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Experimental dataThe dataset used in this study is the global long-term air quality indicator data of 5577 regions from 2010 to 2014 extracted by Betancourt et al.14 based on the TOAR database (https://gitlab.jsc.fz-juelich.de/esde/machine-learning/aq-bench/-/blob/master/resources/AQbench_dataset.csv)29. As shown in Fig. 3, the monitoring sites include 15 regions, including EUR (Europe), NAM (North America), and EAS (East Asia), and are mainly distributed in NAM (North America), EUR (Europe) and EAS (East Asia). The dataset mainly includes the geographical location information of the monitoring site, such as longitude and latitude, the area to which it belongs, altitude, etc., and the site environment information, such as population density, night light intensity, and vegetation coverage. Since it is difficult to directly quantify factors such as the degree of industrial activity and the degree of human activity, environmental information such as the average light intensity at night and population density are used as proxy variables for the above factors. The ozone indicator records the hourly ozone concentration from air quality observation points in various regions and aggregates the collected ozone time series in units of one year into one indicator. Using a longer aggregation period can be used to average short-term weather fluctuations. The experimental data have a total of 35 input variables, including 4 categorical attributes and 31 continuous attributes. The predictor variable is the average ozone concentration in each region from 2010 to 2014. The specific variable names and descriptions14 are shown in the supplementary materials. A total of 4/5 of the total samples were used as the training set, and 1/5 were used as the test set.Figure 3Global distribution of monitoring sites.Full size imageResults of BO-XGBoost-RFEAccording to the XGBoost-RFE algorithm for feature selection, XGBoost-RFE combined with the cross-validation method is used to calculate the selected feature set in each RFE stage for fivefold cross-validation, and the mean absolute error (MAE) is used as the evaluation criterion to finally determine the number of features with the lowest mean absolute error (MAE). At the same time, the Bayesian optimization algorithm is used to adjust the hyper-parameters of XGBoost-RFE, and then the feature subset with the lowest cross-validation mean absolute error (MAE) is obtained. The main parameters of the XGBoost model in this article include the learning_rate, n_estimators, max_depth, gamma, reg_alpha, reg_lambda, colsample_bytree, and subsample. All parameters used in the model are shown in the supplementary material. Within the given parameter range, the Bayesian optimization algorithm is used, the mean absolute error (MAE) of the XGBoost-RFE fivefold cross-validation is used as the objective function, and the number of iterations is controlled to be 100. We obtained the hyperparameter combination corresponding to the lowest MAE and the corresponding optimal feature subset. The iterative process of Bayesian optimization is shown in Fig. 4.Figure 4Iterative process of Bayesian optimization.Full size imageThe parameter range and optimized value of XGBoost-RFE are shown in Table 1. The XGBoost-RFE feature selection results under the above optimized hyperparameters are shown in Fig. 5. The number of features in the feature subset with the lowest mean absolute error is 22, and the MAE is 2.410.Table 1 Main hyper-parameter range and optimized value.Full size tableFigure 5XGBoost-RFE feature selection results: Cross-validation MAE under optimal hyperparameter combination.Full size imageAdditionally, the XGBoost-RFE feature selection model without Bayesian optimization is compared with the algorithm in this study. The default parameters of the underlying model XGBoost are set to learning_rate as 0.3, max_depth as 6, gamma as 0, colsample_bytree as 1, subsample as 1, reg_alpha as 1, and reg_lambda as 0. The comparison results are shown in Table 2. The results show that the XGBoost-RFE cross-validation MAE without parameter tuning is larger than that of the algorithm in this study, and the dimension of the feature subset obtained is also higher than that of the algorithm in this study.Table 2 Comparison of MAE and feature num before and after BO.Full size tablePrediction resultsTo test the prediction accuracy of the prediction model with the optimal subset obtained by BO-XGBoost-RFE, three indexes, MAE, RMSE and R2, are used to evaluate the prediction results, and the expressions are as follows:$$begin{array}{*{20}c} {MAE = frac{1}{n}mathop sum limits_{i = 1}^{n} left| {left( {y_{i} – widehat{{y_{i} }}} right)} right|} \ end{array}$$
(8)
$$begin{array}{*{20}c} {RMSE = sqrt {frac{1}{n}mathop sum limits_{i = 1}^{n} left( {y_{i} – widehat{{y_{i} }}} right)^{2} } } \ end{array}$$
(9)
$$begin{array}{*{20}c} {R^{2} = 1 – frac{{mathop sum nolimits_{i = 1}^{n} left( {widehat{{y_{i} }} – y_{i} } right)^{2} }}{{mathop sum nolimits_{i = 1}^{n} left( {y_{i} – overline{{y_{i} }} } right)^{2} }}} \ end{array}$$
(10)
n indicates the number of samples, yi is the true value, (widehat{{y_{i} }}) is the predicted value and (overline{{y_{i} }}) indicates the mean value of the predicted value.The XGBoost-RFE feature selection algorithm based on Bayesian optimization in this study is compared with feature selection using full features and features selected by the Pearson correlation coefficient, which measures the correlation between two variables. In this study, the correlation with predictor variables was selected to be less than 0.1, and the variables with correlations greater than 0.9 were deleted to avoid multicollinearity.XGBoost, random forest, support vector regression machine, and KNN algorithms were used to predict ozone concentration with full features, features selected by Pearson’s correlation coefficient, and features based on BO-XGBoost-RFE. According to the evaluation indicators described above, the comparison of the prediction performance results of the three algorithms before and after dimensionality reduction can be obtained. The MAE, RMSE and R2 results of each prediction model are shown in Table 3.Table 3 MAE, RMSE and R2 of each prediction model.Full size tableAmong the four prediction models, random forest has the lowest MAE and RMSE and the highest R2 based on three different dimensions of data and therefore has the best prediction performance. The prediction accuracy of all four prediction models based on Pearson correlation is lower than that based on BO-XGBoost-RFE, indicating that only selecting features by correlation cannot accurately extract important variables. Although the RMSE of the support vector regression model based on BO-XGBoost-RFE is slightly lower than the RMSE based on full features, the prediction accuracy of XGBoost, RF, KNN after feature selection of BO-XGBoost-RFE is higher than that based on full features and Pearson correlation. Among the four prediction models, random forest has obtained the highest prediction accuracy. The MAE based on BO-XGBoost-RFE is 5.0% and 1.4% lower than that based on the Pearson correlation coefficient and the full-feature-based model, and the RMSE is reduced by 5.1%, 1.8%, R2 improved by 4.3%, 1.4%. Additionally, the XGBoost model achieved the greatest improvement in accuracy. The MAE was reduced by 5.9% and 1.7%, the RMSE was reduced by 5.2% and 1.7%, and the R2 was improved by 4.9% and 1.4% compared with the Pearson correlation coefficient-based and full-feature-based models, respectively. This indicates that feature selection based on BO-XGBoost-RFE effectively extracts important features, improves prediction accuracy based on multiple prediction models, and has better dimensionality reduction performance.Figure 6 shows the importance of each feature obtained by using the random forest prediction model, reflecting the degree of influence of each variable on the prediction results of the global multi-year average near-ground ozone concentration. The most important variables that affect the prediction results according to the ranking of feature importance are altitude, relative altitude, and latitude, followed by night light intensity within a radius of 5 km, population density and nitrogen dioxide concentration, while the proxy variables for vegetation cover have a relatively weak effect on the prediction of ozone concentration.Figure 6Feature importance in random forest.Full size image More

General observation and methods for ploidy analysis on aphid bacteriome cellsConsistent with previous observations9,21,22,40, the bacteriome of viviparous aphids consisted of two types of cells: bacteriocytes and sheath cells (Fig. 2). Bacteriocytes contained Buchnera cells and were much larger than sheath cells. Sheath cells exhibited a flattened morphology and surrounded the bacteriocytes. Both cell types possessed a single nucleus. Bacteriocytes had a single prominent nucleolus, which was not stained using DAPI, but using “Nucleolus Bright Red” staining (Fig. 2). Most sheath cells also had a single nucleolus, yet a small number had two. “Nucleolus Bright Red” also stained the peripheral region of Buchnera, probably because of the richness of RNA around Buchnera cells.Figure 2Morphology of bacteriocytes and sheath cells from each morph of aphids visualized using DAPI/Phalloidin/Nucleolus Bright Red staining. DNA and F-actin were stained by DAPI (gray or blue) and Phalloidin (green), respectively. The nucleolus, which is the site of ribosome biogenesis, was visualized by Nucleolus Bright Red (red). This dye binds RNA electrostatically, therefore the cytoplasm of bacteriocytes and Buchnera cells were also stained. Bacteriocytes (white arrows) had single prominent nucleolus, and the cell sizes were much larger than sheath cells (white arrowheads) in all aphid morphs.Full size imageTo determine the most suitable methods for ploidy analysis of aphid bacteriocytes, three types of methods, flow cytometry, Feulgen densitometry, and fluorometry were compared. First, flow cytometry successfully detected the nuclei of bacteriome cells and heads, and distinct peaks were present (Fig. S3). There were several peaks, which can be categorized as ploidy classes based on head peaks, assuming that the smallest peaks correspond to a diploid population. We recognized peaks up to 256C (256-ploidy) cells but could not distinguish cell types (i.e., bacteriocytes or sheath cells) in this method due to a lack of cytological information. Note that “C” means haploid genome size, for example, 2C = diploid and 8C = octoploid. Second, Feulgen densitometry also showed several ploidy levels of up to 128C (Fig. S4) in bacteriocytes. Sheath cells mainly consisted of 16-32C cells. However, we found that many cells were lost during the experimental procedures, probably due to the repeated washing processes and the long incubation time.We found the third method, image-based fluorometry for isolated nuclei, the best for quantitative ploidy analysis of aphid bacteriocytes (Fig. 3). Fluorometry showed distinct peaks of integrated fluorescence intensity, and they could be categorized as each ploidy class based on the intensity of the smallest peak in head cells (diploid population). The results were consistent with other methods; ploidy levels were 32C-256C in bacteriocytes and 16C-32C in sheath cells. In this analysis, the nucleolus size was used to discriminate between cell types. During cytological observation, we obtained the size distribution of the nucleolus, and it was revealed that the nucleolus of bacteriocytes was always larger than that of sheath cells (Fig. S5). Based on the results, we determined the threshold of the size of the nucleolus. More specifically, in viviparous females, nuclei that have nucleoli larger than 20 μm2 were categorized into bacteriocytes. Note that the peaks of sheath cells were not distinct or reliable for categorizing their ploidy class; therefore, we showed results focusing on bacteriocytes in the following sections.Figure 3Ploidy analysis of aphid bacteriocytes using DAPI-fluorometry. A representative result from the analysis of adult viviparous females is presented. An image of DAPI-stained nuclei was also shown (the blue channel was extracted). Isolated nuclei of bacteriome cells were stained using DAPI, image-captured with a CCD camera, and their integrated fluorescence intensity was measured using ImageJ software. Nuclei were categorized into “bacteriocytes” or “sheath cells,” based on the size distribution of nucleolus (see “Materials and Methods”). Relative ploidy levels were calculated based on the data from head cells which are mainly diploid. Bacteriocytes of adult viviparous aphids consisted of 16C-256C cells, and 64–128 cells were dominant, while sheath cells exhibited lower ploidy levels (mainly 16C). “C” means haploid genome size, for example, 2C = diploid and 8C = octoploid.Full size imageCellular features of bacteriome cells in viviparous and oviparous females, and malesThe cellular features were generally consistent among young adults (within 5 days of adult eclosion) of three morphs, viviparous and oviparous females, and males (Fig. 2). Nevertheless, Buchnera-absence zones in the cytoplasm of bacteriocytes, which are considered to be degeneration of Buchnera45, and bacteriocytes degeneration46 were both observed more frequently in male bacteriocytes than in females (Fig. 2). The cell size of bacteriocytes was significantly different among morphs (LM with type II test, F = 286.15, df = 2, p  More

Swedish environment minister Annika Strandhäll before the start of the Stockholm +50 Climate Summit. Few world leaders will be attending.Credit: Fredrik Persson/TT News Agency/AFP/Getty

Sustainability is now a household term, but it wasn’t always so.Fifty years ago, the United Nations held its Conference on the Human Environment in Stockholm. This landmark event gave the concept of sustainable development its first international recognition. Sweden and the UN are marking the occasion this week with Stockholm+50, an international meeting that serves as both commemoration and call to action.The world is deep in planetary and human crises, with the UN’s Sustainable Development Goals off track and multilateral agreements on climate change and biodiversity behind schedule. Governments need to integrate sustainability into economic planning — and listen to researchers, who are ready with evidence-based arguments and tools to help them do so.Fifty years ago, the time was ripe for an environmental agenda to enter the world stage. Optimistic ideas of economic growth as a driver of progress, propelled by the Industrial Revolution, needed to accommodate concerns over damage to the natural environment. Books such as Rachel Carson’s Silent Spring (1962) — which raised awareness about harms caused by pesticides — brought scientific information about environmental risks into the mainstream.In March 1972, a team of researchers and policymakers sounded another alarm in The Limits to Growth, one of the first reports to forecast catastrophic consequences if humans kept exploiting Earth’s limited supply of natural resources. The conference in Stockholm followed a few months later, steered to success by its secretary-general, Canadian industrialist Maurice Strong. That set crucial institutions in motion, starting with the establishment of the UN Environment Programme (UNEP), based in Nairobi — the first UN body to be headquartered in a developing country. UNEP went on to facilitate a new international law — the 1987 Montreal Protocol to phase out ozone-depleting substances — and co-founded the Intergovernmental Panel on Climate Change (IPCC). It assisted in establishing the first action plans for sustainable development through landmark international agreements on biodiversity, climate and desertification.But there were mistakes and missed opportunities. The establishment of multiple agencies and policy instruments created a disjointed governance system. Newly created environment ministers wielded little power. In national budgets, environmental protection was siloed away from economic development and social concerns. For a long time, action on climate change remained unfocused. And the economic drivers of environmental change were overlooked.And so, 50 years after that momentous conference, the world remains in crisis. With impending climate and biodiversity crises, the warnings issued by visionaries now hit even closer.Stockholm+50 promises “clear and concrete recommendations and messages for action at all levels”. More than 90 ministers are expected to attend, but only 10 heads of government. That’s a missed opportunity for high-level action. World leaders are needed because their presence signals that sustainability remains at the top of their agendas.Awareness of the need to embed sustainability into policymaking has broken into the mainstream, although much of it is still talk. City governments around the world are implementing ambitious climate action plans through the C40 Cities network. Some companies, too, are adopting sustainability principles, from reporting (and reducing) their carbon footprints to ensuring that investments, as far as possible, do not harm the environment.But this urgency has not ascended to heads of state and government. With a handful of exceptions — such as Finland, Iceland, New Zealand, Scotland and Wales — most nations seem unwilling to systemically integrate their economic, environmental and social policymaking.Doing so is not only good for the environment; it is also sound economics and good for well-being. The food and energy crisis driving poverty and diminishing living standards around the world might have been triggered by the shocks of a pandemic and war on Ukraine — but it is driven just as much by the depletion of natural resources.Ahead of the 1972 conference, 2,200 environmental scientists signed a letter — called the Menton Message — to then UN secretary-general U Thant. The signatories had a sense that the world was moving towards multiple crises. They urged “massive research into the problems that threaten the survival of mankind”, such as hunger, wars, environmental degradation and natural-resource depletion. The UN system went on to play a big part in building the body of knowledge that has shown why sustainability is necessary, and in creating the policy architecture to make it happen. But to do the Stockholm vision justice, there must be bolder action from heads of government and from the UN system. The planned creation of a board of science advisers to UN secretary-general António Guterres needs to be accelerated. Once established, the board must find a way to bring joined-up action on sustainability closer to world leaders.Researchers can now join a successor to the Menton Message that has been organized by the International Science Council, the global science network Future Earth and the Stockholm Environment Institute. In an open letter addressed to world citizens, the authors write: “After 50 years, pro-environmental action seems like one step forward and two back. The world produces more food than needed, yet many people still go hungry. We continue to subsidize and invest in fossil fuels, even though renewable energy is increasingly cost-effective. We extract resources where the price is lowest, often in direct disregard of local rights and values.”World leaders must listen to the research community, and accept the evidence and narrative offered to help them to navigate meaningful change. Environmental sustainability does not impede prosperity and well-being — in fact, it is vital to them. People in power need to sit up and take notice. More

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In this study, the five main characteristics of green spaces that were measured were area, perimeter, perimeter-area ratio, leaf area index, and canopy density. The structure of parameter between them is shown in Table 3.Table 3 Parameter structure of the cooling and humidification effect based on the spatial characteristics of green spaces.Full size tableCorrelation between various spatial characteristics and cooling and humidifying intensity in green spacesSmall-size green spacesFigures 4 and 6 shows the results of linear regressions between spatial characteristics and the cooling effect in small-size green spaces. There were relatively weak correlations between area, perimeter, perimeter-area ratio, leaf area index and cooling intensity, and a strong correlation between canopy density and cooling intensity. Small-size green space has the weakest positive correlation between perimeter-area ratio and cooling intensity (R2 = 0.11), and its canopy density and cooling intensity have the strongest positive correlation (R2 = 0.64). Meanwhile, small-size green space has weakest negative correlation between perimeter and humidifying intensity (R2 = 0.17), and its leaf area index and humidifying intensity have significant positive correlation (R2 = 0.42). Figures 4a and 5a show that for every 1 ha increase in area of small-size green spaces, the cooling intensity increased by 1.026 °C, and the humidifying intensity decreased by 1.56%. Figures 4b and 5b show that for every 100 m increase in perimeter, the cooling intensity decreases by 1.06 °C, and the humidifying intensity decreased by 1.19%. Figures 4c and 5c show that for every 0.01 increase in the perimeter-area ratio, the cooling intensity increases by 1.12 °C, and the humidifying intensity increased by 1.46%. Figures 4d and 5d show that for every 0.1 increase in the leaf area index, the cooling intensity increases by 1.11 °C, and the humidifying intensity increased by 1.12%. Figures 4e and 5e show that each 0.01 increase in the canopy density, the cooling intensity increases by 1.60 °C, and each 0.1 increase in canopy density, the humidifying intensity increased by 1.15% (Fig. 6).
Figure 4Linear regressions between spatial characteristics and cooling intensity of small-size green spaces.Full size imageFigure 5Linear regressions of spatial characteristics and humidifying intensity of small-size green spaces.Full size imageFigure 6The correlation between the spatial characteristics of small-size green spaces and the intensity of cooling and humidifying (GA means green area; GP means green perimeter; GPAR means green perimeter-area ratio; LAI means leaf area index; CD means canopy density).Full size imageMedium-size green spacesFigures 7 and 9 shows the linear regressions between spatial characteristics and cooling intensity in medium-size green spaces. There was an extremely significant positive correlation between area and cooling intensity, an insignificant positive correlation between the leaf area index and cooling intensity, and a relatively weak negative correlation between the other three characteristics and cooling intensity. Medium-size green space has the weakest negative correlation between canopy density and cooling intensity (R2 = 0.12), and its green area and cooling intensity have the strongest positive correlation (R2 = 0.83). Meanwhile, medium-size green space has weakest negative correlation between perimeter-area ratio and humidifying intensity (R2 = 0.41), and its area and humidifying intensity have most significant positive correlation (R2 = 0.81). Figures 7a and 8a show that for every 1 ha increase in area of medium-size green spaces, the cooling intensity increased by 1.19 °C, and the humidifying intensity increased by 1.24%. Figures 7b and 8b show that for every 100 m increase in perimeter, the cooling intensity decreases by 1.02 °C, and the humidifying intensity increased by 1.17%. Figures 7c and 8c show that for every 0.01 increase in the perimeter-area ratio, the cooling intensity decreases by 1.29 °C, and the humidifying intensity decreased by 2.40%. Figures 7d and 8d show that for every 0.1 increase in the leaf area index, the cooling intensity increases by 1.37 °C, and the humidifying intensity decreased by 1.92%. Figures 7e and 8e show that each 0.01 increase in the canopy density, increases the cooling intensity decreases by 1.23 °C, and the humidifying intensity decreased by 6.48% (Fig. 9).Figure 7Linear regressions between spatial characteristics and cooling intensity of medium-size green spaces.Full size imageFigure 8Linear regressions of spatial characteristics and humidifying intensity of medium-size green spaces.Full size imageFigure 9The correlation between the spatial characteristics of medium-size green spaces and the intensity of cooling and humidifying (GA means green area; GP means green perimeter; GPAR means green perimeter-area ratio; LAI means leaf area index; CD means canopy density).Full size imageLarge-size green spacesFigures 10 and 12 shows the linear regressions between spatial characteristics and cooling intensity in large-size green spaces. There was an insignificant correlation between area and cooling intensity, a weak correlation between canopy density and cooling intensity, and a significant correlation between perimeter, perimeter-area ratio and the leaf area index and cooling intensity. Medium-size green space has the weakest negative correlation between green area and cooling intensity (R2 = 0.35), and its leaf area index and cooling intensity have the strongest positive correlation (R2 = 0.92). Meanwhile, medium-size green space has weakest negative correlation between perimeter-area ratio and humidifying intensity (R2 = 0.11), and its leaf area index and humidifying intensity have most significant positive correlation (R2 = 0.39). Figures 10a and 11a show that for every 1 ha increase in area of large-size green spaces, the cooling intensity decreased by 1.02 °C, and the humidifying intensity decreased by 1.22%. Figures 10b and 11b show that for every 100 m increase in perimeter, the cooling intensity decreases by 1.05 °C, and the humidifying intensity decreased by 1.34%. Figures 10c and 11c show that for every 0.005 increase in the perimeter-area ratio, the cooling intensity decreases by 1.43 °C, and each 0.01 increase in perimeter-area ratio, the humidifying intensity decreased by 1.27%. Figures 10d and 11d show that for every 0.1 increase in the leaf area index, the cooling intensity increases by 2.41 °C, and the humidifying intensity increased by 1.37%. Figures 10e and 11e show that each 0.1 increase in the canopy density, the cooling intensity increased by 3.69 °C, and the humidifying intensity decreased by 2.84% (Fig. 12).Figure 10Linear regressions of spatial characteristics and cooling intensity of large-size green spaces.Full size imageFigure 11Linear regressions of spatial characteristics and humidifying intensity of large-size green spaces.Full size imageFigure 12The correlation between the spatial characteristics of large-size green spaces and the intensity of cooling and humidifying (GA means green area; GP means green perimeter; GPAR means green perimeter-area ratio; LAI means leaf area index; CD means canopy density).Full size imageQuantitative analysis of the microclimatic effects of different types of green spacesQuantitative analysis of the effects of different types of green space on cooling intensityFigure 13 shows the linear regressions between the different types of green spaces and cooling intensity. There were negative correlations between green spaces a short, medium, and long distance from a water body and cooling intensity in small-size green spaces, medium-size green spaces and large-size green spaces. The negative correlation between the distance to a water body and cooling intensity in medium-size green spaces was most significant (R2 = 0.985). The greater the distance to a water body, the lower the cooling intensity. For medium-size green spaces, for every 1/4 increase in the distance ratio, the cooling intensity decreased by 0.81 °C. For small-size green spaces, for every 1/4 increase in the distance ratio, the cooling intensity decreased by 1.04 °C. For large-size green spaces, for every 1/4 increase in the distance ratio, the cooling intensity decreased by 1.36 °C. For small-, medium-, and large-size green spaces, there was a positive correlation between canopy density and cooling intensity. There was a most significant positive correlation between canopy density and cooling intensity in large-size green spaces (R2 = 0.941). The greater the canopy density, the greater the cooling intensity. For large green spaces, for every 0.5 increase in canopy density, the cooling intensity increased by 0.16 °C. For small-size green spaces, for every 0.5 increase in canopy density, the cooling effect increased by 0.15 °C. For medium-size green spaces, for every 0.5 increase in canopy density, the cooling intensity increased by 0.16 °C.Figure 13Linear regressions between the distance from different types of green spaces to water areas, canopy density and cooling intensity.Full size imageQuantitative analysis of the effects of different types of green space on humidifying intensityFigure 14 shows the linear regression between the distance of a green space from a water body, canopy density and humidifying intensity. There was a negative correlation between the distance to a water body and humidifying intensity in small, medium, and large green spaces. The negative correlation between the distance to a water body and humidifying intensity in small green spaces was most significant (R2 = 0.996). The longer the distance, the lower the humidifying intensity. For small green spaces, for every 1/4 in-crease in the distance ratio, the humidifying intensity decreased by 4.23%. For medium-size green spaces, for every 1/4 increase in the distance ratio, the humidifying intensity decreased by 3.02%. For large-size green spaces, for every 1/4 increase in the distance ratio, the humidifying intensity de-creased by 6.14%. For small, medium, and large green spaces, there was a positive correlation between canopy density and humidifying intensity. The positive correlation between canopy density and humidifying intensity in medium-size green spaces was extremely significant (R2 = 0.925). The greater the canopy density, the greater the humidifying intensity. For medium-size green spaces, for every 0.5 increase in canopy density, the humidifying intensity increased by 3.29%. For small-size green spaces, for every 0.5 increase in canopy density, the humidifying intensity increased by 3.17%. For large-size green spaces, for every 0.5 increase in canopy density, the humidifying intensity increased by 4.06% (Fig. 15).
Figure 14Linear regressions between the distance from different types of green space to water area, canopy density and humidifying intensity.Full size imageFigure 15Correlation of different green space types with water distance, canopy density and cooling and humidifying intensity.Full size imageEffect of shape and area of water bodies on microclimatic effects based on numerical simulationBanded waterWe constructed a numerical simulation model to explore the effects of a simulated increase in water body area on cooling and humidification. Figure 16 shows the simulated distribution characteristics of temperature and relative humidity after a 5% and 10% increase in water area at 14:00 when temperatures were high. The results suggest that between 7:00 and 10:00, with a 5% and 10% increase in water area, the air temperature was basically the same and the cooling effect was insignificant. However, between 12:00 and 19:00 and particularly in the hours between 13:00 and 16:00 when temperatures were highest, a 5% increase in water area produced a significant cooling effect, with a daily average value of 0.05 °C and a maximum value of 0.09 °C. A 10% increase in water area produced an extremely significant cooling effect, with a daily average value of 0.07 °C and a maximum value of 0.14 °C. From 11:00 to 19:00, a 5% increase in water area produced a significant humidifying effect, with a daily average value of 0.08% and a maximum value of 0.17%. A 10% increase produced an extremely significant humidifying effect, with a daily average value of 0.13% and a maximum value of 0.26% (See supplementary file).Figure 16Distribution characteristics of cooling and humidifying effects of simulated increase of banded water area at 14:00. (a) original cooling effect of banded water in the sample area; (b) cooling effect of 5% increase in water area; (c) cooling effect of 10% increase in water area; (d) original humidifying effect of banded water in the sample area; (e) humidifying effect of 5% increase in water area; (f) humidifying effect of 10% increase of water area.Full size imageMassive waterFigure 17 shows the simulated distribution characteristics of the cooling and humidifying effects after a 5% and 10% increase in the water area at 14:00 when temperatures were high. Between 8:00 and 19:00, a 5% and 10% increase in water area produced a significant cooling effect. At 19:00, the numerical simulation result was abnormal when the water area increased by 5% and 10%; at 13:00, the numerical simulation result was also ab-normal when the water area increased by 10%. After excluding the abnormal simulated data, a 5% increase in water area produced a cooling effect, with a daily average value of 0.06 °C and a maximum value of 0.10 °C. A 10% increase in water area produced an extremely significant cooling effect, with a daily average value of 0.10 °C and a maximum value of 0.18 °C. Between 11:00 and 19:00, a 5% increase in water area produced a significant humidifying effect, with a daily average value of 0.05% and a maximum value of 0.13%. A 10% increase in water area produced an extremely significant humidifying effect, with a daily average value of 0.13% and a maximum value of 0.27% (See supplementary file).Figure 17Distribution characteristics of cooling and humidifying effects of simulated increase of massive water area at 14:00. (a) original cooling effect of massive water in the sample area; (b) cooling effect of 5% increase in water area; (c) cooling effect of 10% increase in water area; (d) original humidifying effect of massive water in the sample area; (e) humidifying effect of 5% increase in water area; (f) humidifying effect of 10% increase of water area.Full size imageAnnular waterFigure 18 shows the simulated distribution characteristics of the cooling and humidifying effects after a 5% and 10% increase in the area of the annular water body at 14:00 when temperatures were high. Between 7:00 and 19:00, a 5% and 10% increase in water area produced a significant cooling effect. Between 11:00 and 16:00 when temperatures were high, a 5% increase in water area produced a cooling effect, with a daily average value of 0.06 °C and a maximum value of 0.14 °C°C and a 10% increase in water area produced an extremely significant cooling effect, with a daily average value of 0.13 °C and a maximum value of 0.28 °C. Between 7:00 and 19:00, a 5% and 10% increase in water area produced significant humidifying effects. Between 11:00 and 16:00 when temperatures were high, a 5% increase in water area produced an extremely significant humidifying effect, with a daily average value of 0.17% and a maximum value of 0.39% and a 10% increase in water area produced an extremely significant humidifying effect with a daily average value of 0.38% and a maximum value of 0.81% (See supplementary file).Figure 18Distribution characteristics of cooling and humidifying effects of simulated increase of annular water area at 14:00. (a) original cooling effect of annular water in the sample area; (b) cooling effect of 5% increase in water area; (c) cooling effect of 10% increase in water area; (d) original humidifying effect of annular water in the sample area; (e) humidifying effect of 5% increase in water area; (f) humidifying effect of 10% increase of water area.Full size image More

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In the present work, we extend the base model for the spatial mosquito population dynamics24 to include wild male mosquitoes and genetically modified male mosquitoes. Thus, five populations will be considered: the aquatic mosquito population, including larvae and pupae, the egg mosquito population, the reproductive female mosquito population, the wild male mosquito population, and the genetically modified male population. Similar approaches can be found in the literature25,26.In the following system, we represent mosquito population densities (mosquitoes per m(^2)) by: E – in the egg phase, A – in the aquatic phase, F – female in the reproductive phase, M – wild males, and G – genetically modified male mosquitoes. Due to the very high resistance of the egg phase (up to 450 days27) and as we are interested in an urban spatial macro-scale modeling, we do not consider the mortality in the egg phase. The model is described by the following system of partial differential equations:$$begin{aligned} {left{ begin{array}{ll} partial _t E &{} = alpha beta F M -e E, \ partial _t A &{} = e left( 1 – dfrac{A}{k} right) E -(eta _a+{mu _a})A, \ partial _t F &{} = nabla cdot (D_m nabla F) -mu _f F + reta _{a} A, \ partial _t M &{} = nabla cdot (D_m nabla M) -mu _m M + (1-r)eta _{a} A, \ partial _t G &{} = nabla cdot (D_g nabla G) -mu _{g}G + l, end{array}right. } end{aligned}$$
(1)
where ( alpha ) represents the proportion of wild male mosquitoes to the total number of male mosquitoes (wild males + genetically modified males); (beta ) represents the expected quantity of eggs from the successful encounter between wild females and males; e is the egg hatching rate; k is the carrying capacity of the aquatic phase; ( eta _a ) is the emergence rate for mosquitoes from the aquatic phase to the female or male phases; ( mu _a), (mu _f), (mu _m), and (mu _{g}) are the mortality rates of mosquitoes in the aquatic phase, females, males, and genetically modified males, respectively; r is the proportion of females to males (typically (r=0.5)); (l=l(x,y,t)) is the function representing the number of genetically modified mosquitoes released in a unit of time at any point of the domain; (D_m) is the diffusion coefficient of wild mobiles females and males; (D_g) is the diffusion coefficient of genetically modified males. The proposed model (1) can naturally deal with heterogeneous parameters, such as mortality, diffusion, and carrying capacity coefficients. Thus it is possible to model the influence of rain, wind, and human action. In the context of this work, we are considering that the city neighborhood is divided into two environments: houses and streets. Due to lack of data, we restrict the investigated heterogeneity only to the carrying capacity coefficient.The proposed model can be regarded as an extension of other “economic” models20,24 in the effort to qualitatively reproduce the complex phenomena by using as few parameters as possible. Following this idea, the carrying capacity was neglected in the egg phase because of the skip oviposition phenomenon28 i.e., the female lays the number of eggs that the place holds, without more space, she migrates to other environments to finish laying the eggs. We also do not consider this coefficient in the winged phase as limitations in the winged phase were not reported in any study. On the other hand, we consider it in the aquatic phases (larvae and pupae), where it is effective29.The term ( alpha ), which multiplies the probability of encounters between male and female, represents the impact of the insertion of genetically modified males in the mosquito population to the immobile phase and is defined as$$begin{aligned} alpha = left{ begin{array}{cc} 1, &{} text{ if } M=G= 0, \ dfrac{M}{M + G}, &{} text{ otherwise }. end{array} right. end{aligned}$$
(2)
Similar modeling approach can be found in the literature16. As the release rate of genetically modified males increases, the alpha value decreases, and, consequently, the probability of encounter between females and wild males also decreases. Thus, there is a greater probability of encounter between genetically modified males and females. This approach presents an advantage, when compared to the models found in the literature25, as System  (1) does not present singularities at the equilibrium states, allowing mathematical analysis and numerical simulations. From the biological point of view, the increment of male wild mosquitoes over some critical value does not affect the egg deposition. At first glance, the term FM can lead to a misunderstanding that such property is not satisfied in the presented model. However, in Section “Equilibrium points considering the application of genetically modified male mosquitoes,” we argue that both male and female populations possess mathematical attractor equilibria, blocking the wild male population from growing beyond this value.Finally, any acceptable population model should be invariant in the definition domain, meaning its solution does not present senseless values. Setting the variable domain as$$begin{aligned} 0 le E(x,y,t)< infty ,;; 0 le A(x,y,t) le k, ;; 0 le F(x,y,t)< infty ,;; 0 le M(x,y,t)< infty ,;; 0 le G(x,y,t) < infty , end{aligned}$$ (3) we can verify that it is invariant under the time evolution by the System (1). To prove this statement, it is sufficient to verify that the vector field defined by the right side of (1) points into the domain when (E, A, F, M, G) approaches the domain boundary. When E approaches zero, the right side of the first equation in (1) is not negative. When A approaches zero, the right side of the second equation in (1) is not negative. When A approaches k (bottom), the first term on the right side of the second equation in (1) tends to zero, while the second term remains negative. Since the term ( nabla cdot (D_m nabla F) ) cannot change the F sign, when F approaches zero, the right side of the third equation in (1) is not negative Since the term ( nabla cdot (D_m nabla M) ) cannot change the M sign, when M approaches zero, the right side of the fourth equation in (1) is not negative. Since the term ( nabla cdot (D_g nabla G) ) cannot change the G sign, when G approaches zero, the right side of the fifth equation in (1) is not negative. In the rest of this section, let us explain how to estimate one-by-one all the parameters used in this model from experimental data available in the literature. It is a challenging task as, typically, the development of the Ae. aegypti mosquito depends on food variation30, temperature variations14,15 and rainfall31. This data is not available in the literature in the organized and systematic form. Because of that, we assume the environment is under optimal conditions of temperature, availability of food, and humidity.How to estimate emergence rate ((eta _a)) The emergence rate describes the rate at which the aquatic phase of the mosquito emerges into the adult phases. In the present model, for simplicity, it was considered that no mosquito from the crossing between genetically modified males and females reaches adulthood. Thus, the emergence rate is calculated on the crossing between females and wild males. Under optimal conditions and feeding distribution, based on the literature30, the emergence rate is 0.5596 (text{ day}^{-1}).How to estimate diffusion coefficients ((D_m,D_g)) The diffusion coefficient is one of the most important parameters describing the mosquitoes’ movement. We use the methodology proposed in the previous work24 to obtain the diffusion coefficient of adult mosquitoes (females and males) and genetically modified males.The estimate is done by assuming that all mosquitoes are released at (0, 0), and their movement is described by the corresponding equation in (1) neglecting other terms than diffusion. The population starts spreading in all directions. We define the spreading distance R(t) as the radius of the region centered in (0, 0) where (90%) of the initial mosquitoes population density is present. In Silva et al.24 it is shown that$$begin{aligned} R(t) = sqrt{4Dt} ;text {erf}^{-1}(0.9). end{aligned}$$ (4) Now corresponding diffusion coefficient is estimated by using the average flight distance of the mosquitoes and the characteristic time related to their life expectancy. Under favorable weather conditions, the average lifetime flight distance of females and males is approximately32,33 65 m, while the same for GM males is34 67.3 m. Based on the literature, we consider that the characteristic time for wild females and males32 is 7 days, and the same for genetically modified males is34 2.17 days. Using (4) we estimate the values for (D_m) and (D_g) summarized in Table 1. It would be natural to consider that the mosquitoes’ movement changes in different environments. Unfortunately, we were unable to find the corresponding experimental data, and because of that, we considered that (D_m) and (D_g) are the same in streets and house blocks.How to estimate mortality rates ((mu _a), (mu _f), (mu _m), (mu _{g}))The mortality coefficient represents an average quantity of mosquitoes in the corresponding phase dying each day. As mentioned before, we disregard the mortality rate in the egg phase, as it is negligible due to its great durability27, it does not affect the numerical results, and it complicates analytical estimates. Thus, the aquatic phase mortality rate coefficient is equal to the same for larvae’s coefficient, which is approximately29 (mu _a = 0.025) (1/day).There is no solid agreement on the mortality rate of male and female wild mosquitoes in the literature. Although some results29,30 suggest they are similar, we follow these authors and consider them equal. Considering both natural death and accidental ones, approximately (10%) of females and male mosquitoes in the adult phase die at each day35. Under optimal conditions, the mortality coefficient can be estimated from this data by using the proposed model (1) by neglecting diffusion and emergence terms in the corresponding equation; details can be found in the previous work24. The resulting parameter values are summarized in Table 1.It would be natural to consider that the mosquitoes mortality rate depends on the environment. Unfortunately, we were unable to find the corresponding experimental data, and because of that, we considered that (mu _a), (mu _f), (mu _m), and (mu _{g}) are the same in streets and house blocks.How to estimate the expected egg number ((beta ))This coefficient represents the average quantity of eggs a wild female lays per day, assuming a successful meeting with a wild male. Considering the number of times a female lays eggs in its lifetime36, the average quantity of eggs per lay and the mosquito’s life expectancy, under favorable conditions, this coefficient is estimated as (beta = 34).How to estimate the hatching rate (e)This coefficient determines the average number of eggs hatching in one day. Experimental data37 suggest that, under optimal humidity conditions, the mean value of the hatch rate coefficient is 0.24 given a temperature of 28 ((^{circ })C), which is considered ideal for mosquito development. This is the value used in the present work.How to estimate carrying capacity coefficient (k)The carrying capacity k represents the space limitation of one phase due to situations present in the environment37,38, such as competition for food among the larvae39. In general, it depends on external factors such as food availability, climate, terrain properties, making direct estimation almost impossible. In the Analytical results section, we show how to estimate this coefficient for each grid block. When considering spatial population dynamics in a heterogeneous environment, carrying capacity is one of the most influential parameters as it varies significantly. For example, house block offer more food and a shelter against natural predators resulting to a larger carrying capacity when compared with street environment. Following the literature32 we assume that the 80% of the mosquito’s breeding places are in houses resulting in the relation (k_h=5k_s), where (k_h) and (k_s) are the carrying capacities of the house blocks and in the streets.Genetically modified mosquitoes release rate (l)Function l(x, y, t) determines how many genetically modified mosquitoes are released in the location (x, y) at time t.In a normal situation, the sex ratio between males and females is 1 : 1. The increment of this proportion favoring GM males increases the probability of females to mate with these mosquitoes. As reported in the literature12,30 the initial launch size is 11 times larger than the adult female population, and it is done in some spots in the city. In this work, we analyze different release strategies maintaining the (11times 1) proportion in some scenarios.Table 1 All parameter values are directly taken or estimated from the literature as explained in section Modeling.Full size table More