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China is the world’s most populous country, with a population of over 1.4 billion people, or 18% of the world human population1. However, China has only about 9% of the 1.4 billion hectares of total arable land in the world2. The question of “who will feed China?” raised by Dr. Lester R. Brown in 1995 is still worthy of consideration today, and ensuring food security remains a top priority for the Chinese government3.Rice is the staple food on dining-tables of over 65% of the population in China; thus, adequate rice production is critical to ensure food security in China4. In order to produce more rice on the limited amount of arable land available, double-season rice cropping systems, which involve successively growing early-season rice (ESR) and late-season rice (LSR) from March to November within a single calendar year, have been extensively developed in southern China5. The development of double-season rice cropping systems has made a considerable contribution toward achieving rice self-sufficiency in China6.Hunan and Jiangxi are the top two double-season rice producing provinces in China7. However, in recent years, the planting area devoted to double-season rice has sharply decreased in the Hunan-Jiangxi region as a result of the conversion from double- to single-season rice (SSR) cropping systems (referred as the rice “double-to-single” phenomenon) (Fig. 1A). A reduced rural labor supply and rising labor wages due to urbanization and economic growth are the key driving forces for the rice “double-to-single” phenomenon11. Fortunately, the rice “double-to-single” phenomenon has not resulted in a decrease in total rice production in the Hunan-Jiangxi region (Fig. 1B). During the most recent 10 years (2011–2020), the total rice production in the Hunan-Jiangxi region has been ranged from 45.3 to 48.7 million tons (Mt) with an average of 46.6 Mt, and the contribution of the Hunan-Jiangxi region to rice production in China has been maintained at ~ 22%.Figure 1(A) Planting areas (million hectares, Mha) for early-season rice (ESR), late-season rice (LSR), and single-season rice (SSR) in the Hunan-Jiangxi region and (B) total rice production (million tons, Mt) in the Hunan-Jiangxi region and the contribution of the Hunan-Jiangxi region to total rice production in China from 2011 to 2020. In (B), the dashed line represents the average rice production during 2011–2020. The rice planting area and total rice production in the Hunan-Jiangxi region were calculated based on data collected from the Hunan Provincial Bureau of Statistics8 and the Jiangxi Provincial Bureau of Statistics9. The contribution of the Hunan-Jiangxi region to rice production in China is the percentage of total rice production in the Hunan-Jiangxi region to the total rice production in China. Data for total rice production in China were collected from the National Bureau of Statistics of China10.Full size imageBecause China’s population is still growing12, China must continue to increase rice production. The domestic demand for rice grain in China is expected to reach 217 Mt by 2030, when the population of China is expected to stabilize6. To meet this demand, the Hunan-Jiangxi region will need to produce 47.7 Mt of rice grains, assuming that the contribution of the Hunan-Jiangxi region to rice production in China remains at the level of the most recent 10 years (~ 22%) (Fig. 1B). This expected rice production (ERP) is 1.1 Mt higher than the average total rice production during the most recent 10 years. In order to avoid the negative effect of the “double-to-single” phenomenon on achieving the ERP in the Hunan-Jiangxi region by 2030, it is necessary to estimate how much planting area of double-season rice will be needed in this region by this point in time.The ERP can be expressed by the following formula: ERP = EPAESR × EGYESR + EPALSR × EGYLSR + EPASSR × EGYSSR, where EGYESR, EGYLSR, and EGYSSR are the estimated grain yields of ESR, LSR, and SSR, respectively; and EPAESR, EPALSR, and EPASSR are the estimated planting areas for ESR, LSR, and SSR, respectively. We assume the following conditions in the Hunan-Jiangxi region by 2030: (1) the total paddy field area will be maintained in the range of 4.57–5.02 million hectares (Mha) that was planted during the years 2011–20208,9; (2) the ratio of EPALSR to EPAESR is the same as the average ratio of planting area of LSR to ESR during 2011–2020 (i.e., 1.07) (Fig. 1A); (3) EPASSR is the difference between the total paddy field area and the EPALSR; and (4) EGYESR, EGYLSR, and EGYSSR are projected under three scenarios: (1) constant yield scenario, (2) 5% yield increase scenario, and (3) 10% yield increase scenario (Fig. 2). The baseline yield for all three scenarios is the average grain yields during 2011–2020. The EPAESR, EPALSR, and EPASSR in the Hunan-Jiangxi region needed to achieve the expected rice production by 2030 were obtained by solving the above formula and are shown in Fig. 3.Figure 2(A) Grain yields from 2011 to 2020 and (B) estimated grain yields by 2030 under three scenarios for early-season rice (ESR), late-season rice (LSR), and single-season rice (SSR) in the Hunan-Jiangxi region. The grain yields from 2011 to 2020 were calculated based on data collected from the Hunan Provincial Bureau of Statistics8 and the Jiangxi Provincial Bureau of Statistics9. In (A), ns denotes non-significant trend at the 0.05 probability level (Statistix 8.0, Analytical software, Tallahassee, FL, USA). In (B), the baseline yield for all three scenarios is the average grain yields during 2011–2020.Full size imageFigure 3Estimated planting areas for early-season rice (ESR), late-season rice (LSR), and single-season rice (SSR) in the Hunan-Jiangxi region that will be required to achieve the expected rice production by 2030 under three scenarios: (A) constant yield scenario, (B) 5% yield increase scenario, and (C) 10% yield increase scenario. Mha is million hectares.Full size imageThe results presented in Fig. 3 provide guidance and models for the government’s decision-making process in the planning planting areas for ESR, LSR, and SSR in the Hunan-Jiangxi region. In brief, farmers will need to plant 2.55–3.18 Mha of ESR, 2.73–3.40 Mha of LSR, and 1.17–2.29 Mha of SSR under the constant yield scenario, 2.09–2.72 Mha of ESR, 2.24–2.91 Mha of LSR, and 1.66–2.78 Mha of SSR under the 5% yield increase scenario, and 1.67–2.31 Mha of ESR, 1.79–2.47 Mha of LSR, and 2.10–3.23 Mha of SSR under the 10% yield increase scenario in the Hunan-Jiangxi region by 2030 depending on the total available paddy field area.One thing to note here is that the actual planting areas for ESR (2.44 Mha) and LSR (2.57 Mha) in 2020 are below the estimated lower limits of planting areas for ESR (2.55 Mha) and LSR (2.73 Mha) that will be needed by 2030 under the constant yield scenario, while the actual planting area for SSR in 2020 (2.42 Mha) is above the estimated upper limit for SSR (2.29 Mha) that will be needed by 2030 under the constant yield scenario (Figs. 1A and 3A). This finding indicates that it is urgent to avoid a further aggravated “double-to-single” phenomenon while maintaining the total paddy field area in the Hunan-Jiangxi region. Because it is not an easy task to maintain the total paddy field area under the projected scenario for urban expansion13, the government should prepare an alternative to reverse the “double-to-single” phenomenon in the Hunan-Jiangxi region. Increasing the mechanized level of farming operation and improving economic returns to farmers are two key aspects for the government to take into account to promote the development of double-season rice.Although the current planting area of double-season rice can fully meet the requirement for achieving the ERP in the Hunan-Jiangxi region by 2030 under both the 5% and 10% yield increase scenarios, there is some difficulty in reaching the yield increase targets. In recent years, the planting area of high-quality rice varieties has been rapidly increased in China14. However, grain yield is generally not very high for high-quality rice varieties, although no genetic linkage has been identified between grain yield and quality in rice15. Hence, great efforts are required to develop rice varieties with both high quality and high yield. In addition, rice yields are determined not only by the variety but also by environments and crop management practices. Soil nutrient deficiencies, unfavorable climatic conditions (e.g., heat, cold, and drought), and pest infestations have always been major yield-limiting factors for rice production in China16. Therefore, great efforts are also required to: (1) improve soil fertility of low- and medium-yielding rice fields and optimize nutrient management practices; (2) develop climate-smart agriculture practices for alleviating climatic stresses; and (3) promote integrated pest management practices. More

Experimental setupThis research was approved by the Carnegie Mellon University Committee of the Use of Human Subjects. All methods were performed in accordance with the relevant guidelines and regulations. Informed consent was obtained from all participants. Our data includes no identifying information of human participants. We conducted experiments from February to August 2021 (except for the preliminary sessions of random information; we ran the condition from June to November 2020). We preregistered the main experiment settings using AsPredicted (https://aspredicted.org/sm4k5.pdf).A total of 2786 subjects participated in our incentivized decision-making game experiments. We recruited subjects using Amazon Mechanical Turk (MTurk)52,53. Supplementary Table 1 shows the subject demographics. Our participants interacted anonymously over the Internet using customized software playable in a browser window (available at http://breadboard.yale.edu). All participants provided explicit consent and passed a series of human verification checks and a screening test of understanding game rules and payoffs before playing the game (see SI). We prohibited subjects from participating in more than one session of the experiment by using unique identifications for each subject on MTurk.In each session, subjects were paid a $2.00 show-up fee and a bonus depending on whether they took the appropriate disaster decision in four rounds. Furthermore, subjects earned $1.00 when they completed all four rounds. In each round, when a disaster stroke before they evacuated, the subjects earned no bonus. Otherwise, they earned a bonus of $1.00 without disaster or $0.50 with disaster by spending $0.50 for evacuation, plus $0.05 per other players who took the correct action accordingly (Supplementary Table 2). We have confirmed with prior work that the amount of evacuation cost, if any, makes no significant difference in the game’s performance23.At the start, subjects were required to pass a series of human verification checks. They needed to pass Google’s reCAPTCHA using the “I’m not a robot” checkbox. They were also requested to answer whether they were human players. The exact question asked was: “Please select an applicable answer about you.” The options were: “I am not a bot. I am a real person.” “I am not a real person. I am a bot.” “I am anything but a human.” and “I am a computer program working for a person.” The option’s order was randomized. Only the participants who selected “I am not a bot. I am a real person.” moved to the step of informed consent.When subjects provided explicit consent, they were asked to take a tutorial before the actual game would begin. In the tutorial, each subject separately interacted with three dummy players in two rounds of a 45-s practice game. In the actual game, some subjects would be informed in advance whether a disaster would indeed strike or not. In the practice game, while all subjects were not informed of such information in the first round, they were informed of the information in the second round. Thus, they practiced both conditions in terms of prior information on the disaster (see SI).After the practice game, subjects were assessed for their comprehension of the game rules and payment structure using four multiple-choice questions with three options. If they failed to select the correct answer in one of the questions, they could reselect it only once through the entire test. If they failed to select the correct answer more than once, they were unable to join the actual game.At 720 s after the tutorial beginning, a “Ready” button became visible simultaneously to all the subjects who completed the tutorial and passed the comprehension tests. The actual games started 30 s after the “Ready” button showed up. If subjects did not click the button before the game started, they were dropped. The game required a certain number of subjects. When the subjects who successfully clicked the button were more than 16, surplus subjects, randomly selected, were dropped from the game. When the number of qualified subjects was less than 12, the game did not start. As a result, subjects started the game in a group with an average size of 15.5 (s.d. = 1.1).At the start of the actual game, we selected one subject (the “informant”) at random who was informed in advance whether a disaster would indeed strike or not. The other subjects were informed that some players had accurate information about the disaster, but they were not informed who the informant was. The exact sentence that the informants received in their game screen was “A disaster is going to strike!” when a disaster would strike or “There is no disaster.” when a disaster would not strike. The one that the other uninformed subjects received was “A disaster may or may not strike.” Then, the group had the same informant across the four rounds except for a supplement condition of random informants. In the random informant condition, an informant was randomly selected every round.To prevent an end-of-game effect, we randomly set the game time with a normal distribution of a mean of 75 s and a standard deviation of 10 s. Prior work has confirmed that the game time is sufficient for players to communicate and make an evacuation decision23. As a result, each round ended at 75.0 s on average (s.d. = 9.5) without prior notice. In half of the sessions, a disaster struck at the end of the game. We did not inform any subjects, including the informants, when their sessions would end, the global network structure they were embedded in, or how many informants were in the game. After making their evacuation choice, subjects were informed of their success and failure along with overall results in their group. Then, subjects played another round of the evacuation game until they completed four total rounds. They had the same local network environment across four rounds except for the dynamic network condition.Network structure and tie rewiringIn the network sessions, subjects played the game in a directed network with a random graph configuration. A certain number of ties were present at the game’s onset as the initial density was set to 0.25.In the dynamic network conditions, subjects also could change their neighbors by making or breaking ties between rounds. In the tie-rewiring step, 40% of all the possible subject pairs were chosen at random. Thus, subjects could choose every other player at least once throughout the entire session (i.e., a set of four rounds) with a probability of about 80%. When the chosen pairs were connected, the pairs (the ties) were dissolved if the predecessor subject of the directed ties chose to break the tie. When the chosen pairs were not connected, the pairs (the ties) were newly created when the predecessor of the potential tie chose to create the tie. Subjects were not informed of the rewiring rate.To equalize the game time, we made subjects in the independent and static network conditions wait for additional 10 s after each game round ended. Despite the adjustment, the game time was significantly longer in the dynamic network sessions than in the independent and static network sessions. The average game time is 429.5 s (s.d. = 20.2) for the independent condition; 428.8 s (s.d. = 19.0) for the static network condition; and 564.7 s (s.d. = 36.3) for the dynamic network condition.To clarify mechanisms for dynamic networks to facilitate collective intelligence, we added one supplementary condition. In the supplementary condition, subjects were assigned to one of the 40 isomorphic networks that other subjects had developed with tie-rewiring options through the three rounds in the dynamic network condition (567 subjects in 40 groups). Network structure and other game settings (i.e., whether a disaster stroke, how long the game was, and which node was the informant) were identical to where the others played the game at the final round. However, players were different, and they had no prior experience in the game. They played the game in a network with a topology created by others ostensibly to optimize the accurate flow of information. In contrast to other conditions, subjects played only one round in the isomorphic network condition.Signal buttonsDuring the game of network sessions, subjects were allowed to share information about the possibly impending “disaster” by using “Safe” and “Danger” buttons that indicated their assessment (see SI). The default node color was grey. Then, when they clicked the Safe button, their node turned blue and, after 5 s, automatically returned to grey. Likewise, the Danger button turned their node to red for 5 s. Subjects could see only the colors of neighbors to whom they were directly connected. Since the signal exchange occurred through directed connections, an individual could send, but not receive, information from another subject (and vice versa). Once subjects chose to evacuate, they could no longer send signals, and their node showed grey (the default color) for the rest of the game. The neighbors of evacuated subjects were not informed of their evacuation. We have confirmed with prior work that collective performance does not vary with the communication continuity and the evacuation visibility23. Subjects could use the Safe and Danger buttons any time unless they evacuated, or they did not have to.Players dropping during the gameAfter each game round, when a player was inactive for 10 s, they were warned about being dropped. When they remained inactive after 10 s, they were dropped. When the selected informant was dropped, the session stopped at the round, and we did not use the data. Furthermore, as too many dropped players could affect the network structure and the behavioral dynamics of remaining players, we did not use the sessions where more than 25% of initial players were dropped during the game. Overall, 4 players dropped in 15 sessions; 3 players dropped in 22 sessions; 2 players dropped in 41 sessions; 1 player dropped in 44 sessions; and no player dropped in 58 sessions. The dropped players were prohibited from joining another session of this experiment.As noted above, players took the additional tie-rewiring step every round in the dynamic network sessions. Thus, the total game time was longer in the dynamic network sessions than in the independent and static network sessions even with the adjustment. As a result, more players were dropped in the dynamic network sessions than in the independent and static network sessions. The average number of dropped players across the four rounds is 0.40 (s.d. = 0.60) for the independent condition; 1.15 (s.d. = 0.86) for the static network condition; 1.75 (s.d. = 1.19) for the dynamic network condition. Although group size could affect collective performance, we found the differences in group size small enough for our study. We have confirmed the dynamic network’s performance improvement with a comprehensive analysis controlling the effect of group size (Supplementary Table 3). Also, there was no statistically significant difference in the dropped players’ performance of the dynamic network condition, compared with the other two conditions. The rate of correct actions of dropped players is 0.456 (s.d. = 0.322) for the independent condition, 0.594 (s.d. = 0.387) for the static network condition, and 0.558 (s.d. = 0.411) for the dynamic network condition; P = 0.106 between the independent condition and the dynamic network condition; P = 0.599 between the static network condition and the dynamic network condition (Welch two-sample t test).Analysis of signal diffusionsTo examine the change in signal diffusion, we analyzed “diffusion chains” for each signal type in the network sessions. We first identified the subjects who sent a signal when their neighbors had never sent one as spontaneous “diffusion sources.” When a subject sent a signal after at least one neighbor had sent the same type of signal, we regarded the subject’s signaling (and evacuation with danger signals) as occurring in a chain of signal diffusion and the total number of the responded subjects (including the diffusion source) as the diffusion size.We analyzed the distribution of signal diffusion chains with complementary cumulative distribution functions, measuring the fraction of diffusion chains that exhibit a given number of diffusion sizes. We found that the number of diffusions of both signals did not change across rounds. Safe-signal diffusions were more likely to occur than danger-signal diffusions regardless of whether a “disaster” would strike and how many rounds subjects played. On the other hand, the diffusion size varied greatly across rounds in disaster situations. With “disaster,” false safe signals spread further than true danger signals at the first round, but after that, warnings outperformed safe signals in terms of diffusion size. Figure 2B and Supplementary Fig. 3 scrutinize the changes in diffusion chains with their distributions.Analysis of individual responsivenessWe analyzed how individual evacuation behavior varies with exposure to signals from neighbors54. Let$${a}_{i}^{evacuate},, (t)=left{begin{array}{ll}1&quad text{if subject } i text{ evacuates at time } t\ 0&quad text{otherwise}end{array}right.$$$${a}_{i}^{show, safe},, (t)=left{begin{array}{ll}1&quad text{if subject } i mathrm{ shows a safe signal at time } t\ 0&quad text{otherwise}end{array}right.$$$${a}_{i}^{show , danger} ,, (t)=left{begin{array}{ll}1&quad text{if subject } i text{ shows a danger signal at time } t\ 0&quad text{otherwise}end{array}right.$$The hazard function, or instantaneous rate of occurrence of subject (i)’s evacuation at time t, is defined as:$${lambda }_{i},, (t)=underset{mathit{dt}to 0}{{mathrm{lim}}}frac{{mathrm{Pr}}({a}_{i}^{evacuate}=1;,, tt)}{dt}$$To model the time to evacuation, We used a Cox proportional hazards model with time-varying covariates for the number of signals, incorporating an individual actor-specific random effect55:$${lambda }_{i} ,, left{t|{{P}_{i}, X}_{i}(t), {G}_{i},{Y}_{i}(t)right}={lambda }_{0}(t)mathrm{exp}left{{{beta }_{P}^{{prime}}{P}_{i}+beta }_{X}^{{prime}}{X}_{i}(t)+{beta }_{G}^{{prime}}{G}_{i}+{beta }_{Y}^{{prime}}{Y}_{i}(t)+{gamma }_{i}right}$$where λ0(t) is a baseline hazard at time t.In the model, the hazard λi(t) depends on the covariates Pi, Xi(t), Gi, and Yi(t). The covariate Pi is the vector of subject i’s experiences before the sessions; that is, the number of rounds, the number of disasters that she has experienced, and the number of disasters that she has been struck by.The covariate Xi(t) is the vector of the number of safe signals ({x}_{i}^{safe} (t)), the number of danger signals ({x}_{i}^{danger} (t)). When subject j is a neighbor of subject i (i.e., (jin {N}_{i})), subject i is exposed to the signal of subject j, so that:$${x}_{i}^{safe},, (t)=sum_{jin {N}_{i}}{a}_{j}^{show, safe}(t)$$$${x}_{i}^{danger},, (t)=sum_{jin {N}_{i}}{a}_{j}^{show, danger}(t)$$The covariate Gi is the vector of the properties of the network in which subject i is embedded, out-degree, in-degree, and a network plasticity indicator. The covariate Yi(t) is the vector of the number of the subject i’s actions of sending safe and danger signals before time t. The coefficients β are the fixed effects and γi is the random effect for individual i. We assumed that waiting times to evacuation in different actors are conditionally independent given the sequence of signals they receive from network neighbors. This model shows how the hazard of an individual’s evacuation depends on the signaling actions of others, their network position, and experience (Supplementary Table 4). We applied the same model to the first signaling behavior. More

From the popular algorithms, we chose the Random forest model as the most suitable for our case. The data required for predictions can be divided into plant occurrence records and environmental features. Bioclimatic variables and soil properties were selected as the main environmental features. All of the data were obtained from open sources.Heracleum Sosnowskiy plant descriptionHeracleum sosnowskyi is a monocarpic perennial plant of the Apiaceae family. The height is up to 3–5 m with a straight stem up to 12 cm in diameter. HS compound steam leaves can reach 150 cm, both long and wide38. The blooming period starts in July and continues until the end of September. Plant reproduction is performed by seeds only. The seeds’ depth of germination is reported as mainly in the upper 5 cm down to 15 cm of soil. One plant can produce 10–20,000 seeds39,40. Seeds germinate in the early spring, while some have reported that a period of cold stratification for the dormancy break is obligatory for germination development. Suitable conditions for HS include a temperate climate with warm humid summers and cold winters, while it is probably not drought resistant. Plants of HS tend to neutral soils with a pH range from 6 to 7, rich in nutrients, and being reported as nitrophilous, so the eutrophication of the environment favours HS development. HS plants do not tolerate shade conditions in the first growing period.HS is mostly spread in artificial and semi-natural habitats, including grasslands, pastures, parks, roadsides, agricultural fields, riverbanks or canal sides, and other distributed habitats. Currently, the main pathways of spread include an involuntary entry with soil on vehicles, machinery, footwear or the use of soil as a commodity (as the growing medium rich in organic matter)39.Study areaThe area for modelling extends from approximately 41(^{circ }) to 70(^{circ }) N and from 27(^{circ }) to 60(^{circ }) E, and Kaliningrad region, it equals to approximately 4 mln km2 (Fig. 4).Figure 4Map of the study area: white colour represents the territory used for prediction, red points correspond to the dataset of HS occurrence, collected from the available sources.Full size imageThe European part of Russia is the most inhabited part of the country, and it is the home of approximately 80% of the total population of Russia. It includes the East European Plain, Caucasus mountains and Ural mountains, with the predominance of the East European Plain. Environmental characteristics across the territory of study vary significantly. The climate is changing from semi-arid in the south to subarctic in the north, including humid continental climate conditions. Natural vegetation is represented by almost all types of biomes with the prevalence of different types of forests: broadleaf and mixed forests, coniferous forests, and boreal forests (taiga), while the area of arable lands is reported to be approximately 650,000 km241,42. The territory is subjected to the constant land-use types and cover changes due to the urbanization and switch of the status of arable lands—i.e. reduction of croplands and development of fallows and forests, and, vice versa, returning of some of them into the cultivation process43. The soil cover is represented by the contrast by their physicochemical properties groups, in the northern part of Luvisols, Podzols, Histosols, while of the southern part—by Chernozems, Kastanozems, Solonetz44.Collection of the input dataPlant occurrence dataPlant occurrence coordinates were collected from several publicly available sources related to citizen science projects: the Global Biodiversity Information Facility database45, iNaturalist database46, and the database of the “Antiborschevik” community47. Records were documented by human observation and collected from 2000 to 2021. The overall number of initial occurrence points from combined sources is 7637.Environmental predictorsClimate data Modelling was performed for current and future climate conditions at its two scenarios, selected year ranges were 2000–2018 and 2040–2060 respectively.Climatic variables were collected from the Worldclim database48, containing the average seasonal information relevant to the physiological characteristics of species and available at different resolutions. We chose 10 arc-minutes spatial resolution taking into account the size of the studied area. Table 1 provides a short description of the used bioclimatic features, and we refer the reader to the Worldclim project for detailed information on the variables’ calculation.For the future climate scenarios, we used two Shared Socioeconomic Pathways (SSPs)49—1-2.6 and 5-8.5, corresponding to the lowest (keeping global mean temperature increase below 2 (^{circ })C) and the highest (at the increase of population without technological change) predicted future greenhouse gases emission scenarios. For these data, we took the same resolution (10 arc-minutes) as discussed above.We used the Equilibrium Climate Sensitivity to select the climate model to model future HS distribution. Equilibrium climate sensitivity (ECS) is defined as the global mean surface air temperature change due to a rapid doubling of carbon dioxide concentrations as soon as the associated ocean-atmosphere-sea ice system reaches equilibrium. As the ECS value increases, the model’s sensitivity to the CO(_2) concentration in the atmosphere increases. We have chosen CanESM5 model (ECS—5.6), CNRM-CM6-1 model (ECS—4.3) and BCC-CSM2-MR model (ECS—3.0)50.Table 1 Description of used bioclimatic variables.Full size tableFor the future climate scenarios we selected three climate models:

BCC-CSM2-MR Beijing Climate Center climate system model developed in Beijing Climate Center, China Meteorological Administration51. Model has horizontal resolution 1.125(^{circ }) by 1.125(^{circ }).

CanESM5 Canadian Earth System Model version 5 developed in Canadian Center for Climate Modelling and Analysis, Canada52. Horizontal resolution 2.81(^{circ }) by 2.81(^{circ }).

CNRM-CM6-1 Climate model developed in National Center of Meteorological Research, France53. Horizontal resolution 1.4(^{circ }) by 1.4(^{circ }).

Authors of the WorldClim project prepared historical and future climate data to a uniform spatial (10 arc-minutes) and temporal resolution.Soil data Soil data were downloaded from the SoilGrids database54—a system for global digital soil mapping. SoilGrids provides continuous data at several depths of the spatial distribution of soil properties across the globe with selected resolution. It uses a machine learning approach to reconstruct continuous data from 230,000 soil profile observations from the WoSIS (The World Soil Information Service) database and a series of environmental covariates.From the whole set of the data provided by SoilGrids several properties were chosen for the forecasting: relative percentage of silt (Silt, %), sand (Sand, %), a volumetric fraction of coarse fragments (CF, %), cation exchange capacity (CEC, ({text{cmol}}_{c}/{text{kg}})) and soil organic carbon (SOC, g/kg) at the depth 5–15 cm, where the HS seeds are assumed to be located. These variables are expected to be more stable over time than bioclimatic predictors; thus, chosen soil properties could be implemented for the future time the same as in the present.Data pre-processingAll the data were transformed to the ASCII format by R script and using software DIVA-GIS following the tutorial for the preparation of WorldClim files for use in SDM (http://www.lep-net.org/wp-content/uploads/2016/08/WorldClim_to_MaxEnt_Tutorial.pdf) with unified selected resolution 340 sq.km.Optimization of the occurrence points amountThe general problem in using the available data collected from the databases of the citizen science projects is that the points of observation are distributed non-uniformly. For instance, the frequency of the records depends on the density of the population directly. The spatial filtering of the data (reducing the number of points) can be performed to reduce the sampling bias55. We prepared three datasets with a distance between points of 4, 7 and 10 km with 2402, 1846 and 1504 occurrence points correspondingly filtering the initial dataset. For the thinning step thin() function was used within the R package spThin with 100 iterations for each of chosen thinning distances. To understand how much data we could lose, we used the analysis of feature distribution and evaluated the general fairness of the model performance.Pseudo-absence generationDue to the availability only of the presence points, it is important to generate the absence points for further implementation of the selected algorithm. Although the generation of pseudo-absence points in SDM research is a widespread solution, a closer look at the literature reveals several gaps and shortcomings. Since the raw dataset of the HS distribution demonstrates strong sampling bias, the generation of pseudo-absence points using the usual ‘random’ strategy can aggravate the sampling bias problem. Thus, the combination of the ‘disk’ and ‘random’ strategies was applied for the generation of the pseudo-absence points using the biomod R package17.

The ‘disk’ strategy is established on the geographic distance works as separation from truth presence and possible absence points. The optimal geographic distance for HS was chosen as 25 km. This distance was chosen empirically by trial-and-error. We started with 18 km (because the size of the cell is   9–18 km depending on location) and finished with 50 km. Using distances such as 30–50 km lead to a positive spatial autocorrelation. Thus, we decided to set 25 km which finally provided both optimal model performance and reduced spatial autocorrelation.

The second part of the generation was based on the ‘random’ strategy with filtration: according to the different range of climate conditions on the territory of Russia, there are several places where HS is not detected, thus not growing. The selection of unsuitable places for HS related to the north of Russia, where it is might be too cold for plant species. From all amount of randomly generated generated points we selected points with condition latitude ( > 64^{circ }), according to tundra board line.

Features selection procedureTo avoid over-fitting and to choose the most conscientious set of parameters for final modelling, two approaches were combined. We searched features that are not correlated with others by a selected threshold is equal to 0.8 in absolute values56 and estimated variable importance using the Mean Decrease Gini (MDG) and the Mean Decrease Accuracy (MDA) as the result of modelling on enumerated parameters’ combinations. MDG score is related to the homogeneity of the nodes and leaves coefficient. With the rise of the MDG score the importance of the corresponding feature is also increasing. MDA describes how much accuracy decrease by removing the feature. We selected the most important features according to the MDG and MDA scores by the highest values of both metrics using a sequential search from an initial set of variables.Modelling approachRandom forestChoosing the appropriate method for creating the tool for accurate SDM is crucial because the overall performance could vary dramatically, depending on the selected model and particular use case. There is a limited amount of acceptable machine learning methods that can be used in SDM. Several popular methods demonstrated high performance in modelling on large areas: GBM, RF, and GLM. In particular, for modelling and prediction of the potential distribution of invasive species, GLM and RF were used57. We decided to use RF because this model was successfully implemented for solving a variety of tasks such as predictions of animal and plant distributions, and also was used for making predictions on a large territory58. The other important advantage that should be noticed is the straightforward interpretability of RF, which means that it is possible to evaluate the impact of each environmental parameter on the occurrence of the invasive species.Approach to the cross-validation of the modelA unique approach for the model calibration is needed to reduce spatial autocorrelation caused by the absence of a strict sampling design. In our case, the data was split into training and testing folds using the spatial blocks technique in a scheme of 13-fold cross-validation. Random spatial splitting was performed 20 times to calibrate the model, with a distance between blocks set as 100 km. To calibrate the model we used a spatial blocks approach with random type from R package blockCV.Evaluation of the model performanceTo evaluate the performance of the model a classic approach for ecology was used—Area Under Curve (AUC) or Receiver operating characteristic (ROC), related to the independent threshold techniques16. The principle of methods lies in the standard confusion matrix, where rows and columns represent actual and predicted classes. The construction of ROC curves uses all possible thresholds to obtain different confusion matrices which leads to the reproduction of the curve with two-dimensional space: (1) on y-axis is True Positive Rate (sensitivity, recall); (2) on x-axis is False Positive Rate (equal to 1 − specificity). In our case true positive (TP, sensitivity) rate means that predicted places where HS grows correspond to actual. Similarly, true negative rate (TN, specificity) indicates correctly classified locations as absence points. In contrast, the missteps when the model predicted places as presence points for plants that are incorrect are False Positive, FP, and places where HS is absent, according to the model, while this is not true are recognised as False Negative, FN. More

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doi: https://doi.org/10.1038/d41586-022-00974-y

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History

Archaeology

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