Saproxylic beetles respond to habitat variables at different spatial scales depending on variable type and species’ mobility: the need for multi-scale forest structure management

The response of species to the environment is scale-dependent and the spatial scale at which this relationships are measured may affect conservation recommendations. Saproxylic beetles depend on decaying- and deadwood which occur in lower quantities in managed compared to natural forests. Most studies have investigated the habitat selection of saproxylic beetles at the stand scale, however depending on the species mobility, the amounts and distribution of forest attributes across the landscape may be equally important, and thus crucial to frame quantitative conservation targets. To address this gap, we evaluated the influence of environmental variables, derived from remote sensing across multiple spatial scales (50, 100, 250, 500 and 1000 m radius), on saproxylic beetles habitat selection. Focusing on four mobile and four flightless species, we hypothesized that mobile species respond to habitat variables at broader scales compared to flightless species, and that variables describing forest structure explain species presence better at smaller scales than variables describing other landscape features. Forest structure variables explained around 40% of the habitat selection, followed by variables describing forest type, topography and climate. Contrary to our expectations, mobile species responded to variables at smaller scales than flightless species. Saproxylic beetle species therefore respond to the availability of habitat features at spatial scales that are inversely related to their dispersal capacities, suggesting that less mobile species require larger areas with suitable habitat characteristics while mobile species can also make use of small, distributed patches with locally concentrated habitat features.


Introduction
Forested areas cover about one-third of the terrestrial earth surface (FAO 2010) and provide habitats for many species. However, this biome is strongly altered by the need to reconcile multiple anthropogenic and ecological demands resulting in multifunctional forest management (Lindenmayer and Franklin 2002). In densely populated regions such as Central Europe, close-to nature forestry is the predominant management regime, targeting economical goals while attempting to conserve biodiversity (Bauhus et al. 2013). Close-to nature forestry focuses on selective logging and natural regeneration. By doing so, it promotes vertical structural complexity at the stand-scale, however it also results in a structural homogenization at the landscape scale (Bauhus et al. 2013) for example by the lack of disturbances and the resulting early successional stages and light availability (Gustafsson et al. 2020). In addition, as harvesting takes place when trees reach maturity, these stands lack late successional stages with senescent trees and high amounts and diversity of deadwood. This largescale homogenization and impoverishment of key structures has led to a decrease in forest species richness (Paillet et al. 2010), which becomes particularly evident in the ongoing insect decline, even in forest ecosystems (Seibold et al. 2019).
Forest specialist species like saproxylic beetles represent a group that is particularly sensitive to current forest management practices (Schmidl and Bussler 2004), which is evident in the high proportion (27%) of threatened species in Germany (Seibold et al. 2015). As saproxylic beetles depend on deadwood in at least one stage of their life cycle (Speight 1989), they are frequently used as indicators for deadwood amount and diversity, which is associated with forest naturalness and structural complexity (Lachat et al. 2012;Gao et al. 2015). Although the amount (Müller et al. 2007) and the diversity of deadwood (Seibold et al. 2016) has been identified as the most influential structural habitat requisite, saproxylic beetles greatly vary in their habitat requirements and different forest structural elements such as decay stage of deadwood or light availability (Müller et al. 2015;Seibold et al. 2016).
Environmental conditions and forest structures at the stand scale are important for saproxylic beetle habitat selection (e.g. Hjältén et al. 2012;Kraut et al. 2016;Seibold et al. 2016). However, the drivers of species presence are not only operating at the stand scale, but as well at the landscape scale (Seibold et al. 2019). Selecting the right spatial scale is important, as ecological processes and patterns can only be detected, when being addressed at the spatial scale they occur (Levin 1992). Spatial scale has two components, namely the spatial grain and spatial extent. Spatial grain (in the following used synonymously with spatial scale) is defined as the resolution of the analysis, while spatial extent defines the area covered by the study.
For beetles, various spatial scales have been used to study species-environment relationships, with single-scale models ranging between 20 m (Dittrich et al. 2019), 60 m (Crawford and Hoagland 2010), 100 m (Judas et al. 2002;Kärvemo et al. 2014;Della Rocca et al. 2017), 1 km (Hof and Svahlin 2016;Silva et al. 2016;Brunetti et al. 2019) or even 10 km resolution for Great Britain (Eyre et al. 2005;Jiménez-Valverde et al. 2007). However, little is known about the optimal spatial scale at which the selection of particular resources or habitat structures actually takes place (Sverdrup-Thygeson et al. 2014). A few studies have evaluated the optimum spatial scale for different habitat variables for predicting saproxylic beetles presence in forests (Økland et al. 1996;Holland et al. 2004;Bergman et al. 2012;Jacobsen et al. 2015). The evaluated optimal scales ranged between 20 and 2000 m for forest cover (Holland et al. 2004), 50-5000 m for substrate density (Bergman et al. 2012), 2000-3000 m for forest age and volume (Jacobsen et al. 2015) and up to 1000-4000 m for various other habitat characteristics. The spatial scale at which habitat selection occurs is generally related to the species' perception of the landscape and thus varies greatly among taxonomic groups (Turner et al. 2019). One trait that may affect scale selection is the species mobility. Species with the capacity to fly may have larger ranges and a higher capacity to move through unsuitable habitat (Steffan-Dewenter et al. 2002;Chust et al. 2004;Percel et al. 2019).
There is growing evidence, that habitat models including variables at multiple scales (multi-scale models) perform better than models using all predictors at the same scale (single-scale models) (Bergman et al. 2012). The advancement in the field of remote sensing has led to area wide datasets with different spatial resolutions and facilitated studies about environment-habitat relationships at multiple scales (He et al. 2015;Reddy et al. 2021).
In order to explore the effects of spatial scales on the occurrence of eight saproxylic beetle species we applied species distribution models. In the following we will use the term habitat selection (sensu McGarigal et al. 2016) when referring to the performance of environmental variables in explaining species presences'. We used high-resolution remote sensing data measured within incrementally increasing radii to predict the presence of species with different dispersal abilities (mobility), four flying (in the following termed as "mobile") and four flightless species. Evaluating the spatial scales at which different variables performed best, we hypothesized, that (i) flightless species respond at smaller spatial scales compared to mobile species (Gehring and Swihart 2003), and that (ii) variables representing forest structure and resources are responding at smaller spatial scales compared to variables describing general conditions such as topography and forest type in all species. In addition, we (iii) hypothesize a better performance of multi-scale models compared to single-scale models for area-wide predictions of species distributions. With the identification of important habitat requisites and the corresponding scales at which they support the presence of species belonging to a conservation-relevant taxonomic group, our results will provide quantitative target values for large-scale conservation strategies enhancing structural complexity in managed temperate forests.

Study area
The study was conducted in the Black Forest in southwestern Germany (see Fig. 1). It is a lower mountain range with altitudes ranging from 120 to 1493 m.a.s.l. and 75% of the area is covered by forests, with Picea abies (42.8%), Abies alba (18.5%) and Fagus sylvatica (15.3%) being the dominant tree species. The forests are managed with a close-to-nature management strategy leading to continuous-cover forests, see Storch et al. (2020) for more details. Within the study area of 7167 km 2 in size, beetles were collected at 180 one hectare plots, that had been established in two large-scale research programs run by the University of Freiburg (for details see: Storch et al. (2020), and the Forest Research Institute of Baden-Württemberg (FVA, for details see Eckerter et al. (2022). Plots were selected to represent a gradient of standing deadwood and amount of forest surrounding these plots and restricted to locations with < 35° slope, elevation of > 400 m.a.s.l. and stand age > 60 years (Storch et al. 2020). The maximum possible distance between the surveyed plots was 138 km.

Collection and selection of model species
We selected four flying species (mobile), namely Ampedus balteatus, Salpingus ruficollus, Hedobia imperialis and Ostoma ferruginea as they represented different families and preference for different forest types, from coniferous to broadleaved-mixed dominated forests. As flightless species we selected Pterostichus pumilio (non-saproxylic), Adexius scrobipen- Fig. 1 The study area (black) is located in the Black Forest in the state of Baden-Württemberg (grey) in south west of Germany (white, A). Beetles were collected at 180 study plots (B) with flight interception traps for flying species only (blue triangles), and a combination of pitfall traps or hand collection for flightless species and flight interception traps (pink triangles). Forest above 400 m.a.s.l. is highlighted in green, grey represents forest below that threshold and nonforested area nis, Acalles micros and Echinodera hypocrita. An overview of all species including mobility, forest type preference and their ecological guild is given in Table 1.
Species presence data were obtained using different methods: Flying beetles were sampled with two flight interception traps per plot over a growing season as described in Knuff et al. (2019). Flightless beetles were sampled by hand (leave litter sifting) next to deadwood and with three pitfall traps over one month or more. More details about sampling locations, methods and sampling effort can be retrieved from table S1. As we used a presence-only model for the analyses, only one presence location per species was retained per plot and allocated to the plot center. Moreover, we reduced the dataset allowing a minimal distance of 400 m between presence locations using the function thin from the SDMtune R-package (Vignali et al. 2020). The number of presence locations per species varied and are listed below and in Table 2.

Environmental variables
We used environmental variables describing climate, topography, forest type and forest structure (Table 3). Forest structure variables were derived mainly from vegetation height models and orthophotos based on stereo aerial photographs of a ground resolution of 0.2 × 0.2 m, dated from 2015 to 2017 and supplied by the State Office for Geoinformation and Land Development Baden-Württemberg (2018). Digital orthophotos and 3D  (Freude et al. 1979;Möller 2009;Kraut et al. 2016) Consumer or inhabitant of wood containing fungal mycelium.

Adexius scrobipennis
Curculionidae Broadleaved and mixed (Freude et al. 1983;Rheinheimer and Hassler 2013) Inhabitant of fungal infected branches and wood splinters embedded in litter (Koch 1992).  % Table 3 Overview of the variables used to predict saproxylic beetle presence including variable type, abbreviation, short description and unit. Variables are classified into four variable types. Details about the forest structure variables are provided in Table S2 Sentinel 2 data (downloaded from the Copernicus Open Access Hub https://scihub. copernicus.eu/) originating from the years 2016-2018 were used for modelling tree volume according to Schumacher et al. (2019) as well as forest type. For forest type classification support vector machine regression models were applied using optical remote sensing data. Pure broadleaved forests were classified as having more than 80% estimated proportion of trees per pixel, mixed broadleaved 20-100%, mixed 20-80%, coniferous mixed 0-80% and pure coniferous less than 20% deciduous trees. Most variables were developed at the Forest Research Institute (FVA) of Baden-Württemberg and provided through the MoBiTools project (https://www.fva-bw.de/top-meta-navigation/fachabteilungen/biometrie-informatik/ mobitools). Tree cover density was retrieved from Copernicus Land Monitoring Service (https://land.copernicus.eu) for the year 2017.

Acalles micros
Topographic variables were calculated using a digital elevation model with an original resolution of 1 × 1 m, as supplied by the LGL (2018). Slope, eastness, northness and roughness were generated using the terrain function from the raster R-package (Hijmans et al. 2022

Variable preparation
All environmental variables were resampled to the same resolution (20 × 20 m) using bilinear interpolation for continuous, and the nearest neighbor method for discrete raster values and cropped to the extent of the study area. In addition, variables were masked to areas with an elevation > 400 m.a.s.l. and defined as forest, including temporarily treeless forest areas, e.g. windthrow areas and gaps (Ganz et al. 2020).
We calculated average values within circular moving windows with radii of 50, 100, 250, 500 and 1000 m for all of the variables, except those representing climate, which were kept at their original resolution of 250 m. We did not exceed the scale of 1000 m as we did not assume that beetles' respond to landscape elements operates beyond this scale and to limit the maximum overlap between the radii of neighboring presence plots.

Univariate species distribution models and scale selection
To model species habitat selection we used a presence only approach (Maxent, Phillips et al. 2006) as sampling effort per plot was not standardized. The Maxent algorithm is known for its high predictive accuracy, even with small sample sizes (Elith et al. 2006;Guisan et al. 2007;Turner et al. 2019). The presence locations were contrasted against 10,000 random background locations, that were selected with the RandomPoints function in the R-package dismo (Hijmans et al. 2020). Model calibration, tuning and evaluation was performed using the R-package SDMtune (Vignali et al. 2020). First, the presence data for each species were split in test (30%) and training (70%) datasets. For each species univariate SDM's were then trained with each variable at each scale separately. In order to account for slight differences between evaluation metrics and obtain more stable results, we used three different metrics to evaluate the univariate models: Akaike's information criterion corrected for small sample sizes (AICc) (Burnham and Anderson 2002), as well as the area under the receiver operating characteristic (ROC) curve (AUC) (Fielding and Bell 1997) and the true skill statistic (TSS) (Allouche et al. 2006), both applied to test the model's fit on the training dataset ("train") and the predictive accuracy on the test dataset ("test"). Scale selection was then performed using an ensemble metric approach, based on the five different evaluation metrics calculated on the univariate models for each variable and scale (table S3). For this purpose, for each metric the difference between the best and least performing scale of the same variable was scaled to a value between 0 and 1, and the relative score for each scale calculated. The values for AICc were reversed (as the lowest value represents the best performing models) and the resulting scores of the different metrics summed up to an ensemble value. The scale with the lowest ensemble value was selected as the "best scale". Finally, we retained only variables which explained species presence better than random at their best-performing scale, i.e. when the respective model had an AUC test of more than 0.5.
We performed a Wilcox test to investigate the differences in scale selection between flightless and mobile species and a Kruskal-Wallis test for testing differences between scales at which the different variable types were selected. In addition, we used a generalized mixed effect model (nlme R-package; Pinheiro et al. 2020) to test if the ensemble values, as a measure of consistency in scale selection, differed in relation to variable type and species mobility.

Multivariate species distribution models/habitat selection
The retained variables at their "best scale" were included in a multivariate model. Of pairs or groups of correlated variables (Spearman's R > |0.7|) only the one was retained that performed best (based on the AICc) in univariate models. For each species, multivariate models were then trained with the feature class combinations depending on the number of presence locations as recommended by Phillips and Dudík (2008): For Acalles micros (9 presence points) only linear features ("l") were used, for Adexius scrobipennis (10), O. ferruginea (17), E. hypocrita (26), P. pumilio (39), Ampedus balteatus (63) and H. imperialis (67) linear and quadratic features ("lq") were tested, and for S. ruficollis (123) product features ("lqp") were additionally allowed. In order to optimize model parsimony, variables were reduced using the reduceVar function (R-package SDMtune) for each species with more than 20 presence locations. This function stepwise removes the least performing variables until all variables have a permutation importance > 7% (based on 10 permutations). To avoid overparameterization of models for species with 10-20 presence points (i.e. O. ferruginea and Adexius scrobipennis), we reduced the predictor variable set to two variables (Harrell et al. 1996) testing all possible variable combinations. For Acalles micros with only nine presence locations we allowed only one variable.
For the best models and the second-best candidate models (AICc difference < 2) hyperparameters were tuned using the optimizeModel function. This method relies on a genetic algorithm to find the optimal hyperparameter combination (for details see: Vignali et al. (2020). Regularization multiplier values between 0.1 and 5 with an increment of 0.05 were tested, and possible feature class combinations allowed as described above. Among the candidate models the model with the lowest AICc was selected as final model.
In order to compare multi-scale with single-grain models, we repeated the workflow described above, but selected all variables at the same scale (50, 100, 250, 500 and 1000 m radius). The resulting five models were then evaluated and compared with the multi-scale model using the AICc and AUC.

Scale selection
The "best scale" at which each variable was selected by each species is reported in Table 4. Both mobility and variable types affected scale selection (see Fig. 2). Mobile species responded to variables at smaller scales (median = 50) than flightless species (median = 250; Wilcoxon rank sum test: p = 0.003). Forest structure variables were selected at smaller scales (median = 100) than forest type (median = 250) and topographic variables (median = 250; Kruksal-Wallis chi squared = 10.08, p = 0.006). Neither did the ensemble value significantly differ between flightless and mobile species (p = 0.152), nor between forest structure and forest type (0.414) but for the topographic variables (p = 0.023), with the latter correlation being characterized by higher ensemble values, i.e. lower consistency in scale selection.

Habitat selection
The multivariate models showed a moderate (O. ferruginea AUC = 0.77) to excellent (Adexius scrobipennis AUC = 0.95) performance, with the flightless species presences being predicted with an overall higher accuracy (Table 2). Projected probabilities of species occurrence are shown in Fig. 3. Over all species, forest structure variables were contributing most to the final models with on average 40.25%, closely followed by forest type 38.32%. Topographic and climatic variables explained 13.69% and 7.72%, respectively.
The presence of Ampedus balteatus was positively influenced by a high proportion of coniferous forest at a 50 m scale and of gaps at a 1000 m scale, low humidity and to a lesser extent by tree cover at a 50 m scale. Additionally, east facing slopes (1000 m) and positive topographic position index values (100 m), i.e. exposed positions, were increasing the probability of occurrence. Salpingus ruficollis occurred at high elevations (50 m scale), flat terrain (i.e. low roughness) (50 m) and north facing slopes (1000 m). It preferred

Single versus multi-scale models
Multi-scale models performed generally better than the corresponding single-scale models, although some single-scale models outperformed the multi-scale models when the AUC was used as evaluation metric (see Fig. 4). The multi-scale models for Ampedus balteatus, S. ruficollis, H. imperialis and E. hypocrita predicted better than any of the single-scale models. However, the single-scale models for Acalles micros, Adexius scrobipennis, O. ferruginea and P. pumilio at the scales 100, 50 and 100, 250 and 50, respectively had slightly higher AUC values. However, when model quality was assessed using the AICc, all multiscale models performed better or just as good (delta AICc < 2) as the single-scale models (see table S4).

Discussion
We evaluated scale-dependent habitat selection of saproxylic beetles, comparing species with different dispersal capacities, i.e. highly mobile vs. flightless species. The selected species showed distinct requirements with regard to forest structure, forest type, topography and climate, with scale selection varying considerably between variables and species. Contrary to our expectations mobile species did not respond at larger spatial scales, but at smaller than flightless species. Moreover, scale selection was related to the variable type, with forest structures being selected at smaller scales than variables describing the topography and forest type. Our results confirm that multi-scale models perform better than models including variables at one, a-priori selected scale, highlighting the importance of evidencebased scale-selection for species distribution models and management recommendations based thereon.

Scale selection
Variables at different spatial scales performed differently in predicting species presences. Most variables were selected at small scales with an overall median of 100 m, but with a high variance between variables and species. This variance is in line with previous studies investigating the effect of scale in Coleoptera (Økland et al. 1996;Bergman et al. 2012;Jacobsen et al. 2015), however, most of them used multispecies presence or species richness as response variables, where a greater variance can be expected compared to single species studies. For example, Holland et al. (2004) showed that species of the same family responded to forest cover at spatial scales between 20 and 2000 m. Smaller scales reflect the Fig. 2 "Optimal scale", as identified by an ensemble evaluation metric, at which saproxylic beetles responded to variables (N = 8), in relation to the variable type (with STRUC = forest structure, TOPO = topography, TYPE = forest type) (A) and the species mobility (B). Ensemble metric values of the responding "best scales" showing the uncertainty in scale selection, with higher values reflecting higher variability between the optimal scales obtained with different evaluation metrics, in relation to variable type (C) and species mobility (D) variability in local environmental conditions, but if chosen too small, information can get redundant. In contrast, larger scales are reducing the variability by integrating (i.e. averaging) habitat conditions of a wider surrounding which could obscure their effect ). Contrary to our expectations and literature (Chust et al. 2004;Percel et al. 2019) we found a reversed pattern, that mobile species responded to variables at smaller spatial scales compared to flightless species. We propose that this pattern is explained by their ecological use of the landscape by the mobile species, as they might be able to reach and find small patches of habitat in an unsuitable forest matrix. Flightless species, in contrast, might depend on a sufficiently high density of key habitat features within a larger surrounding in order to ensure the survival of the entire population. Flightlessness is usually associated with stable habitats (Ikeda et al. 2012), where ephemeral habitat features such as deadwood have to be continuously supplied in close proximity. Richness of species with low-mobility has been shown to be highest in forests larger than 100 ha and older than 130 years, i.e. forest size and continuity determining habitat selection (Irmler et al. 2010). A similar pattern was found in butterflies, where the richness of sedentary species was positively correlated with habitat area, while there was no such correlation in mobile species (Wilcox et al. 1986). Our results suggest that the spatial scales at which habitat features were selected do not reflect individual home range size, but rather the density at which key habitat features are available in the landscape to sustain species populations. In this context, the largest of the investigated scales (1000 m) might have still been too small to encompass flying species populations, and the smallest (50 m) too large for capturing flightless species individual home ranges. Even though there is little research on effective dispersal distances in saproxylic beetles (Komonen and Müller 2018), we assume that dispersal ability and therefore range size differs strongly between flightless and mobile species. For example, males of the flying Lucanus cervus have a home range of 7585 m 2 (minimum convex polygon, logNorm) or 14,487 m 2 (95% kernel density estimates) (Tini et al. 2018), which would correspond to a spatial scale of 50-68 m radius. Comparatively, home range sizes of two flightless beetles in an arid environment did not exceed 700 m 2 (r = 8.4 m) (Matyukhin and Gongalskii 2007). The largest analyzed scale in this study was not exceeding 1000 m, even though other studies have found the optimal scale for certain environmental variables above 1000 m (Økland et al. 1996;Holland et al. 2004;Bergman et al. 2012;Jacobsen et al. 2015;Percel et al. 2019). In our case scales above 1000 m radius would have led to overlapping windows and spatial autocorrelation. Independent of species mobility, forest structure variables were selected at smaller scales than variables describing forest type or topography. This reflects their hierarchical clustering from fine to coarse: Forest structure variables are nested within forest type, with the latter representing available habitat, while the former rather representing resources which are selected at smaller spatial scales. Topographic variables are "independent" from the other variable types and may thus predict at different scales. Elevation is highly correlated with climatic variables such as temperature, windspeed and daily mean saturation deficit, which are expected to act at larger spatial scales than land cover (Pearson and Dawson 2003;Luoto et al. 2006). In our study both, topographic and forest type variables were predicting species occurrence probabilities at similar, larger spatial scales, since the study area is characterized by a high variation in elevation and associated topographical conditions.
In line with previous studies (e.g. Graf et al. 2005) multi-scale models performed better than single-scale models, highlighting the importance of selecting variables at their best performing scale. A-priori univariate scale selection resulted in better or equally good models (AICc delta > 2) than using all variables at the same, often arbitrarily selected, scale (Fig. 4, Table S4; Wheatley and Johnson 2009). Moreover, it has been shown that multi-scale models are especially important for mobile species, while predictions for sedentary species are less influenced if multi-or single-scaled variables are used (Meyer and Thuiller 2006).

Species habitat selection
Model performance (AUC) was higher for the flightless beetles (with fewer presence locations) than for mobile species. This result is in line with Pöyry et al. (2008) who found better predictions for less mobile butterfly species than high mobile butterflies. Although the low number of presence locations for some species like O. ferruginea and most flightless species limited the number of predictor variables and thus also model performance (Guisan et al. 2007), all models showed a sufficiently high model accuracy (AUC > 0.75), making them useful for conservation planning and downstream applications (Pearce and Ferrier 2000).
Most of the studied species preferred a mixed forest type. Echinodera hypocrita and H. imperialis were both related to mixed forests (Möller 2009;Rheinheimer and Hassler 2013;Horák and Rébl 2013), while Acalles micros and Adexius scrobipennis preferred broadleaved mixed forests. This is reflected in their prediction maps, where they are restricted to the edge of the study area, where forests are dominated by broadleaved trees. Salpingus ruficollis and Ampedus balteatus on the other hand were relying on high amounts of coniferous or coniferous mixed forest, with the former also being linked to broadleaved forest at a larger scale. Their predictions are more evenly distributed throughout the study area, as the Black Forest is mainly dominated by coniferous and mixed forests.
Forest height, a proxy for old forest, positively affected the presence of three species Adexius scrobipennis, E. hypocrita and H. imperialis. The former two flightless species are known to occur in old forests with a high degree of naturalness (Stüben 2005;Bahr and Stüben 2007), with E. hypocrita considered a relict species of ancient woodlands (Buse 2012). Even though deadwood is an ephemeral resource, old forests may continuously provide sufficient amounts not only of standing, but also of lying deadwood, which could not be assessed by remote sensing. Forest height may thus reflect the continuous availability of deadwood better than the standing deadwood variable per se. Standing deadwood was only selected into the final models of two species, P. pumilio and O. ferruginea. While P. pumilio is not classified as obligatory saproxylic, its preference to hide in leave litter and lay its eggs below woody debris or stones (Wachmann et al. 1995) may classify it as facultative saproxylic (Graf et al. 2022). Saproxylic species depend on a wide diversity of decaying deadwood and in different abiotic conditions (Seibold et al. 2016). Unfortunately, the identification of deadwood from remote sensing data does not yet provide information about deadwood quality or the stage of decay that might have improved the predictions. Moreover, lying deadwood below the canopy can neither be detected nor quantified with stereo aerial imagery. However, this information of more detailed forest attributes and deadwood is most likely necessary to make better predictions, as they represent elementary resources. As O. ferruginea is inhabiting particularly large, sun exposed standing dead trees (Möller 2009), the relationship of this species with standing deadwood can be well captured by the deadwood detection method used here (Zielewska-Büttner 2020). The presence of S. ruficollis, P. pumilio and H. imperialis was favored by high tree density, high tree volume and few gaps. All these variables reflect the species' preference for rather dense forests (Müller et al. 2010) or indifference to sun exposure (Ranius and Jansson 2000), other than Ampedus balteatus which preferred both high tree cover and gaps.
Climate variables, especially temperature, are important drivers of the distribution of saproxylic beetles and insects in general (Bale et al. 2002), but played a minor role in our models, due to the restricted climatic range of the study area. The presence of Ampedus balteatus was best explained by low values of saturation deficit, a measure for humidity. Salpingus ruficollis, H. imperialis and E. hypocrita were found at high elevations, and P. pumilio, a cold adapted species of colline to montane altitudes (Trautner 2017), was associated with low maximum temperatures.
In this study we were focusing on the effect of different landscape elements at varying spatial scales on the presence of saproxylic beetles. However, also temporal scales of habitat and resources availability influence saproxylic beetles. The decay stage of deadwood is for example influencing the spatial scale at which saproxylic beetles respond to this resource (Jonsell et al. 2019). This is in line with theory, which predicts the colonization of ephemeral resources to be related with more mobile species, whereas more long-lasting resources to be related with less mobile species (Southwood 1977). Yet, the ecological patterns explaining the influence of temporal and spatial scales to species distributions still needs further investigations, also to derive sound management recommendations (Sverdrup-Thygeson et al. 2014).

Conclusions
Understanding species' habitat requirements at relevant spatial scales is elementary to frame appropriate target values for forest management and conservation recommendations (Percel et al. 2019). Our study provides this information for seven obligatory and one facultative saproxylic species: Ensuring sufficient densities of resources and key habitat structures within the surrounding landscape is crucial to compensate for low dispersal ability of flightless species and to sustain viable populations. Mobile species, in contrast, are able to colonize smaller habitat patches with a high density of key structures within a larger surrounding of seemingly unsuitable forest matrix. Less mobile species may thus particularly benefit from the designation of forest reserves that locally provide high densities of key forest structural attributes within areas large enough to harbor viable populations. Retention approaches, in contrast, designed to enhance structural complexity in managed forests by sparing groups of trees or small forest patches from harvesting (Lindenmayer et al. 2012;Gustafsson et al. 2020), may be particularly beneficial for mobile species. Further investigation into effective dispersal distances of saproxylic species and their capacity to move through the landscape, would help to better understand the underlying population processes (Komonen and Müller 2018) and refine recommendations in terms of size and spacing of key structural elements at the landscape scale. In future, more saproxylic species, especially indicator species representing different ecological groups would be needed to broaden management recommendations. Investigating the requirements of single species rather than focusing on species diversity would allow to identify scale-specific response patterns in relation to species' dispersal ability (Komonen 2008) and to derive targets for habitat management at both local and landscape scales.