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This research aims to establish the possible habitat suitability of Heracleum sosnowskyi ( HS ), one of the most aggressive invasive plants, in current and future climate conditions across the territory of the European part of Russia. We utilised a species distribution modelling framework using publicly available data of plant occurrence collected in citizen science projects ( CSP ). Climatic variables and soil characteristics were considered to follow possible dependencies with environmental factors. We applied Random Forest to classify the study area. We addressed the problem of sampling bias in CSP data by optimising the sampling size and implementing a spatial cross-validation scheme. According to the Random Forest model built on the finally selected data shape, more than half of the studied territory in the current climate corresponds to a suitability prediction score higher than 0.25. The forecast of habitat suitability in future climate was highly similar for all climate models. Almost the whole studied territory showed the possibility for spread with an average suitability score of 0.4. The mean temperature of the wettest quarter and precipitation of wettest month demonstrated the highest influence on the HS distribution. Thus, currently, the whole study area, excluding the north, may be considered as s territory with a high risk of HS spreading, while in the future suitable locations for the HS habitat will include high latitudes. We showed that chosen geodata pre-processing, and cross-validation based on geospatial blocks reduced significantly the sampling bias. Obtained predictions could help to assess the risks accompanying the studied plant invasion capturing the patterns of the spread, and can be used for the conservation actions planning.
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Large‑scale forecasting
of Heracleum sosnowskyi habitat
suitability under the climate
change on publicly available data
Diana Koldasbayeva1*, Polina Tregubova2, Dmitrii Shadrin2,3, Mikhail Gasanov2 &
Maria Pukalchik4
This research aims to establish the possible habitat suitability of Heracleum sosnowskyi (HS), one of
the most aggressive invasive plants, in current and future climate conditions across the territory of
the European part of Russia. We utilised a species distribution modelling framework using publicly
available data of plant occurrence collected in citizen science projects (CSP). Climatic variables and
soil characteristics were considered to follow possible dependencies with environmental factors. We
applied Random Forest to classify the study area. We addressed the problem of sampling bias in CSP
data by optimising the sampling size and implementing a spatial cross‑validation scheme. According
to the Random Forest model built on the nally selected data shape, more than half of the studied
territory in the current climate corresponds to a suitability prediction score higher than 0.25. The
forecast of habitat suitability in future climate was highly similar for all climate models. Almost the
whole studied territory showed the possibility for spread with an average suitability score of 0.4.
The mean temperature of the wettest quarter and precipitation of wettest month demonstrated the
highest inuence on the HS distribution. Thus, currently, the whole study area, excluding the north,
may be considered as s territory with a high risk of HS spreading, while in the future suitable locations
for the HS habitat will include high latitudes. We showed that chosen geodata pre‑processing,
and cross‑validation based on geospatial blocks reduced signicantly the sampling bias. Obtained
predictions could help to assess the risks accompanying the studied plant invasion capturing the
patterns of the spread, and can be used for the conservation actions planning.
e relocation and introducing of alien species into new habitats are recognised as one of the major drivers of
global biodiversity loss13. Invasive alien (non-indigenous) species IAS tend to spread rapidly and pose a seri-
ous threat to endemic species due to e.g. the competition in the resource use, allelopathy occurrence, toxicity
of IAS4,5. us, the emergence of IAS can dramatically change the functioning of the natural communities and
overall ecosystem structure68.
Such common occurrences as human living territory expansion, globalization of transport, and changing
of the land-use types favor species invasion. With that, the estimated costs of the elimination of IAS are usually
quite high. e specic of individual IAS limits the implementation of such practices. e other constraints are
the territory’s size that needs to be treated, the possibility of negative side outcomes because of the use of chemi-
cal and biological control agents, andthe development of the invasion process911. IAS disproportionally aect
the most vulnerable communities in poor areas, at the locations of abandoned and disturbed lands. us, their
spread is clearly pulling up the achievement of the Sustainable Development Goals12.
Heracleum sosnowskyi Manden (Hogweed, HS) is one of the examples of extremely dangerous invasive species.
e natural habitat of HS is the central and eastern Caucasus area and adjacent regions, Transcaucasia region
and Turkey13. Large biomass and the ability to live and develop in cold climates became HSa popular crop in
agriculture in the middle of the 20th century14. However, soon the unpleasant odor of milk and meat of animals
OPEN
1Center of Life Sciences, Skolkovo Institute of Science and Technology, Moscow, Russian Federation 121205. 2RAIC,
Skolkovo Institute of Science and Technology, Moscow, Russian Federation 121205. 3Irkutsk National Research
Technical University, Irkutsk, Russian Federation 664074. 4Digital Agriculture Laboratory, Skolkovo Institute of
Science and Technology, Moscow, Russian Federation 121205. *email: Diana.Koldasbayeva@skoltech.ru
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that were fed with HS fodder andthe phototoxic eect of above-ground parts of HS were revealed, and as a
result, the cultivation was abandoned.
e need to forecast the potential extinction of dierent species in dierent spatial and temporal contexts,
has led to the Species Distribution Modelling (SDM) development. SDM framework is based on the ecological
concept assuming that the distribution of species is explained by the set of factors, such as environmental require-
ments and interactions with other living organisms, physiology characteristics, evolution history15,16. General
workow of correlative SDM consists of (1) obtaining the data about the species of study occurrences: presence-
only data, presence/absence data, abundance data; environmental characteristics data, sometimes considering
biotic interactions as well, (2) search of the interconnections between these data, and (3) building the map of
predicted distributions across the region of interest. SDM framework is implemented in a variety of packages
and libraries in most common programming languages, such R or Python, and allows to use several dierent
statistical or machine learning (ML) models, e.g., generalized linear models, classication and regression trees,
random forest (RF), support vector machine, articial neural networks, and others, and ensemble of them1721.
In terms of data availability these models mostly dier from each other by the requirements to occurrence
records, i.e., should the occurrence data be represented by two classes—presence and absence, or it can be only
presence data22. e choice of the appropriate modelling method signicantly aects outcomes and depends
on multiple factors: size of the territory of study, type of the environment considering its changing dynamics,
characteristics of modelling species, data availability, while it has become more popular to use ensembles-across-
methods forecasting23. However, there are no strict directives on how to implement the ensemble, e.g. should
one estimate an average prediction or weighted average prediction—thus, this solution is not so straightforward
in comparison with basic modelling methods24. Some studies demonstrate higher performance of a particular
model above others for specic cases. For example, it has been shown that RF approach is highly suitable for
forecasting on large territories with a limited amount of data25, while for marine environments, ensemble models
are recommended to use26.
Correlative SDM has a conceptual limitation—it is assumed to capture realized ecological niche, which
is confusing when IAS is the object of the study27. Another struggle is the quality of using data, precisely, the
occurrence and absence of the species. It is stated that pseudoabsence data should be eld corrected, otherwise
it shows strong bias, decreasing the species prediction perfomance28. In reality, such correction is almost impos-
sible for large territories and requires signicant collections of remote sensing data with appropriate resolution.
It is much more controversial issue when the spread of IAS is the case. In case of a sucient number of veried
absence points of the studied IAS, a question that remains: is this location unsuitable indeed for the selected
IAS, or the IAS has not reached it yet29. However, despite all the mentioned limitations, correlative SDM still is
the primary tool for the IAS distribution modelling30. Another possibility is to use mechanistic SDM, which is
developed on the process-based approach, e.g. phenology model31, but such models require calibration of many
internal parameters.
While it is extremely dicult to eliminate all growing populations of the invasive species, HS including, the
information from the modelling of habitat suitability can aid in prioritizing the management of invaded areas.
Precisely, it can help to mark out the territories where the possibility of development of rapidly growing popula-
tions poses the largest threat to native species, agriculture, and populated areas. Considering this context use of
data from CSP is of particular interest, however, it may have its limitations. In this work large-scale HS distribu-
tion modelling is performed. We estimated habitat suitability for the current climate as average from 2000 to 2018
and possible future climate from 2040 to 2060 according to three climate models—BCC-CSM2-MR, CanESM5,
and CNRM-CM6-1—in two scenarios, the worst and the best in terms of greenhouse gas emissions (Fig.1).
e general workow of the presented research included the following steps: (i) collection of the required
data from public sources, (ii) data pre-processing, (iii) feature selection, (iv) model training and validation, (v)
receiving of the outputs of the best model, (vi) building the maps, showing the spatial distribution of the occur-
rence probability (habitat suitability) across the territory of the study, expressed in the range from 0 to 1, for
current and possible future climate conditions. Presented methodology and results of HS spread modelling can
be used for invasion risk assessment.
Results
Optimisation of the occurrence data distribution based on the thinning procedure. Ideally,
thinning removes the optimal number of records to substantially reduce the eects of sampling bias, as in our
case when most of the locations are concentrated in a few places—while simultaneously retaining most of the
valuable information. Figure2 demonstrates the results of model prediction for (1) initial dataset with data col-
lected from all available sources; (2) dataset with thinning distance 4 km, (3) dataset with thinning distance 7
km, (4) dataset with thinning distance 10 km. It is also important to know how the predictors’ distribution would
change at the dierent thinning intervals. In our case, there were no signicant dierences between distribu-
tions’ shapes of environmental features that corresponded to the dierent thinned data (Fig.S1).
e outputs of models vary signicantly depending on the number of points at dierent input datasets. e
ROC-AUC scores of the models built on the complete data, datasets at 10, 7, and 4 km thinning distances are
0.877, 0.83, 0.85, and 0.82 correspondingly (Fig.S4). Modelling results obtained from the complete dataset
represent the territory of the study as mostly unsuitable for HS spread, 84% of the territory is characterised by
the prediction value of less than 0.25. On the most contrast variant of the model built on the data at 10 km thin-
ning distance, the suitability rose considerably: thepercent of territory wherethe prediction value is above 0.5
increased to 22% compared to 3% inthe case of full data, the area of territory under less than 0.25 prediction
values is decreased to 31% and 44% at thinning distances of 10 and 7 km respectively. We further need to choose
which model to use for the next step of future prediction by nding a reasonable output.
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From the results visualised as maps, we can notice, that the model built on the full dataset is overtted, does
not cover northern latitudes, and poorly represent theoriginal habitat located inthe Caucasus area. It mostly
repeats the points of observation thus the possible distribution of habitat suitability of HS obtained from the
full dataset is built in a learn-by-heart manner. On the contrary, the model built on the dataset obtained due to
thinning at the distanceof 7 km seems to be the most suitable in terms of both prediction results and keepingas
much information as possible. Additionally, while we cannot lean on the evaluation scores to support this con-
clusion, we estimated the variability of prediction values across the territory of the study. It was the highest for
the datasets obtained at 10 and 7 km thinning distances. e outputs of the model built on 7 km distance data
were more diverse at the 100 km blocks, as was used for spatial cross-validation (Figs.S2, S3).
Features selected for modelling. To avoid over-tting because of using redundant variables, animpor-
tant part of the SDM procedure was choosing the most meaningful set of them, corresponding to the observed
HS occurrence. To do this several approaches were combined: search of highly correlated features and estima-
tion of the importance of features bythe Mean Decrease Gini (MDG) andthe Mean Decrease Accuracy (MDA)
scores. us, the general workow consisted of 3 general steps: (1) generation of correlation matrix; (2) estima-
tion of MDG and MDA scores; (3) picking up highly important non-correlated features and choosing the fea-
tures that have correlates but demonstrate higher importance according to both MDG and MDA scores. e rst
step of selection includes a search of highly correlated features andthe formation ofsets of mutually exclusive
covariates according to the absolute value ofPearson correlation coecient greater than 0.8. e correlations are
demonstrated in Fig.S5. From the group of bioclimatic variables, the following subset of features demonstrated
ahigh correlations’ coecients between each other:
BIO1, BIO6, BIO9, BIO11;
BIO6, BIO4, BIO7;
BIO4, BIO7, BIO16;
BIO5, BIO10;
BIO16, BIO13;
BIO13, BIO14, BIO18, BIO17, BIO12.
en, based on the variable importance results obtained by MDA and MDG, the most important features were
selected and included in the core list for the predictions: BIO8, BIO10, BIO13, BIO15, BIO19. Additionally,
BIO1 and BIO9 features demonstrated approximately equal importance in corresponding forecastings. us,
we built dierent RF models with the core list of features including only BIO9 for the rst variant and only BIO1
for the second one. By comparing the results from modelling, BIO1 demonstrated higher importance, so it was
included in the nal list of features.
Using the same approach, described above, the selection of soil properties was performed. According to the
correlation matrix (Fig.S5), soil properties do not have correlationcoecients equal to 0.8 or more in absolute
Figure1. Flowchart of the approach.
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values with bioclimatic variables. However, SOC and Sand content demonstrated a high enough correlation. CF,
Silt and Sand did not show high importance in the corresponding analyses. us, from the soil features, the nal
list included only CEC and SOC. erefore, the following list of features was used to train the algorithm: SOC,
CEC, BIO1, BIO8, BIO10, BIO13, BIO15 and BIO19 (Fig.S6).
According to Fig.S6, BIO13 and BIO8 demonstrated the highest importance in predicting HS distribution.
Based on MDA, soil properties are considered to be more important comparedto MDG. BIO1 and BIO10
demonstrated less importance related to MDA, whereas CEC and BIO19 had the same pattern related to MDG.
Possible habitat suitability in the future. Using the set of environmental predictors obtained inatthe
feature selection stage, we modelled the possible future spread of HS across the territory ofthe study. To do this,
we estimated the distribution of bioclimatic variables according to the available global climate models. From
obtained results, we see that CNRM-CM6-1 and BCC-CSM2-MR show almost identical results in general, as
well as between chosen SSP (Fig.3, Fig.S7). According to them, only 6–8 % of the study territory in the future
are characterised by prediction values less than 0.25. e CanESM5 results show a slightly dierent picture: the
percent of the likely unsuitable territory is down even more to 3% at the better SSP126, and to 0.7% at the worst
CO
2
atmosphere concentration scenario—SSP585.
Figure2. Maps of prediction of possible distribution of HS in current climate conditions using dierent
thinning distances and, consequently, amounts of input points. e quality of prediction varies signicantly,
while the model built on the full dataset is obviously overtted.
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Discussion
Sampling bias is a frequent problem in SDM because presence-only data is collected predominantly in more
accessible locations32. e spatial sampling bias also leads to environmental bias in the data set33. Ignoring the
problem leads to inaccurate forecasting and can be followed by an inappropriate risk assessment of invasive
species and mistakes in conservation planning. e number of methods to tackle the problem of sampling bias
is limited. For rare records, a new Poisson point process model is proposed34, where environmental eect and
sampling bias are explicitly modelled in separate clusters in a framework of quasi-linear modelling. Another
example of solving this problem is the incorporation of background (pseudo-absence) points with the same
sampling bias asthe distribution of occurrence points33. If the number of records is enough, spatial ltering is
commonly used when some part of occurrence points is discarded. We combined two methods to overcomethe
sampling bias of HS occurrence points: spatial ltering andthe creation of the same eect of sampling bias
among pseudo-absence points.
e main limitation of the data thinning method is that we should assume the particular level of sampling
bias to proceed to the following modelling, while in reality, it is actually unknown. is is whythe search for
the most appropriate amount of discarded records for occurrence pointsis notstraightforward. erefore we
used three distances: 4 km, 7 km and 10 km to compare with the initial dataset. e estimates forthe current
climate (Fig.2) demonstrate signicant dierences in predicted habitat suitability that are highly dependent on
the thinning process. At the same time, using the initial dataset in forecasting leads to inaccurate results, which
demonstrates over-tting. Extensive results carried out show that spatial ltering improves forecasting, the higher
number of discarded points—the higher number of locations that are more suitable for HS. Nevertheless, the
big distance of 10 km excludes the largest amount of points which leads to an increase in the uncertainty of the
model. erefore, the distance of 7 km was considered as optimum in our study. However, it must not be forgot-
ten thatthe suspense ofthe level of sampling bias is one limitation of our implementation.
Figure3. Maps of prediction for possible distribution in future climate conditions on the example of selected
global climate models CNRM-CM6-1, CanESM5, BCC-CSM2-MR, in two scenarios of Shared Socioeconomic
Pathways—SSP126 and SSP585.
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e characterization ofthe possible future expansion of invasive species might be a powerful tool for the
highlighting of the importance of conservation management. Research results allow considering possible shis
in the ecosystem components on dierent levels without actions to be taken.
According to the modelling results the main change between current and possible future distributions is in
the noticeable increase of the average possible suitability across the territory from 0.28 in current climate condi-
tions to 0.37–0.4 at SSP126 and to 0.37–0.43 at SSP585 in future climate considering the results of the selected
models (TableS1). Moreover, in the future conditions, the territory of study is covered more or less uniformly
by the prediction values higher than 0.25—on average 89% is potentially suitable for HS spread, which is two
times more, compared to the current climate predictions based on the selected data shape. At the same time,
the maximum prediction value in future climate is decreased from 1 to 0.7. e territory covered by prediction
values more than 0.25 includes the high latitudes above 60
, especially in the SSP585 scenario according to the
CanESM5 model.
According to established knowledge, the light availability in combination with disturbed upper soil coverage is
necessary for the development of HS plants atthe early stages35. us, the conditions of long daylight in northern
latitudes during the period of active vegetation might especially favourthe plants’ growth in the lighted cover
locations with suitable wetness regime. erefore, HS in future climate might impose a serious danger to the
territories thatare currently characterised by low biodiversity and productivity. It can be additionally considered,
thatthe active spread of HS can inuence the carbon cycle by reducing biodiversity and changing the structure
of soil prole. HS is reported not to form litter36, so the structure of microorganisms’ community should shi,
while soil properties are expected to degrade due toa decrease of carbon stock37.
Methods
From the popular algorithms, we chose the Random forest model as the most suitable for our case.e 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 description. Heracleum sosnowskyi is a monocarpic perennial plant of
the Apiaceae family. e 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. e blooming period starts in July and continues until the end of
September. Plant reproduction is performed by seeds only. e 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 stratication for the dormancy break is obligatory for ger-
mination 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 rst growing period.
HS is mostly spread in articial and semi-natural habitats, including grasslands, pastures, parks, roadsides,
agricultural elds, 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 area. e area for modelling extends from approximately 41
to 70
N and from 27
to 60
E, and
Kaliningrad region, it equals to approximately 4 mln km2 (Fig.4).
e 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 moun-
tains, with the predominance of the East European Plain. Environmental characteristics across the territory of
study vary signicantly. e 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 dierent 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. e 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. e 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 data. Plant occurrence data. Plant 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 docu-
mented by human observation and collected from 2000 to 2021. e overall number of initial occurrence points
from combined sources is 7637.
Environmental predictors. Climate 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 dierent resolutions. We chose 10 arc-
minutes spatial resolution taking into account the size of the studied area. Table1 provides ashort description
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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
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.
Figure4. Map 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.
Table 1. Description of used bioclimatic variables.
Parameter Full name
BIO1 Annual mean temperature
BIO2 Mean diurnal range
BIO3 Isothermality
BIO4 Temperature seasonality
BIO5 Max temperature of warmest month
BIO6 Min temperature of coldest month
BIO7 Temperature annual range
BIO8 Mean temperature of wettest quarter
BIO9 Mean temperature of driest quarter
BIO10 Mean temperature of warmest quarter
BIO11 Mean temperature of coldest quarter
BIO12 Annual precipitation
BIO13 Precipitation of wettest month
BIO14 Precipitation of driest month
BIO15 Precipitation seasonality
BIO16 Precipitation of wettest quarter
BIO17 Precipitation of driest quarter
BIO18 Precipitation of warmest quarter
BIO19 Precipitation of coldest quarter
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We used the Equilibrium Climate Sensitivity to select the climate model to model future HS distribution.
Equilibrium climate sensitivity (ECS) is dened 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.
For 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
by 1.125
.
CanESM5 Canadian Earth System Model version 5 developed in Canadian Center for Climate Modelling
and Analysis, Canada52. Horizontal resolution 2.81
by 2.81
.
CNRM-CM6-1 Climate model developed in National Center of Meteorological Research, France53. Horizontal
resolution 1.4
by 1.4
.
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 map-
ping. 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 prole observations from the WoSIS (e 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: rela-
tive percentage of silt (Silt, %), sand (Sand, %), a volumetric fraction of coarse fragments (CF, %), cation exchange
capacity (CEC,
cmol
c
/kg
) and soil organic carbon (SOC, g/kg) at the depth 5–15 cm, where the HS seeds are
assumed to be located. ese 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‑processing. All the data were transformed to the ASCII format by R script and using soware
DIVA-GIS following the tutorial forthe preparation of WorldClim les for use in SDM (http:// www. lep- net. org/
wp- conte nt/ uploa ds/ 2016/ 08/ World Clim_ to_ MaxEnt_ Tutor ial. pdf) with unied selected resolution 340 sq.km.
Optimization of the occurrence points amount. e 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. e spatial ltering 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 cor-
respondingly lteringthe initial dataset. For the thinning step thin() function was used within the R package
spin 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 generation. Due 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. us, the
combination of the ‘disk’ and ‘random’ strategies was applied for the generation of the pseudo-absence points
using the biomod R package17.
e ‘disk’ strategy is established on the geographic distance works as separation from truth presence and pos-
sible absence points. e optimal geographic distance for HS was chosen as 25 km. is 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 nished with 50 km. Using distances such as 30–50 km lead to a positive spatial autocorrela-
tion. us, we decided to set 25 km which nally provided both optimal model performance and reduced
spatial autocorrelation.
e second part ofthe generation was based onthe ‘random’ strategy with ltration: according to the dier-
ent range of climate conditions on the territory of Russia, there are several places where HS is not detected,
thus not growing. e 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
, according to tundra board line.
Features selection procedure. To avoid over-tting and to choose the most conscientious set of parameters
for nal 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 coecient. With the
rise of the MDG score the importance of the corresponding feature is also increasing. MDA describes how much
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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 approach. Random forest. Choosing 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. ere 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.
e 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 spe-
cies.
Approach to the cross-validation of the model. A 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 performance. To 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. e principle of methods lies in the standard confusion matrix, where rows and columns
represent actual and predicted classes. e construction of ROC curves uses all possible thresholds to obtain
dierent 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 − specicity). In our
case true positive (TP, sensitivity) rate means that predicted places where HS grows correspond to actual. Simi-
larly, true negative rate (TN, specicity) indicates correctly classied 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.
Code availability
For the data, preprocessing and modelling details to reproduce the calculations, we refer the reader to the reposi-
tory of the project https:// github. com/ herac leums osnow skyi/ Herac leum_ Sosno wskyi.
Received: 11 February 2022; Accepted: 30 March 2022
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Acknowledgements
The work was supported by the Analytical center under the RF Government (subsidy agreement
000000D730321P5Q0002, Grant No. 70-2021-00145 02.11.2021). We thank the “Antiborschevik” community,
Maria Popova and Nikolay Petrov personally, for help with territorial research and providing the occurrence data.
Author contributions
M.P., P.T., D.S., M.G. contributed to the original concept of the study, D.K., M.G., P.T. collected the data, D.K.
developed the modelling design, performed calculations, D.K., P.T., D.S., M.G. reviewed and interpreted model-
ling output, D.K., P.T., M.G. visualised the results. D.K., P.T., D.S., M.G. wrote original dra.
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Competing interests
e authors declare no competing interests.
Additional information
Supplementary Information e online version contains supplementary material available at https:// doi. org/
10. 1038/ s41598- 022- 09953-9.
Correspondence and requests for materials should be addressed to D.K.
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