Ecology

Our results suggest that certain plant functional traits can be retrieved from simple RGB photographs. The key for this trait retrieval are deep learning-based Convolutional Neural Networks in concert with Big Data derived from open and citizen science projects. Although these models are subject to some noise, there is a wealth of applications for this approach, such as global trait maps, monitoring of trait shifts in time and the identification of large-scale ecological gradients. This way, the problem of limited data that still impedes us to picture global gradients7 could be alleviated by harnessing the exponentially growing iNaturalist database16. The performance of the CNN models across traits varied strongly, but revealed a clear trend: As expected, the more a trait referred to morphological features, the more accurate the predictions were. The models of the Baseline setup explained a substantial amount of the variance for LA and GH, whereas traits that are partly related to morphological features, SLA and SM, show moderate (R^2) values. The predictions of LNC and SSD explain almost none of the variance, suggesting that tissue constituents are not directly expressed or related to visible features. It also indicates that the strong covariance among these traits13 does not suffice in supporting their predictions from photographs. If the RGB images do not contain relevant information, the model will minimise the prediction errors by the regression-to-the-mean bias seen in Fig. 3 (especially lower panels).The value of informing the model on the known trait variability through an augmentation of the target values (Plasticity setup) depended on the results of the Baseline setup of the trait. That is, the better the predictive performance of the Baseline setup, the more the trait seemed to profit from the Plasticity setup, rendering it ineffective for SSD, LNC and SM (Fig. 3). Refraining to cling to species mean values by considering within-species trait variation has been applied before using conventional methods26, but to our knowledge has never been tried in CNN models, yet. We expected that providing a distribution of trait values rather than a single mean for each species can convey to the CNN that different trait realisations can be expected from the same species. Obviously, this idea can only work if a distribution rather than a single value is available for each species. The SM dataset, for instance, contained only one image per species (Table 1). In this case, the Plasticity setup reduced the predictive performance compared to the Baseline setup, possibly by increasing the discrepancy to the true trait value. Since the traits with more accurate predictions profited most from the Plasticity setup, we assume that it supports the model in learning to predict the trait expressions themselves rather than extracting them indirectly through taxa-specific morphological features. Given that we restricted the number of images per species to a maximum of 8, while successful deep learning-based plant species identification usually requires thousands of images12,22, it seems very unlikely that the models inferred traits from species-specific plant features visible in the imagery. The latter was underpinned by our finding that the predictions of most traits are void of phylogenetic autocorrelation (Supplementary Information 1 and Supplementary Table 5), indicating that taxonomic relationships were insignificant for the trait predictions. The absence of phylogenetic autocorrelation of the prediction errors underlines that the models did not learn species-specific features for most traits, as this would imply similar trait predictions for related species.On the contrary, the SSD model predictions express a phylogenetic signal (Supplementary Information 1 and Supplementary Table 5). Trait expressions are generally clustered under similar climatic conditions29,30,31. Simultaneously, climatic conditions constrain the geographic distribution of species and growth forms29,30,31,32. The SSD dataset is biased towards woody species (Table 1), which confines it to a smaller taxonomic range. Hence, the phylogenetic signal of SSD might result from its phylogenetic clustering and predominant dependence on bioclimatic information rather than on RGB imagery (Fig. 2).Nevertheless, the benefit of including climate information on temperature, precipitation and their seasonality8,20,21,26 on predicting trait expressions was confirmed for all traits in this study, which underlines the value of contextual constraints in CNN models10 (see below for a discussion of the relevance of climate vs. image data). This also highlights the general flexibility of deep learning frameworks in adapting to variable input data from different scales and sensors10, which makes them a promising tool for ecological research. Our results particularly revealed this effect for SSD, SLA and LA, whereas it was smaller for GH, LNC and SM (Fig. 2). For the latter traits, other physical constraints such as disturbance33,34, seasonal variation35,36 and soil conditions6,26,28 come into consideration. As the focus of the Worldclim setup was to show that contextual cues can improve the trait retrieval from photographs rather than identifying the best set of auxiliary data, we confined the analysis to the most promising20,26 data source (WorldClim37).In the Worldclim setup, a single model accumulated knowledge about the trait learning task. Combined predictions of different CNN models, however, have shown to surpass the predictive performance of single CNN, e.g. in plant species identification tasks22. Each of the CNN models is prone to literally ‘look’ at different aspects of the learning task by focusing on different image features. Previous research also showed increased model performance in a trait prediction task in case of ensembles of regression and machine learning models26. Accordingly, and as demonstrated by our results, an ensemble approach seems promising to further enhance predictive performance of CNN models concerning trait prediction.The predictive performance of these Ensembles has shown to be reproducible with different sets of training images (cp. Figs. 2, 3, Supplementary Fig. 2). In our heterogeneous dataset, model performance was not affected by different growth forms, image qualities and image-target distances (Fig. 4). Different growth forms and plant functional types show their own characteristic trait spectrum13. Possibly, contextual cues within the image might have supported the CNN in inferring the plant functional type of a species, e.g. by a long-distance image being indicative of a tree species. Yet, since the majority of the images only shows single plant organs on close-up photographs (Fig. 4), we assume that the trait predictions are not confounded by the identification of growth forms. Furthermore, the absence of a phylogenetic signal in the prediction errors for most traits highlights the model’s ability to generalise by extracting trait information independent of taxonomic relationships, meaning that the models (except for SSD) did not learn species-specific mean trait expressions (see Supplementary Information 1 and Supplementary Table 5).Additionally, we disclosed the high generalisability of these results by investigating the datasets’ underlying distributions both spatially (Supplementary Fig. 3) and across biomes (Supplementary Fig. 4). Although some regions such as Central Europe and North America show higher data coverage, the datasets used for this study contain data across all biomes and regions on Earth. Therefore and despite this clustering, we expect the models to be applicable for all biomes around the globe. This was highlighted by an additional analysis showing that the predictive performance of the models is reasonably constant across biomes (Supplementary Fig. 5). As suggested by refs.38,39, we tolerated a certain spatial bias in favor of larger datasets. Although the SSD dataset predominantly contained woody species, neither of the six datasets expressed an exclusion of either growth form (Table 1, Fig. 4).The application of our models to global gradients of traits revealed that our GTDM indeed cover macroecological patterns and trends known from other publications: The latitudinal distributions could roughly be confirmed for GH26, LNC26,27 and SM6,8 (Fig. 5). Predicted trends for maximum leaf size hint at the applicability of our GTDM of LA40. The trait gradients for North America were confirmed for SLA6,8,26,27,28, SM6,8, LNC27 and SSD6 alike. Although based on different input data and modelling methods, the major global latitudinal gradients found in previous studies could be reproduced by our GTDM, which indicates the plausibility of the latter6,8,26,27.We further validated the GTDM quantitatively by means of correlations with other GTDM. Regarding SSD, the detected high correlations might be due to method similarity, as our GTDM product of SSD primarily builds upon climate data (see above), just as ref.6,26. For GH, SLA and SM, however, the high correlations are unlikely to result from climate data exclusively, as the explained variances of the RGB imagery ((R^2) of Plasticity setup) are higher than the additional contributions of the Worldclim setup (approx. 94%, 70% and 79% share of imagery on total explained variance, respectively; Supplementary Table 2). We decoupled the GTDM products from bioclimatic information in an additional analysis (Supplementary Fig. 6). Remarkably, the macroecological patterns could roughly be reproduced when the GTDM were based exclusively on RGB imagery, which shows that the bioclimatic information merely serves to smooth the macroecological trait patterns for most of the traits.Despite of all GTDM being at least partly build upon climate data and using trait data from the same source (TRY database), some GTDM of SLA and all GTDM of LNC vary strongly in their correlations (Supplementary Fig. 1). On the one hand, this might indicate that LNC varies at a different scale, e.g. on account of its seasonal and within-species variation35,36. On the other hand, other GTDM products are based on mean trait values weighted by abundances of plant functional types27,28 rather than single trait predictions, which might explain negative or non-significant correlations as well.Hence, a potential pitfall of the presented approach is that it is prone to express an observation bias, e.g. by citizen scientists only taking pictures of the most striking species. The sampling design underlying the GTDM does not account for plant community composition, meaning that we cannot tell if plant photographs at a certain location represent the actual community structure. Since many images contain more than one individual plant and different species, the CNN model predictions, however, might be based on more than one species, thereby partly resembling trait expressions of the community. The representativeness of trait data for plant communities, though, remains an ubiquitous problem of global trait maps, including those fully based on trait data from the TRY database7, since every available dataset is far from representing the actual plant community composition7. Hence, at present our GTDM have to be considered a plausibility check of the model predictions rather than an application-ready trait map product, not least because the sampling of images might not be representative of the respective plant community.Nevertheless, our results indicate that exploiting a Big Data approach is viable to reveal macroecological trait patterns, maybe because the most striking species of an ecosystem are likely to suffice in describing its functional footprint5. Since the strong growth of the iNaturalist database leads to a steadily increasing geographic coverage, the representativeness of these data is likely to grow as well. A recent study investigating the records of FloraIncognita12, a citizen-science and deep learning-based application for identifying plant species from photographs, suggested that such crowd-sourced data can reproduce primary dimensions in plant community composition41. This underlines the future potential of harnessing citizen science databases for identifying these patterns. Here, we demonstrated the practical value and applicability of the CNN models by producing GTDM that were able to reproduce known macroecological trait patterns while displaying one anticipated application of this method. Additionally, in these GTDM we bypass the issue of spatial error analysis that is challenging for most GTDM products26 by obtaining a potentially arbitrary number of observations in light of the strongly increasing number of observations in iNaturalist, almost rendering an extrapolation obsolete. Our GTDM are based on individual trait measurements rather than estimated on behalf of a small set of covariates, which is typical for climate-based GTDM26. Since plant traits vary strongly within species17,18,19, these measurements express a high practical relevance. As the iNaturalist plant photograph database is witnessing an exponential growth of data inputs, the potential of exploiting this data source for plant trait predictions is growing rapidly. It is worth mentioning that this approach also led to the first publication of a GTDM of mean LA (available for download under https://doi.org/10.6084/m9.figshare.13312040), since former publications were limited to modelling upper limits of LA based on climatic constraints40.Future studies building on our work, which benefit from the ever-growing data accumulation of both the iNaturalist and TRY database, might not face restrictions of dataset size as we did in our study. This might allow for more representative samples in future studies, e.g. enabling to stratify training data by species while simultaneously balancing the trait distribution. This might support a reduction of the regression-to-the-mean bias seen in all of the results (Fig. 3) by avoiding to overrepresent common trait expressions. Another possible approach would be to select only species with particularly low variability for model training, since it decreases the chance of incorporating images showing plants with an extreme trait expression that differ strongly from the chosen mean trait values from TRY. By that, we might be able to derive more reliable and accurate predictions in the context of weakly supervised learning by reducing noise in the training data.Although weakly supervised learning approaches generally have shown to be an effective way of compensating a shortage of individually labeled data42,43, an image dataset including in-field trait measurements under natural conditions representing the global trait spectrum would be necessary for a conclusive validation. In our study, it even remains unclear to what extent the trait values actually refer to the individual plant shown in an image, particularly as the images sometimes show more than one individual plant and more than one species (Supplementary Fig. 7). This may hinder the model from predicting a trait value corresponding to the dominant species in the image (but might also partly resemble the community composition, see above). Although we attempted to compensate the lack of a dataset that enables a conclusive validation by eliminating possible biases concerning image settings (Fig. 4), growth forms (Fig. 4), phylogenetic autocorrelation (Supplementary Information 1, Supplementary Table 5), predictions based only on climate data (Supplementary Fig. 6), predictive performance across biomes (Supplementary Fig. 5), a training dataset subject to limited geographic or climatic coverage (Supplementary Figs. 3, 4) and effects of a specific set of training data (Supplementary Fig. 2), we cannot conclusively prove that the model predictions are based on causal relationships. Our model results suggest that the trait predictions reflect the feature space of natural trait expressions (Fig. 3), but an in-depth analysis of the image features the models learned for inferring the respective traits will be necessary to rule out any possible biases in future studies. An explicit analysis might involve investigating which plant organs are relevant for the trait predictions by means of feature attribution techniques and could ultimately provide clear evidence. This may not only enable to build trust in such artificial intelligence (AI) models, but also to generate new knowledge from them in order to deepen our understanding of plant morphology and trait covariance.Nevertheless, this study can only be considered a pioneering work testing the feasibility of the approach, as application-ready models require a conclusive and explicit validation. A dataset enabling this has to incorporate image-trait pairs measured and photographed on the same individuals. One possible solution would be to generate a database of plant traits including respective photographs, which then can serve as a benchmark for future studies. More

Log normal concentrations in the environmentEmpirical concentration distributions in the environment exhibit a wide variability, ranging from familiar parametric forms, e.g., normal and log-normal distributions, to more complex shapes9,10,11,12. Overall, the concentration distribution reflects the different processes that govern environmental fate, e.g., emissions/formation, transport processes, source mixing, sinks and dependences on other variables and processes. In principle, we may therefore extract mechanistic insights into the lifecycle of an environmental component from analysis of the concentration distribution. Although such deconvolution is intangible in the general case, there are specific cases where there are known mechanistic origins for certain distributions. For instance, source mixing in the environment will tend the distribution towards normal.In this paper we present a model for how log-normal distributions may emerge in the environment (Fig. 1A). This topic has been addressed in a few earlier studies6,7,8. A joint argument in these is the implication of the ‘Multiplicative Central Limit Theorem’ (or ‘Gibrat’s law’), which applies to processes that include the product of many random variables. If we take the logarithm of the product of many random variables, we have the sum of many random variables, by which the Central Limit Theorem applies, which predict a normal distribution. Back-transforming the logarithm, yields a log-normal distribution. Although this heuristic argumentation does not provide specific physico/chemical mechanisms as to how the multiplication of multiple random variables may commonly appear in the environment, it does provide an intuitive framework.The present contribution is based on a physico/chemical first order exponential kinetics model (Fig. 1B). Starting with an ordinary differential equation (Eq. 1), we introduce a stochastically variable rate, resulting in a stochastic differential equation (Eq. 2). By solving the corresponding Fokker–Planck equation (FPE) (see Theory section and SI for details) we derive the log-normal distribution (Eq. 3), under certain assumptions about stochastic variability. Since exponential kinetics are commonly observed for many processes in the environment, this model provides a potential explanation for the relative ubiquity of lognormal distributions in the environment.Observations of lognormal-like concentration distributions in the environment include a wide array of components (e.g., aerosols; bulk organic carbon; heavy metals; organic pollutants; minerals; trace gases; inorganic ions; humic matter; biomarkers; radionuclides; microplastics; pharmaceuticals and pesticides) in various environmental sub-compartments (e.g., groundwater; watersheds; urban air; precipitation; rocks; stormwater; indoor air; soils; wastewater; marine sediments; landfills; lake sediments; peat; glaciers; background air; biota and humans)2,3,12,13,14,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38. However, even though log normality is relatively common in the environment, we emphasize that it by no means is generally observed10,11,12: see discussion in the next section.Ascribing a data set to a specific parametric form, e.g., log-normal, may provide mechanistic insights, but also typically simplifies statistical treatment11. Among multiple approaches, a straight-forward approach to test for log-normality is by log-transforming the data and then use one of the many well-established tests for normality, e.g., the Shapiro-Wilks test9,39,40. Specific aspects of analysis of log-normal data sets, e.g., the impact of non-detects or data averaging, or data sampling strategies, have been discussed in some detail in the literature12,41,42,43. However, even though we may attribute a certain data set to a parametric distribution, there are many empirical situations where the data appears to follow a complex/un-known distribution. Can we identify some general principles that may help disentangle observed variability, even beyond common parametric forms?Three mechanisms influencing concentration distributionsAny environmental system is governed by a multitude of different processes, occurring simultaneously. Fortunately, some mechanisms appears to be more prevalent than others, and we can make simplifications, allowing modeling, e.g., the currently presented model for log-normal dependence. To attempt a more general description for concentration distributions, it may prove useful to consider a few different principal mechanisms. Here we explore three such mechanisms:KineticsThe model presented here is a common first order approximation of kinetics, e.g., of source and sink processes (Fig. 2A–B). In reality, dynamical systems may be highly complex, beyond the present formulation with a constant deterministic part (μk, Eq. 2), with multiple coupled components, non-linearities, feedbacks and heterogenous interactions. How such more complex kinetics influence concentration distributions is a topic for further scientific discovery.Figure 2Numerical simulations (random sampling) of time-series concentration data and corresponding distributions, illustrating how different processes may influence concentration distributions. Panels (A)–(B): Log normally-distributed data (Eq. 3), e.g., influenced by exponential kinetics. Panels (C)–(D): Data reflecting the random fluctuation between three different log-normally distributed states (green, blue and red), yielding a multi-modal (mixture) distribution. Panels (E)–(F): Random mixing of the three distributions from panels (C)–(D), yielding a convolution distribution, tending towards a normal distribution. Panels (G)–(H): The log-normal distribution of panels (A)–(B), modulated by an oscillatory function (here sine function), illustrating the impact of, e.g. diurnal or seasonal cycles on observed distributions. The simulations were conducted using Matlab (ver. R2019b).Full size imageMixingThe concentration of a component in the environment is typically the sum of emissions from many sources. If these combine randomly, the concentration distribution approach normality (Fig. 2E–F). However, this type represents one limit of mixing—where the resulting distribution at each time point is the sum distribution (convolution) of many variables. Another limit is where the contributions from different sources are separated, such that the concentration at any given measurement point (e.g., time point) reflects one individual source (Fig. 2C–D). An example could be an atmospheric measurement site located between two cities: by wind direction each time point is mainly dominated by either city. In this limit the concentration data will tend to a multi-modal (or ‘mixture’) distribution.External variablesIn the model described in the Theory section the non-stochastic part of Eq. (2) is a constant (μk). But this parameter may also vary with external parameters, e.g., state variables. For instance, diurnal or seasonal variations of temperature, pressure or sunlight, including phase transitions, may strongly influence concentration distributions (Fig. 2G–H).These three classes of mechanisms influence the lifecycle of a component in the environment, but their relative importance regarding how concentration distributions are affected may be highly variable. For certain instances it may be possible to ascribe a certain parametric function to the data, e.g., a normal distribution for well-mixed sources or a log-normal suggesting a kinetic domain. However, for situations with more complex, multi-modal or broad distributions both statistical treatment and interpretations are more challenging. For instance, quite similarly looking distributions may emerge from rather different mechanisms, e.g., dependence on an externally oscillating parameter or a stochastically jumping mixture distribution (e.g., compare Fig. 2C–D with Fig. 2G–H).OutlookThe shape of empirical concentration distributions is determined by the lifecycle dynamics and thereby contain information of environmental fate. In this paper we show that log-normality suggests influence by first order exponential kinetics (Eqs. 1 and 5; Fig. 1A–B). Reflecting the overall non-equilibrium state of environmental systems, there are a number of different processes/mechanisms that may exhibit exponential kinetics and thereby drive concentrations towards log-normality, e.g., emissions/chemical formation (e.g., of primary or secondary pollutants), degradation/decomposition (e.g., chemical reactions or deposition), kinetic transfer between different pools/layers/reservoirs (e.g., between the troposphere and the stratosphere) or kinetic partitioning (e.g., between gas and liquid phases). Some of these processes, e.g., sink kinetics, are active throughout the lifecycle of a component, and thereby continuously push concentrations towards log-normality.Overall, the implications of log-normal concentration distributions span a broad spectrum of potential applications, ranging from data analysis methodologies, sampling strategies, emissions estimation, source apportionment calculations, modelling of chemical fate, estimation of toxic exposure to future climate scenarios9,25,29,41,42,43,44,45,46,47,48,49,50,51,52. Given the general mathematical formulation of the model (Eq. 2), we note that the applicability extends to log-normal concentration distributions also beyond Environmental systems53,54.A specific example, where mechanistic insights may be derived from analysis of concentration distributions is the estimation of lifetimes (τ = 1/k, Eq. 1)55,56. Our present findings suggest that observation of log-normally distributed concentration data, perhaps especially at remote or receptor sites, may indicate sink kinetics, and may therefore provide insights into the sink rate (Eqs. 4a–b and 5). Another specific situation where concentration distribution analysis is of importance is the common challenge of trend detection in environmental data11. For certain time-series data, log-transformation is commonly used prior to statistical analysis51,57. The present analysis may provide a physico-chemical motivation for such transformations, potentially contributing to interpretations. A third specific example regards the analysis of ratios of diagnostic markers, which are common tools to assess sources and processes across Earth and Environmental sciences. Examples include ratios of chemical markers and isotope signatures, where the latter commonly are reported as concentration ratios. The ratio of two log-normal random variables is another log-normal variable58. We may then predict that if the overall concentrations are log-normal, then, e.g., isotope signatures should also be log-normal, with potential implications for data analysis methodology and interpretation.Finally, we note that rates in environmental systems often are proportional to concentrations, e.g., reactants. As an example, the sink rate for CO is proportional to the OH concentration (see Theory). Consequently, if the concentration is log-normal, so is the rate. Furthermore, fluxes (e.g., emission or sink fluxes) are often defined as the product of a rate and a concentration (or at least the amount, by some proportional measure). Taken together, this suggests that log-normal concentration distributions may imply log-normal distributions also for rates and/or fluxes for certain systems, with implications for, e.g., emission estimation or box models47,49,59.All-in-all, this paper presents a mechanistic model for how log-normal concentrations may emerge in the environment, which in turn suggests an explanation for the relative abundance. More

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Understanding the spatial patterns and drivers of animal movement is a crucial first step to controlling disease spread4. Our study provides novel information about where, how and when cattle move in a region beset by endemic pathogens2,39,40. Because contacts occur heterogeneously through time and space, interventions targeting areas and times of high contact risk could effectively break the chain of transmission across wide areas. We found that cattle herds had the highest probability of contact at dipping sites, far from their bomas, in small herds and during periods of low rainfall, indicating that transmission of all pathogens may be particularly elevated under these conditions (Figs. 5, 6). Nonetheless, cattle spent most of their time in other areas (i.e. near bomas or in grazing areas) where the direction and magnitude of effect of spatiotemporal scale on contact rates varies. This suggests that interventions for different pathogens in these systems will likely require a consideration of scale of transmission and be tailored to particular pathogens. Overall, our study provides a framework for risk-based livestock disease control approaches for the most dominant management systems in sub-Saharan Africa.Daily movement patterns of cattle in pastoral and agropastoral settings in sub-Saharan Africa largely reflect the distribution of shared resources, which determines the distance animals move each day and the probability of contacting each other. Our results are similar to those reported in other regions of Africa, suggesting broadly comparable patterns of daily displacement. For instance, cattle in our agropastoral study area travel to grazing, watering and dipping locations that are ~ 4 km from their bomas and primarily during daylight hours (Fig. 2). Similarly, in Kenya, cattle in the pastoral Mara and Ol Pajeta regions move less than 6 km from their bomas and movements peak around 12:00–14:00 h each day9,41. Despite the predominance of short-distance daily movements, we observed occasional long-distance movements (i.e. up to 12 km), particularly by larger herds. Transhumant cattle in Cameroon also moved up to 23 km/day for short periods, while relocating to seasonal grazing areas on the edge of the Sahel, though in most observations (86%) they moved less than 5 km/day8. Although we observed no contacts among cattle from bomas  > 17 km apart (Supplementary Fig. S5), regardless of how contact was defined, infrequent long-distance movements by large herds may provide a conduit for disease transmission between villages42. Indeed, larger herds actually had a lower relative probability of contact across spatiotemporal scales (Fig. 5), which may reflect the fact that large herds were more likely to move to areas away from other collared cattle, either because they were moving outside the study area, or because they had exclusive use of particular areas, whereas smaller herds that were mostly moved around bomas mixed more frequently. While interventions (e.g. vaccination or quarantine) targeting small herds would address local disease events, particularly within villages, halting larger-scale transmission requires an understanding of livestock pathways enabling inter-village connectivity and strategies tailored to herds driving these processes.A key difference between the movement of cattle in agropastoral and pastoral systems lies in the seasonal variation of daily movement. In our study, agropastoralists move their herds farther in the wet compared to the dry season, while the opposite has been reported for pastoralists8,9,41. During the wet season, agropastoralists cultivate crops near their homesteads, which increases competition for space and displaces cattle to reserved grazing areas far from cultivated land11. During the dry season, particularly in the early period, cattle graze harvested fields around the homestead and tend to move short distances each day. In our study, although individual herds travelled more (marginally) in the wet compared to the dry season, there were more contacts following low rainfall periods when resources were typically scarce (Fig. 5). Similarly, a previous study has shown that more villages were connected at shared resource areas during dry spells, which resulted in higher contacts11. This suggests a higher disease risk in the dry compared to wet seasons in agropastoral management systems.Translating movements into contact between individuals is challenging because the definition of a “contact” depends on the distance at which pathogens can travel in space, and the time period that pathogens survive, or mature to an infectious state, in the environment. Most studies that attempt to measure contact, however, focus only on a single scale. Here, we show that pairwise contact rates between cattle herds generally increase with broader spatiotemporal definitions of contact. Yet, there was no difference at spatial scales between 50 m, 100 m and 200 m for a temporal scale of one hour, suggesting these scales are functionally equivalent definitions of contact. Thus, we define “close contact” as proximity of livestock herds within 200 m in any given hour, which would be applicable to multiple disease systems and vital for understanding infectious disease spread in traditionally managed herds. However, given that herds tracked in our study ranged in size from 30 to 500 cattle, for households with herds of  More

Soil physicochemical propertiesThe test results of physicochemical factors of the soil are shown in Table 2. In the soil with 15-year vines, the average contents of TK and SK were highest and the contents of SOM and TN were lowest. In the soil with 5-year vines, the contents of XN and SK were relatively higher, and the soil pH was between 7.86 and 7.98, thus it is alkaline soil.Table 2 Determined results of soil physicochemical properties.Full size tableThe analysis of variance showed that grape planting year had significant effect on TK and SP (P  More

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Data sourcesThe data come from the Ministry of Commerce of the People’s Republic of China’s 2019 Guide to Foreign Investment and Cooperation Country, as well as the websites and research literature from the Fraser Institute and the World Bank. The datasets include 14 factors that influence the environmental risk of overseas mining investment in the Philippines are summarized in Tables 1 and 2. The specific reasons that we choose these data in the Philippines are as follows:Table 1 Evaluation factors and grading standards of environmental risk for an evaluation of overseas mining investment in the Philippines.Full size tableTable 2 Risk index data.Full size tableTable 3 Correlation function value of each evaluation index used in an evaluation of overseas mining investment in the Philippines.Full size tableThe Philippines is a multi-ethnic island nation in Southeast Asia located in the western Pacific Ocean. The country has a total land area of 299,700 km2 and a population of 101 million. The Philippines is rich in mineral resources, and the area of known mineralization accounts for 30% of the land area in the country. According to the National Bureau of Geology and Mining in the Philippines, gold, copper, nickel, and chromium reserves rank third, fourth, fifth, and sixth in the world, respectively, in terms of mineral reserves per unit area. Nonferrous metal mining in the Philippines has great potential. To date, 13 types of metal minerals have been discovered, including gold, copper, nickel, aluminium, chromium, silver, lead, and zinc, with total reserves of 7.1 billion tons. Twenty-nine types of nonmetallic minerals have also been discovered with total reserves of 51 billion tons. The Philippines is an important producer and exporter of metallic mineral resources such as copper and nickel6,33.The Philippines has been one of the countries most in favour of overseas mining investment in the region near China. Before the mid-1990s, the Philippines was a favoured country for international mining investors; however, in the late 1990s, changes to national policies and social unrest led to a decline in the mining investment environment. Since January 2003, President Arroyo has proposed a reform of the mining development strategy in the Philippines, and the mining investment environment has improved. However, combined with the political, religious and security issues in the Philippines, especially the peoples’ attitude towards foreign investment, the current mining policy environment in the Philippines is not ideal. Therefore, to comprehensively and objectively understand and analyse the mining investment environment in the Philippines, relevant documents were collated and analysed. Following the principles of importance, practicality, scientificity and systematicness in the design of the index system, the accepted classification rules and data released by authoritative agencies such as the World Bank were used for the evaluation basis1,2,3,4,5,6,7,8, which selected 14 factors that have bearing on political policy, economic, financial, sociocultural, and infrastructure risks. The classification standard and valuation of each index are provided in Table 1. According to the classification standard and valuation index objectives, the risks were divided into five levels (i.e., I–V, which reflect high, higher, general, lower, and low risks, respectively). The Philippines’ risk index data are listed in Table 2.Determination of index weights: analytical hierarchy processThis method integrates quantitative and qualitative evaluations to improve the accuracy of decision making32,33,34,35,36,37,38. The basic principles and steps of the AHP method are as follows:Step 1: The complex problem is decomposed to make it multi-element in nature.Step 2: These elements are grouped, and a hierarchical structural model is established.Step 3: A discrimination matrix is constructed, and any two factors are compared with a 1–9 scaling method to obtain the relative importance of each index at each level, which can be expressed quantitatively.Step 4: The largest eigenvalue and the corresponding eigenvector of the discrimination matrix are calculated using the mathematical method, where the eigenvectors and weight coefficient values are listed in terms of the importance of the evaluation factors.Step 5: The consistency of the discrimination matrix is tested based on the consistency index ( CI) calculated as (CI = frac{{{lambda_{max }} – n}}{n – 1}) as well as with the average random consistency index (RI). If the random consistency ratio (CR = frac{CI}{{RI}} < 0.10), then the results of the hierarchy analysis are considered to be consistent, and the resulting weight distribution values are reasonable. If this is not the case, then the weight coefficient values should be redistributed to adjust the values.Entropy weight theoryIn information theory, the importance of studying the degree of dispersion of the whole system is central to the entropy method. The specific steps for these calculations are as follows:Step 1: Data collection and sorting: The initial evaluation matrix composed of (m) evaluation indexes and (n) evaluation objects is as follows:$$ {{text{X}}_{{text{ij}}}} = left[ {begin{array}{*{20}{c}} {{x_{11}}}&{{x_{12}}}& cdots &{{x_{1{text{n}}}}} \ {{x_{21}}}&{{x_{22}}}& cdots &{{x_{2n}}} \ vdots & vdots & vdots & vdots \ {{x_{m1}}}&{{x_{m2}}}& cdots &{{x_{mn}}} end{array}} right] $$ (1) Step 2: Data standardization: All index values ( {x_{ij}}) in matrix ( {X_{ij}}) are normalized as follows:$$ {text{x}}_{ij}^{prime} = {raise0.7exhbox{${{x_{ij}}}$} !mathord{left/ {vphantom {{{x_{ij}}} {sumlimits_{i = 1}^m {{x_{ij}}} }}}right.kern-nulldelimiterspace}!lower0.7exhbox{${sumlimits_{i = 1}^m {{x_{ij}}} }$}} $$ (2) Step 3: Calculation of information entropy: The entropy of each evaluation index can be obtained from$$ {E_i} = frac{{sumlimits_{j = 1}^n {x_{ij}^{prime}ln x_{ij}^{prime}} }}{ln n} $$ (3) Step 4: Calculation weight: The weight of each evaluation index can be calculated as follows:$$ {w_i} = frac{{1 - {E_i}}}{{sumlimits_{i = 1}^m {left( {1 - {E_i}} right)} }} $$ (4) where ( {w_j}) is the index weight and ( sumlimits_{j = 1}^n {{w_j} = 1} ). The larger the entropy weight is, the greater the effect of the index on the scheme, in that it contains and transmits more decision information that has a greater influence on the final evaluation decision39,40,41,42,43,44.Combination weighting model based on game theoryThis approach differs from the traditional simple linear combination weighting method. The central idea of this approach is to “coordinate conflicts and maximize benefits” by comprehensively considering the relationship between the indexes, balancing the subjective and objective weights, and optimising the index weight values. The basic algorithm is as follows:Construction of the basic weight vector setAssuming that ( H) weight values are obtained using the ( H) weighting method, the basic weight vector set of the ( H) method is$$ {w_k} = left( {{w_{k1}},{w_{k2}}, cdots {w_{kn}}} right),k = 1,2, cdots ,H $$ (5) Any linear combination of ( H) weight vectors is$$ w = sumlimits_{k = 1}^H {{a_k}{w_k}^T} ,{a_k} > 0 $$
(6)
where ( {a_k}) is the linear combination coefficient, and ( w) is the comprehensive index weight value of the ( H) weight set.Optimal combination weightTo find the balance between the different weights, the optimal effect weight vector ( W) was obtained. In the calculation process, it is converted into an optimisation of the weight coefficient ( {a_k}) to minimise the deviation between ( w) and ( {w_k}), as follows:$$ minleft| {sumlimits_{j = 1}^H {{a_j}{W_j}^T – {W_i}^T} } right|,i = 1,2, cdots ,H;j = 1,2 cdots ,H $$
(7)
From the differential properties of the matrix, the first-order derivative condition for the optimisation of Eq. (7) becomes$$ sumlimits_{j = 1}^H {a_j} {W_i}W_j^T = {W_i}W_i^T $$
(8)
By solving Eq. (8), the combination coefficients ( left[ {{a_1},{a_2}, cdots ,{a_H}} right]) can be obtained and normalised according to ( a_k^* = {a_k}/sumlimits_{k = 1}^H {a_k} ). The final combination index weight is ( W = sumlimits_{k = 1}^H {a_k^*W_k^T} ,k = 1,2, cdots ,H) 31,32.Workflow of extension matter element theoryThe theoretical basis of extenics involves the matter element and extension set theories, and its logical cell is the matter element. As such, extenics introduces the concept of the matter element that organically combines quality and quantity. It is a triple group composed of things, features, and quantity values for things, which are depicted as R = (things, features, quantity values). The matter element concept correctly describes the relationship between quality and quantity, and it can be more appropriate to describe the change process of objective things. Different objects can have the same characteristic element and are represented by the matter element with the same characteristics. For convenience, many matter elements with the same characteristics are expressed in a simple way.Determination of the classical and joint domains$$ {R_{ij}} = left( {{N_j},{C_i},{V_{ij}}} right) = left[ {begin{array}{*{20}{c}} {N_j}&{C_1}&{{V_{1j}}} \ {}&{C_2}&{{V_{2j}}} \ {}& vdots & vdots \ {}&{C_i}&{{V_{ij}}} end{array}} right] = left[ {begin{array}{*{20}{c}} {N_j}&{C_1}&{left( {{a_{1j}},{b_{1j}}} right)} \ {}&{C_2}&{left( {{a_{2j}},{b_{2j}}} right)} \ {}& vdots & vdots \ {}&{C_i}&{({a_{ij}},{b_{ij}})} end{array}} right] $$
(9)

Equation (9) is a matter element body with the same characteristics of a matter element with the same characteristics ( {R_{ij}}), in which ( {N_j}) is the ( j) evaluation category, ( {C_i}) is the ( i) evaluation index, and ({V_{ij}} = left( {{a_{ij}},{b_{ij}}} right)left( {i = 1,2, cdots ,n;j = 1,2, cdots ,m} right)) is the range of quantity values ( {N_j}) for the index ( {C_i}), which is the classical domain of the data range taken by each category for the corresponding evaluation index.$$ {R_P} = left( {P,{C_i},{V_{iP}}} right) = left[ {begin{array}{*{20}{c}} P&{C_1}&{{V_{1P}}} \ {}&{C_2}&{{V_2}_P} \ {}& vdots & vdots \ {}&{C_n}&{{V_{nP}}} end{array}} right] = left[ {begin{array}{*{20}{c}} P&{C_1}&{left( {{a_{1P}},{b_{1P}}} right)} \ {}&{C_2}&{left( {{a_{2P}},{b_{2P}}} right)} \ {}& vdots & vdots \ {}&{C_n}&{({a_{nP}},{b_{nP}})} end{array}} right] $$
(10)
where ( P) is the whole of the category, ( {V_{iP}}) is the range of quantity values taken of ( P) for ( {C_i}), and ( {R_P}) is the ( P) joint domain.Determination of the matter element to be evaluatedFor ( q) to be evaluated and using the matter element to express the detected data or analysis results, the matter element ( {R_q}) to be evaluated can be expressed as$$ {R_q} = left( {q,{C_i},{v_i}} right) = left[ {begin{array}{*{20}{c}} q&{C_1}&{v_1} \ {}&{C_2}&{v_2} \ {}& vdots & vdots \ {}&{C_n}&{v_n} end{array}} right] $$
(11)
where ( q) is some thing and ( {v_i}) is the quantity value ( q) for ( {C_i}), which are the specific data obtained by the monitoring of the things that are to be evaluated.Determination and calculation of the degree of relationDetermination of the degree of relation for the thing to be evaluated in each category is expressed as follows:$$ {K_j}left( {v_i} right) = = left[ {begin{array}{*{20}{c}} {frac{{rho left( {{v_i},{V_{ij}}} right)}}{{rho left( {{v_i},{V_{iP}}} right) – rho left( {{v_i},{V_{ij}}} right)}}begin{array}{*{20}{c}} {}&{} end{array}rho left( {{v_i},{V_{iP}}} right) – rho left( {{v_i},{V_{ij}}} right) ne 0} \ {begin{array}{*{20}{c}} {}&{} end{array} – rho left( {{v_i},{V_{ij}}} right) – 1begin{array}{*{20}{c}} {}&{}&{} end{array}rho left( {{v_i},{V_{iP}}} right) – rho left( {{v_i},{V_{ij}}} right) = 0} end{array}} right] $$where ( rho left( {{v_i},{V_{ij}}} right) = rho left( {{v_i},left( {{a_{ij}},{b_{ij}}} right)} right) = left| {{v_i} – frac{{{a_{ij}} + {b_{ij}}}}{2}} right|-frac{{{b_{ij}} – {a_{ij}}}}{2}).The calculation of the thing ( q) to be evaluated for the degree of relation ( j) is expressed as$$ {K_j}left( q right) = sumlimits_{i = 1}^n {{a_i}{K_j}left( {v_i} right)} $$Determination of the levelDetermination of the level is expressed as follows:If ( {K_{j0}} = max left{ {K{}_jleft( q right)} right},j in left( {1,2, cdots ,m} right)), ( q) belongs to level ( {j_0}).In the extension set, the concept of a relational function is established. Any element in ( U) can be quantitatively described by the relational function value, which can belong to the positive, negative, or zero domains (i.e., belongs to the elements in the same domain). It is also possible to separate different levels from the size of the relational function valu27,28,29,30. More

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