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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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