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Our results show that Chl a alone is not an adequate proxy for prey growth rates in dilution grazing experiments when mixoplankton are present5,10. Chlorophyll is, in any case, a poor proxy for phototrophic plankton biomass31 because of inter-species variations, and also for the photoacclimation abilities of some species (for which very significant changes can occur within a few hours). The problem extends to the involvement of mixoplanktonic prey and grazers. Nevertheless, even very recent studies continue to rely on this parameter for quantifications of grazing despite acknowledging the dominance, both in biomass and abundance, of mixoplanktonic predators in their system30. Moreover, the detailed analysis of the species-specific dynamics revealed that different prey species are consumed at very different rates. In our experiments, and contrary to expectations (see32,33, and Fig. S1 in the Supplementary Information), C. weissflogii was only actively ingested in the ciliate experiment and, according to the results from the control bottles (Table 2), not by M. rubrum (see Fig. 4 and Fig. S1a).Certainly, it is not the first time that a negative selection against diatoms has been seen; for example, Burkill et al.34 noticed that diatoms were less grazed by protist grazers than other phytoplankton species, as assessed by a dilution technique paired with High-Performance Liquid Chromatography for pigment analysis. Using the same method, Suzuki et al.35 reported that diatoms became the dominant phytoplankton group, which suggests that other groups were preferentially fed upon. Calbet et al.36, in the Arctic, also found only occasional grazing over the local diatoms. In our study, diatoms were not only not consumed, but the presence of dinoflagellates appeared to contribute to their growth (Fig. 4), this relationship being partly dependent on the concentration of the predator (see Fig. 2c, d). This result could be a direct consequence of assimilation and use of compounds (e.g.,37,38) released by microplankton such as ammonium (e.g.,39,40) and urea (e.g.,41), which were not supplied in the growth medium, but which would have supported prey growth. Alternatively, this unexpected outcome may have been a consequence of the selective ingestion of R. salina by the two predators, relieving the competition for nutrients and light and resulting in a higher growth rate of the diatom in the presence of the predators. We cannot rule out the fact that diatoms sink faster than flagellates which, as the bottles were not mixed during most of the incubation period (although gently mixed at every sampling point), may have also involuntarily decreased ingestion rates on C. weissflogii. Still, one C. weissflogii cell contains, on average, ca. 2.5 times more Chl a than one R. salina cell (initial value excluded, see Table 3). Taken together with the preference for R. salina it is not surprising that the proportion of total Chl a represented by the diatoms increased over time, in particular in the L/D treatment (Figs. 6a, c and 7a, c).Table 3 Chl a content (pg Chl a cell−1) of the target species at each sampling point as calculated from the control bottles.Full size tableAnother factor clearly highlighted by our experiments, is that protozooplankton themselves contribute a significant portion of the total chlorophyll of the system (due to ingested Chl a), in particular at the beginning of the incubation (see Figs. 6 and 7); this being invariably ignored in a traditional dilution experiment. The high Chl a detected inside the protozooplanktonic grazers at the beginning of the incubations could suggest that the system was initially not in equilibrium, and that this was the result of superfluous feeding (e.g.,42). This would, nevertheless, be surprising since we required ca. 1 h to collect the initial samples (t = 0 h) after joining all the organisms together (see the section “Dilution grazing experiments” in the “Methods” section); previous studies, like the one on G. dominans and Oxyrrhis marina by Calbet et al.42, showed that the hunger response and consequent vacuole replenishment occurred in ca. 100 min for very high prey concentrations and it is expected to decrease at lower prey concentrations as the ones used in our study. Therefore, even if one assumes that the first 4 h of incubation are a result of superfluous feeding, after 24 h, the “estimated”, “observed”, and “from dilution slope” grazing estimates are not significantly different to those displayed in Fig. 5 (P  > 0.05 in all instances) and, therefore, we can assume that the hunger response was likely irrelevant (e.g.,43) and did not mask our results. In any case, as stated before, an actual field grazing dilution experiment also suffers from similar problems, because grazers and prey are suddenly diluted and not pre-adapted to distinct food concentrations. Nevertheless, this is not novel information, since Chl a and its degradation products have been found inside several protozooplankton species from different phylogenetic groups immediately after feeding44 and even after some days without food45. An increase in intracellular Chl a concentrations immediately after feeding has also been found in mixoplankton46,47, on which this increase is derived both from ingested prey as well as from new synthesis of their own Chl a. Additionally, several experiments with Live Fluorescently Labelled Algae (LFLA) show that predators (irrespective of their trophic mode) seem to maximise the concentration of intracellular prey shortly after the initiation of the incubation (e.g.,48; Ferreira et al., submitted). Indeed, some authors have even been able to measure photosynthesis in protozooplankton, like the ciliates Mesodinium pulex49 and Strombidinopsis sp.50.The fact that Chl a is a poor indicator of phytoplankton biomass and the inherent consequences discussed so far can be solved by the quantification of the prey community abundance (e.g.,51) by microscopy or by the use of signature pigments for each major phytoplankton group. The latter method, however, is not as thorough as the former, since rare are the cases where one pigment is exclusively associated with a single group of organisms (see52 and references therein). In any case, any pigment-based proxy is subject to the same problems, as identified by Kruskopf & Flynn31. Irrespective of the quantification method, it has been made evident that the different algae are consumed at different rates (e.g., pigments10,34,35; microscopy5,36).Prey selection in protistan grazers is a common feature (e.g.,23,26,27,28). Given the diversity of grazers in natural communities and the array of preferred prey that each particular species possesses, it is logical to think that dilution experiments will capture the net community response properly. Likewise, grazers interact with each other through toxins, competition, and intraguild predation among other factors. An example of intraguild predation could be the observed on K. armiger by G. dominans (see Figs. 2f and 4 and Table 1), which caused an average loss of ca. 18.72 pg of K. armiger carbon per G. dominans per hour in the D treatment. Interestingly, in the same treatment, a slight negative effect of K. armiger on its predator G. dominans can also be deduced (i.e., positive g, Table 1), resulting in an average loss of ca. 0.33 pg G. dominans carbon per K. armiger per hour. This could be a consequence of algal toxins, since K. armiger is a known producer of karmitoxin22, whose presence may have negative effects even on metazoan grazers21. Regarding ciliates, none of the species used is a known producer of toxic compounds, which suggests that the average loss of ca. 1.25 pg M. rubrum carbon per hour in the D treatment was due to S. arenicola predation. Altogether, it seems clear from our data that intraguild predation cannot be ignored when analysing dilution experiments (Fig. 4). Furthermore, our results clearly show that single functional responses cannot be used to extrapolate community grazing impacts, as evidenced by the differences in estimated and measured ingestion rates based on the disappearance of prey in combined grazers experiments (Fig. 5). Nevertheless, this is a relatively common procedure (e.g.,53 and references therein). Often in modelling approaches, individual predator’s functional responses have been used to extrapolate prey selectivity and community grazing responses27; in reality complex prey selectivity functions are required to satisfactorily describe prey selectivity and inter-prey allelopathic interactions54.It is, however, also evident that the measured ingestion rates in combined grazers experiments were not the same as those calculated from the slope of the dilution grazing experiment. This raises the question of why was that the case. It is well known that phytoplankton cultures, when extremely diluted, show a lag phase of different duration55 which has been attributed to the net leakage of metabolites56. Assuming that the duration of the lag phase will be dependent on the level of dilution, it seems reasonable to deduce that after ca. 24 h the instantaneous growth rates (µ) in the most diluted treatments will be lower than that of the undiluted treatments. This has consequences, not only for the estimated prey growth rates but also for the whole assessment of the grazing rate, due to the flattening of the regression line (i.e., the decrease in the computed growth rate). This artefact may be more evident in cultures acclimated to very particular conditions (as the laboratory cultures used in this study) than in nature.Another important finding of our research is the importance of light on the correct expression of the feeding activity by both mixoplankton and protozooplankton. We noticed that irrespective of the light conditions, all species exhibited a diurnal feeding rhythm (R. salina panels in Figs. 2 and 3), which is in accordance with earlier observations on protists (e.g.,29,57,58). The presence of light typically increased the ingestion rates. Additionally, the ingestion rates differed during the night period between L/D and D treatments, which implies that receiving light during the day is also vital in modulating the night behaviour of protoozoo- and mixoplankton. In particular, mixoplankton grazing is usually affected by light conditions, typically increasing (e.g.,32,59), but also sometimes decreasing(e.g.,60) in the presence of light. Different irradiance levels can also affect the magnitude of ingestion rates both in protozoo- and mixoplankton (see61 and references therein).For those reasons, we hoped for a rather consistent pattern among our protists that would help us discriminate mixoplankton in dilution grazing experiments. As a matter of fact, based on the results from Arias et al.29, we expected that in the dinoflagellate experiment, the D treatment would have inhibited only the grazing of K. armiger, enabling a simple discrimination between trophic modes. The reality did not meet the expectations since the day and night-time carbon-specific ingestion rates (as assessed using the control bottles, Table 2) of K. armiger were respectively higher and equal than those of G. dominans. Conversely, in the ciliate experiment, protozooplankton were the major grazers in our incubations regardless of the day period and light conditions. This response was not as straightforward as one would expect it to be because M. rubrum has been recently suggested to be a species complex containing at least 7 different species (62 and references therein), which hinders any possible conjecture on their grazing impact. Indeed, the uneven responses found between and within trophic modes precluded such optimistic hypothetical procedure.The D treatment in the present paper illustrated the importance of mimicking natural light conditions, a factor also addressed in the original description of the technique by Landry and Hassett1. It is crucial for the whole interpretation of the dilution technique that incubations should be conducted in similar light (and temperature) conditions as the natural ones to allow for the continued growth of the phototrophic prey. However, here we want to stress another aspect of the incubations: should they start during the day or the night? Considering our (and previous) results on diel feeding rhythms, and on the contribution of each species to the total Chl a pool, it is clear that different results will be obtained if the incubations are started during the day or the night. Besides, whether day or night, organisms are also likely to be in a very different physiological state (either growing or decreasing). Therefore, we recommend that dilution experiments conducted in the field should always be started at the same period of the day to enable comparisons (see also Anderson et al.14 for similar conclusions on bacterivory exerted by small flagellates). Ideally, incubations would be started at different times of the day to capture the intricacies of the community dynamics on a diel cycle. Nevertheless, should the segmented analysis be impossible, we argue that the right time to begin the incubations would be during the night, as this is the time where ingestion rates by protozooplankton are typically lower (e.g.,29,57,58, this study) and would, consequently, reduce their quota of Chl a in the system.Lastly, we want to stress that we are aware that our study does not represent natural biodiversity because our experiments were conducted in the laboratory with a few species. Nevertheless, we attempted to use common species of wide distribution for each major group of protists to provide a better institutionalisation of our conclusions. Further to the choice of predator and prey is their concentrations and proportions. Being a laboratory experiment designed to understand fundamental mechanisms within a dilution grazing experiment, we departed from near saturating food conditions from where we started the dilution series. In nature, the concentrations that we used may be high but are not unrealistic, and actually lower than in many bloom scenarios. We included diatoms at high concentrations, even knowing that they are not the preferred prey of most grazers34, because diatoms are very abundant in many natural ecosystems and to stress the point of food selection within the experiment. For sure, using different proportions of prey would have rendered different results. However, as previously mentioned, our aim was not to seek flaws in the dilution technique, but to understand the role of mixoplankton in these experiments and the complex trophic interactions that may occur within. Ultimately, with our choice of prey and their concentrations, we have proven that when there is no selection for a massively abundant prey, the use of Chl a as a proxy for community abundances may underestimate actual grazing rates.Some other aspects of our experiments may also be criticised because they do not fully match a standard dilution experiment. For instance, we manipulated light, adding complexity to the study. However, this manipulation enabled the deepening into the drivers of the mixoplanktonic and protozooplanktonic grazing responses. Another characteristic, perhaps awkward, of our study is that we allowed the grazers to deplete their prey before starting the experiment. One may argue this procedure does not mimic the natural previous trophic history a grazer may have in nature. Yet, in nature, when facing a dilution experiment, it is impossible to ascertain whether the organisms are encountering novel prey or not. Indeed, they (prey and predator) could have just migrated into such conditions, or be subject to famine, or just moved from a food patch. In any case, it is true that a consistent “hunger response” would have affected our initial grazing values, biasing grazing rate estimates. To overcome this artefact, we let the grazers feed for about one hour before starting the actual dilution assay (see the “Methods” section). From that point on, any dilution is, in fact, an abrupt alteration of the food scenario, which is likely more important than the previous trophic history of the grazer.In summary, with these laboratory experiments, we have presented evidence calling for a revision of the use of chlorophyll in dilution grazing experiments5,10, and we have highlighted the need to observe the organismal composition of both initial and final communities to better understand the dynamics during the dilution grazing experiments51. This approach will not incorporate mixoplanktonic activity into the dilution technique per se however if combined with LFLA (see5,17), a semi-quantitative approach to disentangle the contribution of mixoplankton to community grazing could be achieved (although not perfect). An alternative (and perhaps more elegant) solution could be the integration of the experimental technique with in silico modelling. The modelling approaches of the dilution technique have already been used, for example, to disentangle niche competition63 and to explore nonlinear grazer responses20. We believe that our experimental design and knowledge of the previously indicated data could be of use for the configuration of a dilution grazing model, which could then be validated in the field (and, optimistically, coupled to the ubiquitous application of the dilution technique across the globe). We cannot guarantee that having a properly constructed model that mimics the dilution technique will be the solution to the mixoplankton paradigm. However, it may provide a step towards that goal as it could finally shed much-needed light on the mixo- and heterotrophic contributions to the grazing pressure of a given system. To quote from the commentary of Flynn et al.6, it could provide the answer to the question of whether mixoplankton are de facto “another of the Emperor’s New Suit of Clothes” or, “on the other hand (…) collectively worthy of more detailed inclusion in models”. More

Our results showed that covariates at different geographical scales (national and local) may have important effects on the risk of snakebite, both for humans and animals. The results indicate that the risk of snakebite in the Terai varies at national scale between clusters and at local scale between households. The evaluation of the final models without spatial random components and the worsening of the models’ goodness of fit as a result highlighted how snakebite risk and its determining factors are indeed spatially structured.A strong association between high snakebite incidence and mortality, and poverty was established from the analysis of 138 countries affected by the disease32. In this study, we identified the PPI, an indicator for poverty, as a highly influential risk-increasing factor for humans. This not only confirms the critical role of poverty as a driver for this Neglected Tropical Disease, but also offers the possibility to use a standardized index at individual household scale for similar studies. Chaves et al.33 used the Poverty Gap, which is a simpler index expressing how far a person is from the average national poverty line, but to our knowledge, no study has used PPI for snakebite in any way. Applying PPI as a snakebite risk predictor also addresses previous expert calls for an Ecohealth approach to consider the relationship between the structural characteristics of houses, poverty, and snakebite34.Three of the survey covariates had significant effects on the odds of snakebite. Food storage and straw storage increased them, while sleeping on the floor reduce them. The effect of the first two covariates is likely to be related to prey availability, represented by rodents, which are attracted by food and shelter sources. Both food and straw are very often stored near dwellings, which in the end multiply the number of possible encounters between humans, domestic animals, and the hunting snakes20. The expected snakebite risk reduction effect by sleeping on the floor is more complex though. Previously, a higher snakebite incidence was reported among rural Hindus in Maharashtra, India, due to their custom of sleeping on the floor35,36, while in Nepal, Chappuis et al. did not find any protective effect or significant difference in snakebite cases between sleeping on a cot or on the floor37. This result, nevertheless, might be influenced again by regional customs that make sleeping on the floor more common in eastern Terai (71.1% of all affirmative answers to this question), and second, by the commonly acknowledged prevalence of kraits (Bungarus spp.) in western Terai, which are the species most commonly linked to bites to people sleeping on the floor while hunting at night inside houses22,38. This geographic separation, between the human behaviour and the distribution of the species considered to cause most bites linked to it, could explain the observed shift in the odds towards a reduction effect. This effect should be further explored in localized studies designed to capture behavioural differences in humans and snakes.For both the general human risk model and its equivalent prediction model, the covariate Distance to water had a significant risk-increasing effect. For each additional km in distance from permanent water sources, the odds of snakebite increased by 1.38 and 1.51 times, respectively. From a human perspective and in this socio-economic framework, it would be important to consider not only the distance to water, but also the path taken to get the water (or any other resource). If this path would lead a person through grasslands and open fields, this could imply an increased risk of snakebite. From an ecological perspective, there are two important aspects to consider in relation to water sources. One is, as in this study, the distance from large, constant water sources, which usually represent stable environments subject to less hydric stress. The second (not considered here) are the human-made water sources, such as ponds, reservoirs, and paddy fields that change often, are usually closer to human dwellings, and are known to attract some medically important venomous snakes (MIVS)5. Studies on snake migration and home range use have concluded that depending on species and ecological conditions, snakes can move between a few tens of meters per day and more than 10 km between seasons, while searching for water and prey resources38,39,40,41. In sub-tropical regions like the Terai, snakes living closer to continuous sources of water and vegetation should have easier access to a wider variety of prey. On the contrary, those living in agricultural areas might need to scout farther in the search for resources, encountering human-made waterbodies and prey, such as rodents42 and amphibians, abundant in this region10. Further studies considering all sources of water, and species ecology, biology and richness would be necessary to completely understand the effect of this and similar eco-physiological covariates.Another important factor was the NDVI, which is a commonly used value to express photosynthetic activity, leaf production and in summary the ‘greenness’ of the environment43. As is the case for other covariates, its interpretation depends on the study circumstances. In Iran, it was considered an indicator of prey availability for snakes and linked to snake habitat suitability14. Elevated NDVI values have been associated with higher number of hospitalizations in Nigeria and northern Ghana, in particular during the periods of high agricultural activity, which is also related to higher snake-human contact and higher snakebite incidence43. In our study, its ‘protective’ effect can indeed be the consequence of better access to prey associated with healthier ecosystems, explained in the Terai by the higher NDVI values of the multiple dense forests distributed along the region. In addition, the averaged NDVI values for agricultural areas should be lower than those for perennial forests, because they include the highs and lows of production and harvest.Environmental drivers like temperature and precipitation are common factors in geospatial analyses of snakebite13,14,17,44. They are found in many cases to be the main factors modulating the incidence or risk of snakebite, while varying in importance according to study conditions. For example, in Iran, precipitation seasonality was the most prevalent climatic covariate determining the habitat suitability leading to snakebite risk14, while in Mozambique, temperature seasonality was the predominant covariate13. Despite the Terai’s sub-tropical climate, the range of the average minimum temperature of the coldest month (BIO6) was 1.8–10.9 °C. For our snakebite risk analysis in animals, an increase of 10 °C of BIO6 between any two points represented an increase in the odds of snakebite of 23.41 times. For snakes, this range could be the difference between total lethargy and partial activity45, which could lead to increased numbers of snakebites. In addition, and according to the production and holding practices of domestic animals in the Terai, this temperature range can also represent the difference between animals (mainly ruminants) being kept in sheds when at the lower range limits, or being let out of them at the upper limits, which would again increase the chances of encounters with snakes.Similarly, for the animal model, pig density and sheep density, significantly influenced the variation in the risk of snakebite for animals in the Terai. This could be due to the conditions in which the animals and their feed are kept, favouring environments that are beneficial for either snakes or their prey. At more local scales, rather than the distribution, the presence of other animal species could instead be the factor associated with higher snakebite rates12. However, since the available data on domestic animal density was produced more than 10 years ago, and the animal population has grown substantially in the last years in Nepal, this outcome should be interpreted with caution.For the animal risk, the possession of an animal shed also significantly increased the odds of snakebite. Similar to straw storage, animal sheds and similar constructions offer some shelter and at the same time attract small (prey) animals, both of which are likely to attract snakes, increasing snakebite risk for the animals using the shed. If in addition, the sheds function as poultry coops, the snake hunting behaviour might be instead targeted towards chicks and chickens12. Mitigation measures such as raising the coop’s floor or securing openings with fine metal mesh have been suggested to reduce this risk12.The human modification of terrestrial systems was the only non-significant covariate in the animal risk model. However, as its strong, risk-reducing effect still seems to explain a lot of the response variation, it was retained. Its change in one unit, i.e., going from a pristine to fully modified environment, decreased the odds of snakebite by 0.13 (equivalent to 7.69 times), which agrees with previous national survey results from Sri Lanka21.For our human risk prediction model, four covariates were either significant or helped to explain the changes in the response. Distance to water and NDVI were clearly significant, and precipitation of the driest quarter (BIO17) and the mean annual temperature (BIO1) helped to explain some of the response variation with convincing, unambiguous effects. For BIO17, an increase of 100 mm of rain during the driest months of the year represented an odds-reduction effect equivalent to 8.33 times. This agrees with the results of distance to water, suggesting that the additional availability of resources during water shortage periods, i.e., almost four times more rain (BIO17 range: 18–71 mm), could locally improve ecological conditions for snakes also leading to less scouting and fewer human encounters. Previous studies have analysed the multilevel ecological effects of droughts, e.g., reducing snake prey and leading snakes to engage in riskier behaviours46,47. For BIO1, the protective effect was weaker. An increase of 10 °C represented a reduction of the odds of snakebite equivalent to 3.57 times. Average temperatures for specific locations are difficult to interpret, since they might depend on mild highs and lows, strong highs and lows, or relative combinations of both. Thus, despite having a relatively important effect on the response, this effect still might be the consequence of confounding and unknown interactions.Several other evaluated covariates, for both humans and animals, showed a negligible effect on describing the response, were not significant while having very large uncertainties, or both. Consequently, they were discarded as predicting factors. For the list of baseline covariates evaluated, see supplementary Table S1. For a complete list of available survey covariates, see Alcoba et al.27.Some of our discarded covariates have been important in other studies, for example, to quantify snakebite risk based on reclassification methods of covariates such as habitat suitability, species presence, or envenoming severity13,14,17,44,48. These methods are especially relevant when one species (or very few) is the cause of most snakebite cases, and has differentiated optimal and sub-optimal habitats. In Nepal, and particularly in the Terai, there are at least two, and sometimes more than 10 MIVS with overlapping distributions49. Thus, it could be said that practically the whole region offers suitable habitat for multiple MIVS. In addition, the impossibility of reliably identifying the species having bitten the surveyed victims hindered the use of single species in the analysis. In our analysis, species richness was removed, as it showed almost no effect on the response. A recent meta-analysis reported an equivalent result at global scale, finding no significant difference between the number of venomous snake species in tropical and temperate locations, while the number of snakebites is clearly higher in tropical areas50. These results suggested that high incidence of snakebite is unrelated to species richness, but instead related to other factors like the number of people working in agricultural environments21,32,50. Another important driver of snakebite incidence has been population density50. In our study, however, any possible effect from population density on the risk was diminished by the random selection of households at specific numbers during study design. This was later confirmed by the minimal effect of population density as covariate in the human risk analysis.This study presents a few limitations. For instance, despite the capacity of the INLA method to borrow strength from neighbouring observations and areas, the selection of adequate covariates with enough explanatory power still depends greatly on the number of snakebite cases, which even for a national scale study like this remains small. Also, some of the covariates with the strongest explanatory power came from our household survey, which prevented their use for generalized spatial prediction models. Concerning the animal risk analysis, due to the small number of snakebite cases we opted to aggregate all animal species and consider a grouped response. Thus, for a spatial analysis of animal risk, it was not worth it to consider each species, since that would dilute further an already sparse dataset in individual models and selection processes. Moreover, the data gathered for animals was dependent on the random selection of (human) households and unrelated to the current distribution of animal populations. This, in addition to the possible number of dry bites that go unnoticed, might be responsible for the low number of animal victims recorded (even combined across all species), making a more detailed analysis unfeasible.Despite the large number of covariates examined during our analysis, very few were useful to predict snakebite risk along the Terai. It is possible that confounders or other difficult-to-measure covariates could better explain the complex relationship between the ecology and biology of MIVS, socio-economic factors, human behavioural traits, and the circumstances around domestic animal keeping. This needs to be further explored, following a recent call for an overarching One Health and Ecohealth approach to better understand the drivers for snakebite risk, incidence, and mortality under specific situations34.In conclusion, snakebite is a multi-factorial disease and there is no possible universal approach to model its risk. Each model should be individually designed for each set of socio-economical, geographic, ecological, cultural, and environmental circumstances19. To better understand and address the snakebite problem, it is necessary to approach it, whenever possible, with local data collected at a national scale, so that the conclusions drawn can fuel appropriate national public health policies and actions. As long as people work, live, and keep their domestic animals in close contact with natural environments with MIVS, the risk of snakebite will be present. However, better understanding of the factors influencing that risk at the most granular scale possible, and the estimation of the populations at risk, can help to better target prevention and mitigation measures. For humans, this evidence can channel efforts towards improved access to treatment through the optimized stockpiling of antivenom, and the improvement, relocation or new construction of treating facilities, but more importantly, towards community education and sensitization in preventive campaigns51. Part of that preventive and educative efforts can be done at household level, by promoting and facilitating the use of protective equipment such as rubber boots, or the guidance on how to improve and adapt their immediate surroundings to make them ecologically less attractive for snakes and their prey. For domestic animals, this information could help better target awareness-raising activities for animal owners and implement mitigation strategies. For animals at higher risk, tailored interventions such as the improvement of housing conditions, regular cleaning of sheds and surrounding areas (e.g., from food waste and surrounding vegetation), and using light when animals are walked out of the enclosure at night could be deployed specifically as snakebite prevention measures52. It is also important to highlight that many of the factors analysed in this study affect most directly the snakes themselves, not only as snakebite agents, but also as a diverse group of species, differently affected by ecological, climatic and environmental factors in a multiplicity of settings shared with humans and domestic animals. It is therefore necessary to further investigate how those factors influence the behavioural and ecological traits of MIVS in order to truly understand this disease from a One Health viewpoint. At stake is the reduction of snakebite envenoming incidence rates in humans and animals, and of its possible long-term sequelae on human populations. More

Study site and populationThe study was conducted between July and October 2019 in the North of Peru. We focused on populations of coexisting Morpho species present in the regional park of the Cordillera Escalera (San Martin Department) near the city of Tarapoto. Both the capture-recapture and the dummy experiment were performed at the exact same location, on the bank of the Shilcayo river (06°27′14.364″S, 76°20′45.852″W).DNA extraction and RAD-SequencingThirty-one wild males caught on the study site were sequenced to perform population genomic analyses (M. achilles—n = 13, M. helenor—n = 10 and M. deidamia—n = 8). DNA was extracted from each sample from a slice of the thorax, using Qiagen kit DNeasy Blood & Tissue. DNA quantification (using the microfluorimetric method) and quality controls (using electrophoresis and spectrophotometric method) were performed prior to sequencing. RAD-library preparation and sequencing were performed at the MGX-Montpellier GenomiX platform (Montpellier, France). DNA was digested with the Pst1 enzyme and the library was prepared according to Baird and Etter’ protocol47 in a slightly modified version. Paired-end RAD-sequencing was performed on a 2 lanes flow cell of an Illumina HiSeq2500 in a rapid mode so that reads (125 bp) were expected to be of high quality with no missing base (N content). We obtained 299 million sequences, comprising R1 and R2 reads for each sequenced fragment. Adapters were removed from the reads.Read quality control, alignment and dataset generationRead quality was assessed with FastQC v0.11.9 (http://www.bioinformatics.babraham.ac.uk/projects/fastqc/). The per base sequence quality was high across all reads (no lower than 36 for R1 and 32 for R2) with an average quality score of 39 (40 being the maximum). Overall, FastQC highlighted the high quality of the sequencing data, allowing us to skip the step of read trimming.The data were demultiplexed, assigning each sequence to its sample ID and the reads were aligned using Stacks V2.5 (http://catchenlab.life.illinois.edu/stacks/)48,49. Parameters were set following the 80% polymorphic (r80) loci rule, which only considers loci shared by at least 80% of the samples50. The optimised parameters are ‘max distance between stacks’ (inside each sample) and ‘number of mismatches between stacks’ (between samples). Every other parameter was kept to default values. After aligning all reads, we selected 2740 biallelic loci shared by all samples, including 88,889 SNPs in total. Each locus had a length of 463.12 bp on average (range [343; 908]). These loci are assumed to be evenly distributed throughout the genome but cover only a limited portion of the genome (around 0.5%). Datasets were stored in a VCF file (containing all the SNPs found in the alignment) and a fasta file (containing the two alleles found at every locus for each sample). To run DILS-ABC inferences, Stacks fasta files were converted to another fasta format compatible with DILS (https://github.com/CoBiG2/RAD_Tools).Demographic inferencesEight categories of demographic models were compared, according to temporal patterns of introgression. This was done to answer two questions on gene flow in Morpho: (1) is there ongoing migration between M. helenor and M. achilles? (2) do M. helenor and/or M. achilles exchange alleles with M. deidamia? This was assessed by an ABC approach using a version of DILS adapted to samples of three populations/species32. Since Stacks does not report monomorphic RAD loci, the ABC analysis was conditioned in the same way, by excluding monomorphic loci from the simulations. Focusing on polymorphic loci may only limit our ability to estimate the absolute values of parameters (i.e. population sizes expressed in numbers of individuals, and ages of past events expressed in numbers of generations); nevertheless, this framework excluding monomorphic loci still allows reliable comparisons of models51 and estimations of relative parameter values, as performed to investigate the human history51.A generalist model was studied (Supplementary Fig. 12). This model describes an ancestral population subdivided in two populations: the ancestor of M. deidamia and the common ancestor of M. helenor/M. achilles. The latter population was further subdivided into the three species/populations currently sampled. Each split event is accompanied by a change in demographic size, the value of which is independent of the ancestral size. In addition, given clear genomic signatures for recent demographic changes with largely negative Tajima’s D, we implemented variations for the effective sizes of the three modern lineages at independent times. Finally, migration can occur between each pair of species/populations. Migration affecting the M. helenor/M. achilles pair can either be the result of secondary contact after a period of isolation (ongoing migration), or of ancestral migration (current isolation) as in50,52.As this model is over-parameterised, our general strategy is to investigate the above two questions by comparing variations of this generalist model. Thus, to test the gene flow between M. helenor and M. achilles, we compared two categories of models. (1) With random parameter values for all model parameters including the ongoing migration between M. helenor and M. achilles (gene flow resulting from a secondary contact between them); (2) as above, but with the migration between M. helenor and M. achilles set to zero after a randomly drawn number of generations following their split. An overlap between ‘current isolation’ and ‘ongoing migration’ models can occur when the transition time (from ancestral migration to current isolation forward in time for a ‘current isolation’ model; or from ancestral isolation to ongoing migration forward in time for an ‘ongoing migration’ model) tends towards the extreme values 0 or Tsplit hel-ach (Supplementary Fig. 12). To reduce this effect, the transition times were drawn in a Beta distribution with parameters (α = 5, β = 1) when migration has to be restricted to a past period, and in a Beta distribution with parameters (α = 1, β = 5) when migration is assumed to occur after a recent secondary contact.When two broad categories of models are statistically compared, each category is represented by simulations performed under the four sub-models allowing or not allowing genomic heterogeneities for effective sizes (Ne) and for migration rates (N.m). For instance, to test for gene flow between M. helenor and M. achilles, the model of ‘ongoing migration’ is actually represented by simulations with the four possible combinations of homogeneity/heterogeneity, all labelled as being ‘ongoing migration’.As for any inferential analysis, it is important to recognise that the best-supported model is based on a classification of models within a studied set. Intermediate models, with more subtle cycles of genetic isolation and secondary contact could produce a better fit to the data, but it would be surprising to detect a strong support for the model assuming a lack of recent gene flow, if the most recent secondary contact of such cyclicity induced elevated gene flow.For each model, 50,000 simulations using random combinations of parameters were performed. Parameters were drawn from uniform prior distributions. Population sizes were sampled from the uniform prior [0–1,000,000] (in diploid individuals); the older time of split was sampled from the uniform prior [0–8,000,000] (generations); ages of the subsequent demographic events were sampled in a uniform prior between 0 and the sampled time of split. Migration rates 4.N.m were sampled from the uniform prior [0–50]. Both migration rates and effective population sizes are allowed to vary throughout the genomes as a result of linked selection, following refs. 53,54,55.On each simulated dataset, we calculated a vector of means and standard deviations for different summary statistics: intraspecific statistics (π for M. helenor, π for M. achilles, π for M. deidamia, θW for M. helenor, θW for M. achilles, θW for M. deidamia, Tajima’s D for M. helenor, Tajima’s D for M. achilles, Tajima’s D for M. deidamia) and interspecific statistics (gross divergence, net divergence and FST for all three possible pairs; ABBA-BABA D). Our version of DILS includes part of the DaDi56 and Moments57 strategy involving the identification of the best model proposed demographic model from the molecular patterns of polymorphism and divergence (proportion of shared polymorphisms, fixed differences between species, exclusive polymorphisms, etc.), excluding monomorphic loci. Thus, only loci containing at least one SNP in an alignment of the three species studied are considered, including singletons. Importantly, each locus carrying at least one SNP in a tri-specific alignment is associated with a mutation rate assumed to be 3 · 10−9 mutations per generation and per base pair to convert demographic parameters into demographic units from coalescence units.We first conditioned the mutations occurring during coalescent simulations by using theta (=4 · N · µ · Li; where N is the effective population size, µ the mutation rate per nucleotide and per generation; Li the length of locus i). The number of simulated segregating sites for a given locus strongly depends on the coalescent history (i.e the total length of the simulated coalescent tree), occasionally generating monomorphic loci. To confirm that the inferences are not impacted by differences in the number of monomorphic loci in the simulated datasets, we then used an alternative simulation approach, by randomly placing in simulated coalescent trees a fixed number of mutations corresponding to the observed number of SNPs for each locus. Thus, a randomly simulated dataset consists of 2740 loci whose lengths (ranging from 339 to 894 nucleotides) and number of SNPs (ranging from 1 to 91) individually match the properties of the observed loci in the actual dataset. Since the results drawn from both approaches were similar, we report only the estimations provided by the simulations based on the actual number of SNPs. Comparisons between the two approaches can be found in supplementary (Supplementary Tables 8, 9).Statistical comparisons between simulated and observed statistics were performed using the R package abcrf version 1.8.158,59.Mark-recapture experimentTo estimate the timing of patrolling activity among Morpho species, we performed capture-mark-recapture between 9 a.m. and 2 p.m. (flight activity in Morpho is drastically reduced in the afternoons at this site) during 17 sunny days. Although on a few days, capture was cancelled because of bad weather annihilating butterfly activity, the 17 capture sessions were mostly consecutives, as they were performed in a 22 days period (Supplementary Table 1 and Supplementary Fig. 15). All butterflies were captured with hand-nets, identified at the species level, and numbered on their dorsal wing surface using a black marker. The exact time of each capture was annotated. Butterflies captured while inactive, such as those laying on a branch or on the ground were excluded from the analysis to focus exclusively on actively patrolling individuals. We measured patrolling time for a total of 295 occasions, including 78 recaptures (i.e. 217 individuals were captured at least once). All captured individuals were males. Individuals M. achilles were the most frequently captured (n = 121), followed by M. helenor (n = 95). Individuals M. deidamia were about half less captured (n = 48), and individual M. menelaus were the least captured (n = 34). Because striking differences in patrolling time were observed among Morpho species, we used time of the day as a predictor of species identity in order to distinguish between M. helenor and M. achilles in the below-described experiment because butterflies from these two species are morphologically too similar to be identified while flying (Supplementary Fig. 13). After the 17 nearly-consecutive days of capture, one day of capture was repeated every 2 weeks during 2 months in parallel to the dummy experiment (described below), to verify that temporal activity was stable over time (Supplementary Fig. 13).Estimating population size from mark-recapture dataBased on capture-recapture histories, we estimated individual abundance for each species using a loglinear model implemented in the R package Rcapture version 1.4.360 (Supplementary Fig. 15). Given the short duration the sampling period (22 days) relative to the longevity of adult Morpho butterflies (several months61), we used a closed-population model assuming no effect of births, deaths, immigration and emigration. Abundance was estimated in Morpho helenor and M. achilles only, as capture and recapture events were too few in the other species (M. deidamia and M. menelaus) to allow estimating population size (Supplementary Table 1).Experiment with dummy butterfliesWe investigated the response of patrolling males to sympatric conspecifics, congeners and of exotic conspecifics, using dummies placed on their flight path. Dummies were built with real wings dissected and washed with hexane to remove volatile compounds and cuticular hydrocarbons, ensuring to test only the visual aspect of the dummies. We mounted the wings on a solar-powered fluttering device (Butterfly Solar Héliobil R029br) that mimics a flying butterfly, thereby increasing the attractiveness of the dummy. The fluttering dummy was positioned on the riverbank, and placed at the centre of a 1 m3 space delimitated with four vertical stacks (Fig. 1a). The set-up was continuously monitored by a human observer and filmed using a camera (Gopro Hero5 Black set at 120 images per second) mounted on a tripod. Patrolling Morpho butterflies that deviated from their flight path to approach the dummy but did not enter the cubic space were categorised as approaching. Any Morpho butterfly entering the cubic space was considered as interacting with the dummy. Those passing without showing interest to the setup were categorised as passing. The category of behaviour and the exact time of the butterfly responses were annotated on site by the human observer. Patrolling individuals were mainly identified at the species level by the observer on the site: M. menelaus can be easily distinguished from M. deidamia, and these two species are also quite different from M. helenor and M. achilles. However, the sister species M. helenor and M. achilles cannot be discriminated during flight, and we thus rely on an indirect method, based on flight hours, to infer the species identity of wild visitors looking as a M. helenor/M. achilles (Supplementary Fig. 13). Note that removing data with the highest levels of uncertainty in species identity (i.e. when discarding visits performed in the period where M. helenor/M. achilles temporally overlap) does not quantitively affect our results (Supplementary Fig. 14 and Supplementary Tables 5, 6). Using the recorded video, we also measured the duration of the interactions (i.e. the time spent in the cubic space) occurring between patrolling male and the dummy. The ten dummies were each tested during 4 sunny days from 9 a.m. to 2 p.m. (i.e. during 5 h). This resulted in 40 days of experiment over which each dummy was left fluttering on the river bank for a combined duration of 20 h. Dummies were randomly attributed to each day of the experiment. Mark-recapture data suggested a very low rate of individuals passing through the site several times per day (mean percentage of recapture within the same day = 0.95%), thus limiting potential pseudoreplication within each dummy replicate. We recently showed that intraspecific variation in wing colour pattern within the locality is very low in these species25. Using a single dummy per sex and species, as done here, should thus have little impact on the observed behaviours.In order to control for variation in weather (affecting both the activity of patrolling butterflies and of the solar-powered device), we collected hourly data on the percentage of cloud cover for the period and location of our experiment (available at https://www.visualcrossing.com/). A percentage of cloud cover was then associated with all the behavioural observations, and used as a control variable in all statistical analyses.Three-dimensional kinematics of flight interaction with the dummiesTo test whether Morpho males showed different flight behaviours when interacting with the male and female dummy, we filmed the flight interactions using two orthogonally positioned video cameras (Gopro Hero5 Black, recording at 120 images per second) around the dummy setup (Fig. 1a). Stereoscopic video sequences obtained from the two cameras were synchronised with respect to a reference frame (here using a clapperboard). Prior to each filming session, the camera system was calibrated with the direct linear transformation (DLT) technique62 by digitising the positions of a wand moved around the dummy. Wand tracking was done using DLTdv863, and computation of the DLT coefficients was performed using easyWand64. After spatial and temporal calibration, we also used DLTdv8 to digitise the three-dimensional positions of both the visiting (real) butterfly and the dummy butterfly at each video frame by manually tracking the body centroid in each camera view. Butterfly positions throughout the flight trajectory were post-processed using a linear Kalman filter65, providing smoothed temporal dynamics of spatial position, velocity and acceleration of the body centroid. Based on these data, we investigated how spatial position, speed and acceleration of the visitor butterfly varied over the course of the interaction. We proceeded by dividing space into 10 cm spherical intervals around the dummy position ranging from 0 to 1.2 m distance (this step standardises interactions of different durations), and computed the proportion of time spent, the mean speed and acceleration of the interacting butterfly within each distance interval (Fig. 2). We analysed a total of 28 interactions performed by individual Morpho achilles male, including 14 with the dummy of its conspecific male and 14 with the dummy of its conspecific female. Analysed interactions lasted in average 1.44 ± 0.87 (mean ± sd) s.Statistical analysis of behavioural experimentsDifferences in patrolling time were assessed by testing the effect of species on time of capture using Kruskal–Wallis test. To test the effect of visitor identity and dummy characteristics on the number of approaches and interactions, we performed logistic regressions. Approach was treated as a binary variable, where 0 meant ‘passing without approaching’ and 1 meant ‘approaching the dummy setup’. For the interactions, we only considered individuals approaching the setup, such as 0 meant ‘approaching without entering the cubic space’ and 1 meant ‘entering the cubic space’. This allowed getting rid of the uncertainties on whether passing individuals had actually seen the setup or not. We first tested the effect of visiting species on approach and interaction while controlling for dummy’s characteristics to test for intrinsic differences in territoriality (or ‘curiosity’) among species. We then tested the effect of the dummy sex and identity on approach and interaction separately in Morpho helenor and M. achilles. The percentage of cloud cover was also included in the models to control for variation in dummy movements (generated by the solar-powered device), potentially affecting the butterfly response (Supplementary Tables 3 and 4). We further tested if variation in wing area and proportion of iridescent blue among dummies affected the frequency of approach and interaction, again using logistic regression analyses (Supplementary Fig. 7). Statistical significance of each variables was assessed using likelihood ratio tests comparing logistic regression models66. Finally, we tested the effect of dummy sex and identity on the duration of interaction using Kruskal–Wallis tests.Based on the flight kinematic data, we investigated whether flight behaviour during the interaction differed with male vs. female dummies. We ran a mixed-effects model testing the effect of (1) the sex of the dummy and of (2) the distance from dummy (fixed effects), on the proportion of time spent (fixed effects), using the flight ID as a random effect. The flight ID corresponds to the behaviour of a single wild males flying within the ‘interaction space’. Specifically, we tested for the statistical interaction between the sex of the dummy and distance from dummy on the proportion of time spent in the different distance intervals. We then similarly tested for difference in acceleration over the course of the flight interaction, by testing the effect of (1) the sex of the dummy and of (2) the distance from dummy (fixed effects), on the acceleration, with the flight ID as a random effect. We focused on the statistical interaction between the sex of the dummy and the distance from dummy on the mean acceleration in the different distance intervals.Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

Climate change and the urban heat island effect threaten the sustainability of rapidly growing urban settlements and urban population worldwide1. Such threats may be ameliorated by the ecosystem service of local climate regulation provided by green–blue urban areas (natural, restored, or (re)constructed ecosystems, such as forested land, wetlands, parks)2,3,4. The spatiotemporal relationships existing between natural ecosystems and human societies form the basis of the ecosystem service framework, used to represent such benefits from nature to human well-being5,6. Areas of ecosystem service provision (nature contribution of some supply) and ecosystem service use (human beneficiaries with some ecosystem service demand) in a landscape are then often connected by some form of carrier flow, which can be natural (air and water movement) or depend on human-made infrastructure (e.g., pipelines for water, road network and vehicles for human movement)7,8. Additionally, ecosystem service relevance is scale-dependent, e.g., with carbon sequestration being globally relevant, while recreational areas provide mostly local and regional benefits9,10,11. Over each scale of relevance, it is essential to distinguish the supply and demand sides of spatial ecosystem services relationships2, and the degree to which potential supply (left, Fig. 1) can actually reach and fulfill some actual demand (right, Fig. 1). This may be referred to as the degree of realization of ecosystem service supply and demand12. Conceptually, we define a potential as the hypothetical maximum capacity for a service (supply) or need (demand). In contrast, a realized service quantifies the actual ecosystem service, after consideration of proper spatial flow connections between natural ecosystems and humans. For example, for a city, only part of its total potential ecosystem service demand (Pd) may be actually fulfilled (referred to as the realized ecosystem service demand, Rd, right in Fig. 1) by only part (the realized supply part, Rs, left in Fig. 1) of the city’s total potential ecosystem service supply (Ps). Thus, Rd measures the part of the human demand (for the ecosystem service) actually fulfilled, while Rd quantify the part of the supply used to provide the ecosystem service. The Methods section describes and discusses in further detail this and other term definitions used in the analysis, the relationships between terms, and the calculation methods employed to quantify them.Figure 1Spatial flow dependence of ecosystem services and studied city locations. Schematic of potential and realized supply and demand of flow-dependent ecosystem service (for explanation, see “Methods”).Full size imageIn practice, implementing the concept of ecosystem services into urban landscape management and decision making is still problematic5, with one reason being the challenge to link spatially disaggregated areas of service provision with the human beneficiaries13. In addition, considerable ambiguity still remains, conceptually and in practice, regarding the distinction and quantification of potential and realized ecosystem services supply and demand14. For example, without consideration of the spatial relationship between supply and demand (implicitly or explicitly), it becomes difficult to determine or quantify, in practice, if an actual ecosystem service exists. To contribute to its resolution, we here investigate the degree of supply and demand realization for the urban ecosystem service of local climate regulation using comparative quantitative indicators in and across 660 cities of different sizes and in different parts of Europe (Fig. 2).Figure 2Studied city locations. Map of the European study region and locations of the cities studied. See Supplementary Table 1 for further city data.Full size imageThe potential of green–blue urban areas for cooling cities is generally well established, and has been studied using direct observations15,16, remote sensing17 or modelling based approaches18,19. The regulation of local urban air temperatures by such areas can increase thermal comfort and decrease health risks related to urban heat island (UHI) effects20,21 for urban populations. The UHI effects relate to often-observed higher ambient air temperatures in urban environments compared to their close surroundings20,21. The spatial extents of cities in this study are then considered according to their respective administrative unit definitions.The investigation focuses on urban realization of this ecosystem service because the proportion of the global human population living in urban areas is steadily rising22, and cities are critical for both climate change mitigation and societal adaptation to warming23,24. For adaptation, cities need to handle exacerbated urban warming by UHI effects and provide livable environments for their residents while avoiding detrimental consequences from competing development interests25,26. The UHI effects emphasize the importance of local climate regulation as an essential urban ecosystem service, the actual realization of which depends on city function and form, with the latter including the spatial distribution of green–blue urban areas, as well as temporal changes in this by growing urbanization. The degree to which such growth leads to replacement of moist soils and vegetative cover with paved and impervious surfaces also affects urban surface energy and radiation balances27, and associated land surface temperatures at local human scale, although the relationship with air temperature is complex27. For example the proportion of vegetation in a particular area will regulate the resulting ratio of sensitive to latent heat flux (known as Bowen ratio), which will in turn affect properties of the urban climate27.In reality, a city’s climate consists of a variety of smaller-scale microclimates, which can be modified and leveraged through deliberate design20. This emphasizes the importance of good city planning28, including for conservation, restoration, and construction of new urban green–blue areas29,30. Such areas can provide various services to urban populations, e.g., urban flood mitigation12 and more general health31 and well-being32 benefits, including cooling required to mitigate UHI effects. The latter can be achieved, e.g., by enhanced latent heat flux associated with higher evapotranspiration from green areas and evaporation from blue areas. Through the flow of air and its lateral heat advection, green–blue urban areas can also cool surrounding built parts of the city that would commonly have a demand for such ecosystem service of local climate regulation2. How to measure and predictively quantify the zones of influence of such air cooling by green–blue areas is still a challenging research question, but such zones are reported to be in the range of several hundred meters29,33,34.The aim of the indicators developed and used in this study is to quantify actual realized urban ecosystem service supply in terms of its fulfillment of some actual demand for that ecosystem service of the urban human population. Over each city, such realization and associated indicator values depend both on local conditions (such as natural land-cover areas that can supply the considered ecosystem service) and overall urban form and spatial configuration of the natural and built areas in the urban landscape. At larger scales spanned by multiple cities (such as those over Europe studied in this paper, Fig. 2), the quantitative indicators can be used to detect main ecosystem service realization patterns, similarities and differences among cities. This is done by quantifying indicator statistics across the cities, and assessing ecosystem service realization patterns in terms of how these statistics depend on city characteristics, or associated country or sub-region characteristics, such as population density or socio-economic measures like Human Development Index (HDI) and GDP per capita.A few studies have evaluated spatial dependencies of ecosystem services35,36 and mostly focused on multiple services in a specific study area. Our comparative multi-city study aims instead at revealing possible overarching statistical patterns of the spatially dependent ecosystem service of local climate regulation, and its realization in and across European urban systems. While this urban ecosystem service is important per se, the dependence of its realization on spatial proximity to green–blue areas may also provide useful guidance for further study of other urban ecosystem services that depend on the spatial distribution of green–blue areas and their proximity to human needs within cities2,12,32.Previous multi-city explorations of urban socio-economic growth and human-made infrastructure have revealed and quantified various statistical cross-city patterns37,38,39. Our study hypothesizes that such patterns may also emerge in the cross-city statistics of ecosystem service realization indicators related to green–blue city areas and their provision to urban populations. Identification of such quantitative ecosystem service indicator patterns can increase fundamental understanding of urban ecosystem service conditions, as well as projection capabilities for changes in these conditions under city growth, e.g., in terms of population density, HDI, and GDP per capita.To explore and test the main study hypothesis, we compile and synthesize for all 660 European cities (Fig. 2) high-resolution datasets for city morphology (e.g., land cover) and bio-physical characteristics (e.g. degree of imperviousness, vegetation type and vegetation density), based on previous study reports of the relevance of these parameters for the ecosystem service of local climate regulation2,12, along with city-scale measures of human population, city area, and resulting population density ratio (Supplementary Table 1). Using these data, we evaluate and map total potential ecosystem service supply and demand in each city (Figs. 1, 2, Supplementary Figures 1–3, Methods), and further apply a model of radially decaying ecosystem service supply and demand realization at 20 m resolution (Supplementary Figure 2–3, Methods) to also account for the spatial influence reach of local climate regulation from each location in the city. Furthermore, for comparative multi-city analysis, we quantify a set of directly comparable ecosystem service realization indicators for each city (explained further below) and their resulting statistics across all 660 cities over Europe, and comparatively for cities in different European countries and sub-regions.Indicator definitions and calculationsFor each of the 660 cities, we consider and calculate two basic metrics of urban ecosystem service realization: the ratio of realized to potential ecosystem service supply (Rs/Ps), and the ratio of realized to potential ecosystem service demand (Rd/Pd). For each discretized city pixel within a city, we first calculate its local net potential ecosystem service supply (Ps) or demand (Pd) directly from the urban morphology and bio-physical data (Supplementary Figure 1). For each net supply pixel, we further calculate (as illustrated bottom right in Supplementary Figure 2) that pixel’s ecosystem service realized supply contributions to the surrounding net demand pixels within its spatial influence radius (top, Supplementary Figure 2). Analogously, for each net demand pixel, we calculate the contributions to fulfilling (realizing) its ecosystem service demand from the surrounding net supply pixels that have that net demand pixel within their spatial influence radius. For each pixel of any type, we thus calculate its realized ecosystem service supply Rs or demand Rd in relation to its potential net local supply Ps or demand Pd, respectively (Supplementary Figure 2; see also Supplementary Figure 3 and Supplementary Information for further calculation and mapping details). We further calculate comparative indicators of city-average relative realized ecosystem service supply and demand, Rs/Ps and Rd/Pd, respectively, from the sums of local Rs, Rd, Ps and Pd over all pixels in the city. The city-average supply indicator Rs/Ps thus quantifies the average degree of realized (actually used) ecosystem service supply from all green–blue areas over the whole city (left in Fig. 1). Analogously, the city-average demand indicator Rd/Pd quantifies the average degree of realized (actually fulfilled) ecosystem service demand over each city (right in Fig. 1). For further cross-city comparison, we also calculate indicators for how large area fraction of total city area has a relatively high degree of ecosystem service supply and demand realization, respectively. Local Rs/Ps ≥ 0.5 and Rd/Pd ≥ 0.5 are then selected as illustrative thresholds for such relatively high degree of ecosystem service supply and demand realization, respectively, with the area fractions calculated from the number of pixels with Rs/Ps ≥ 0.5 or Rd/Pd ≥ 0.5 relative to the total number of pixels in each city.Based on the power-law relationships with population density results found for both previous city-average and city-fraction indicators of ecosystem service realization, we also have an opportunity to project indicator values for future scenarios of changed population density, as$$r_{i} = frac{Ri}{{Pi}} = Ai cdot left( {PD} right)^{beta i} le 1$$
(1)
where index i = d represents demand and i = s supply. Furthermore, for city-average indicators, Ri and Pi represent realized and potential ecosystem service, respectively, while for area-fraction indicators, they represent city area with high degree of ecosystem service realization (≥ 0.5) and total city area, respectively. The constraint of (r_{i} le 1) is due to the upper limit of Ri ≤ Pi for both indicator types, with Ai the scale factor and βi the exponent of a power law relationship ri with population density (denoted PD). Based on Eq. (1), a relative measure of ecosystem service realization effectiveness can be estimated from the demand fulfillment ((r_{d})) relative to the supply use ((r_{s})), as:$$Effectiveness = frac{{r_{d} }}{{r_{s} }} = frac{{Ad cdot left( {PD} right)^{beta d} }}{{As cdot left( {PD} right)^{beta s} }} = frac{Ad}{{As}}PD^{{left( {beta d – beta s} right)}}$$
(2a)
with$$r_{d} = Ad cdot left( {PD} right)^{beta d} quad ifquad r_{d} le 1,,,,,r_{d} = 1quad otherwise$$
(2b)
$$r_{s} = As cdot left( {PD} right)^{beta s} quad if,r_{s} le 1,,,,r_{s} = 1quad otherwise.$$
(2c) More

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