Title: Geostatistical models with the use of hyperspectral data and seasonal variation - a new approach for evaluating the risk posed by invasive plants

Author: Katarzyna Bzdęga, Adrian Zarychta, Alina Urbisz, Sylwia Szporak- Wasilewska, Michał Ludynia, Barbara Fojcik, Barbara Tokarska-Guzik

Citation style: Bzdęga Katarzyna, Zarychta Adrian, Urbisz Alina, Szporak- Wasilewska Sylwia, Ludynia Michał, Fojcik Barbara, Tokarska-Guzik Barbara. (2021). Geostatistical models with the use of hyperspectral data and seasonal variation - a new approach for evaluating the risk posed by invasive plants. "Ecological Indicators" (2021), vol. 121, art. no. 107204, s. 1-21. DOI: 10.1016/j.ecolind.2020.107204

Ecological Indicators 121 (2021) 107204

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Ecological Indicators

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Geostatistical models with the use of hyperspectral data and seasonal variation – A new approach for evaluating the risk posed by invasive plants

Katarzyna Bzdęga a,*, Adrian Zarychta a, Alina Urbisz a, Sylwia Szporak-Wasilewska b, Michał Ludynia a, Barbara Fojcik a, Barbara Tokarska-Guzik a a Institute of Biology, Biotechnology and Environmental Protection, Faculty of Natural Sciences, University of Silesia in Katowice, Jagiellonska 28, 40-032 Katowice, Poland b Water Centre, Warsaw University of Life Science - SGGW, Nowoursynowska 166, 02-787 Warsaw, Poland

ARTICLE INFO ABSTRACT

Keywords: The general trend of ongoing plant invasion and the increasing number of species that may become invasive in Heracleum sosnowskyi the future, force seeking solutions that can improve the efficiency and economy of their management. Thus, we Fallopia spp. applied a novel approach combining the use of geostatistical interpolators such as ordinary kriging (OK) and co- Spatial distribution kriging (CK) with environmental and hyperspectral data to evaluate the potential threat associated with the Spectral vegetation index distribution of invasive plant species and to predict their probabilities of occurrence above the selected threshold Remote sensing Kriging of 10%. The specific spatial patterns of the probability of occurrence of Heracleum sosnowskyi and Fallopia spp. were modelled in two study areas in southern Poland. The significant achievement of this study was the application of geostatistical tools producing results characterized by a degree of precision quantified by cross- validation errors, and prediction errors after field verification. OK and CK returned root mean squared error (RMSE) values in a range from 0.21 to 0.51 and 0.21 to 0.47, respectively. For OK and CK, the prediction errors resulting from field verification in the following year were between 0.03–0.39, and 0.03–0.29, respectively. Additionally, the study provided the first prediction maps (2D) and Digital Prediction Models (DPMs) (3D) vi­ sualizations of the probability of occurrence of both invasive plants. Although the proposed approach is illus­ trated with real case studies related to Heracleum sosnowskyi and Fallopia spp., it could be extended to other species. This demonstrates the potential of an effective alternative strategy for evaluating the risk posed by invasive plants, that will be able to provide fast, low cost and effective prediction and monitoring of their spread. For institutions dealing with invasive plants, this may be beneficialand help to reduce the negative consequences of their improper management.

1. Introduction development of Geographic Information System (GIS), remote sensing and geostatistics may help to achieve the above-mentioned research The classical approach to research on the occurrence of invasive goals and deserves attention - in particular the possibilities offered by plant species requires both fieldand off-site studies. These are methods these tools (Hutchinson and Gallant, 1999; Ai and Li, 2010). For pre­ and techniques well known for controlling the spread of invasive species dicting the potential distribution of invasive taxa in their invaded range, (cartographic studies of distribution ranges, monitoring, management ecological or climatic niche modelling is used (Broennimann and Gui­ and other methods to control these species) (Tokarska-Guzik, 2005 and san, 2008; Fernandez´ and Hamilton, 2015; Ramírez-Albores et al., 2016; the literature cited therein). However, modern methodological and Jovanovi´c et al., 2018). technical facilities are often used to refine and automate the whole Remote sensing is increasingly being used to study invasive species research. These may enable a more detailed analysis of ranges of inva­ of plants as it allows modelling their spread and may be a tool for rapid sive species occurrence and the dynamic of invasiveness, as well as and efficient monitoring in the future (Ishii and Washitani, 2013; Roc­ preparation of more effective activities aiming to combat them. The chini et al., 2015; Chance et al., 2016; Müllerova´ et al., 2017; Martin

* Corresponding author. E-mail addresses: [email protected] (K. Bzdęga), [email protected] (A. Zarychta), [email protected] (A. Urbisz), [email protected] (S. Szporak-Wasilewska), [email protected] (M. Ludynia), [email protected] (B. Fojcik), [email protected] (B. Tokarska-Guzik). https://doi.org/10.1016/j.ecolind.2020.107204 Received 28 November 2019; Received in revised form 13 November 2020; Accepted 18 November 2020 Available online 8 December 2020 1470-160X/© 2020 University of Silesia. Published by Elsevier Ltd. This is an open access article under the CC BY license

(http://creativecommons.org/licenses/by/4.0/). K. Bzdęga et al. Ecological Indicators 121 (2021) 107204 et al., 2018). 2011). Geostatistics as a branch of applied statistics began in the mining Therefore, many legal conditions are being implemented to minimize ′ industry in the early 1950 s (Krige, 1951), and the first geostatistical or prevent this phenomenon. Identification of priority invasive plant concepts were developed by Matheron (1962), Matheron (1965). The species and identification of various pathways and vectors of their dynamic development of geostatistical methods has contributed to their introduction seems particularly important. Attention should also be paid use in other fields, mainly in earth and environmental sciences. Apart to techniques for rapid detection of newly arrived alien species and from mining geology (Van der Meer, 2006; Mucha and Wasilewska- monitoring of previously established ones (Genovesi and Shine, 2004; Błaszczyk, 2012; Shirazi et al., 2018), these methods are used in a va­ COM, 2011; Convention on Biological Diversity, 2014; Regulation UE, riety of studies and fields, such as hydrogeology (Dai et al., 2017), hy­ 2014). drology (Shaqour et al., 2016), climatology and meteorology (Ishida and Currently, a marked growing interest in research on prediction of Kawashima, 1993; Kwiatkowska-Malina and Borkowski, 2014; Pravi­ plant spread from the place of their introduction may be observed lovic et al., 2018), geomorphology (Zarychta, 2015), soil science (Ferr´e (Gallien et al., 2010; Elith, 2014; Gillard et al., 2017). et al., 2015; Zarychta and Zarychta, 2015; Veronesi and Schillaci, 2019), Due to the fact that data on the current distribution of invasive alien and remote sensing (Ciampalini et al., 2012). plants is essential for understanding the process of their spreading and Geostatistical methods are also used to analyse spatial patterns of occupying new habitat types, different concepts of invasion ecology, insect populations and their spatial structural dynamic in different types environmental variables, types and data sources (e.g. literature data of environments. This can be important in ecological studies and pest such as scientific publications, unpublished floristic data, distribution management (Zhou et al., 2012). maps provided from online databases, herbarium collections and field Geostatistical modelling and remote sensing data have allowed to observation data) are used and analyzed. estimate the spatiotemporal dynamics of an agrocoenosis vegetative A thorough estimation of the occurrence of invasive species together cover (Zhukov et al., 2013) and describe spatial variations in Leaf Area with their potential to occupy new areas is especially important for Index (LAI) in subtropical forests (Zhu et al., 2016). Despite the management policy and protection of valuable natural areas (Robertson demonstrated usefulness of geostatistical methods in natural sciences, et al., 2010; Groom, 2013a, 2013b). the number of studies using them in plant species spatial distribution is Such data are collected in different online information systems with still small. Among the available geostatistical techniques, ordinary different coverage: global such as CABI (2018), GISD (2018), and GISP kriging is the most used, while multivariate estimation techniques (e.g. (2018); European such as DAISIE (2017), EASIN (2018), NOBANIS co-kriging) are less frequent in plant science studies. Works worth (2018), and EPPO (2018); and regional such as the National Biodiversity mentioning, address among others, the analyses of spatial distribution Data Centre - Ireland (2018), Alien Species in Poland (2018), and BFIS and preservation of the species richness and diversity in a shrub savanna (2018). (Batista et al., 2016), estimation of changes in the distribution of There is an urgent need to develop and apply an effective alternative vascular plants (Groom, 2013a), mapping of Posidonia oceanica cover approach combining the use of geostatistical tools to model environ­ using geostatistical analysis of seabed images (March et al., 2013), mental parameters affecting the future distribution of selected alien spatiotemporal dynamics of tree species in a natural mixed tropical plant species in order to support effective management of invasive plant forest (Pelissari et al., 2017), use of geostatistical methods for assessing species. The study aimed: (1) to determine the relationship impacting biodiversity forest reserve zones located within reforestation of Euca­ upon selected aspects of seasonal variability (e.g. cover, phenological lyptus sp. and Pinus sp. (Neves et al., 2010), as well as use of remotely stages, co-dominants) for Heracleum sosnowskyi and Fallopia spp., and (2) sensed data for classification of forest ecosystems (Zawadzki et al., to obtain prediction maps and Digital Prediction Models (DPMs) of alien 2004a), and determination of inventory measures and biophysical pa­ plant species occurrence by applying two geostatistical estimators, or­ rameters of forests (Zawadzki et al., 2004b). Geostatistical tools were dinary kriging and co-kriging. also used for the generation of plant distribution ranges (Groom, 2013a). The development of civilization has contributed to the spread of 2. Materials and methods plant species from geographically distant regions of the world. Crossing geographical barriers is known as geographic or chorological expansion, 2.1. Characterization of invasive plant species while the spreading of species to anthropogenic habitats within a natural range is named ecological expansion (Tokarska-Guzik, 2005 and the The main object of our interests was a group of alien invasive plant literature cited therein) or invasion (Richardson et al., 2000; Pyˇsek et al., species of diverse biology (Table 1): Heracleum sosnowskyi and Fallopia 2004). The term ‘invasive species’ refers to species of foreign origin that species. Heracleum sosnowskyi (Sosnowsky’s hogweed) is a biennial or become introduced and established outside their native range, success­ perennial plant, and reproduces exclusively by seeds. The two knotweed fully producing viable offspring, often in large numbers, spreading at a taxa: Fallopia japonica (Japanese knotweed), the parental species, and considerable distance away from the mother plants (Richardson et al., F. × bohemica (Bohemian knotweed), the hybrid, belong to perennials 2000; Hulme, 2007). with a clonal (iterative) type of growth, that use two reproductive The problem related to the spread of invasive species is important, modes: vegetative through quick-growing rhizomes and generative by because they pose a threat to native species and to natural or semi- seeds, rare in the European parts of the invasive (secondary) range. natural ecosystems or habitats by competing for sunlight, nutrients, These species are recognized as the most troublesome alien invasive water and growing space, often preventing their regeneration, limiting species (Lowe et al. 2000) introduced outside their natural range: Cau­ access to light, changing the rate of organic matter degradation, limiting casus and South-West Asia - Heracleum, and East Asia - Fallopia, to or even preventing seed germination, as well as modifying soil physical different parts of the world (Bailey, 2003; Nielsen et al., 2005; Bailey and chemical properties and activity of soil microorganisms and alle­ et al., 2007; Jahodova´ et al., 2007). They spread mostly along rivers, but lopathic effects (Aguilera et al., 2010; Butchart et al., 2010; Chmura are also found in anthropogenic habitats (Pyˇsek and Prach, 1993; et al., 2015; McGeoch et al., 2010; Vila` et al., 2011; Simberloff et al., Tokarska-Guzik, 2005; Richards et al., 2008; Wilson et al., 2017). Such 2013). plants cause growing concern, as they pose a serious threat to native The spreading of invasive plant species also affects the economy and biodiversity and result in significant ecological and economic costs human health. These plants limit and often prevent, the use of agricul­ (Rajmis et al., 2016; Fennel et al., 2018), as well as pose health risk to tural land for cultivation, destroy flood protection, and significantly humans and cattle, as is the case with Heracleum species (Hipkin, 1991; lower the attractiveness of areas in terms of landscape, recreation and Maguire et al., 2008; Chmielewski et al., 2017). In Poland, Sosnowskyi’s tourism, causing huge economic losses (Vila` et al., 2009; Pimental, hogweed occurs in the northern and southern part of the country, but the

2 K. Bzdęga et al. Ecological Indicators 121 (2021) 107204

Table 1 (Kondracki, 2001), the study was carried out in two regions located in List of characteristics of two invasive plant species selected for analysis and the southern Poland. In the Central Beskidian Piedmont region, the research processing approach. was conducted in two areas, HE1 and HE2 with Heracleum sosnowskyi. Heracleum sosnowskyi (Sosnowsky’s References Similarly in the Upper Vistula River Valley, the study was performed in hogweed) two areas, RE1 and RE2, where Fallopia species grow (Fig. 1). Flowering time from mid-June to late Nielsen et al., 2005; Kabuce and The areas HE1 and HE2 are situated in the eastern part of the Central July (August) Priede, 2010 Beskidian Piedmont that represents an area between the Dunajec and Fruiting time from late July to Nielsen et al., 2005; Vladimirov et al., Wiar valleys. Here, there is a belt of hills and valleys of several dozen October 2017 kilometres wide, and their height above sea level ranges between 300 Type of growth not clonal Nielsen et al., 2005; Kabuce and + ◦ Priede, 2010; Vladimirov et al., 2017 and 500 m. The average annual air temperature is 14 C, while the Modes of exclusively by seeds Nielsen et al., 2005; Kabuce and total annual precipitation is 800 mm. reproduction Priede, 2010; Baleˇzentiene˙ and The areas RE1 and RE2 are located in the central area of the Bartkevicius, 2013 O´swięcim Basin, part of the Upper Vistula River Valley and is bordered Fallopia spp. (knotweeds) References by sandy terraces with a relative height of 10 to 20 m. The average + ◦ Flowering time from (July) August to Alberternst and Bohmer,¨ 2011 annual temperature is about 8.6 C and the average amount of pre­ September (October) cipitation reaches 719 mm. Fruiting time from September to Parkinson and Mangold, 2010; Both HE areas are located near the town of Sanok (administratively October personal observation in the Podkarpackie Province), while RE1 and RE2 are situated between Type of growth clonal / an iterative Adachi et al., 1996; Bailey et al., ´ ę 2009; Alberternst and Bohmer,¨ 2011 the towns of Pszczyna and Oswi cim (Silesia Province). Modes of vegetative through Bailey et al., 2009; Alberternst and In HE1 and HE2, a larger share of abandoned fields is present, sur­ reproduction quick-growing Bohmer,¨ 2011 rounded by forests consisting of Pinus sylvestris, Picea abies and Fagus rhizomes sylvatica, among others. The areas with Fallopia species (RE1 and RE2) generative by seeds Forman and Kesseli, 2003; Grimsby are dominated by willow (Salix spp.) and poplar (Populus spp.) riparian et al., 2007; Ti´ebre´ et al., 2007 forests, typical of the Vistula River Valley, surrounded by arable fields. The area of HE1 is 168 ha, and that of HE2 is 240 ha, while the area knotweeds are especially common in the southern regions (Zając and of RE1 is 389 ha and includes the RE2 area consisting of two smaller Zając, 2001, 2015). parts: western (208 ha) and eastern (70 ha) (Fig. 1, Table 2).

2.2. Study area

According to the physico-geographical division of Poland

Fig. 1. Location of the study areas in the Central Beskidian Piedmont (HE1, HE2 - Heracleum sosnowskyi) and the Upper Vistula River Valley (RE1, western RE2, eastern RE2 - Fallopia spp.).

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Table 2 Overview of research areas with dates of field and remote sensing data acquisition.

Species ID of the Latitude Longitude Size of the research area Campaign Seasons Field data Aerial data Phenological research area (ha) collection date acquisition date stage

Heracleum HE1 22.11712 49.42794 168.1 K1 spring 21.5.2016 21.5.2016** leaves sosnowskyi K2 high 11–12.7.2016 17.7.2016** peak of summer flowering K3 late 11.9.2016 4.9.2016** late senescence summer

K4 – – K5 high 21–22.6.2017 30.6.2017** peak of summer flowering K6 – –

HE2 22.51386 49.59334 240.3 K1 – – K2 – – K3 – –

K4 – – K5 high 23–24.6.2017 22.6.2017** peak of summer flowering K6 – –

Fallopia spp. RE1 19.06254 49.95383 389.1 K1 high 1.6.2016 22.6.2016** leaves summer K2 high 30.7.2016 24.7.2016** leaves summer K3 autumn 20.9.2016 11.9.2016** peak of flowering

K4 spring 24.5.2017* – K5 – – K6 late – 29.8.2017* summer

RE2 19.04736 49.95259 western part 208.1 K1 – – 19.08834 49.95657 eastern part 70.3 K2 – – K3 – –

K4 high 12.6.2017* – summer K5 – – K6 late 29.9.2017 29.8.2017** peak of summer flowering

Notes: *: data collected from fieldmeasurements or acquired with airborne remote sensing; **: hyperspectral data used in calculating spectral vegetation indices (SVIs) (subsection 2.3.2).

2.3. Sampling strategy invasive plant species was not less than 2 m. Similarly, the distance between sampling locations without invasive plant species, defined as 2.3.1. Botanical data ‘background’, was not less than 2 m. Once the two criteria were met, the Field data were collected during 2016 and 2017: three times within sampling locations were randomly selected from the species presence the growing season in 2016 to assess the ability to detect invasive plant patches. For all areas of HE and RE, during 2016–2017, at least 100 species at different phases of the life-cycle and plant cover stages, and locations were sampled for each invasive plant species (Table 3), again in 2017: on dates of species optimum development determined on together with a similar number of locations for other species with the basis of expert knowledge and the results obtained in the firstyear of diverse morphology or frequently with concomitant species (e.g. research. The presence-absence of a specified invasive species was also Arrhenatherum elatius, Urtica dioica) with a plant cover > 20% at each confirmed during a single visit in the field verification of 2018. sampling location (Fig. 2, Tables 3 and 4). In the first year, the research was conducted on test areas HE1 and For each co-dominant species, at each sampling location, plant cover RE1. Within these areas, field data were acquired in three campaigns state from 20% to 100% was recorded at 10% intervals. The observed (K1, K2 and K3) corresponding to the period of the growing season values were then divided into three frequency classes: A class - between (Table 2). The compliance of the botanical reference data obtained in the 20 and 40%, B - between 50 and 70%, and C - between 80 and 100%, firstyear was verifiedby revisited research on areas HE1 and RE1 in the respectively. The vegetative (1), flowering(2) and fruiting phases (3) for following year, in which new data were also acquired at the optimal Heracleum sosnowskyi and the vegetative (1) and fruiting phases (2) for floweringand fruiting stages of the analyzed species. Additionally, in the Fallopia species were also recorded. The value of necromass coverage second year of the study, the distribution of Heracleum and Fallopia plant was recorded with 10% accuracy, in the range from 10 to 100 (values species was analyzed in the new areas (HE2 and RE2), using the <10 were considered as 0). Among collected sampling locations without botanical sampling method developed during the first year. The sam­ invasive plant species (‘background’) were those in which the total cover pling technique was performed at the species optimal flowering and of non-invasive plants exceeded 20%, and thus were treated as co- fruiting stage, i.e. campaigns K4, K5 and K6 (Table 2). All sampling dominants. The coordinates of all locations were stored in Spectra Pre­ locations were polygons with a shape similar to a circle with a diameter cision MobileMapper 120 GNSS receivers (Spectra Geospatial, West­ of 2 m. The criteria for allocation of sampling locations in each area were minster, USA). The field botanical sampling data, including species as follows: (1) the presence of a given invasive plant species observed in characteristics, e.g. percentage cover, the life-cycle stages (phenological the patch of the species with percentage cover equal to or above 10%, phase), height and co-dominants (coexisting species) and others, were and (2) the distance between neighbouring sampling locations with written down on survey forms and finally stored in a database. At the

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Table 3 maps with the distribution of Heracleum sosnowskyi and Fallopia species The number of sampling locations in each research area in the given campaign. were produced (Fig. 2). ID of the research Class Campaign Number of sampling Finally, in 2018, the accuracy of predictions from geostatistical area locations modelling (Section 3) was assessed with actual species distribution. 2016 2017 2018 Therefore, a given number of sampling locations in each research area (Table 3) were inspected during a single visit in 2018 to confirm the HE1 Heracleum K1 104 – sosnowskyi presence-absence of a specified invasive species at the sampling K2 104 – 146* location. K3 108 – K5 – 38 2.3.2. Remote sensing data ’ ‘background 60 89 149 The encroachment of invasive plant species requires comprehensive HE2 Heracleum K5 – 107 107 and efficientsolutions that are repeatable and applicable to other areas sosnowskyi where these plants pose a threat. To this goal, spectral vegetation indices ‘background’ – 127 127

RE1 Fallopia spp. K1 107 – – K2 107 Table 4 K3 106 – 263* List of species co-occurring with the Heracleum and Fallopia invasive plant spe­ K4 – 146 cies with more than 20% cover, present in the sampling locations within the K6 – 10 areas: HE and RE. ‘background’ 41 170 211 Coexisting species ID of the research area RE2 Fallopia spp. K4 – 102 111 K6 – 9 HE RE + ‘background’ – 131 131 Agrostis vulgaris Alopecurus pratensis + Notes: *: the sum of sampling locations, including the highest number of loca­ Anthriscus sylvestris + tions, in the campaign of 2016 and all remaining locations collected in 2017 that Arrhenatherum elatius + were verified in 2018. Avenula pubescens + Bromus mollis + Calystegia sepium + same time of field data acquisition , airborne data (hyperspectral im­ Chaerophyllum aromaticum + agery) were also acquired (Tables 2 and 5). Deschampsia caespitosa + For the purpose of this study (subsection 2.3.4), field data i.e. per­ Elymus repens + + centage cover of Heracleum sosnowskyi and Fallopia species (Table 5) Humulus lupulus Phleum pratense + were binary coded. We assumed a binary threshold value equal to 10%, Urtica dioica + + i.e. 0 for coverage < 10% and 1 for coverage ≥ 10%. After data analysis,

Fig. 2. Schematic diagram showing stages in preparing a sampling strategy for the analyzed invasive plant species.

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Table 5 Variables required for statistical and geostatistical modelling of the target species.

Data Heracleum sosnowskyi Fallopia spp. Type of method

(Sosnowsky’s hogweed) (knotweeds) KW test Ordinary kriging Ordinary co-kriging

Botanical field data* percentage of ground cover + + + + + phenological stage (the life-cycle stages) + + + co-dominants (coexisting species) + + + necromass measurement + + + Airborne hyperspectral data spectral vegetation indices + + +

Notes: *: all botanical data are referred to each sampling location; KW test: Kruskal-Wallis test (See subsection 2.3.3).

(SVIs) were calculated using hyperspectral data from remote sensing result, it is more sensitive to variations in chlorophyll concentrations. (Table 2) and used as covariate in the geostatistical analysis (co-kriging). The Simple Ratio (SR) was developed mainly to identify green vegeta­ The airborne platform consisted of HySpex scanners (451 bands in tion. The use of the highest absorption (red range of electromagnetic VNIR and SWIR) that recorded images with a 1-metre spatial resolution. spectrum) and reflectance (near-infrared) regions of chlorophyll makes Images were atmospherically, radiometrically and geometrically cor­ this index suitable for many different plant studies. rected. Based on the acquired hyperspectral data, 65 spectral vegetation indices implemented in ENVI (Broomfield, CO, USA) version 5.3 were 2.3.3. Statistical analysis calculated for each research area and date of acquisition. Analysis of the Field and airborne hyperspectral data (Table 5) were analyzed using spectral properties of the target plant species showed that the best re­ Statistica (StatSoft Inc., USA) version 12.0. The assumptions of sults were provided by indices covering two or more of the following normality distribution and homogeneity of variance were not ensured. spectral bands: 550, 650, 670, 700, 800 and 860 nm. The following three When statistically significant differences were found, two non- narrow hyperspectral bands combinations were then selected: 550.4, parametric tests were applied to indicate the degree of differences be­ 668.6, and 700.6 nm; 550.4, 700.6, and 799.7 nm, and 652.7, and tween distinguished groups. The Mann-Whitney U test was used to 860.4 nm. examine the differences between two groups, while the Kruskal-Wallis Among the 65 indices that meet the criteria mentioned above, in test was conducted to test differences between more than two groups each research area, we selected for further analysis using geostatistical (Zar, 2014). methods, four with the highest correlation coefficients with the The boxplots graphs were created using MATLAB R2009a (The observed probability of occurrence at sampling locations after binary Mathworks, Natick, MA, United States). For all analysis we assumed a transformation (Table 6). The time of acquisition of aerial data and the significance level of 0.05. related environmental components, i.e. the changes in the cover of plants during the growing season, their phase of the life cycle and the 2.3.4. Geostatistical analysis presence-absence of coexisting species, the amount of necromass, the The variables used in the geostatistical analysis (OK, CK) referred to proportion of different land-use types (meadows, fields, forests, rivers, the probability of occurrence of a given invasive species for the selected etc.) and the type of soil may affect the values of the correlation co­ threshold of 10%. For the purpose of the geostatistical analysis the efficients.All these indices were calculated from the hyperspectral data original data set was enriched by randomly located mask points repre­ of 2017, except in the case of ARI2 which was computed from the senting urban land cover (buildings, roads), forest communities, open hyperspectral image of each campaign of 2016 (Section 3.3). water bodies, and rivers where the value was equal to zero. The total Simultaneously, from the 2016 data, ARI2 and TCARI were used in number of sampling locations used in geostatistical modelling for each the analysis of seasonal variability (Section 3.1). research area in this study is given in Table 7. The Anthocyanin ReflectanceIndex 2 (ARI2) uses reflectancevalues The resulting interpolation maps and Digital Prediction Models in the visible spectrum to take advantage of the absorption signatures of (DPMs) showed the probabilities of exceeding (or being below) the 10% stress-related pigments such as anthocyanins. Vegetation with a large threshold. Point ordinary kriging (OK) and point co-kriging (CK) (Goo­ share of newly forming leaves or those undergoing senescence are better vaerts, 1997) were the geostatistical estimators used to perform the recognized with the use of indices that detect higher concentrations of analyses. anthocyanins. The Transformed Chlorophyll Absorption Reflectance For each area, ordinary kriging and ordinary co-kriging with two Index (TCARI) and Modified Chlorophyll Absorption Ratio Index variables (i.e. probability of occurrence above 10% as primary variable (MCARI) values depend on the relative abundance of chlorophyll. The and spectral vegetation indices as secondary variable - Table 6) were advantage of TCARI in relation to MCARI is that the former was devel­ preceded by the computation of the empirical semivariogram (Goo­ oped to minimise the impact of soil and other non-photosynthetic sur­ vaerts, 1997) in Eq. (1): faces on the index value, especially in sparse vegetation cover, and, as a

Table 6 Spectral vegetation indices (SVIs) used in this study.

SVI ID of the research area r Equation References [ ] ARI2 RE1 0.67 1 1 Gitelson et al., 2001 ARI2 = ρ 800 ρ ρ ( ) 550 700 ρ MCARI RE2 western 0.79 = [(ρ ρ ) . (ρ ρ ) ] 700 Haboudane et al., 2004 MCARI 700 670 0 2 700 550 ρ ρ 670 SR RE2 eastern 0.85 SR = 860 Birth and McVey, 1968 ρ ( ) 653 ρ TCARI HE1 0.71 = [ ( ) . ( ) ] 700 Haboudane et al., 2004 TCARI 3 ρ700 ρ670 0 2 ρ700 ρ550 HE2 0.45 ρ670 Notes: ARI2: Anthocyanin ReflectanceIndex 2; MCARI: ModifiedChlorophyll Absorption Ratio Index; SR: Simple Ratio; TCARI: Transformed Chlorophyll Absorption Reflectance Index; r: Pearson correlation coefficient; ρ: the reflectance at the given wavelength (nm).

6 K. Bzdęga et al. Ecological Indicators 121 (2021) 107204

Table 7 where Z*(uα) is the predicted value from CV obtained via point ordinary The number of sampling locations for geostatistical modelling in each research kriging, z(uα) is the observed value and n is the number of sampling area. locations, ID of the Sampling locations from field Mask Sum of all the √̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ √ n research area measurements* points samples √∑ 2 √ (Z*(uα) z(uα) ) √α=1 HE1 503 956 1459 RMSE = (7) HE2 234 1183 1417 n RE1 687 514 1201 √̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ RE2 western 518 242 760 √ n √∑ 2 RE2 eastern 118 78 196 √ [( *( ) ( ) )/ *( ) ] √ Z uα z uα σ uα RMSSE = α=1 Notes: *: the sum of sampling locations including points with invasive plant n (8) species and ‘background’ collected in 2016–2017.

where σ*(uα) is the ordinary kriging standard deviation for location uα. N(h) 1 ∑ * ( ) γ(h) = [z(u ) z(u + h) ]2 Estimated values for the ordinary kriging ZOK u were calculated ( ) α α (1) 2N h α=1 using the formulae expressed in Eq. (9): ∑n(u) ∑n(u) where N(h) is the number of pairs of data locationsz(uα) and * OK OK ZOK (u) = λα (u)Z(uα) with λα (u) = 1 (9) z(uα +h)separated by a distance vector h. α=1 α=1 In the case of ordinary co-kriging, the cross-covariance was OK computed as Eq. (2): where λα is the weight assigned to n(u) random variables Z(uα) In ordinary co-kriging, the estimates were computed using Eq. (10): 1 ∑N(h) C (h) = z (u )z (u + h) m m ( ) ( ) ij N(h) i α j α i h j+h (2) n∑1 u n∑2 u α=1 Z* (u) = λOCK (u)Z (u ) + λOCK (u)Z (u ) OCK α1 1 α1 α2 2 α2 (10) α1=1 α2=1 where ziand zj are the covariates at two points i and j, respectively, at a ∑ ∑ distance h apart, N(h) is the number of pairs of data locations separated n1(u) OCK n2(u) OCK λα (u) = 1 and λα (u) = 0 (11) α1=1 1 α2=1 2 by the distance vector h, and mi h ,mj+h are the means of values of the two covariates considered (mi, mj) separated by vectors h and + h, where λα is the primary data weights and λα is the secondary data respectively. 1 2 weights at two locations u in Eq. (11). Prior to the computation of the experimental semivariograms, a Mean prediction error (MPE) and root mean square prediction error detrend function was used to remove from the data a quadratic trend by (RMSPE) were used to assess the accuracy of the prediction methods a second-order polynomial expression. A theoretical model was then (OK, CK). These were calculated by comparing the estimated values fitted to the experimental semivariograms. From the authorized semi­ retrieved at sampling locations from the prediction maps of probability variogram models, three were selected, as described by the following of occurrence of a given invasive species with an independent data set formulas: collected within each research area in the field verification of 2018. Nugget effect: { These errors were computed based on formulas in Eqs. (6) and (7), but in 0, h = 0 this case, Z*(uα) is the predicted value from OK or CK, while z(uα) is the γ(h) = (3) c0, h ∕= 0 observed value in 2018, and n is the number of sampling locations. For this purpose, the data shown in Table 7 were applied. In this study, for where c0 is the spatially uncorrelated variance (‘nugget’). both estimators (OK and CK), a 1-metre spatial interpolation grid was Exponential model with a practical range a: used. Each interpolated value of the grid cell was assigned to a location [ ( ) ] 3h at a given point after performing binary transformation stage as γ(h) = c + c 1 exp 0 a (4) mentioned previously (Section 2.3.1). Overall, the validation was run to verify the magnitude of differences between the estimated (continuosly Spherical model with a range a: varying between 1 and 0) and measured (1 or 0) values. ⎧ [ ( ) ] Ordinary kriging and ordinary co-kriging were performed by ⎪ 3 [ ( ) ] ⎨⎪ h h h c0 + c 1.5 0.5 , h ≤ a applying the commercial software Surfer (Golden Software, Golden, CO) γ(h) = c + c Sph = a a 0 ⎪ (5) version 12 and ArcGIS (ESRI, Redlands, CA) version 10.6.1. These a ⎩⎪ c0 + c, h > a software packages were also used for creating prediction and standard deviation maps. where c is the spatially correlated variance (‘partial sill’). The quantity c0 +c is known as the ‘sill’. 3. Results Fitted semivariograms and cross-covariance models were tested by cross-validation (CV), which quantified the accuracy of predictions at 3.1. Seasonal variability sampling locations for the target species. The basic idea of typical cross- validation is to remove iteratively some of the data from the data set and The seasonal variability of Heracleum sosnowskyi and Fallopia spp. use the remaining data to predict the deleted observations by applying was analyzed with regard to their cover during the growing season, the the selected semivariogram model (Cressie, 1991). In order to verify the phase of the life cycle (subsection 2.3.1) and the presence-absence of correctness of the models, the following errors indexes were calculated: coexisting species at sampling locations in 2016 and 2017 (Table 3). In mean error (ME), root mean square error (RMSE), and root mean square addition, the relationship between previously mentioned aspects of standardized error (RMSSE), defined as: seasonal variability and herbaceous plants (excluding the invasive spe­ ∑ n * cies), as well as the necromass was determined (subsection 2.3.1). = (Z (uα) z(uα) ) ME = α 1 Furthermore, the analysis of seasonal variability of the examined species n (6) was based on the following spectral indices: TCARI for Heracleum sos­ nowskyi, and ARI2 for Fallopia spp. in each campaign of 2016 (subsection

7 K. Bzdęga et al. Ecological Indicators 121 (2021) 107204

2.3.2). plants was close to 100% in both spring and high summer 2016 (K1 and A complete description of the evaluation of the percentage coverage K2, respectively). In contrast, coverage was above 90% in late summer of plants at sampling locations, number of locations and the sampling 2016 (K3) and also in high summer 2017 (K5, Fig. 3d). The differences method can be found in subsection 2.3.1 and Table 3. between K1, K2 and K3, K5 proved to be statistically significant.In the Our research showed that the percentage coverage of Heracleum case of RE areas, the cover of herbs was at a level of 100% for all sosnowskyi and Fallopia species changed during both growing seasons campaigns in both growing seasons except in spring and high summer (Figs. 3a-c and 4a-c). In the case of Heracleum sosnowskyi, the highest (K4) 2017 (Fig. 4d). cover of about 80% was recorded in spring 2016 (K1) and for the high In the case of the presence-absence of coexisting species with Her­ summer in both 2016 and 2017 (K2 and K5), respectively. In contrast, a acleum (campaigns K1-K3 and K5) and Fallopia species (campaigns K1- lower cover of hogweed, about 60% was observed in late summer 2016 K6), no changes were detected in coexisting species coverage as their (K3, Fig. 3a, Table 2). For Fallopia species, the highest cover at a level of level was always close to 100% (Figs. 3f and 4f). 100% was observed during the first growing season, the high summer The percentage cover of necromass defined as the total mass of all (K2), while the lowest species coverage value of at least 80% was in dead plant parts (including invasive species) changed druring consid­ spring and high summer in K4 of the second season (Fig. 4a, Table 2). ered two growing seasons (Figs. 3g, h and 4g, h, 1, Table 2). As for lo­ As for the phase of the life cycle, the highest cover of Heracleum cations with hogweed, the necromass cover reached the highest value in sosnowskyi, about 90%, was noted in the floweringand fruiting phases of late summer 2016 (K3), and in the high summer 2017 (K5, Fig. 3g, the species (Fig. 3b). As for Fallopia species, their cover reached 100% in Table 2). In the locations with knotweeds, a considerable amount of the flowering stage (Fig. 4b). necromass, above 20%, was identifiedin spring and high summer 2017 Regarding the occurrence of coexisting species with Heracleum (for (K4), and subsequently below the value of 20% in high summer 2016 campaigns K1-K3 and K5) and Fallopia species (for campaigns K1-K6) at (K1, Fig. 4g, Table 2). the same sites, their presence leads to a reduction of invasive species With regard to the phase of the invasive species life cycle, the cover coverage. The cover for Heracleum was reduced from 80% to 70% by co- of necromass was highest in the same vegetative phase for both Herac­ occurring species (Fig. 3c). Similarly, as in the case of previous species, leum and Fallopia species (Figs. 3h and 4h, respectively). The presence- the cover of Fallopia species was lowered from 100% to 80% and thus absence of coexisting species with Heracleum (campaigns K1-K3 and was the strongest reduction recorded of approximately 20% (Fig. 4c). K5) and Fallopia species (campaigns K1-K6) did not affect the cover of The values of percentage cover of herbaceous plants (excluding the the necromass (Figs. 3i and 4i). Similarly, their influence on the per­ invasive species) also changed over both the growing seasons (Figs. 3d-f centage coverage of herbaceous plants was also not observed (Figs. 3f and 4d-f, Table 2). In regard to the HE areas, the cover of herbaceous and 4f).

Fig. 3. Boxplots of the observations for coverage of Heracleum sosnowskyi, herbaceous plants and necromass divided into the campaigns corresponding to the period of the growing season (2016 in K1-K3 and 2017 in K5), the phases of the life cycle (vegetative, flowering,fruiting) in regard to the coexisting species (presence - yes, absence - no). Each box includes the median (central red line), the 25th and 75th percentiles (the edges of the box), extreme data points (whiskers), outliers (red pluses). Both campaigns and the phase of the life cycle were subject to the Kruskal-Wallis test (the values were presented in blue). Means with the same red letters close to the median are not significantly different from each other. A significance level of 5% where ∝=0.05 (critical value) and a p (probability) value determined from the distribution of test statistics were used for all analyses. The coverage analysis due to the presence-absence of co-occurring species was performed with the Mann-Whitney U test. In all analyses, median values that are followed by the same letter within the group were not significant.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).

8 K. Bzdęga et al. Ecological Indicators 121 (2021) 107204

Fig. 4. Boxplots of the observations for coverage of Fallopia species, herbaceous plants and necromass divided into the campaigns corresponding to the period of growing the season (2016 in K1-K3 and 2017 in K4, K6), the phases of the life cycle (vegetative, flowering,fruiting) in regard to the coexisting species (presence - yes, absence - no). (Descriptive statistics in boxplots are analogous to those in Fig. 3.).

Analysis of spectral indices allowed us to state that TCARI differen­ so evident due to the fact that the latter also has a high coverage at this tiates Heracleum sosnowskyi from other herbaceous vegetation in a time. The presence of flowers and fruits seems to play a pivotal role in satisfactory way. The average values of the indice for areas with species species identification by remote sensing methods. occurrence were significantly higher compared to those where the Slightly less explicit results of spectral indices analysis were obtained hogweed was not found, regardless of the campaign (Table 8). The in the case of Fallopia species. The highest average values of the ARI2 highest average values of the index for Heracleum were observed during were observed during high summer in K2, and the lowest in autumn in high summer in K2, and the lowest in spring in K1 (Fig. 5a). As for the K3 (Fig. 5b). As for herbaceous plants, similarly to the previously re­ values of TCARI for herbaceous plants, no significant differences were ported results for TCARI2, no differences in ARI2 were recorded be­ found between K2 and K3 (Fig. 5c). Differences between average TCARI tween K1 and K2 (Fig. 5d). As in the case of Heracleum sosnowskyi, the values for all sampling locations with the occurrence of Heracleum average values of the chosen indice for areas with Fallopia species were compared to others were observed in K2 (46.7%) and K3 (81.8%) with significantly higher in comparison to those areas where the knotweeds the lowest in K1 (27.2%). This suggests that the optimal time for the were not present irrespective of the campaign (Table 8). The highest identificationof Heracleum with remote sensing is high summer (peak of differences between index values for sampling locations with Fallopia flowering)or late summer (late senescence - fruiting phase). Despite the spp. compared to others were detected in K2 (70.1%) and K3 (112.5%) high coverage of Heracleum sosnowskyi found in spring, the spectral and the lowest in K1 (7.7%). It seems that in the case of Fallopia spp. the differences between Heracleum and other herbaceous vegetation are not optimal time for species identification by remote sensing methods is

Table 8 The values of TCARI (for Heracleum sosnowskyi) and ARI2 (for Fallopia spp.) indices for the campaigns of 2016 in HE1 and RE1 research areas, respectively.

HE1: TCARI

Campaign Heracleum sosnowskyi Other herbaceous plants

Min Average Max Min Average Max

K1 692.59 1341.73 2069.03 86.35 1130.02 1631.38 K2 866.38 2035.85 3221.18 764.14 1359.47 1846.7 K3 1065 1887.18 2784.39 515.9 1383.49 1880.44

RE1: ARI2

Campaign Fallopia spp. Other herbaceous plants

Min Average Max Min Average Max

K1 1.27 3.11 5.23 0.80 2.50 4.99 K2 1.41 4.46 6.74 1.09 2.76 5.01 K3 1.00 2.77 4.60 0.89 1.77 4.53

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Fig. 5. Boxplots of the TCARI values of Heracleum sosnowskyi and ARI2 values of Fallopia spp. as well as other herbaceous plants divided into the campaigns cor­ responding to the period of the growing season in 2016 (K1, K2 and K3). Each box includes the median (central red line), the 25th and 75th percentiles (the edges of the box), extreme data points (whiskers), outliers (red pluses). (Descriptive statistics in boxplots are analogous to those in Fig. 3.). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article). high summer (full leaves development) and autumn (peak of flowering). means of ME, RMSE and RMSSE from cross-validation (Table 10a). As all In general, high coverage of Heracleum sosnowskyi (about 80%), as values of ME were close to zero, this indicated that only small differ­ well as Fallopia species (80% and more) in spring and high summer ences exist between the measured and estimated values. In contrast, OK proved to be crucial for mapping the occurrence of these plants by produced the lowest RMSE value for HE1 (0.213) and the highest for geostatistical methods regardless of the remote sensing results. RE2 eastern (0.509). Furthermore, the value of RMSSE (above 1) revealed an underestimation of the variables at sampling locations for all areas, except HE1 (0.991). 3.2. Ordinary kriging (OK) On average, the magnitude of the errors deviation from the obser­ vations in each research area (See Tables S1 and S2 in Suppl. Mat.) were In the case of ordinary kriging of the Heracleum sosnowskyi data set, in the range 0.002 to 0.013 and 0.21 to 0.51 for ME and RMSE, two theoretical models were fitted to the empirical variograms in both respectively. HE areas, i.e. an exponential model with a nugget effect, and a spherical The correct variogram structural analysis allowed for obtaining model with a nugget effect for HE1 and HE2, respectively (Table 9). The predicted probabilities of occurrence with quantified adequacy of the same protocol was used for ordinary kriging of the Fallopia spp. data set, underpinning models for the targed species, Heracleum sosnowskyi, as in both RE areas, where empirical variograms were computed and a well as for Fallopia spp. for ordinary kriging (Fig. 6). theoretical model was fittedto it using: a spherical model with a nugget The prediction and standard deviation maps based on semivariogram effect (Table 9). The variograms values were calculated for each distance ◦ models for H. sosnowskyi in both HE1 and HE2 areas are shown in Fig. 7. value by averaging the values obtained in four different directions of 0 , ’ ◦ ◦ ◦ ◦ Sosnowskyi s hogweed was estimated with high probability to be above 45 , 90 and 135 , with tolerance of 45 . All variograms were consid­ the 10% threshold of occurrence in the western and mid-western portion ered to be isotropic. of HE1. Moreover, predicted probabilities between 0.35 and 0.65 were The experimental semivariograms and their models are shown in observed in the southern and eastern parts of the area. No occurrences of Fig. 6. The performance of the semivariogram models was evaluated by

Table 9 Parameters of theoretical models for ordinary kriging of Heracleum sosnowskyi and Fallopia spp. data sets.

Species ID of the research area Model Partial sill Range (m)* Nugget effect Max / min neighbours**

Heracleum sosnowskyi HE1 exponential 0.120 170 0.005 10–4 HE2 spherical 0.140 142 0.040 10–4 Fallopia spp. RE1 spherical 0.099 220 0.106 10–4 RE2 western spherical 0.114 200 0.090 10–4 RE2 eastern spherical 0.122 80 0.115 10–4 ◦ Notes: *: the range, in this case, means the same as the search ellipse radius, simultaneously, the ellipse was divided into 4 sectors with 45 offset type; **: maximum and minimum number of neighbours within the search ellipse.

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Fig. 6. Experimental variograms and fitted theoretical models for the variables of ordinary kriging and co-kriging complemented by the cross-covariance models. Notes: Z, Z1: primary variable as probability of occurrence above 10% of Heracleum sosnowskyi and Fallopia species cover; Z2: secondary variable, i.e. spectral vegetation indices.

Table 10 Cross-validation test (a) and prediction errors (b) of ordinary kriging for Heracleum sosnowskyi and Fallopia spp. data sets.

Species ID of the research area Cross-validation test (a) Prediction errors (b)

ME RMSE RMSSE MPEOK RMSPEOK

Heracleum sosnowskyi HE1 0.013 0.213 0.991 0.00016 0.03061 HE2 0.002 0.286 1.06 0.00002 0.16321

Fallopia spp. RE1 0.003 0.391 1.05 0.00277 0.30321 RE2 western 0.005 0.390 1.105 0.03271 0.38623 RE2 eastern 0.008 0.509 1.164 0.00172 0.31024

Notes: to prevent loss of information in the presented values, the 5 places past the decimal were kept. this species are recorded in the southwest, southeast, north, as well as occurrence were recorded in the mid portion of the area, while lower mid-eastern portion of HE1 (Fig. 7a and e). These results were confirmed values were observed in the neighbouring parts, in the east and west of by field verification in 2018. the area (Fig. 7c and f). For hogweed, the predicted probability of In the case of HE2, the maximum predicted values of species occurrence above the 10% threshold was close to zero (between 0 and

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Fig. 7. The probability of occurrence of Heracleum sosnowskyi in areas HE1 and HE2 as obtained via ordinary kriging: prediction (a, c), standard deviation maps (b, d), and Digital Prediction Models - DPMs (e, f) with sampling locations (black dots). Notes: the greater a given numerical value assigned to the colour scale on prediction maps, the greater the probability that the species occurs above the selected threshold at a location.

0.05), in the northern and southern parts of the area, which is equivalent (Table 10b). to an estimated low frequency of species occurrence, and this was sup­ Semivariogram models used for mapping the probability of occur­ ported by field verification in 2018. rence above 10% and its standard deviation for Fallopia spp. in RE1 and The standard deviation maps for both HE1 and HE2 areas resulted RE2, which consists of the western and eastern parts, respectively (See from the unbiased estimation process ensured by kriging. For the areas Table 9), returned the outputs presented in Fig. 8. without sampling locations, the values of kriging standard deviation In the case of knotweed species, the highest predicted probability of were ca. 0.3 (Fig. 7b and d), as reflected by the prediction errors their occurrence (>0.75) is observed mainly in the central and western

12 K. Bzdęga et al. Ecological Indicators 121 (2021) 107204 portions of RE1, as well as (ca. 0.5) in the eastern and mid-western parts River, which is reflected very well in the resulting map. Additionally, of the area (Fig. 8a and g). This pattern of probability distribution is due locations far from the river were characterised by lower values of to the presence of the Vistula River, and its effect upon the linear pattern probability (between 0.05 and 0.35) that, however, do not exclude the of the distribution of the target species along the river. The aforemen­ presence of the species (Fig. 8c, h and e). The field verification con­ tioned was confirmed by observations made in 2018. ducted in 2018 revealed that most of the knotweeds occurred in the The highest probability of occurrence above 10% for the target immediate vicinity of the Vistula River and in nearby cultivated fields,at species in the eastern and western portions were estimated in the a distance of about 100 m from the river. On the other hand, there were western RE2 area (first part of RE2 area), while the lowest values (be­ few cases of knotweeds existing close to the borders of the research areas tween 0.25 and 0.5) were observed in the middle of the area. However, (Fig. 8c, h and e). in the eastern RE2 area (the other part of RE2 area) the higher proba­ Similarly, as in the case of RE1, the distribution of knotweed in RE2 bility of occurrence of species is mainly concentrated along the Vistula is conditioned by the presence of the river, flowing eastward in the

Fig. 8. The probability of occurrence of Fallopia species in areas RE1 and RE2, consisting of two smaller parts, western and eastern, obtained via ordinary kriging: prediction (a, c, e), standard deviation maps (b, d, f), and selected Digital Prediction Models - DPMs (g, h) with sampling locations (black dots). Notes: the greater the numerical value assigned to the colour scale on prediction maps, the greater the probability that the species occurs above the selected threshold at the location.

13 K. Bzdęga et al. Ecological Indicators 121 (2021) 107204 entire area. Table 12 The values for the kriging’s standard deviation for RE areas were Cross-validation test (a) and prediction errors (b) of ordinary co-kriging for very similar to those obtained for values of MPE and RMSPE errors, and Heracleum sosnowskyi and Fallopia spp. data sets. were slightly higher than prediction errors values from HE areas. This Species ID of the Cross-validation test (a) Prediction errors (b) outcome was probably due to the higher nugget effects and to the lowest research ME RMSE RMSSE MPECK RMSPECK sampling density in RE2 eastern (Figs. 8b, d, f and 7b, d, Table 10b). area

Heracleum HE1 0.013 0.213 0.932 0.00049 0.03815 sosnowskyi 3.3. Ordinary co-kriging (CK) HE2 0.001 0.285 1.042 0.00086 0.11155

Fallopia spp. RE1 0.009 0.389 1.035 0.01077 0.29572 A similar approach was used in the case of ordinary co-kriging for the RE2 0.015 0.387 1.106 0.01715 0.27278 Heracleum sosnowskyi data set: in both the HE areas, experimental western semivariograms were computed for the primary and the secondary RE2 0.026 0.473 1.085 0.00595 0.08267 variables, and then modelled resorting to an exponential model with a eastern nugget effect. Moreover, the cross-covariance was also calculated and Notes: to prevent loss of information in the presented values, the 5 places past the modelled (Table 11). decimal were kept. As for ordinary co-kriging of the Fallopia spp. data set, in both RE areas, this resorted to the same number of empirical variograms, as well from both HE and RE areas. as to the same theoretical models, adopted in the HE areas (Table 11). In In the HE1 area, our results showed that the probability of hogweed this case too, the resulting experimental variograms were calculated by occurrence, was clearly visible particularly in its western portion, where averaging the directional semivariograms (in four different directions, its occurrence had been confirmed in 2018. In the HE2 area, the prob­ ◦ with angular tolerance of 45 ). All were considered to be isotropic, as the ability of occurrence of the species was concentrated in the middle targeted variables did not exhibit spatial anisotropy within the spatial section of the prediction map, and was closely correlated with the range of the selected theoretical models. location where its presence was confirmedin the 2018 fieldverification The performance of the variogram models was assessed via cross- (subsection 2.3.1, Fig. 9a, e, c and f). validation by means of ME, RMSE and RMSSE for each research area In the RE areas, the highest probabilities of knotweed occurrence (Table 12a), as in the case of ordinary kriging. CK generated the lowest were primarily in the middle and western part of RE1. They also cor­ RMSE value for HE1 (0.213) and the highest for RE2 eastern (0.473). responded in terms of estimated probabilites and locations of species to Meanwhile, for the HE1 and HE2, RMSSE areas indicated a slight those observed in the maps of the RE2 western area (Fig. 10a, g, c and h). overestimation (0.932) and underestimation (1.042) of the variability of Within the RE2 eastern area, the occurrences of the invasive Fallopia the predictions; however, there is only a slight underestimation for both species extended clearly along the Vistula River from the west and RE areas. In all these cases, the results were consistent and similar to the farther east (Fig. 10e). These results highlight the existence of a spatial ones obtained for the previous cross-validation of ordinary kriging for pattern in the presence of the species, which was confirmed by obser­ Heracleum sosnowskyi and Fallopia spp. (See Table 10a). vations made in 2018. Overall, the magnitude of the errors with reference to the mean of For both the RE and HE areas, each estimation was characterized by the target variable in each area (See Tables S1 and S2 in Suppl. Mat.) is standard deviation values ranging from 0.17 to 0.48 and from 0.10 to of the order of 0.001 to 0.026 and 0.21 to 0.47 for ME and RMSE, 0.36, respectively (Figs. 9b, d and 10b, d, f), and validated by prediction respectively. errors after field verification in 2018 (Table 12b). The predicted probabilities of occurrence of Heracleum sosnowskyi CK and OK standard deviations are of the same order of magnitude and Fallopia spp. via co-kriging (CK), integrating the variogram struc­ for both methods at unsampled locations, indicating that in these cases tural analysis with an additional secondary variable are shown in Fig. 6 the two estimators are not significantly different. and Table 11. Figs. 9 and 10 show that the results of the CK models applied in this The CK results based on bivariate estimation are shown in Figs. 9 and study are comparable to the models generated via OK presented in 10. The obtained prediction and standard deviation maps for Figs. 7 and 8, respectively. The CK maps are characterized by an H. sosnowskyi and Fallopia species were similar to those obtained via OK

Table 11 Parameters of theoretical models for ordinary co-kriging of Heracleum sosnowskyi and Fallopia spp. data sets.

Species ID of the research area Variables Model Partial sill Range (m)* Nugget effect Max / min neighbours**

Heracleum sosnowskyi HE1 Z1 0.12 0.001 40–20 Z2d exponential 193 007 100 60 000 5–2 Z12 150 n/a n/a HE2 Z1 0.132 0.027 40–20 Z2d exponential 160 403.5 120 68 987 5–2 Z12 25 n/a n/a Fallopia spp. RE1 Z1 0.11 0.095 10–2 Z2a exponential 0.65 220 0.7 5–2 Z12 0.065 n/a n/a RE2 western Z1 0.135 0.069 20–10 Z2c exponential 164.974 204 187.779 5–2 Z12 1.418 n/a n/a RE2 eastern Z1 0.249 0 50–30 Z2b exponential 1 305 762 40 72 580.13 5–2 Z12 416.291 n/a n/a

Notes: Z1: primary variable as probability of occurrence (threshold 10%) of Heracleum sosnowskyi and Fallopia species cover; Z2: secondary variable as spectral vegetation indices with date of acquisition of the hyperspectral image - ARI2 (2016)a, MCARI (2017)b, SR (2017)c, TCARI (2017)d; *: the range in this case has the same ◦ value as the search ellipse radius, with the ellipse divided into 4 sectors with 45 offset; **: maximum and minimum number of neighbours within the search ellipse; n/ a: not available.

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Fig. 9. The probability of occurrence of Heracleum sosnowskyi in areas HE1 and HE2as obtained via co-kriging: prediction (a, c), standard deviation maps (b, d), and Digital Prediction Models - DPMs (e, f) with sampling locations (black dots). (Descriptive notes for the maps are analogous to those in Figs. 7 and 8). increased level of detail for the targeted species, primarily due to the occurrence for the analyzed taxa. contribution of the secondary variable (e.g. the spectral vegetation The performance of the two geostatistical interpolators (OK, CK) was indices, Table 6). Moreover, the SVIs used as secondary variables in the confirmed by the calculation of Pearson’s correlation coefficient be­ CK method were fully determined by the resolution of the hyperspectral tween the observed and estimated values of 2016–2017. The perfor­ data. Pixels of hyperspectral images with 1-metre spatial high resolution mance comparison between OK and CK showed that in CK, the use of the assumed the reflectancevalues at the given wavelength for all grid cells. secondary variable improved its performance in relation to OK This allowed for obtaining a more exact spatially and spectrally data set (Table 13). that was used as a secondary variable to estimate the probabilities of

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Fig. 10. The probability of occurrence of Fallopia species in areas RE1 and RE2, consisting of two smaller parts, western and eastern, obtained via co-kriging: prediction (a, c, e), standard deviation maps (b, d, f), and selected Digital Prediction Models - DPMs (g, h) with sampling locations (black dots). (Descriptive notes for the maps are analogous to those in Figs. 7 and 8).

4. Discussion Table 13 Pearson’s correlation coefficient between measured and estimated values via To successfully predict plant invasion, and consequently prevent ordinary kriging and ordinary co-kriging for the data of 2016–2017. further spread, new methods that enable rapid and effective monitoring Type of method ID of the research area are required. Geostatistical tools could make invasive plant management HE1 HE2 RE1 RE2 western RE2 eastern more economical and expeditious. The main goal of our study was to Ordinary kriging 0.996 0.918 0.792 0.638 0.821 determine the relationship between the coverage, phenological stage Ordinary co-kriging 0.997 0.965 0.807 0.849 0.996 and co-dominants across seasons for Heracleum sosnowskyi and Fallopia spp. in selected areas, and to test the application of geostatistical tools to generate prediction maps of probability of target species over a large spatial extent. Specifically, our findings extended the previous studies concerning these species by Müllerova´ et al. (2017) and Martin et al.

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(2018), as well as the use of geostatistical methods by Groom (2013a) The current literature on Heracleum and Fallopia species identifica­ and the utilisation of Aircraft Remote Sensing by Müllerova´ et al. (2017 tion using remote sensing is still limited and problematic (Müllerova´ and the literature cited therein). Our study also puts forward a novel et al., 2017; Martin et al., 2018). These invasive species were detected approach for predicting probabilities of occurrence of invasive plant with very high accuracy when in an appropriate phenological phase: species, encompassing models created for single species and using hogweed during flowering; knotweed at the phase of senescence georeferenced fieldobservation with environmental data to evaluate the (Müllerova´ et al., 2017). This is also supported by our fieldobservations risk they pose to native biodiversity and/or human health and the for this species, where the use of TCARI allowed for satisfactory differ­ economy. entiation between hogweed and other species at the peak of the flow­ At present, most research on alien and invasive plant species are ering period, as well as in autumn during the late senescence/fruiting mainly concerned with applying UAV, Aircraft and Satellite Remote phase. Unfortunately, similarly to cited research, their detection in other Sensing (Bradley, 2014; Chance et al., 2016; Müllerova´ et al., 2017; parts of the season was quite difficult as they were indistinguishable Martin et al., 2018; Kattenborn et al., 2019), the maximum entropy from the leaves of other surrounding plants similar to them. In the case model (Elith, 2014; Padalia et al., 2014; Gillard et al., 2017; Srivastava of Fallopia, using ARI2 brought about correct identificationof species in et al., 2018), and, more rarely, geostatistical techniques (Frappier et al., high summer with leaves fully developed. The aforementioned was also 2003; Lortie et al., 2010; Groom, 2013a; Hawthorne et al., 2015). true for autumn and peak of flowering.This result is very similar to those In the literature, there are many examples of research on the negative of Müllerova´ et al. (2017). Furthermore, the same problem was noticed interactions between plant invaders and native flora, while relatively when the canopy of trees obscures knotweeds and hogweeds during the few studies are focused on interactions among invasive plant species. vegetation season or when they are freshly cut or eradicated (Müllerova´ Furthermore, the majority of related studies are concerned with invasive et al., 2017; Martin et al., 2018). In the last case, their detection is much species where a simple scenario includes only one invasive species harder, but may still be achievable if the weeds have more time to affecting the native community (Lenda et al., 2019 and the literature regrow (Martin et al., 2018). The phenological phase, however, is still cited therein). Meanwhile, interactions between native and invasive considered as a crucial factor in detecting invasive plant species by plant species remain understudied. remote sensing (cf. Bradley, 2014; Hill et al., 2016; De Sa´ et al., 2018). The analysis of seasonal variability of invasive Heracleum sosnowskyi In our applied study, the optimal phenological stages for Heracleum (hogweed) and Fallopia spp. (knotweeds) revealed changes in their sosnowskyi and Fallopia spp. were determined on the basis of botanist percentage coverage during the considered growing seasons. Hogweed expert knowledge, but they were not used as variables in the geo­ presented the highest coverage in spring before floweringand during the statistical modelling, in which the occurrence of a given species high summer, at peak flowering, with the lowest cover reported within regardless of its phenological state was mapped (subsection 2.3.1). the late summer at late senescence (Fig. 3a, Table 2). The coverage of However, it should be noted that phenological observations of Olea knotweed species, however, varied considerably according to the europaea have been undertaken to determine olive floweringstatus and growing seasons, the highest was observed in 2016 during the high to measure a flowering-intensity scale that, as a linear variable, has summer, before flowering, while the lowest was in 2017, in spring and become the basis of geostatistical analysis (co-kriging) by Rojo and high summer, also before flowering( Fig. 4a, Table 2). These substantial Perez-Badia (2015). Consequently, phenological models of flowering differences in the cover of Fallopia spp. between 2016 and 2017 were intensity were obtained, which helped to interpret aerobiological data probably due to the influenceon growth during seasonal development of and the factors involved in the airborne dispersal of pollen. Thus, the damages caused by mowing, grazing or spraying. Overall, the cover of phenological phase is not required in geostatistical applications, though both invasive species was high, approximately 80%–100%, but the fig­ it may be used as a secondary variable that is extremely important in ures are slightly lower for H. sosnowskyi at late senescence and for Fal­ target species detection using remote sensing. lopia species mainly before flowering. Still, due to the phase of the life Our 2D maps and 3D visualizations of Heracleum sosnowskyi and cycle, but excluding the campaigns and growing seasons, the highest Fallopia spp. obtained by using two different geostatistical estimators, i. cover of H. sosnowskyi (up to 90%) and Fallopia species (up to 100%) was e. ordinary kriging (OK) and co-kriging (CK), reflecttheir occurrence in reported in the flowering and fruiting phases or only at the fruiting the field, as demonstrated by observations carried out in 2018. With stage, respectively (Figs. 3b and 4b). reference to the values of standard deviation maps, the precision of the Considering the results related to the occurrence of coexisting species predicted probability of species occurrence decreases at unsampled lo­ with Heracleum and Fallopia species, we recorded that their cover was cations. Admittedly, the high probability of occurrence of both species reduced slightly (but nevertheless discernibly) by co-dominants plants - was closely related to that observed at the sampling locations, although up to 10% in the case of hogweed and up to 20% for knotweed species. comparing the results of the two methods showed minor differences in All recorded species co-occurring with invasive species are native and the predictions between them. This is in part due to the well-known their number varied between 11 and 3 for H. sosnowskyi and Fallopia smoothing effect of the ordinary kriging estimator (Yamamoto, 2005). spp., respectively (Figs. 3c and 4c). Noticeable changes were also As a consequence, relatively small values are overestimated and high observed in the cover of herbaceous plants (excluding the invasive values underestimated. Simultaneously, this effect mainly made refer­ species) in the HE and RE areas during both growing seasons. The per­ ence to estimated prediction values of the DPMs for OK and CK. In the centage cover of herbs essentially depended on the phenological phase case of CK, the smoothing effect is partially avoided with the use of a of the invasive species. There was a higher herbaceous cover when secondary variable (e.g. spectral vegetation indices - SVIs). Neverthe­ H. sosnowskyi was at flowering/fruitingphase and Fallopia species were less, the presence of the smoothing effect in OK and CK maps did not in the fruiting phase. Simultaneously, the herbaceous cover was less affect the high probability of species occurrence. Furthermore, regard­ than 100% when hogweed and knotweed species were at the beginning less of the chosen method, the correctness of the estimation results was of their intensive growth phase (spring) (Figs. 3e and 4e). The percent quantified in our study through standard deviation maps for all areas cover of necromass differed slightly in both growing seasons (2016 and wherein values did not exceed 0.51 in each case (the max value of 0.5 2017). Its highest value within the HE areas was recorded for the late was noted only in one case) (cf. Groom, 2013a). and high summer, while in the RE, the maximum was in the late summer The prediction errors of OK and CK for Heracleum sosnowskyi and and spring. With regard to the phase of the invasive species life cycle, the Fallopia spp. were calculated (Tables 10b and 12b) in order to be able to cover of necromass was the highest in the vegetative stage for both compare the values observed in the field verification of 2018, with the Heracleum and Fallopia species, i.e., when the invasive plants did not estimated values. Their low values confirmed the correctness of spatial bloom and fruit. The largest proportion of the necromass came from autocorrelation modelling (subsection 2.3.4). Nevertheless, the predic­ invasive plant species rather than from herbs. tion errors for CK were lower compared to OK (Tables 10b and 12b). In

17 K. Bzdęga et al. Ecological Indicators 121 (2021) 107204 the case of differences in the OK and CK values of prediction and cross- and verification surveys carried out in the field. In the study, we found validation errors for HE and RE areas, all the obtained values were lower that in cross-validation, CK outperformed OK. However, overall, CK and for HE1 and HE2 compared to the observed values of RE1 and RE2 OK standard deviations were of the same order of magnitude for both (Tables 10 and 12). This outcome is probably related to the reduction of methods at unsampled locations, proving that in these cases the two the smoothing effect that is due to the use of spectral vegetation indices estimators are not significantly different. Our study also included (as a secondary variable) derived from high-resolution hyperspectral generating the firstprediction maps (2D) and Digital Prediction Models images. This after-effect is also probably due to the slightly lower nugget (DPMs) as a 3D visualization for H. sosnowskyi and Fallopia spp. though effect in the variogram models for the primary variable (Tables 9 and applying the geostatistical techniques of ordinary kriging (OK) and co- 11). kriging (CK). The DPMs could provide the support required to inter­ Taking into consideration the cross-validation results, the use of pret prediction maps (2D) of other invasive plant species. They can also hyperspectral images does not lead to significantly improve the valida­ be helpful resources for government agencies, private businesses, citi­ tion results. Overall, the predictive accuracy of our models was rather zens groups and research institutions dealing with the management of satisfactory, and was supported with evidence stemming from cross- invasive plants so as to minimize the negative consequences associated validation errors which in the case of RMSE were in the ranges 0.21 to with the presence of these species. The specific spatial patterns (refer­ 0.51 for OK and 0.2 to 0.47 for CK, and from the prediction errors where ring to the semivariogram and the cross-covariance for OK and CK, RMSPE were at the level of 0.03 to 0.38 and 0.03 to 0.29 for OK and CK, respectively) underpinning the occurrence of both species within each respectively (Tables 10 and 12). area were also identified. Considering our results, it seems that Moreover, there is a noticeable visual difference between the two H. sosnowskyi and Fallopia spp. may be satisfactorily mapped and geostatistical estimators. Herein, the maps obtained via OK are smoother monitored via OK and CK methods at the (large) spatial scale of the than the CK maps wherein the spatial details are determined by the invaded area. greater resolution of the secondary variable. The use of co-kriging in plant mapping distribution is valuable CRediT authorship contribution statement because it enables the possibility of combining information derived from different sources, e.g. remote sensing, with dispersed botanical data. Katarzyna Bzdęga: Conceptualization, Methodology, Validation, Nevertheless, ordinary kriging is particularly useful when e.g. access to Formal analysis, Investigation, Data curation, Writing - original draft, expensive hyperspectral images is not possible. Writing - review & editing, Visualization, Supervision, Project admin­ A comparison of our results with those reported by Müllerova´ et al. istration. Adrian Zarychta: Conceptualization, Methodology, Valida­ (2017) also revealed noticeable differences at the level of the spatial tion, Formal analysis, Investigation, Writing - original draft, Writing - scale of the performed studies on invasive plants. The size of study sites review & editing, Visualization. Alina Urbisz: Data curation, Writing - ranged from 60 ha to 100 ha in Müllerova´ et al. (2017), while the extent original draft. Sylwia Szporak-Wasilewska: Conceptualization, Meth­ of our areas included sites above 70 ha - with one exceeding 380 ha. odology, Validation, Formal analysis, Writing - original draft, Writing - However, the main methodological limitation in both cases was the size review & editing. Michał Ludynia: Validation, Formal analysis, Visu­ of the acquisition of the hyperspectral imagery which is decisive for the alization. Barbara Fojcik: Investigation, Writing - original draft. Bar­ size of the area for interpolation/classification. bara Tokarska-Guzik: Investigation, Funding acquisition. In our study, the spatial extent of the survey was not as relevant as the quantity and density of sampling locations dependant upon the Declaration of Competing Interest distribution of H. sosnowskyi and Fallopia species. Simultaneously, auxiliary variables obtained from hyperspectral imagery were not a The authors declare that they have no known competing financial problem to the outcome of our proffered procedure because in CK interests or personal relationships that could have appeared to influence modelling they are replaceable by other less expensive and easier to the work reported in this paper. obtain covariates (e.g. DEM, distance from river stream, soil type, land- use types) in order to derive better spatial model with quantified accu­ Acknowledgments racy, for example sequential simulations with regression kriging (Borůvkaet al., 2014; Zhang et al., 2020). The study was co-financedby the Polish National Centre for Research Our research provides an effective, quick and low cost alternative and Development (NCBR) and MGGP Aero under the programme Nat­ approach for evaluating the risk posed by invasive plants, as well as for ural Environment, Agriculture and Forestry BIOSTRATEG II.: The efficient, prediction and monitoring of the spread of invasive plant innovative approach supporting monitoring of non-forest Natura 2000 species - especially the H. sosnowskyi and Fallopia species. Moreover, habitats, using remote sensing methods (HabitARS), project number: they constitute a response to other solutions in which the phenological DZP/BIOSTRATEG-II/390/2015. Special thanks also to Monika Jędr­ phase plays a crucial role in the detection of invasive plant species. zejczyk-Korycinska´ (University of Silesia in Katowice) for her technical support while collecting field data set. 5. Conclusions Finally we would like to thank the anonymous native speaker who had carefully read and checked our manuscript. The combination of geostatistical tools with environmental and hyperspectral data makes it possible to predict the distribution of Her­ Appendix A. Supplementary data acleum sosnowskyi and Fallopia species, which are recognized worldwide as some the most troublesome alien invasive plant species. They Supplementary data to this article can be found online at https://doi. constitute a unique model system for studies of their spreading processes org/10.1016/j.ecolind.2020.107204. and for the creation of novel strategies to improve the effectiveness and efficiency of their management. In the research, we adopted various References analytical approaches and different types of data to evaluate the po­ tential threat associated with the distribution of H. sosnowskyi and Fal­ Adachi, N., Terashima, I., Takahashi, M., 1996. 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