# Spatial Connections between Microplastics and Heavy Metal Pollution within Floodplain Soils
## 2 Materials and Methods
### Statistics and Data Evaluation  
Basic statistical operations were performed in Microsoft Excel 2013 (Microsoft; Redmond, WA, USA), in R (R Core Team, 2020), and in RStudio (Version 3.4.1; RStudio Inc.; Boston, MA, USA). Statistical tests were applied to examine relationships and differences between the collected datasets based on regression and correlation analyses, as well as to identify significant differences between concentrations and sampling locations or depths. Data visualization, tests for normal distribution (Shapiro-Wilk), linear regression analyses, Spearman correlation analyses, and variance analyses (ANOVA) were conducted with the standard R-packages as well as \"graphics\", \"stats\", \"vioplot\", \"ggplot2\", \"ggridges\", and \"scatterplot3d\". Significances were tested on different levels. We interpreted the results of statistical analysis to be significant when reaching a \(p\)-value \(<\) 0.05. Basic geoinformatics evaluations were carried out in ArcMap (Version 10.3, Esri Deutschland GmbH, Kranzberg, Germany).  
For the spatial and absolute comparison of plastic and heavy metal contents in floodplain soils, the total amount of plastic (P\({}_{tot}\)) was calculated (Equation (1)) and documented as unit particles per kg soil dry mass (p kg\({}^{-1}\)).  
\[P_{tot}=\sum MEP+CMP+LMP+MMP. \tag{1}\]  
In order to provide an effective risk assessment--and ascertain the pollution characteristics--of heavy metals, as well as conducting a spatial comparison with plastic contamination, we calculated different pollution indices according to [PERSON] et al. (2018). Each of the applied indices shows an effective assessment of contamination and the spatial contamination differences ([PERSON] et al., 2018). To measure the potential impact of anthropogenic heavy metal pollution, we calculated the \"Enrichment factor\" (EF) (Equation (2)),  
\[EF=\frac{\left[\frac{HM}{LV}\right]sample}{\left[\frac{HM}{LV}\right]geochemical\ background}. \tag{2}\]  
where HM is the concentration of individual heavy metals and LV is the reference concentration of Fe. Geochemical background (GB) concentrations for the calculation of EF and PLI, as well as comparative values, were calculated based on the average values for Hesse floodplain soils provided in [PERSON] and [PERSON] (2011) ([PERSON], 2011). A total of 341 samples (64 floodplain silt substrates and 277 floodplain sand substrates) were averaged. Additionally, the \"Pollution Load Index\" (PLI) (Equation (3)), based on the \"Single Pollution Index\" (PI) for each heavy metal, was calculated,  
\[PLI=\sqrt[n]{PI_{1}x\ PI_{2}xPI_{3}xPI_{n}}. \tag{3}\]  
where PI is the single pollution index of each heavy metal calculated as \(PI=\frac{HM}{CB}\).  
To assess the potential toxicity a of heavy metal contamination, the \"Contamination Security Index\" (CSI) (Equation (4)) was calculated  
\[CSI=\sum\
olimits_{n=1}^{n}\omega\left(\left(\frac{HM}{ERL}\right)^{\frac{1}{2 }}+\left(\frac{HM}{ERM}\right)^{2}\right). \tag{4}\]  
with W (the weight of each heavy metal) computed according to [PERSON] et al. (2015) ([PERSON] et al., 2015), and HM (the individual concentration of each heavy metal), ERM (median value of the effect range), and ERL (lowest value of the effect range) calculated according to [PERSON] et al. (1995) ([PERSON] et al., 2019). Finally, the \"Potential Ecological Risk Index\" (RI) (Equation (5)) was calculated according to [PERSON] (1980) ([PERSON], 1980) to assess potential ecological risks of heavy metal concentrations in floodplain soils  
\[RI=\sum_{i=1}^{n}E_{r}^{i} \tag{5}\]  
with \(n\) (the number of heavy metals) and Er (the single index of the ecological risk factor) calculated by \(E_{r}^{i}=T_{r}^{i}\ x\ PI\) with \(T_{r}^{i}\) (toxic response coefficient) and PI (the Single Pollution Index).  
Heavy metal concentrations were also compared to legal standards for soils (German national legislation) (German, 1980; [PERSON], 1980).