# Multiple Threshold-Selection Methods Are Needed to Binarise Species Distribution Model Predictions

Marjon Hellegers, Arjen van Hinsberg, Jonathan Lenoir, Jürgen Dengler,

Mark a J Huijbregts, Aafke M Schipper

► To cite this version:

Marjon Hellegers, Arjen van Hinsberg, Jonathan Lenoir, Jürgen Dengler, Mark a J Huijbregts, et al. Multiple Threshold-Selection Methods Are Needed to Binarise Species Distribution Model Predictions. Diversity and Distributions, 2025, 31 (4), 10.1111/ddi.70019. hal-05355920

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RESEARCH ARTICLE

OPEN ACCESS

# Multiple Threshold-Selection Methods Are Needed to Binarise Species Distribution Model Predictions

Marjon Hellegers¹,² ID | Arjen van Hinsberg¹ | Jonathan Lenoir³ | Jürgen Dengler⁴,⁵ | Mark A. J. Huijbregts² | Aafke M. Schipper¹,²

<figure><img src="image_2.png" /></figure>

¹PBL Netherlands Environmental Assessment Agency, The Hague, the Netherlands | ²Department of Environmental Science, Radboud Institute for Biological and Environmental Sciences, Radboud University, Nijmegen, the Netherlands | ³UMR CNRS 7058 'Ecologie et Dynamique des Systèmes Anthropisés' (EDYSAN), Université de Picardie Jules Verne, Amiens, France | ⁴Vegetation Ecology Research Group, Institute of Natural Resource Sciences (IUNR), Zurich University of Applied Sciences (ZHAW), Wädenswil, Switzerland | ⁵Plant Ecology Group, Bayreuth Center of Ecology and Environmental Research (BayCEER), University of Bayreuth, Bayreuth, Germany

**Correspondence:** Marjon Hellegers (marjon.hellegers@pbl.nl)

**Received:** 10 May 2024 | **Revised:** 11 March 2025 | **Accepted:** 15 March 2025

**Editor:** Cesar Capinha

**Funding:** The authors received no specific funding for this work.

**Keywords:** binarisation | cut-off value | F-measure | habitat suitability models | Matthew's correlation coefficient | sensitivity | similarity index | specificity | true skill statistic

## ABSTRACT

**Aim:** Probabilities of occurrence predicted by species distribution models (SDMs) are routinely binarised based on a threshold that maximises the true skill statistic. Recently, the true skill statistic is criticised for favouring overprediction when species' prevalence is low. We aim to assess the effect of three alternative threshold-selection methods on predicted range sizes and changes therein under climate change across a large number of species in Europe.

**Location:** Europe.

**Methods:** We fitted SDMs for 1677 vascular plant species, using species observations from 431,179 vegetation plots as response variables and climate, soil and topographic variables as predictors. We used the SDMs to quantify current and future range sizes of each species under mild and severe climate change scenarios, each combined with two dispersal assumptions (no and unlimited dispersal) and using four threshold-selection methods: maximising true skill statistic (TSS), minimising the difference between sensitivity and specificity (DSS), maximising Matthew's correlation coefficient (MCC) and maximising F-measure (F). Further, we assessed prediction errors for each threshold-selection method in relation to species prevalence.

**Results:** We found that SDM outputs binarised with TSS resulted in the largest predicted ranges and the smallest future range contractions. For current climate conditions, median range sizes were 1.3, 3.6 and 9.2 times larger when binarised with TSS than with DSS, MCC and F, respectively. Under severe climate change without dispersal, median range size declines were 56%, 61%, 79% and 88% with TSS, DSS, MCC and F, respectively. Binarisation based on TSS tended to result in the highest overprediction rates and lowest underprediction rates, while this was the opposite with F.

**Main Conclusions:** We recommend choosing the threshold-selection method based on the goals and scope of the study, while carefully considering the trade-offs between overprediction and underprediction. Alternatively, we recommend using multiple threshold-selection methods to quantify the uncertainty in the binarisation.

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

© 2025 The Author(s). Diversity and Distributions published by John Wiley & Sons Ltd.
# 1 | Introduction

Species distribution models (SDMs) are routinely used to predict the potential distribution and redistribution of species in space and time, in order to address various topics in conservation biology and climate change research (Kok et al. 2023; Newbold 2018; Visconti et al. 2016). For example, SDMs can be used to identify areas for conservation and restoration, to determine locations at risk from invasive alien species and to assess the effects of global warming on biodiversity (see reviews in Elith and Leathwick 2009; Franklin and Miller 2010; Guisan and Thuiller 2005). Studies using SDMs provide vital information to underpin biodiversity policy, and are amongst other applications used to inform the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services and the Intergovernmental Panel on Climate Change (IPBES 2016; Warren, Price, Graham, et al. 2018; Warren, Price, VanDerWal, et al. 2018).

Modelling techniques used to establish SDMs usually generate probabilities of occurrence (PoO) for the focal species (Guisan et al. 2017). For many applications, however, it is desirable or required to binarise these probabilities into presence and absence predictions. For example, expected changes in species' range sizes in response to climate change are typically based on binarised SDM outputs (Santini et al. 2021). Binarisation involves identifying a threshold to transform the predicted PoO into presence or absence. There are many possible threshold-selection methods, including data-driven approaches, which derive a threshold value directly from the species observations and predicted PoOs and accuracy-based thresholds, which derive a threshold value that maximises the agreement between species observations and model predictions (e.g., Liu et al. 2005; Nenzén and Araújo 2011). It is most common to use the accuracy-based threshold derived with the true skill statistics (TSS) (Fielding and Bell 1997; Guisan et al. 2017; Nenzén and Araújo 2011). The TSS metric is a performance metric that considers both the sensitivity and specificity of the model (i.e., the true positive rate and true negative rate), hence both omission (false negatives) and commission (false positives) errors are accounted for. Selecting a threshold value by maximising TSS is implemented as a standard threshold-selection method in the widely used R-package 'biomod2' (Thuiller et al. 2016). It is recommended and applied in this form in numerous highly cited papers (Barbet-Massin et al. 2012; Jiménez-Valverde and Lobo 2007; Liu et al. 2005, 2016; Santini et al. 2021; Thuiller et al. 2019).

Recently, however, the TSS metric is criticised for being dependent on prevalence, that is, the proportion of sites where a species is present relative to all recorded sites (Jimenez-Valverde 2021; Leroy et al. 2018; Somodi et al. 2017; Wunderlich et al. 2019). For example, Leroy et al. (2018) find that TSS favours overprediction when species' prevalence is low. Yet, studies exploring the effects of maximising TSS and alternative threshold-selection methods on SDM outputs are largely restricted to theoretical analyses and simulations based on virtual species (Leroy et al. 2018; Somodi et al. 2017; Wunderlich et al. 2019). While these studies provide valuable insights into the differences between, and possible limitations of, different approaches, they do not reveal the extent to which the choice of threshold-selection method affects the binarised outputs of SDMs of actual species.

Nenzén and Araújo (2011) are an exception. They fitted SDMs for 116 endemic European tree species to quantify the extent to which the choice of threshold-selection method, amongst which maximising TSS, affected the proportions of species categorised as threatened, based on the projected changes in range size under different climate change scenarios. However, they do not assess how the choice of threshold-selection method affects the range size predicted for a given moment. Range size is highly relevant for estimating the extinction risk of a species, and is as such also one of the key parameters for determining the species conservation status in the IUCN Red List and the EU's Birds and Habitats Directives (Bijlsma et al. 2019; Faurby and Antonelli 2018; IUCN 2012; Purvis et al. 2000). Hence, it is of the utmost importance to better understand how alternative threshold-selection methods may affect SDMs' predictions of range sizes and changes therein of actual species, particularly in the context of global biodiversity redistribution due to climate change (Pecl et al. 2017).

Here we evaluated how the choice of threshold-selection method to binarise SDMs' predictions affects range sizes and changes therein under two climate change scenarios (mild and severe) for 1671 vascular plant species across Europe. We focused on TSS and three other accuracy-based threshold-selection methods, because these methods account for the omission and commission errors in the binarised species ranges. Based on our findings, we provide recommendations on the use of accuracy-based approaches to binarise SDMs' predictions.

# 2 | Methods

## 2.1 | Threshold-Selection Methods

We focused on accuracy-based threshold-selection methods to binarise SDM outputs, that is, methods that identify a PoO-threshold by maximising the agreement between observations and model predictions (Nenzén and Araújo 2011). For maximising the agreement, we selected four methods based on threshold-dependent discrimination metrics: maximising the true skill statistic (TSS), minimising the difference between sensitivity and specificity (DSS), maximising the Matthew's correlation coefficient (MCC) and maximising the F-measure (F) (Table 1). These four methods are commonly used in classification tasks (Barbosa et al. 2013; Tharwat 2021) and compare different elements of the confusion matrix, that is, the matrix representing matches and mismatches between presence-absence observations and the binarised predictions (Table S1).

The TSS metric considers both the true positive rate (proportion of observed presences correctly predicted) and the true negative rate (proportion of observed absences correctly predicted), it balances sensitivity and specificity (Allouche et al. 2006; Hanssen and Kuipers 1965; Somodi et al. 2017; Youden 1950). Values range from -1 to 1, where a value of 1 indicates a perfect prediction, a value of -1 indicates a prediction that is exactly opposite to a perfect prediction and a value of 0 indicates a random prediction.

The DSS method sets the PoO-threshold by minimising the absolute difference between sensitivity and specificity (Cantor
<table><caption>**TABLE 1** | Discrimination metrics selected for this study.</caption><thead><tr><th>Discrimination metric</th><th>Alternative names</th><th>Calculation</th></tr></thead><tbody><tr><td>True skill statistic</td><td>Hanssen-Kuipers discriminant, Peirce Skill Score, Youden's J statistic</td><td>TSS = <sup>TP</sup>&frasl;<sub>TP+FN</sub> + <sup>TN</sup>&frasl;<sub>TN+FP</sub> - 1</td></tr><tr><td>Difference between sensitivity and specificity</td><td></td><td>DSS = | <sup>TP</sup>&frasl;<sub>TP+FN</sub> - <sup>TN</sup>&frasl;<sub>TN+FP</sub> |</td></tr><tr><td>Matthews correlation coefficient<sup>a</sup></td><td>Yule phi coefficient, Mean Square Contingency Coefficient</td><td>MCC = <sup>TP &times; TN - FP &times; FN</sup>&frasl;<sub>&radic;(TP+FP)(TP+FN)(TN+FP)(TN+FN)</sub></td></tr><tr><td>F-measure</td><td>F1 score</td><td>F = <sup>2TP</sup>&frasl;<sub>FN + 2TP + FP</sub></td></tr></tbody></table>

Note: Calculations of these metrics are based on the elements of the confusion matrix: True positives (TP), true negatives (TN), false positives (FP) and false negatives (FN) (Table S1).

et al. 1999). Values can range from 0 to 1, where a value of 0 indicates equal sensitivity (i.e., true positive rate) and specificity (i.e., true negative rate), while larger values indicate an imbalance between sensitivity and specificity.

MCC provides a comparison of the true positives and true negatives to the false positives and false negatives (Table S1). In addition to the model's sensitivity and specificity, which are also considered by TSS and DSS, MCC includes the overprediction of the presences (overprediction rate, i.e., the proportion of falsely predicted presences relative to all predicted presences) and the overprediction of the absences (false omission rate, i.e., the proportion of falsely predicted absences relative to all predicted absences) (Chicco and Jurman 2020; Chicco et al. 2021; Matthews 1975; Yule 1912). The MCC values have the same interpretation as the TSS values.

The F-measure increases with true positives and decreases with false negatives and false positives (Li and Guo 2013; Sørensen 1948). Thus, the F-measure penalises the overprediction rate and underprediction rate of the species range, but does not consider the extent to which the absences are correctly predicted (true negatives, Table S1). This can be considered an advantage, particularly when the number of absences is much larger than the number of presences or with presence-only observations (Leroy et al. 2018). Values of F range from 0 to 1, where 1 indicates a perfect prediction and 0 means that none of the predictions were correct. The value representing a random prediction depends on the prevalence (Christen et al. 2023).

## 2.2 | Species Distribution Models

Following Hellegers et al. (2020), we fitted SDMs for 1677 vascular plant species that are representative of all terrestrial natural and semi-natural habitats as classified by the level 3 EUNIS habitat types (Appendix S1: Text S1.1; Chytrý et al. 2020, version 2021-06-01). This species list is restricted to species for which the models converged and with at least 75 presence records, ensuring five presences per environmental variable after setting aside 20% of the observations for model evaluation. Here, we briefly summarise the procedure; for more details, we refer to Hellegers et al. (2020). We obtained empirical observations of

the 1677 species from vegetation plots registered in the European Vegetation Archive (EVA; Chytrý et al. 2016). Following the selection criteria as described in Hellegers et al. (2020), we excluded plots recorded before 1990 to minimise temporal differences between the plots and the environmental variables, plots with a known spatial uncertainty larger than 1 km, plots with missing values for one or more environmental variables and plots allocated to maritime wetlands, freshwater systems, marine waters, man-made habitats or unknown habitats. With these criteria, we retained a total of 431,179 vegetation plots (Figure S1). An overview of all the datasets included in the subsequent analyses is provided in the Table S2.

As predictor variables for fitting SDMs, we used a set of 12 variables, representing climate, soil and topographic conditions, that passed the threshold for multicollinearity, that is, a variance inflation factor (VIF) < 10 (Table S3). Following Hellegers et al. (2020), we used three climatic variables (mean temperature of the coldest month, total annual precipitation and annual growing degree days) for the time period of 1990–2018 at a spatial resolution of 30 arc-sec across Europe, all retrieved from the CHELSA dataset version 2.1 (Karger et al. 2017, 2021). We further included seven soil variables (organic carbon, clay and silt content, bulk density, volume of coarse fragments, cation exchange capacity and soil pH) that we extracted at a 1 km² resolution from the SoilGrids dataset (Hengl et al. 2017). In order to better represent site conditions for plant growth, we added two topographic variables to the set of environmental variables used by Hellegers et al. (2020). First, we generated a binary variable (1 km² resolution) reflecting whether the vegetation could be exposed (1) or not (0) to saltwater inundation, intrusion or salt spray, assuming that the influence of salt water extends 3 km inland from the nearest coastline (Du and Hesp 2020). Second, we added the topographic wetness index, which indicates the propensity of an area to accumulate water given its topographic position. We retrieved this variable at a 15 arc-sec resolution across Europe from Marthews et al. (2015), who calculated it as a function of the local outflow slope of a grid cell and its upstream catchment area. We reprojected all environmental variables to a 1 km² resolution, based on the ETRS89 Lambert Azimuthal Equal-Area projection, and resampled the values using bilinear interpolation. We reprojected and resampled the variables using the 'projectRaster' function from the 'raster' package in R (Hijmans 2025).

<footnote><sup>a</sup>When a whole column or row of the confusion matrix is zero, MCC is undefined. In these cases, values can be assigned following Chicco and Jurman (2020). Specifically, if the confusion matrix has only one non-zero entry, all predictions are either correct or incorrect, in which case MCC is either 1 or -1, respectively. If the confusion matrix contains one row or column with only zero entries, the prediction is equal to what could be expected at random and MCC equals zero.</footnote>
<figure><img src="image_3.png" /><figcaption>**FIGURE 1** | Schematic representation of the modelling approach.</figcaption></figure>

We fitted our SDMs with the biomod2 package using three modelling techniques (generalised linear models, GLMs; generalised additive models, GAMs; and boosted regression trees, BRTs) and kept default settings (ver. 3.5.1; Thuiller et al. 2016). In order to reduce spatial autocorrelation and avoid pseudo-replication, we sampled only one presence record from the vegetation plots per 1 km² grid cell per species (Text S1). Further, we sampled one pseudo-absence record per species per grid cell in those cells containing vegetation plots yet without presence records of the focal species. We assumed the species to be absent in these grid cells. The resulting presence and pseudo-absence records covered 107,201 grid cells. We further refer to this set of observations as the 'bias-corrected observations' (Figure 1). In order to keep the time required for fitting our SDMs within feasible limits, we established a subsample of pseudo-absence records from the set of bias-corrected observations, knowing that the number of pseudo-absences has little influence on SDM performance (Čengić et al. 2020). We used a random subsample of the pseudo-absence records, such that at

least 10,000 pseudo-absence records were used for GLMs and GAMs and at least 1000 pseudo-absence records were used for BRTs (Barbet-Massin et al. 2012). When the number of presence records per species exceeded 1000 or 10,000, we subsampled a number of pseudo-absences equal to the number of presences. We gave equal weights to the presence and pseudo-absence records during model fitting. For each species, we first evaluated the performance of each modelling technique with a single cross-validation round. To this end, we first fitted SDMs with the three modelling techniques using a single random sample of 80% of the presence and pseudo-absence records and evaluated them based on the remaining 20% of the data, ensuring equal prevalences in both datasets (Figure 1). For each modelling technique, we calculated cross-validated performance values in line with each of the four threshold-selection methods. For TSS, MCC and F, we selected the metric values belonging to the PoO-thresholds that maximised the respective metrics. Since DSS is not a performance metric per se, we determined the cross-validated performance value for
this threshold-selection method by calculating the mean of the sensitivity and the specificity belonging to the PoO-threshold that minimised the DSS. Next, we refitted the SDMs with 100% of the observations and built four ensemble models for each species, one per threshold-selection method. We calculated the ensemble models by means of a weighted average across the three modelling techniques, using the cross-validated model performance values specific to each threshold-selection method as weights (Marmion et al. 2009). Finally, we assessed the performance of the resulting ensemble models with a threshold-independent metric, specifically the area under the receiver operating characteristic curve (AUC), using the bias-corrected observations (Figure 1). We removed six species from the analysis for which at least one ensemble model had an AUC ≤ 0.7 (Çorbacıoğlu and Aksel 2023), leaving 1671 species for the analysis.

## 2.3 | Range Sizes and Range Size Changes

For each threshold-selection method, we first used the ensemble model to predict the PoO under current climatic conditions (1990–2018). We binarised the continuous SDM predictions with the threshold value that maximised the agreement between the predictions and bias-corrected observations according to the corresponding threshold-selection method (Figure 1). Using the selected PoO-threshold per threshold-selection method, we then projected the species ranges for two contrasting future climate change scenarios. We used future climate projections averaged across 2071–2100 for a mild and severe CMIP6 climate scenario, SSP1-2.6 (SSP1-RCP2.6) and SSP5-8.5 (SSP5-RCP8.5), obtained from the CHELSA data set (Karger et al. 2017). We selected bias-corrected projections from five climate models, following the suggestions of the ISIMIP3b protocol (Lange 2019, 2021), that is, we selected GFDL-ESM4, UKESM1-0-LL, MPI-ESM1-2-HR, IPSL-CM6A-LR and MRI-ESM2-0 (Boucher et al. 2020; Dunne et al. 2020; Gutjahr et al. 2019; Sellar et al. 2019; Yukimoto et al. 2019). We averaged the climate variables across the five models for each CMIP6 climate scenario. The resulting scenarios correspond to an increase of the global annual mean temperature of +2.3°C (SSP1-2.6) and +5.3°C (SSP5-8.5) relative to the pre-industrial era (1850–1900). We assumed the soil and topographic variables to remain constant under future projections.

We combined each of the two climate change scenarios with two dispersal assumptions, as commonly done in climate change impact studies based on SDMs (Seaborn et al. 2020): unlimited dispersal and no dispersal. With unlimited dispersal, we assumed that the projected future ranges of the plant species will cover all of the study area where the projected future climate is suitable (i.e., the projected PoO is above the threshold). With no dispersal, we assumed that plant species are unable to disperse beyond their current range (i.e., where the PoO in the current climate is above the threshold). Hence, the future range cannot extend beyond grid cells with suitable current climate.

Per species *i* and threshold-selection method (TM), we calculated the species predicted range size (RS) under current climatic conditions (CC) and under each of the four future scenarios (FS), that is, two climate scenarios combined with two

dispersal assumptions, by summing the 1 km² grid cells where the SDM predicted the species to be present. For each future scenario, we also calculated per species and threshold-selection method the relative range size change (RSC), as follows:

$$RSC_{i,TM,FS} = \frac{RS_{i,TM,FS} - RS_{i,TM,CC}}{RS_{i,TM,CC}} \quad (1)$$

We assessed whether the range sizes and range size changes were significantly different between the threshold-selection methods by performing a Kruskal–Wallis test and a Dunn's test with a Bonferroni correction for multiple comparisons using the 'kruskal.test' function from the 'stats' package in R (vers. 4.3.1; R Core Team 2023) and 'dunn.test' function from the 'dunn.test' package in R (vers. 1.3.6, Dinno 2024).

## 2.4 | Relative Influence of the Threshold-Selection Method on SDM Outputs

To assess the relative influence of the choice of the threshold-selection method, climate scenario and dispersal assumption on the projected range sizes and changes in range sizes, we followed the procedure of Thuiller et al. (2019). Specifically, we fitted two GLMs with the identity link function relating the future RS-values and the future RSC-values as response variables to the threshold-selection method (a factor variable with four levels), the climate scenario (a factor variable with two levels) and dispersal assumption (a factor variable with two levels) as explanatory variables. We fitted these models using the 'glm' function from the 'stats' package. To quantify the contribution of each of the explanatory variables to the predicted future range sizes and range size changes, we calculated the percentage of explained deviance using the 'anova' function from the 'stats' package. Because the distributions of the RS- and RSC-values are positively skewed and include zeroes and negative values, respectively, we applied a cube root transformation to these variables.

## 2.5 | Errors in Predicted Ranges

As a final step, we evaluated how the four threshold-selection methods affect type I (false positives) and type II (false negatives) errors in the predicted current ranges as well as potential relationships between errors and species prevalence. For each species and each threshold-selection method, we first calculated the overprediction rate (OPR), the underprediction rate (UPR, i.e., 1—sensitivity), the false positive rate (FPR, i.e., 1—specificity) and the false omission rate (FOR) in the model predictions (Table 2). We did this based on the grid cells with bias-corrected observations. We then calculated the prevalence (Prev) of the species (*i*) as the proportion of presence records (*n*) relative to the sum of all presence and pseudo-absence records (*N*) in the bias-corrected observations:

$$\text{Prev}_i = n_i / N \quad (2)$$

Finally, for each of the error metrics, we fitted a local second order polynomial regression relating the error metric to the species' prevalence (Prev). We fitted these regressions using the 'loess' function from the 'stats' package in R, keeping default
<table><caption>**TABLE 2** | Error metrics measuring type I and type II errors in the predicted ranges under current climatic conditions.</caption><thead><tr><th>Metric</th><th>Calculation</th><th>Interpretation</th></tr></thead><tbody><tr><td>Overprediction rate</td><td>OPR = FP / (FP + TP)</td><td>Fraction of predicted presences that is incorrect</td></tr><tr><td>Underprediction rate</td><td>UPR = FN / (FN + TP)</td><td>Fraction of observed presences that is incorrectly predicted to be absent</td></tr><tr><td>False positive rate</td><td>FPR = FP / (FP + TN)</td><td>Fraction of observed absences that is incorrectly predicted to be present</td></tr><tr><td>False omission rate</td><td>FOR = FN / (FN + TN)</td><td>Fraction of predicted absences that is incorrect</td></tr></tbody></table>

Note: Calculations of these metrics are based on the elements of the confusion matrix: true positives (TP), true negatives (TN), false positives (FP) and false negatives (FN) (Table S1).

settings. Because of the positively skewed distributions of the prevalence values, we log-transformed this variable.

## 3 | Results

### 3.1 | Current and Future Range Sizes

The fitted ensemble SDMs showed an excellent performance for the majority of the species, with AUC ≥ 0.9 for 71% of the species, independent of the metric used to weight the component models in the ensemble (Figure S2). For most of the species, we found the largest predicted current and future range sizes based on the TSS method, compared to the other threshold-selection methods (Figures 2 and 3; Figures S3-S7). Predicted range sizes progressively declined when based on DSS, MCC and F (Figures 2 and 3; Figures S3-S7). Under current climatic conditions, the median range size computed with the TSS method (10.2×10⁵ km²) was 1.3, 3.6 and 9.2 times larger than the median range sizes based on DSS (7.6×10⁵ km²), MCC (2.8×10⁵ km²) and F (1.1×10⁵ km²), respectively (Figure 2; Table S4). Under the mild climate change scenario (SSP1-2.6) with unlimited dispersal (i.e., the most optimistic variant), the TSS method resulted in the median range size being 1.4, 4.3 and 10.9 times larger than median range sizes based on the DSS, MCC and F methods, respectively (Figure 3; Table S4). Under the severe climate change scenario (SSP5-8.5) without dispersal (i.e., the worst-case variant), the median range size as computed with the TSS method was 1.5, 8.0 and 40.0 times larger than the median range sizes as computed with the DSS, MCC and F methods, respectively.

### 3.2 | Range Size Changes

Median range size changes were negative in all combinations of climate change scenario, dispersal assumption and threshold-selection method, pointing at an overall decline in plant species

<figure><img src="image_4.png" /><figcaption>**FIGURE 2** | Distribution of predicted range sizes across 1671 plant species in Europe under current climatic conditions based on each of four methods used to set a binarisation threshold for the probability of occurrence: Maximising the true skill statistic (TSS), minimising the difference between sensitivity and specificity (DSS), maximising Matthew's correlation coefficient (MCC) and maximising F-measure (F). The boxes show the medians and the 25 and 75 percentiles and the whiskers represent 1.5 times the inter-quartile distance. Different letters refer to significantly different predicted range sizes (p < 0.001). The notches represent the 95% confidence interval around the medians (McGill et al. 1978). Outliers are not shown. The full spread in predicted range sizes is provided in Table S4.</figcaption></figure>

ranges under future climate conditions (Figure 4; Table S5). However, the predicted declines were the smallest when the TSS method was used (Figure 4; Table S5), and progressively larger when the DSS, MCC and F methods were used (Table S5; Figures S8-S11). The differences between the four threshold-selection methods in predicted range size changes were most pronounced under the no dispersal assumption (Figure 4). Under the severe climate change scenario without dispersal, the median predicted range decline was -56% for TSS and -61%, -79% and -88% for DSS, MCC and F, respectively (Figure 4; Table S5).

### 3.3 | Relative Importance of the Threshold-Selection Method

The threshold-selection method, dispersal assumption and climate change scenario together explained 26.5% and 22.7% of the total variation in future range sizes and range size changes, respectively (Figure 5). For the predicted future range sizes, the choice of the threshold-selection method explained most of the variation (21.5%). Dispersal assumption and climate change scenario explained each 2.5% of the variation in predicted future range sizes (Figure 5a). In contrast, for the future changes in range sizes, the dispersal assumption and climate change scenario were the most decisive, explaining 20.5% and 1.6% of the variation, respectively (Figure 5b). The choice of a
<figure><img src="image_5.png" /><figcaption>**FIGURE 3** | Box plots of the projected future range sizes of 1671 plant species in Europe for mild (SSP1-2.6; a,c) and severe (SSP5-8.5; b,d) climate change, with unlimited dispersal (a,b) and no dispersal (c,d), based on each of four methods used to set a binarisation threshold for the probability of occurrence: Maximising the true skill statistic (TSS), minimising the difference between sensitivity and specificity (DSS), maximising Matthew's correlation coefficient (MCC) and maximising F-measure (F). The boxes show the medians and the 25 and 75 percentiles, and the whiskers represent 1.5 times the inter-quartile distance. Different letters refer to significantly different projected range sizes (*p* < 0.001). The notches represent the 95% confidence interval around the medians (McGill et al. 1978). Outliers are not shown. The full spread in predicted range sizes is provided in Table S4.</figcaption></figure>

threshold-selection method explained only 0.6% of the variation
in predicted future range size changes.

**3.4 | Prediction Errors of Current Ranges**

Compared to the F and MCC methods, binarisation with the TSS and DSS methods generally resulted in higher overprediction rates and lower underprediction rates (Figure 6a,b). Overprediction rates were high across all threshold-selection methods. Underprediction rates were the largest when F was used as a threshold-selection method. Differences in underprediction rates were most pronounced for species with a prevalence value around 0.002 and declined towards the rarest and more prevalent species in the dataset. For all threshold-selection methods, the false positive rate and false omission rate were relatively small compared to the overprediction and underprediction rates (Figure 6c,d).

4 | Discussion

We assessed how the choice of a threshold-selection method affects
range sizes and changes therein under climate change as predicted
by SDMs of 1671 vascular plant species that are representative of all

European terrestrial natural and semi-natural habitats. We found a
large effect of the choice of the threshold-selection method on pre-
dicted species range sizes, consistent with previous research based
on virtual species (Liu et al. 2016). The choice of the threshold-
selection method was more influential for projecting future range
sizes than the choice of the climate change scenario or dispersal
assumption. We further found differences in the projected changes
in range sizes between the four threshold-selection methods, such
that reductions in range sizes were the smallest when binarised
based on a maximised TSS value and were progressively larger
when binarised by minimising DSS, maximising MCC or maxi-
mising F, particularly when no dispersal was assumed. However,
we found the uncertainty in the predicted changes in range size
related to the choice of threshold-selection method to be smaller
than the uncertainties due to the choice of dispersal assumption or
climate change scenario. The influence of the binarisation method
on predicted range size changes is also reported by Nenzén and
Araújo (2011). They assessed the impact of 14 threshold-selection
methods on SDM predictions under nine climate change scenarios
and find that predictions of the proportions of threatened species,
when assessed based on predicted range size changes, change up
to tenfold due to the choice of the threshold-selection method.
However, a quantitative comparison between their results and
ours is hampered by the differences in climate change scenarios
and indicators used.
<figure><img src="image_6.png" /><figcaption>**FIGURE 4** | Box plots of the projected range size changes of 1671 plant species in Europe for mild (SSP1-2.6; a,c) and severe (SSP5-8.5; b,d) climate change, with unlimited (a,b) and no dispersal (c,d), based on four methods used to set a threshold for the probability of occurrence: Maximising the true skill statistic (TSS), minimising the difference between sensitivity and specificity equality approach (DSS), maximising Matthew's correlation coefficient (MCC) and maximising F-measure (F). The grey line represents no range size change. The boxes show the medians and the 25 and 75 percentiles, and the whiskers represent 1.5 times the inter-quartile distance. Different letters refer to significantly different projected range size changes (*p* < 0.001). The notches represent the 95% confidence interval around the medians (McGill et al. 1978). Outliers are not shown. The full spread in predicted range size changes is provided in Table S5.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**FIGURE 5** | Influence of the choice of threshold-selection method (TM), dispersal assumption and climate change scenario (SSP) on the species range size (a) and range size change (b).</figcaption></figure>

We found that binarising the continuous SDM predictions by maximising the TSS and DSS values resulted, for most species, in larger predicted range sizes than the other two

threshold-selection methods. We also found that the larger predicted range sizes with TSS and DSS come with higher overprediction rates and lower underprediction rates than MCC and F, particularly for relatively rare species (Figure 6a,b). This difference reflects that TSS and DSS only consider the underprediction rate (through the sensitivity) and the false positive rate (through the specificity) and do not explicitly penalise the overprediction rate, in contrast to F and MCC. Previous studies show that TSS values for rare species depend primarily on the underprediction rate and that TSS values can be high even with a large overprediction rate (Leroy et al. 2018; Wunderlich et al. 2019). The similarity in predicted range sizes and error rates that we found between TSS and DSS suggests that the same holds for the DSS method. Hence, TSS and DSS favour thresholds that correctly predict presences and minimise false negatives, at the expense of an increase in false positives. This trade-off increases when species prevalence becomes lower, hereby disproportionally increasing the chance to overestimate future range sizes of rare species and thereby to underestimate their extinction risks under climate change. In line with previous studies (Barbosa et al. 2013; Leroy et al. 2018), our results emphasise the importance of considering the overprediction rate in addition to the underprediction rate and the false positive rate when binarising SDM outputs in climate change impact assessments.
<figure><img src="image_8.png" /><figcaption>**FIGURE 6** | The overprediction rate (a), underprediction rate (b), false positive rate (c) and false omission rate (d) in the predicted ranges of all species in relation to their prevalence, for each of the four methods to set a threshold for the probability of occurrence: Maximising the true skill statistic (TSS), minimising the difference between sensitivity and specificity (DSS), maximising Matthew's correlation coefficient (MCC) and maximising F-measure (F). The shaded areas represent the 95% confidence intervals around the regression lines.</figcaption></figure>

We found that the range sizes binarised with F or MCC were generally smaller than those binarised based on TSS or DSS, a result that can be attributed to the penalisation of the overprediction rate by F and MCC. Thus, compared to ranges binarised with TSS or DSS, ranges binarised based on F or MCC are composed of fewer false positives. Hence, using F or MCC for binarisation reduces the chance of overestimation of the range sizes and therefore underestimation of species extinction risks under climate change, particularly so for rare species or within large study areas. However, this coincides with a larger underprediction rate (more false negatives), in particular for the F method. More specifically, we found that binarisation based on the F method leads to a relatively large share of the observed presences being missed (over 50% for a considerable number of species; see Figure 6b). Thus, our results reflect a dire trade-off between minimising the underprediction and overprediction rates, and with that between correctly predicting presences and decreasing the risk to underestimate climate change impacts. Moreover, we note that F and MCC are also dependent on the sample prevalence (Christen et al. 2023; Hand and Christen 2018; Liu et al. 2016; Zhu 2020), reflecting that the overprediction rate changes with the sample prevalence that is used to determine the threshold value. We found that this dependency was most

pronounced for F, followed by MCC and virtually absent for TSS and DSS (Text S2 and S3).

Ideally, the optimal binarisation threshold value is set based on an independent and representative benchmark of the species' range. For well-studied species for which accurate expert-based range maps are available, these maps could be suitable (Mainali et al. 2020). However, expert-based range maps are not necessarily a good benchmark, as they can be highly subjective, vary in detail between regions and species and generally overestimate actual species ranges (Maiorano et al. 2013; Rondinini et al. 2011; Wiedenfeld and Tognelli 2023). Ranges derived from grid-based occurrences, such as atlas data, are highly dependent on the grid cell size (Gaston and Fuller 2009; Smith et al. 2020). Species observations are also affected by inaccuracies, for example due to low detection probability, phenological mismatch, spatial bias in the monitoring locations and highly dynamic ranges (Chen et al. 2013; Kéry 2011; Yackulic et al. 2013; Zizka et al. 2021). Moreover, even if highly accurate range maps are available, the comparison or benchmarking might be hampered because the predicted range map might depend on fewer environmental variables than the actual range, which might be influenced by additional factors. Consequently, optimising the
binarisation threshold by means of an independent benchmark
is generally not possible.

In absence of high-quality range maps and species observations,
thresholds are generally optimised with imperfect observations.
The uncertainty in absence records can be particularly high as
absences are much more difficult to confirm than presence re-
cords, particularly for cryptic and mobile species (MacKenzie
et al. 2017). Moreover, the uncertainty in absence records in-
creases with the grid cell size. For example, we assumed species
to be absent in grid cells containing vegetation plots without
presence records of the focal species. These vegetation plots
are mostly up to 100 m² in size and thus much smaller in size
than the 1 km² grid cells. Hence, species that are absent in the
vegetation plots could be present elsewhere in the grid cell. In
contrast, a presence record in a vegetation plot guarantees that
the species is present in the respective grid cell. A larger uncer-
tainty in absence than in presence records results in a larger un-
certainty in the overprediction rate than in the underprediction
rate. Consequently, from the overprediction and underprediction
rates cannot be derived whether the range size is overpredicted
(predicted range size is too large) or underpredicted (predicted
range size is too small). Instead, the differences in underpredict-
tion and overprediction rates between threshold-selection meth-
ods reflect a relative difference in the risk to underpredict or
overpredict the actual range size. We recommend future research
to assess the extent to which threshold-selection methods under-
predict or overpredict species ranges with high-quality presence
and absence data, for example, with virtual species.

Our results indicate that binarisation of continuous PoO pre-
dictions generated by SDMs introduces large uncertainties in
the prediction of range sizes and range size changes. Previous
studies have therefore recommended avoiding binarising SDM
outputs (Guillera-Arroita et al. 2015; Santini et al. 2021) or to
categorise the continuous species range map into more than
two classes by setting multiple threshold values to distinguish
the areas where a species is likely present or absent from areas
where the prediction is uncertain (Somodi et al. 2024). However,
the latter approach comes with the challenge of identifying mul-
tiple threshold values. Moreover, some research questions re-
quire a binary prediction of the species range. In these cases, we
recommend selecting the most appropriate threshold-selection
method in light of the goals and the scope of the study (Freeman
and Moisen 2008; Guisan et al. 2017; Nenzén and Araújo 2011),
considering various aspects and trade-offs. First, it is relevant to
consider that presence records are typically more certain than
absence records. From this perspective, one may argue that
false negatives are worse than false positives, representing an
argument in favour of binarisation thresholds that minimise the
underprediction rate (methods of choice: TSS or DSS). This ar-
gument disfavours binarisation based on F, since this method
gives the highest underprediction rates. However, an increasing
capacity to predict presences correctly increases the risk of over-
predicting the range (more false positives). Therefore, a second
relevant aspect to consider is the trade-off between the risks to
overpredict versus underpredict the species' range and identify
which of the two is the least problematic given the goal of the
study. For example, from a precautionary perspective, overpre-
diction is more problematic when assessing impacts of envi-
ronmental change on species ranges and associated extinction

risks. This would be an argument in favour of approaches that
minimise the risk of overprediction (methods of choice: F and to
a lesser extent MCC). However, for other study goals, for exam-
ple for identifying where invasive alien species may establish,
underprediction might be more problematic (Guisan et al. 2013),
in which case the use of TSS or DSS may be more appropriate.
Third, it is relevant to consider the prevalence-dependence of
the various accuracy-based threshold-selection methods, which
we found to be much larger for F and MCC than for DSS and
TSS. Note that prevalence is not only affected by the actual oc-
currence of the species but also by the size of the study area, the
number of pseudo-absences selected and the monitoring inten-
sity. As an alternative to selecting a single threshold-selection
method, one may consider to binarise SDMs based on multiple
threshold-selection methods in order to quantify the uncertainty
associated with this choice.

To conclude, our study demonstrates that the threshold-selection
method chosen to binarise continuous SDM predictions has signif-
icant implications for predicted current and future range sizes of
vascular plant species in Europe, and thus for their perceived ex-
tinction risk and conservation status. For a large number of plant
species in European terrestrial habitats, we show that threshold
selection based on TSS and DSS generally leads to larger predicted
current and future range sizes and, particularly when assuming no
dispersal, also smaller reductions in projected future range sizes,
compared to threshold-selection methods based on MCC and F. We
further show that these differences reflect a trade-off between the
overprediction and underprediction rates and that this trade-off is
affected by the prevalence in the records that are used to set the
threshold. In view of this trade-off, we recommend choosing the
threshold-selection method in light of the goals and scope of the
study. As an alternative, we recommend using multiple threshold-
selection methods, in order to quantify the uncertainty related to
the binarisation of the continuous SDM outputs.

Author Contributions

The research was designed by M.H., M.A.J.H. and A.M.S. and carried
out by M.H. All authors contributed to the analyses and interpretation
of the results and to the writing of the paper.

Acknowledgements

We thank all custodians and deputy custodians of the vegetation data-
bases in the European Vegetation Archive for sharing their vegetation
records. This study was conducted as part of the BioScore project.

Conflicts of Interest

The authors declare no conflicts of interest.

Data Availability Statement

The R-code used to generate the results presented in this study and
the results themselves are openly available in figshare (doi: 10.6084/
m9.fishshare.27002980). The species observations in the vegetation
plots used for this analysis are available via the European Vegetation
Archive (https://euroveg.org/eva-database). A list of vegetation plot
numbers used in the analysis and a list of databases from which these
vegetation plots were derived can be found in Supporting Information
and Table S2, respectively. The climate, soil and topographic variables
from CHELSA (Karger et al. 2017), SoilGrids (Hengl et al. 2017) and
Marthews et al. (2015), respectively, are publicly available.
## Peer Review

The peer review history for this article is available at https://www.webof.science.com/api/gateway/wos/peer-review/10.1111/ddi.70019.

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## Supporting Information

Additional supporting information can be found online in the Supporting Information section.