favored within kingdoms, i.e., within bacteria or within fungi, while negative associations predominate between kingdoms38,39. Given these foundations, concerning H1, we expected an increase in the proportion of positive correlation by drought stress that would be strongest for B-B, followed by F-F, and lastly by B-F; for H2 we expected rewetting to cause a decrease in the proportion of positive correlation, again most strongly for B-B, followed by F-F, and lastly by B-F.Overall, at the all-correlation level, we found no consistent support for the differences postulated for bacterial and fungal responses in H1. For example, strong increases in the proportion of positive correlations under drought could be found in all microbial pairings for some compartments (B-B in leaf and root, F-F in rhizosphere and soil, and B-F in root and rhizosphere) (Fig. 2a, Supplementary Figs. 2, 3). Neither did we find consistent support for the differences ascribed to bacteria and fungi in H2 as the strongest decreases in the proportion of positive correlations during rewetting occurred at F-F in rhizosphere and soil, and B-B in leaf and root (Fig. 2b, Supplementary Figs. 2, 3).Fig. 2: Correlations of microbes in drought stress and drought relief.Estimates of combined correlations (row a) show an increase in positive correlations under drought stress across the four compartments (root, black; rhizosphere, blue; soil, red; leaf, green). Data points underlying the lines in the figure are provided in the alternative version in Supplementary Fig. 2. This result is in line with the stress gradient hypothesis which posits that stressful environments favor positive associations because competition will be less intense than in benign environments32,33,36,37. Note that positive trends in combined correlations can arise in two ways. First, from an increase of positive correlations (row b) that exceeds the rise in negative correlations (row c), e.g., Leaf bacterial-bacterial (Bac-Bac) correlations or rhizosphere fungal-fungal (Fun-Fun) correlations in the drought period (Negative correlations in row C values are multiplied by −1 to facilitate comparison). Second, from a decrease in negative correlations that exceeds a decrease in positive correlations, e.g., root bacterial-bacterial correlations or root bacterial-fungal (Bac-Fun) correlations in drought. Combined (a), positive (b) and negative (c) estimates of correlation (Spearman’s rho, ρ) are given for four compartments (root, rhizosphere, soil and leaf), and three types of correlations (Bacterium-Bacterium, Fungus-Fungus, Bacterium-Fungus). T-tests (two sided) were carried out for linear mixed effect modelling that incorporates link type and compartments as random factors. Detailed distribution densities of correlations are presented in Supplementary Fig. 3. Source data are provided as a Source Data file.Full size imageWe found support for the stress gradient hypothesis because drought increased the relative frequency of positive correlations among microbial taxa (Fig. 2a, Supplementary Figs. 2, 3). The increases were due, largely, to B-B correlations in leaf and F-F correlations in the rhizosphere during drought, when the relative frequency of positive correlations was increased (Fig. 2b, Supplementary Figs. 2, 3) and the frequencies of negative correlations were decreased or weakly increased (Fig. 2c, Supplementary Figs. 2, 3). Less obvious increases in the relative frequency of positive correlations (such as B-B in root, F-F in soil, and B-F in root and rhizosphere) occurred where drought reduced both positive and negative correlations, but the losses of negative correlations exceeded those of positive correlations (Fig. 2, Supplementary Figs. 2, 3).In support of the expectation that correlations would be more negative between taxonomic groups than within taxonomic groups, we found that the relative frequency of positive correlations was generally lower for B-F than B-B and F-F correlations (Fig. 2, Supplementary Figs. 2, 3). Moreover, as ecological modeling has indicated that negative associations should promote stability of communities40, we hypothesize that B-F correlations would be more stable than B-B and F-F networks in response to drought stress. However, we found no support for this hypothesis, as B-F correlations (for example in root) did not always show the least response to drought stress (Fig. 2, Supplementary Figs. 2, 3).Testing H1 and H2 at species co-occurrence levelFor our final test of H1 (resistance) and H2 (resilience) we focused on co-occurrence networks based on significant, positive correlations. These networks have been reported to be destabilized for bacteria but not for fungi in mesocosms subject to drought stress19, and shown to be disrupted for bacteria in natural vegetation studied over gradients of increasing aridity41,42. Using these results as guides, for H1 we expected that drought stress should disrupt co-occurrence networks most strongly for B-B, followed by F-F, and lastly by B-F. For H2 we expected that relief of stress by rewetting should strengthen microbial co-occurrence networks most strongly for B-B, followed by F-F, and lastly by B-F.For this test we constructed microbial co-occurrence networks using significant positive pairwise correlations between microbial taxa, B-B, F-F and B-F, and compared the network complexity between fully irrigated control and drought, and between control and rewetting following drought. In general, we found no consistent support for the difference between bacteria and fungi inherent in H1. Rhizosphere was the one compartment where B-B vertices dropped and F-F vertices rose in response to drought, as expected, but this result was offset in root and soil, where vertices dropped in all networks, B-B, F-F and B-F (Figs. 3, 4; Supplementary Figs. 4, 5). Analysis by co-occurrence networks highlighted the differences between plant compartments. In root drought strongly disrupted networks of B-B, B-F and F-F, but in the other three compartments, network disruption was weaker, and networks were even enhanced by drought for F-F in rhizosphere and B-B in leaf (Figs. 3, 4).Fig. 3: Networks of significant positive cross-taxonomic group correlations (bacteria and fungi).a Fungal operational taxonomic units (OTUs) (blue) and bacterial OTUs (black) are graphed as nodes. Significant positive Spearman correlations are graphed as edges (ρ  > 0.6, false discovery rate adjusted P  More

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Overview of the study areaBased on the actual cultivation of peanuts, the Huang-Huai-Hai region is selected as the study area (Fig. 1). The main body of the study area is the Huang-Huai-Hai Plain (North China Plain), which is a typical alluvial plain resulting from extensive sediment deposition carried by the Yellow River, the Huaihe River and the Haihe River and their tributaries, and the hills in central and southern Shandong Peninsula adjacent to it. Administrative zones include 5 provinces, 2 cities, 53 cities and 376 counties (districts). In China, The Huang-Huai-Hai region is an important production and processing centre for agricultural products, with a total land area of 4.10 × 105 square kilometers and cultivated fields of 2.15 × 107 hm2, accounting for 4.3% and 16.3% of the total amount of the country, respectively. It belongs to temperate continental monsoon climate with distinct seasons, accumulated temperature of 3600–4800 degrees above 10 °C, frost-free period of 170–200 days and annual precipitation of 500–950 mm27. The Huang-huai-hai region is the largest peanut growing area, accounting for more than 50% of the country’s peanut production and area28.Figure 1Location of the study areas. The figure was made in the ArcGIS 10.2 platform (https://www.esri.com/en-us/home).Full size imageData sourcesThe data used in the study mainly include meteorological data, geographic information data and crop data. The meteorological data comes from China Meteorological Information Center (http://data.cma.cn), including the daily maximum temperature (℃), daily minimum temperature (℃), daily average temperature (℃), daily precipitation (mm) and daily average wind speed (M/s) observed by 186 ground observation meteorological stations in the Huang-Huai-Hai region from 1960 to 2019 (Fig. 1). Geographic information data include elevation DEM data (resolution of 1 km × 1 km) and land use data in the study area, which are from the resource and environmental science and data center of Chinese Academy of Sciences (http://www.resdc.cn). Crop data, including peanut sowing area and yield data, are derived from the statistical yearbooks of provinces and cities in the study area and China Agricultural Technology Network (http://www.cast.net.cn).Data processingMeteorological data processingAnusplin software is a tool to interpolate multivariate data based on ordinary thin disks and local thin disk spline functions, enabling the introduction of covariates for simultaneous spatial interpolation of multiple surfaces, suitable for meteorological data time series29. First, the Anusplin software is used to spatially interpolate the meteorological data and suitability data of the peanut growing season (April to September) from 1960 to 2019 based on the elevation data with a resolution of 1 km × 1 km. The Inverse Distance Weight (IDW) interpolation can make the meteorological data after Anusplin interpolation maintain consistency with the original data, and is able to improve the interpolation accuracy. Finally, the meteorological and suitability data set with a resolution of 1 km × 1 km is obtained. ArcGIS and MATLAB software were used to count the median of regional meteorological factors in agricultural fields of different cities (counties), and the meteorological factors and suitability of different periods of peanut growth season in each city (county) were obtained.Yield data processingMany factors affect crop yield formation, which can be generally divided into three main categories: meteorological conditions, agronomic and technological measures, and stochastic factors. Agricultural technical measures reflect the development level of social production in a certain historical period and become time technology trend output, which is referred to as trend output for short, and meteorological production reflects short period yield components that are affected by meteorological elements. Stochastic factors account for a small proportion and are often ignored in actual calculations30. The specific calculation is as follows:$$Y={Y}_{t}+{Y}_{w}$$
(1)

where Y is the actual yield (single production) of the crop, Yt is the trend yield, and Yw is the meteorological yield.In this paper, a straight-line sliding average method is used to simulate the trend yield. The straight-line sliding average method is a very commonly used method to model yield, and it considers the change in the time series of yield within a certain stage as a linear function, showing a straight line, as the stage continuously slides, the straight line continuously changes the position, and the backward slip reflects the continuous change in the evolution trend of the yield history31. The regression models in each stage are obtained in turn, and the mean value of each linear sliding regression simulation value at each time point is taken as its trend yield value. The linear trend equation at some stage is:$${Y}_{i}left(tright)={a}_{i}+{b}_{i}t$$
(2)
where i = n-k + 1, is the number of equations; k is the sliding step; n is the number of sample sequences; t is the time serial number. Yi(t) is the function value of each equation at point t. there are q function values at point t. the number of q is related to n and k. Calculate the average value of each function value at each point:$$overline{{Y }_{i}(t)}=frac{1}{q}sum_{j=1}^{q}{Y}_{i}left(tright)$$
(3)
Connecting the (overline{{Y }_{i}(t)}) value of each point can represent the historical evolution trend of production. Its characteristics depend on the value of k. Only when k is large enough, the trend yield can eliminate the influence of short cycle fluctuation. After comparison and considering the length of yield series, k is taken as 5 in this paper.After the trend yield is obtained, the meteorological yield is calculated using Eq. (1), then the relative meteorological production is$${Y}_{r}=frac{{Y}_{w}}{{Y}_{t}}$$
(4)
The relative meteorological yield shows that the relative variability of yield fluctuation deviating from the trend, that is, the amplitude of yield fluctuation, is not affected by time and space, and is comparable. However, when the value is negative, it indicates that the meteorological conditions are unfavorable to the overall crop production, and the crop yield reduction, that is, the yield reduction rate32.Characteristics of spatial and temporal distribution of climatic resources in the Huang-Huai-Hai regionCollect meteorological resource data from 1960 to 2019. Taking 1960–1989 as the first three decades of the study and 1990–2019 as the last three decades, the climatic resource changes of peanut growth in the Huang-Huai-Hai region are analyzed by interpolation of heat resources (average temperature), water resources (precipitation) and light resources (sunshine hours) in the study area in two periods combined with topographic factors.Establishment of suitability modelAccording to the definition of phenological time and growth period of peanut planting practice in the Huang-Huai-Hai region, the growth season of peanut is divided into three growth periods and five growth stages (Table 1). Temperature, precipitation and sunshine hours are the necessary meteorological factors to determine the normal development of peanut. Therefore, combined with climatic resources in the study area, temperature, precipitation and sunshine suitability model was introduced to quantitatively analyze the suitability of peanut planting.Table 1 Division of peanut growth periods.Full size tableTemperature suitability modelTemperature is a very important factor in the growth period of peanut, and the change of temperature in different growth periods will have a great influence on the yield and quality of peanut. As a warm-loving crop, accumulated temperature plays a decisive role in the budding condition and nutrient growth stage of peanut. Temperature determines the quality of fruit and the final yield of peanut. Beta function33 is used to calculate temperature suitability, which is universal for crop-temperature relationship. The specific calculation is as follows:$${F}_{i}left(tright)=frac{(t-{t}_{1}){({t}_{h}-t)}^{B}}{({t}_{0}-{t}_{1}){({t}_{h}-{t}_{0})}^{B}}$$
(5)
where the value of B is shown in$$B=frac{{t}_{h}-{t}_{0}}{{t}_{0}-{t}_{1}}$$
(6)
where Fi(t) is the temperature suitability of a certain growth period; t is the daily average temperature of peanut at a certain development stage; t1, th and t0 are the lower limit temperature, upper limit temperature and appropriate temperature required for each growth period of peanut. Refer to the corresponding index system and combined with the peanut production practice in Huang-Huai-Hai region34,35,36, determine the three base point temperature of peanut in each growth period, as shown in the Table 2.Table 2 Three fundamental points temperature and crop coefficient of peanut at each growth stage in the study area.Full size tablePrecipitation suitability modelPeanut has a long growth period, which is nearly half a year. Insufficient or excessive water during the growth period has a great impact on the growth and development, pod yield and quality of peanut. Combined with the actual situation of Huang-Huai-Hai region and peanut precipitation / water demand index, the water suitability function is determined and calculated as follows:$${text{F}}_{{text{i}}} left( {text{r}} right) = left{ {begin{array}{*{20}l} {frac{{text{r}}}{{0.9{text{ET}}_{{text{c}}} }}} hfill & {r < 0.9E{text{T}}_{{text{c}}} } hfill \ 1 hfill & {0.9E{text{T}}_{{text{c}}} le r le 1.2E{text{T}}_{{text{c}}} } hfill \ {frac{{1.2{text{ET}}_{{text{c}}} }}{{text{r}}}} hfill & {r > 1.2E{text{T}}_{{text{c}}} } hfill \ end{array} } right.$$
(7)
where Fi(r) is the water suitability of a certain growth period; r is the accumulated precipitation of peanut in a certain development period; ETc is the water demand of peanut in each growth period.$${mathrm{ET}}_{mathrm{c}}={mathrm{K}}_{mathrm{c}}cdot {mathrm{ET}}_{0}$$
(8)
where Kc is the peanut crop coefficient (Table 2) and ET0 is the crop reference evapotranspiration, which is calculated by the Penman Monteith method recommended by the international food and Agriculture Organization (FAO).Sunshine suitability modelSunshine hours are an important condition for photosynthesis. The “light compensation point” and “light saturation point” of peanut are relatively high, and more sunshine hours are required for photosynthesis. Under certain conditions of water, temperature and carbon dioxide, photosynthesis increases or decreases with the increase or decrease of light. Relevant studies show that when the sunshine hours reach more than 55% of the available sunshine hours, the crops reach the appropriate state to reflect the light37. The following formula is used to calculate the sunshine suitability of peanut in each growth period.$${mathrm{F}}_{mathrm{i}}left(mathrm{s}right)=left{begin{array}{l}frac{mathrm{S}}{{mathrm{S}}_{0}} quad S{mathrm{S}}_{0}end{array}right.$$
(9)
where Fi(s) is the sunshine suitability of peanut in a certain development period, S is the actual sunshine hours in a certain growth period, S0 is 55% of the sunshine hours (L0), and the calculation method of L0 refers to the following formula.$${mathrm{L}}_{0}=frac{2mathrm{t}}{15}$$
(10)
$$mathrm{sin}frac{mathrm{t}}{2}=sqrt{frac{mathrm{sin}(45^circ -frac{mathrm{varnothing }-updelta -upgamma }{2})times mathrm{sin}(45^circ +frac{mathrm{varnothing }-updelta -upgamma }{2})}{mathrm{cosvarnothing }times mathrm{cosdelta }}}$$
(11)
where Φ is the geographic latitude, δ is the declination, γ is the astronomical refraction, t is the angle.Comprehensive suitability modelPeanut has different needs for meteorological elements such as temperature, sunshine and precipitation in different growth periods. In order to analyze the impact of meteorological factors in different growth periods on yield, correlation analysis was conducted between the suitability of temperature, precipitation and sunshine in each growth period and the relative meteorological yield of peanut, and the correlation coefficient of each growth period divided by the sum of the correlation coefficients of the whole growth period was used as the weight coefficient of the suitability of temperature, precipitation and sunshine in each growth period (Table 3). The climatic suitability of each single element in peanut growing season is calculated by using formulas (12) and (13):Table 3 The weight coefficients of climatic suitability at each growth stage.Full size table$$left{begin{array}{c}{mathrm{b}}_{mathrm{ti}}=frac{{mathrm{a}}_{mathrm{ti}}}{sum_{mathrm{i}=1}^{mathrm{n}}{mathrm{a}}_{mathrm{ti}}}\ {mathrm{b}}_{mathrm{ri}}=frac{{mathrm{a}}_{mathrm{ri}}}{{sum }_{mathrm{i}=1}^{mathrm{n}}{mathrm{a}}_{mathrm{ri}}}\ {mathrm{b}}_{mathrm{si}}=frac{{mathrm{a}}_{mathrm{si}}}{{sum }_{mathrm{i}=1}^{mathrm{n}}{mathrm{a}}_{mathrm{si}}}end{array}right.$$
(12)
$$left{begin{array}{c}F(t)={sum }_{mathrm{i}=1}^{mathrm{n}}left[{mathrm{b}}_{mathrm{ti}}{mathrm{F}}_{mathrm{i}}(mathrm{t})right]\ F(r)={sum }_{mathrm{i}=1}^{mathrm{n}}left[{mathrm{b}}_{mathrm{ri}}{mathrm{F}}_{mathrm{i}}(mathrm{r})right]\ F(s)={sum }_{mathrm{i}=1}^{mathrm{n}}left[{mathrm{b}}_{mathrm{si}}{mathrm{F}}_{mathrm{i}}(mathrm{s})right]end{array}right.$$
(13)
where bti, bri and bsi are the weight coefficients of temperature, precipitation and sunshine suitability in the i growth period respectively, ati, ari and asi are the correlation coefficients between temperature, precipitation and sunshine suitability and meteorological impact index of peanut yield in the i growth period respectively, and F(t), F(r) and F(s) are the temperature, precipitation and sunshine suitability in peanut growth season respectively.Then, the geometric average method is used to obtain the comprehensive suitability of peanut growth season, as shown in formula (14).$$F(S)=sqrt[3]{F(t)times F(r)times F(s)}$$
(14)
Verification of climatic zoning resultsDrought and flood disaster indexOn the basis of previous studies, in view of the different water demand of peanut in different development stages, this paper adds the water demand of peanut in different development stages as an important index to calculate, and constructs a standardized precipitation crop water demand index (SPRI) that can comprehensively characterize the drought and flood situation of peanut, so as to judge and analyze the occurrence of drought and flood disasters of peanut.Step 1: calculate the difference D between precipitation and crop water demand at each development stage$${D}_{i}={P}_{i}-{ET}_{ci}$$
(15)
where Pi is the precipitation in the i development period (mm), and ETci is the crop water demand in the i development period (mm).Step 2: normalize the data sequence.Since there are negative values in the original sequence, it is necessary to normalize the data when calculating the standardized precipitation crop water demand index. The normalized value is the SPRI value. The normalization method and drought and flood classification are consistent with SPEI index38,39,40.Chilling injury indexBased on the results of previous studies41, the abnormal percentage of caloric index was selected as the index of low-temperature chilling injury of peanut to judge and analyze the occurrence of chilling injury in different growth stages. The specific calculation process and formula are as follows:Step 1: calculate the caloric index of different development stages.Combined with the growth and development characteristics of peanut and considering the appropriate temperature, lower limit temperature and upper limit temperature at different growth stages of peanut, the caloric index can reflect the response of crops to environmental heat conditions. The average value of daily heat index is taken as the heat index of growth stage to reflect the influence of heat conditions in different growth stages on crop growth and development. Refer to formulas (5) and (6) to calculate the heat index Fi(t) at different development stages.Step 2: calculate the percentage of heat index anomaly$${I}_{ci}=frac{{F}_{i}(t)-overline{{F }_{i}(t)}}{overline{{F }_{i}(t)}}times 100%$$
(16)
where Ici is the Chilling injury index of stage i, Fi(t) is the heat index of stage i, and (overline{{F }_{i}(t)}) is the average value of the heat index of stage i over the years.Heat injury indexBased on the results of previous studies42, taking the average temperature of 26 °C, 30 °C and 28 °C and the daily maximum temperature of 35 °C, 35 °C and 37 °C as the critical temperature index to identify the heat damage of peanut in three growth stages, if this condition is met and lasts for more than 3 days, it will be recorded as a high temperature event.Disaster frequencyDisaster frequency (Pi) is defined as the ratio of the number of years of disaster at a certain station to the total number of years in the study period43, which is calculated by formula (17).$${P}_{i}=frac{n}{N}times 100%$$
(17)
where n is the number of years of disaster events to some extent at a certain growth period at a certain station, and N is the total number of years. More

Population genetic data collection from primary data sourcesFigure 4 describes the overall data collection workflow for the four datasets that comprise CaliPopGen. We first identified literature potentially containing population genetic data for California by querying the Web of Science Core Collection (https://webofknowledge.com/) for relevant literature from 1900 to 2020 with the terms: topic = (California*) AND topic = (genetic* OR genomic*) AND topic = (species OR taxa* OR population*). We included only empirical peer-reviewed literature and excluded unreviewed preprints. In using these search terms, our goal was to broadly identify genetic papers focused on California with population or species-level analyses, while avoiding purely phylogenetic studies or those focused on agricultural or model species. This resulted in 4,942 unique records.Fig. 4Flow chart of the data collection process that generated the CaliPopGen databases.Full size imageWe next screened titles and abstracts to retain articles that: (1) provided data on populations of species which are self-sustaining without anthropogenic involvement; (2) included at least some eukaryote species; (3) included population(s) sampled within California; (4) mentioned measures of genetic diversity or differentiation; and (5) were not reviews (thus restricting our search to only primary literature). We retained 1869 studies after this first pass of literature screening (see Technical Validation for estimate of inter- and intra-screener bias).Our second, more in-depth screening pass involved reading the full text of these 1869 studies. We had two goals. First, we confirmed that retained papers fully met all five of our inclusion criteria (the first screen was very liberal with respect to these criteria, and many papers failed to meet at least one criterion after close reading). Second, we eliminated papers where the data were not presented in a way that allowed us to extract population-level information. For example, many of the more systematics-focused studies pooled samples from large, somewhat ill-defined regions (“Sierra Nevada” or “Southern California”); if such regions were larger than 50 km in a linear dimension, we deemed them unusable for making geographically-informative inferences. Other studies presented summaries of population data, often in the form of phylogenetic networks or trees, but did not include information on actual population genetic parameters and therefore were not relevant to our database. We retained 528 publications after this second pass.From this set of papers, we extracted species, locality, and genetic data for each California population or sampling locality described in each study (Fig. 3A). This included Latin binomial/trinomial, English common name, population identifiers, and geographic coordinates of sampling sites. We also noted population/sampling localities that were interpreted as comprised of interspecific hybrids, and listed both parental species. We collected population genetic diversity and differentiation statistics for each unique genetic marker for each population/sampling locality; as a result, a sampling locality may have multiple entry rows, one for each locus or marker type. Parameters extracted for each population/marker combination include sample size, genetic marker type, gene targets, number of loci, years of sampling, and reported values for effective population size (Ne), expected (HE) and observed (HO,) heterozygosity, nucleotide diversity (π, pi), alleles-per-locus (APL), allelic richness (AR), percent polymorphic loci (PPL), haplotype diversity (HDIV), inbreeding coefficient (e.g. FIS, FIT, GIS), and pairwise population genetic comparison parameters (FST, GST, DST, Nei’s D, Jost’s D, or phi). We note that while there are technical differences between allelic richness and alleles-per-locus, source literature often used the terms interchangeably, and we include the parameters and their values as named in the source. We define marker type as the general category of genetic marker used (e.g., “microsatellite” or “nuclear”), while gene targets are the specific locus/loci (e.g., “COI”). We present these data in two separate datasets, one containing all population-level genetic summary statistics (Dataset 121, see Fig. 3C and detailed description in Table 1) and a second for estimates of pairwise genetic differentiation (Dataset 221, see Fig. 3D and detailed description in Table 2).Table 1 Description of the population genetic data in Dataset 121.Full size tableTable 2 Description of the pairwise genetic distance data in Dataset 221.Full size tableAll genetic data were extracted directly from the source literature. However, we also updated or added to the metadata for these population genetic values in several ways. We included kingdom, phylum, and a lower-level taxonomic grouping for each species (usually class), and updated scientific and common names based on the currently accepted taxonomy of the Global Biodiversity Information Facility22. When geographic coordinates were not provided for a sampling locality, as was frequently the case in the older literature, we used Google Maps (https://www.google.com/maps) to georeference localities based on either in-text descriptions or embedded figure maps guided by permanent landmarks like a bend in a river or administrative boundaries. Because this can only yield approximate coordinates, we recorded estimated accuracy as the radius of our best estimate of possible error in kilometers. If coordinates were provided in degree/minute/seconds, we used Google Maps to translate them to decimal degrees. In cases where coordinates were not provided and locality descriptions were too vague to determine coordinates with less than 50 km estimated coordinate error, we did not attempt to extract coordinates but still provide the genetic data. All coordinates are provided in the web Mercator projection (EPSG:3857). We excluded studies that reported genetic parameter values only for samples aggregated regionally (“Southern California” or “Sierra Nevada”). If marker type was not explicitly included, we classified marker type based on the gene targets reported, if provided.Life history trait data collectionTo increase the utility of CaliPopGen, we also assembled data on life history traits for all animal (Dataset 321) and plant (Dataset 421) species contained in Datasets 121 and 221. We assembled trait data that have previously been shown to correlate with genetic diversity, including those related to reproduction, life cycle, and body size, as well as conservation status (e.g.23,24,25,26,). Life history data were compiled by first referencing large online repositories, often specific to taxonomic groups, like the TRY plant trait database27, and the Royal Botanic Gardens Kew Seed Information Database28. If trait data for species of interest were unavailable from these compilations, we conducted keyword literature searches for each combination of species and life history trait, and extracted data from the primary literature. When data were not available for the subspecies or species for which we had genetic data, we report values for the next closest taxonomic level, up to and including family, as available in the literature.For both animals and plants, we defined habitat types as marine, freshwater, diadromous, amphibious, or terrestrial. Marine species include those that are found in brackish or wetland-marine habitats, as well as bird species that primarily reside in marine habitats. Freshwater species include those that are found in wetland-freshwater habitats, as well as species that primarily reside in freshwater. The diadromous category includes fish species that are catadromous or anadromous. We considered species to be amphibious if they have an obligatory aquatic stage in their life cycle, but also spend a significant portion of their life cycle on land. Terrestrial species were defined as those that spend most of their life cycle on land and are not aquatic for any portion of their life cycle. In a few cases (e.g., waterbirds that are both freshwater and marine, semi-aquatic reptiles), a species could reasonably be placed in more than one category, and we did our best to identify the primary life history category for such taxa. If the taxonomic identity of an entry was hybrid between species or subspecies, this was noted in the speciesID column and no life history data were reported.The CaliPopGen Animal Life History Traits Dataset 321 (description of dataset in Table 3) includes habitat type, lifespan, fecundity, lifetime reproductive success, age at sexual maturity, number of breeding events per year, mode of reproduction, adult length and mass, California native status, listing status under the US Endangered Species Act (ESA), listing status under the California Endangered Species Act (CESA), and status as a California Species of Special Concern (SSC). For some traits, value ranges were recorded–for example, minimum to maximum lifespan. In other cases, we recorded single values and, when available, a definition of this single value, (for example, minimum, average, or maximum lifespan). We report either the range of the age of sexual maturity (minimum to maximum), or a single value, depending on the available literature. For sexually dimorphic species, we report female adult length and weight when available, because female body size often correlates with fecundity. Across animal taxonomic groups, different measures of body size and length measurements are often used, reflecting community consensus on how to measure size. Given this variation, we report the type of length measurement, if available, as Standard Length (SL), Fork Length (FL), Total Length (TL), Snout-to-Vent Length (SVL), Straight-Line Carapace (SLC), or Wingspan (WS).Table 3 Description of the animal life-history data in Dataset 321.Full size tableThe CaliPopGen Plant Life History Traits Dataset 421 (description of dataset in Table 4) includes habitat type, lifespan, life cycle, adult height, self-compatibility, monoecious or dioecious, mode of reproduction, pollination and seed dispersal modes, mass per seed, California native status, NatureServe29 element ranks (global and state ranks, see Table 5 for definitions), listing status under the Federal Endangered Species Act (ESA), and listing status under the California Endangered Species Act (CESA). In contrast to most animal species, plant lifespan was typically reported as a single value. We define life cycles as the following: Annual: completes full life cycle in one year; Biennial: completes full life cycle in two years; Perennial: completes full life cycle in more than two years; Perennial-Evergreen: perennial and retains functional leaves throughout the year; Perennial-Deciduous: perennial and loses all leaves synchronously for part of the year. Some species are variable (for example, have annual and biennial individuals), and in those cases we attempted to characterize the most common modality.Table 4 Description of the plant life-history data in Dataset 421.Full size tableTable 5 Description of the Conservation status (Heritage Rank) from California Natural Diversity Database29.Full size tableBecause of the paucity of data available for chromists and fungi, we did not extract life history trait data for the relatively few species in these taxonomic groups.Data visualization and summaryWe used the R-package raster (v3.1–5) to visualize the spatial extent of the data in CaliPopGen in Fig. 3. Panel (A) shows a summary plot of all unique populations of both the Population Genetic Diversity in Dataset 121 and the Pairwise Population Differentiation in Dataset 221. Panel (B) shows the total number of unique populations in each California terrestrial ecoregion. Panel (C) depicts all data entries of Population Genetic Diversity Dataset 121, summed for each 20×20 km grid cell. Panel (D) shows the density of pairwise straight lines drawn between pairs of localities in the Pairwise Population Differentiation Dataset 221, depicted as the total number of lines per 20×20 km grid cell. The number of populations and species of both Datasets 121 & 221 are summarized for each marine and terrestrial ecoregion in Table 6.Table 6 Summary of total numbers of populations and species per California ecoregion, separately for population genetic and pairwise datasets.Full size table More

Systematic reviewA systematic review (PROSPERO Registered: CRD42020165355) of all cluster-randomised control trials currently published on ITNs [including conventional nets (CTNs), pyrethroid-only long-lasting nets (pyrethroid-nets), and pyrethroid-piperonyl butoxide synergist nets (pyrethroid-PBO ITNs)], IRS or a combination of both interventions was completed to validate an established transmission model for Plasmodium falciparum malaria parameterised using entomological assessment of the interventions. Three search platforms, Web of Knowledge, PubMed and Google Scholar were used and further studies were included from three recent Cochrane reviews that have focused on individual- or cluster- randomised control trials testing either ITNs, IRS or both26,27,28. Our search criteria focused on studies within Africa, and those reporting an epidemiological outcome such as parasite prevalence or clinical incidence in a defined age-cohort. A total of 138 studies were initially identified for further assessment (Supplementary Fig. S2).Those papers identified through the systematic review went through another round of screening to ensure they fell within the scope of the work and were compatible with existing modelling parameterisation. These criteria included (i) the intervention falls within an existing World Health Organization recommendation (so trials, or arms of trials, investigating pyrethroid-pyriproxyfen ITNs29 or insecticide-treated curtains30 were excluded), (ii) the entomological impact of the product had been previously statistically characterised as part of the modelling framework (trials investigating DDT31 or propoxur IRS32 were excluded), (iii) the study was within the Africa continent, (iv) the study randomised interventions in the intervention arm across the community (i.e., interventions were not targeted to individuals or risk groups within the community)33,34,35, and (v) the study was not reporting a cluster-randomised design36. A full description of why studies and arms were excluded is provided in Data S1.1.RCTs can assess the public health impact of interventions using different epidemiological endpoints. The two most common metrics used in malaria RCTs is infection prevalence (generally assessing parasitemia in a particular age group using microscopy or rapid diagnostic tests) or clinical incidence (typically assessed using active case detection in a cohort, which had previously been cleared of infection). These metrics are both equally valid though may give different results. For example, it may be harder to change malaria parasite prevalence with a partially effective intervention in a high-transmission setting (where people have a high chance of being reinfected) compared to a low-transmission setting (where reinfection is less common). Similarly, estimates of clinical incidence will vary depending on the study design and regularity of follow-up. For example, there are practical constraints on the number of times people within an active cohort can be tested. In areas of higher transmission incidence estimates will be greater the more regularly the cohort is tested as people infected multiple times between screening will be less common. This information on the regularity of screening is not always reported making it difficult to adjust models accordingly. It is also important to account for cluster-level effects when interpreting trial results, and this cluster-level data is also mostly unavailable37. The systematic review identified more studies that evaluated interventions in their ability to change malaria prevalence, with 13 out of 14 RCTs showing how the intervention changed parasite prevalence between the study arms compared with 8 RCTs, which reported changes in clinical incidence. Therefore, we focus on prevalence as our metric for epidemiology impact in this framework though note this should be repeated with clinical incidence estimates should more data become available. The final dataset had 73 cross-sectional surveys of prevalence in a defined age-cohort, 37 trial arms from 13 different RCTs.Characterising the entomological impact of ITNs and IRSExperimental hut trials (EHTs) measure the outcome of wild, free-flying, mosquito attempting to feed on volunteers resting indoors in the presence of an indoor intervention38. This includes (i) whether or not a mosquito is deterred away from a hut, which has the intervention (calculated by the number of mosquitoes found in the control hut relative to the intervention hut), (ii) whether the mosquito exits without feeding (repellence, measured as the percentage of alive unfed mosquitoes inside the intervention hut), (iii) the percentage entering the hut that successfully blood-feed, or (iv) the percentage of mosquitoes which die. Intervention efficacy is typically summarised for the intervention huts relative to a no-intervention (or untreated net) control huts, be it induced mortality (the increase in the percentage of mosquitoes dying over a 24-h period) or blood-feeding inhibition (the reduction in the percentage of mosquitoes receiving a blood-meal).EHTs use specially built structures that follow a defined floor-plan and set of specifications. There are multiple designs of experimental hut as they were originally intended to replicate the predominant type of housing found in the local area. We recently conducted a systematic review to capture the average behaviours of mosquitoes across different hut designs19. The two most used huts in Africa are the West African design and East Africa hut39 (a third hut—the Ifakara hut—is not considered here39). The meta-analyses showed that the associations describing the probable outcome of a mosquito feeding attempt (deterrence, repellence, successful feeding, or death) varies according to hut design. It is unclear that hut design best predicts epidemiological impact.Meta-analyses of EHT data have shown how the entomological efficacy of pyrethroid-nets has diminished over time, probably due to the rise of pyrethroid-resistant mosquitoes16,19,40, though there may be some manufacturing changes41. EHTs are conducted throughout Africa but are limited to the sites where the huts are built and cannot directly inform estimates of ITN efficacy outside of these areas. The most widely used quantitative measure for approximating the phenotypic level of resistance in the local mosquito population is the discriminating-dose bioassay. There are two main types of discriminating assays, the WHO susceptibility bioassay and the CDC bottle bioassay42,43. Both these assays measure the proportion of local Anopheline mosquitoes that survive 24-h following exposure to a discriminatory dose of pyrethroid for 60 min. Results from these bioassays are highly variable44 though collating data from multiple tests has shown clear trends over time45. The relationship between the level of resistance in the local mosquito population (as measured in a discriminating-dose bioassay) and the mortality induced by ITNs in EHTs can be used to extrapolate the results from hut trials to other geographical regions16.Modelling rationaleThe two main metrics recorded in EHTs do not capture all entomological impacts of ITNs and IRS. Though useful, induced mortality does not consider the sub-lethal impact of interventions whilst blood-feeding inhibition fails to differentiate between preventing blood-meals and killing mosquitoes, which are likely to have very different epidemiological impacts. Killing mosquitoes reduces the force of infection for users and non-users (through a community effect) so the overall effectiveness of treated nets and IRS will vary according to how abundantly and regularly they are used by the local human population. In addition, the impact of ITNs and IRS is likely to vary between sites because of factors such as the disease endemicity itself driven by societal behaviours, seasonality of transmission and the use of other malaria control interventions, amongst others. This means that raw EHT data is unlikely to directly correlate with the results of RCTs.EHTs are widely used to parameterise malaria transmission dynamics mathematical models46,47,48. These models rigorously quantify the outcome of each mosquito feeding attempt and, by making a limited number of assumptions, can estimate an overall entomological efficacy by combining the impact of the level of personal protection elicited by the intervention to the user and the indirect community effect provided to both users and non-users. Transmission dynamics mathematical models are designed to mechanistically capture the underlying processes governing malaria transmission and so can account for known non-linear processes such as the acquisition of human immunity49,50,51. This enables these models to translate the entomological efficacy quantified in an EHT into predictions of epidemiological impact given the characteristics of the site. Unfortunately, to date, there are no published EHTs that have been conducted alongside RCT evaluation of ITNs or IRS products (and therefore evaluated against the same mosquito population). To overcome this issue we parameterise the models using a meta-analyses of 136 EHT results16,19 collated from across Africa, which quantifies how mosquito deterrence, repellence, successful feeding, or death varies with time since the intervention is deployed and according to the level of pyrethroid resistance in the local mosquito population (as measured by the discriminating-dose bioassay). This approach has been able to recreate the epidemiological impact observed in RCTs evaluating a small number of ITNs15 or IRS products9, but this is the first attempt at using this method to validate the modelling framework against all trials evaluating nets and IRS.There is considerable uncertainty in how the entomological efficacy of treated ITNs varies with the level of resistance in the local population. This is a key relationship determining how field discriminating-dose bioassay data should be interpreted yet it is highly uncertain, with a recent meta-analyses indicating that it is equally well explained by two different functional forms (the logistic or log-logistic functions)19. Similarly, it is unclear whether the epidemiological impact of ITNs or IRS is best captured by all experimental hut data combined (Supplementary Fig. S14C, D)19 or if the meta-analyses should be restricted to just West or East African hut design data alone. To rigorously differentiate between these options six different models are run for each trial arm (n = 37), varying both the relationship between discriminating-dose bioassay and EHT mosquito mortality (either the logistic or log-logistic function) and the data used in the EHT meta-analyses (all data, East or West African design huts). The ability of these models to recreate the observed results is statistically compared and the most accurate selected for the main analyses.Transmission dynamics modelThe malaria transmission model that we use here incorporates the transmission dynamics of Plasmodium falciparum between human hosts and Anopheles mosquito vectors. The differential equations and associated assumptions of the original transmission model52 have been comprehensively reported in the Supplementary Material from Griffin et al.53, Walker et al.54 and Winskill et al.55. The model has been extensively fitted to data on the relationship between vector density, entomological inoculation rate, parasite prevalence, uncomplicated malaria, severe disease and death49,52,53,56,57. Model equations and assumptions are provided in the Supplementary Methods and https://github.com/jamiegriffin/Malaria_simulation. Unless stated (Supplementary Data S1), default parameters are taken from these papers.Data requirements for model simulationThe transmission model can be parameterised to describe the specific ecology of each RCT location using data on the mosquito bionomics, seasonal transmission patterns, historic use of various interventions—principally insecticide-treated ITNs or the residual spraying of insecticides (IRS)—and baseline endemicity. These data are recorded within the research articles reporting the trials at the trial arm level (Supplementary Data S1.2 notes where data are available and which resources were used; Supplementary Data S1.3 lists the key data identified for model parameterisation) and Supplementary Fig. S1 provides a diagram of how they are combined to inform the model.Briefly, the Anopheles mosquito species composition at baseline is used to determine the proportion of mosquitoes with bespoke behaviours that could alter exposure risk to mosquito bites and thus transmission risk. Species-specific mosquito behaviours are parameterised from systematic reviews on anthropophagy, using the human blood index47,58,59, and the proportion of mosquito bites that are received indoors or in bed because this impacts the efficacy estimate for indoor interventions60.Other information that are specific to each trial also help interpret our success at predicting, or not, the observed results of an intervention tested in an RCT; the diagnostic used to measure prevalence or incidence is useful because different tests have different sensitivities61, which can be included in the model framework54. The baseline burden of infection is particularly important to enable the model to be calibrated to the endemicity of the study site by varying the number of mosquitoes per person (the human:mosquito ratio). This is determined by a cross-sectional estimate of parasite prevalence in a defined age-cohort at a particular time of year of the baseline survey.For any location, the current level of endemicity is determined by the historic interventions already operating at the site. Therefore, wherever possible, ITN use and the historic use of sprayed insecticides, as well as the estimated proportion of clinical cases that are drug-treated, are included as baseline parameters.In addition to the waning potency of insecticide active ingredient outlined above, the impact of nets can also wane because of changes in the proportion of people using them. This can be driven by the quality of the product, seasonal patterns in humidity or other social patterns of use62,63,64. Where data are available, this waning adherence to net use is captured by fitting an exponential decay function to the proportion of people using nets measured at cross-sectional surveys throughout the trials:$${{{{{{{mathrm{U}}}}}}{{{{{mathrm{sage}}}}}}}}_{i}={e}^{-{sigma }_{i}t}$$
(1)
where σ is a parameter determining how rapidly people stop using nets in an intervention arm i of the trial and t is time in years. Parameter estimates for pyrethroid-only and pyrethroid-PBO ITNs are provided for different levels of resistance for the 6 potential methods of associating bioassays and using data (Supplementary Data S1.4).The IRS product used is equally important as the entomological impact of different products vary, particularly for pyrethroid-based IRS in the presence of resistant mosquitoes9. Supplementary Data S1.5 show the parameter estimates for products included in the analysis.The seasonality of transmission has been defined previously for each RCT site (at the administration subunit 1 level) using normalised rainfall patterns obtained from the US Climate Prediction Center65. The daily time series are aggregated to 64 points per year for years 2002 to 2009. A Fourier function is fitted to these data to capture seasonality by reconstructing annual rainfall patterns54,66. We deliberately do not match rainfall data from the respective RCTs, which would likely improve the model estimates because we are ultimately testing whether this framework has predictive power across future years or alternative ecologies, where we will not know how rainfall will exactly impact mosquito densities and hence malaria transmission.Statistical analysisThe mean simulated malaria prevalence (matching the age-cohort of the trial) is recorded for all RCT surveys timepoints. This equates to a total of 73 cross-sectional surveys post-implementation. The process was repeated using the 6 different entomological parameter sets (the relationship between bioassay and hut trial mortality and the hut design used to summarise treated net entomological impact). An illustration of the different models and their fit to data is demonstrated in Supplementary Fig. S17 for a recent study trialling pyrethroid-only nets, pyrethroid-PBO ITNs alone or in combination with a long-lasting IRS product in Tanzania5. The difference between the observed and predicted prevalence at each timepoint is shown for all RCTs in Supplementary Fig. S18. A simple linear regression is conducted comparing observed and predicted results are summarised in Supplementary Table 3. Let Xi denote the malaria prevalence predicted by the model at timepoint i while Yi is the observed prevalence. The regression,$${Y}_{i}=m{X}_{i}$$
(2)
for i = 1,…,c + n, where m is the gradient between the observed and predicted result (consistent across studies), c is the number of post-intervention datapoints in the control arms and n is the number of post-intervention datapoints in the intervention arms (c + n = 73 for analyses of all RCTs). Better fitting models have a higher adjusted R2 (adjusted R2 values of one indicate the model is perfectly predicting the trial result) whilst the gradient of the regression m indicates any bias (with value of one reporting the model can predict prevalence equally well across the endemicity range). Results are presented for all ITNs and IRS RCTs and separately for RCTs of different types of (pyrethroid-only ITNs, pyrethroid-PBO ITNs and IRS, Supplementary Table 3). The log-logistic model (results 4–6 in Supplementary Table 3) describing the relationship between bioassay and hut trial mortality consistently fits the data better, with models fit using either all hut trial data or East African design huts having a similar accuracy (adjusted R2 = 0.95). This parameter combination also had the least bias, with the best fit regression line being closer to one.The average efficacy of the different ITNs and IRS combinations was calculated by comparing malaria prevalence for the different trial arms to the respective control arms at matched timepoints following the introduction of interventions. Let ({E}_{{jk}}^{l}) be the relative reduction in the malaria prevalence between the control (k = 0) to intervention (k = 1) arms at matched timepoint j in the same trial for either the predicted (l = Xjk) or observed (l = Yjk) malaria prevalence,$${E}_{j}^{X}=({{X}_{j0}-{X}}_{j1})/{X}_{j0},{{{{{rm{ and }}}}}},{E}_{j}^{Y}=({Y}_{j0}-{Y}_{j1})/{Y}_{j0}$$
(3)
for j = 1,…,n. The goodness of fit for the efficacy estimates is calculated in a similar manner to the prevalence estimates by substituting in ({E}_{j}^{X}) and ({E}_{j}^{Y}) into Xi and Yi in E2, respectively. Models are on average able to estimate the efficacy of the interventions at different timepoints (Supplementary Table 3). Estimates for some timepoints diverge substantially (for example, the study testing conventional nets in the Gambia relative to untreated nets67 measured negative effect in one setting; the treated net arm having more infected children whereas the model predicted a 12.5% reduction due to the CTN (with parameters derived from all EHT data and the log-logistic function, 4 in Supplementary Table 3), Supplementary Data S1.8), but in most studies the trial average (averaged across all timepoints) is remarkably consistent. Accuracy is lower than estimates of absolute prevalence, in part because the difference between the percentage of people slide positive in low-endemicity settings may be relatively modest in absolute terms but might represent a substantial difference as a percentage. It is also important to note that when the models do systematically miss some timepoints, this is consistent across the control and treated arms. For example, in the Protopopoff et al. study in Tanzania5 (Figs. S14 and S17) efficacy is over-estimated in all arms 18 months after the start of the trial, but the relative difference between the arms (in terms of ordering, and the efficacy estimate) is relatively consistent. This indicates that unmeasured factors, such as differences in the timing and duration of the rainy season, may have occurred across all trial arms. As previously, the log-logistic functional form describing the relationship between bioassay and hut trial mortality consistently fits the data better (Supplementary Table 3, options 4 to 6). The models fit describing the entomological efficacy of any net using all EHT data predicts efficacy data better with East African design hut data providing similar accuracy (adjusted R2 = 0.64 vs. 0.62, respectively). Following this we select the log-logistic functional form to describe the relationship between mortality in the discriminating-dose bioassay and EHT and characterise the entomological efficacy of treated ITNs using data from both East and West African design huts for the main analyses (Fig. 2B, C).The ability of the best-performing model (Supplementary Table 3, column 4: log-logistic function and all EHT data) to capture the relative drop in prevalence over time compared to the baseline (pre-intervention) estimate is shown in Supplementary Fig. S19. This value is denoted as ({dot{E}}_{t}^{l}) and is calculated as,$${dot{E}}_{t}^{X}=({X}_{0}-{X}_{t}),{{{{{rm{and}}}}}},{dot{E}}_{t}^{Y}=({X}_{0}-{Y}_{t})$$
(4)
where ({X}_{0}) is the malaria prevalence at baseline (prior to intervention deployment with the exception of Chaccour et al.68) observed from the RCT and the model is calibrated to this endemicity. Xt is then the subsequent cross-sectional survey observed for each study, and RCTs have different numbers of surveys ranging from 1 to 4 in the published literature. The corresponding model estimate is represented by Yt. Estimates are calculated for all post-intervention timepoints in both control and intervention arms and are shown in Fig. S19A. The difference between ({dot{E}}_{t}^{X}) and ({dot{E}}_{t}^{Y}) can be used to explore how closely the model is able to predict this absolute difference observed in the trials (a value of 0 indicates exact match, high predictive ability). The model overestimates the performance of IRS only, deployed in 1995 using the pyrethroid IRS ICON CS 10% (Syngenta), but otherwise there is no difference in the models’ ability to estimate different ITN interventions or combination net and IRS interventions, be it the absence of an intervention, conventional dipped-nets, pyrethroid-only nets, pyrethroid-PBO ITNs with or without IRS (Fig. S19B). All code is available69.Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More