Evidence of a spatial auto‐correlation in the browsing level of four major European tree species

Abstract The contribution of spatial processes to the spatial patterns of ecological systems is widely recognized, but spatial patterns in the ecology of plant‐herbivore interactions have rarely been investigated quantitatively owing to limited budget and time associated with ecological research. Studies of the level of browsing on various tree species reported either no spatial auto‐correlation or a small effect size. Further, the effects of disturbance events, such as hurricanes, which create large forest openings on spatial patterns of herbivory are not well understood. In this study, we used forest inventory data obtained from the federal state of Baden‐Württemberg (Southern Germany) between 2001 and 2009 (grid size: 100 × 200 m) and thus, after hurricane Lothar struck Southern Germany in 1999. We investigated whether the browsing level of trees (height ≤ 130 cm) in one location is independent of that of the neighborhood. Our analyses of 1,758,622 saplings (187.632 sampling units) of oak (Quercus), fir (Abies), spruce (Picea), and beech (Fagus) revealed that the browsing level is characterized by a short distance spatial auto‐correlation. The application of indicator variables based on browsed saplings should account for the spatial pattern as the latter may affect the results and therefore also the conclusions of the analysis.

Browsing by large herbivores is frequently perceived as a major challenge for tree recruitment in Europe (Kupferschmid & Heiri, 2019), North America (Devaney, Pullen, Cook-Patton, Burghardt, & Parker, 2020;Saucier, Champagne, Côté, & Tremblay, 2019), and Asia (Tamura & Yamane, 2017). However, forestry management remains largely disconnected from the management of large herbivore populations (Beguin, Tremblay, Thiffault, Pothier, & Côté, 2016;Reimoser, 2003). During the 18th century, forest management in Europe focussed on the consequences of anthropogenic changes for sustainable forestry practices, such as the loss of tree recruitment area due to industrial development and the intensive utilization of domestic animals (see Carlowitz, 1713). Until the early 20th century, the effects of large herbivores on tree recruitment and thus on forest development were largely ignored because large herbivores were of relatively low abundance, both in North America (Leopold, Bean, & Norman, 1943) and in Europe (Breitenmoser, 1998;Jędrzejewska, Jędrzejewski, Bunevich, Miłkowski, & Krasiński, 1997). During the 1940s and 1950s, however, awareness of the effects of large herbivores on tree recruitment in the Northern Hemisphere increased (Aldous, 1944;Leopold et al., 1943). Among the approaches developed to quantify the utilization of forest plants by large herbivores (Aldous, 1944;Reimoser, 2000) was that of Zai (1964), who in 1964 proposed a determination of the percentage of browsed trees (number of trees with browsed terminal buds divided by the total number of trees-the browsing level) as a robust index of roe deer (Capreolus capreolus) browsing. However, it was not until the 1980s that the browsing level of terminal buds was linked to tree growth and tree survival (Eiberle & Nigg, 1984, 1987). Thereafter, browsing-level assessments gained increasing attention (Reimoser & Gossow, 1996;Welch, Staines, Scott, & French, 1992).Thus, the browsing-level approach of Zai (1964), with its minimal required effort and observer independence, seemed to be a promising method to quantify the impact of large herbivores on tree regeneration (Morellet & Guibert, 1999). However, Reimoser, Odermatt, Roth, and Suchant (1997) and Senn and Häsler (2005) argued that a specific browsing level cannot be seen as direct damage caused by herbivores nor can it be related to a specific damage to forestry caused by herbivores. Reimoser (2003) pointed out that a higher browsing level might be a consequence of: (a) an increased need of large herbivores to engage in damaging activities, (b) an increase in the numbers of large herbivores, or (c) a change in forest structure resulting in the increased vulnerability of the saplings.
The home range of roe deer individuals varies between 20 and 60 ha (0.2-0.6 km 2 ) depending on the region, season, and landscape composition (Lovari, Serrao, & Mori, 2017;Morellet et al., 2013;Richard, Said, Hamann, & Gaillard, 2014). Within home range roe deer select not only high-quality forage patches but also high-quality plants within those patches (Moser et al., 2006), and food quantity and quality will likely impact roe deer numbers (Gaillard et al., 2003;Gill et al., 1996). In the study of Gill and coauthors (Gill et al., 1996), roe deer density correlated negatively with total conifer cover with a time lag of 6 years. Thus, based on the ecology of plant-herbivore interactions, it can be expected that the browsing of trees will be characterized by spatial patterns. However, there have been no, or at best few (cf. Champagne et al., 2018;Morellet & Guibert, 1999;Ohse et al., 2017) attempts to quantify the spatial characteristics of the browsing level. Furthermore, the results of those studies indicated either no auto-correlation (Champagne et al., 2018;Morellet & Guibert, 1999) or only negligibly small effect sizes (Ohse et al., 2017).  were analyzed. We tested the assumption that the species-specific browsing level of saplings (height ≤ 130 cm) at one location is independent of the species-specific browsing level of saplings at neighboring locations. The spatial independence not only of the browsing level but also of the number of saplings per sampling unit (sapling density) was determined by calculating Moran's I (Moran, 1950). The results presented for four major tree species (Abies, Picea, Fagus, Quercus) in Europe highlight the need to quantify spatial patterns in plant-herbivore ecology research and practice.

| DATA AND ME THODS
Since 1998, forest cultural undertakings ("Betriebe") of the German federal state of Baden-Württemberg has made use of forest inventory data to estimate timber production (Nothdurft, Borchers, Niggemeyer, Saborowksi, & Kändler, 2009). The inventory is conducted once per decade at the level of one "Betrieb" and collects data on the amount, age, and spatial distribution of tree species within a predefined grid (100 × 200 m, cf. Figure S1)  (Table 1). The annual sample covering several distinct regions in Baden-Württemberg (cf. Figure 1) may or may not have appropriately represented the sapling density and the browsing level for the federal state of Baden-Württemberg. We thus compared the browsing level determined in forest inventories with the results of the "Forstliches Gutachen Baden-Württemberg" (cf. Figure 2), an official management tool to estimate both the browsing level and the possibility to reach forest management objectives. Since 1983, a survey has been conducted every third year for each hunting ground in Baden-Württemberg (N ≈ 6,000, size of the hunting grounds ≈300-400 ha). In December 1999, hurricane Lothar struck Eastern France (Storms et al., 2006) and Southern Germany (

TA B L E 1 (Continued)
solid cubic meters were storm damaged (Erb et al., 2004). The resulting openings led to an increase in the number of saplings and thus to improved habitat quality for large herbivores in subsequent years (Storms et al., 2006;Widmer et al., 2004). Data of the "Forstliches Gutachten Baden-Württemberg" suggested that the browsing intensity in Baden-Württemberg declined to a local minimum in 2001.
Thus, in this study, we used 2001 as the reference year (cf. Figure 2 where N is the number of spatial units, x the browsing level, x mean the mean browsing level, w ij the weight according to the defined neighborhood (w ij = 0 for i = j; w ij = 0 for d(i, j) > d nb ) and W the sum of all w ij .
Thus, I was calculated as the correlation coefficient for pairs of points considered as neighbors.
A calculated value of I significantly less or greater than 0 negated the hypothesis that the browsing of young trees (height ≤ 130 cm) is a spatially independent process. The Bonferroni correction was used to correct for multiple testing effects. Statistical calculations were carried out using R version 3.4.4 (R Core Team 2018) and the R package spdep (Bivand et al., 2006).

| RE SULTS
Between 2001 Figures 3 and S4). Both the browsing level and the sapling density were characterized by a positive spatial auto-correlation (Figures 3 and S4)  (1) and independently of the tree species (Figures 3 and S4) and corresponded to a rather high overall browsing level ( Figure 2) Figures 3 and S4).

| D ISCUSS I ON
In this study, Moran's I (Moran, 1950) was calculated to test for the spatial independence of (a) the sapling density of four tree species resolution of the available data sets and thus in a low power to detect spatial auto-correlations. For example, previous sampling units frequently corresponded to a single year (Morellet & Guibert, 1999), two years (Champagne et al., 2018) or three years (Ohse et al., 2017) and were sampled in relatively small study areas (<6 km 2 Morellet & Guibert, 1999, Champagne et al., 201875 km 2 Ohse et al., 2017).
Our inventory data for the year 2007 provide an example of how incomplete information can result in a failure to detect spatial auto-correlations (Table 1). The estimated value of Morans I (year 2007) supports the hypothesis of spatial independence for both sapling density and browsing level. However, while this conclusion might be true for the sampled year/region, it does not imply that data on sapling density and browsing level can generally be regarded as spatially independent variables (Table 1, Figures 2 and S4). Differences in Moran's I between tree species may be due to the different dispersal strategies of the trees (Dormann, 2007;Yokozawa et al., 1999).  Figures 2 and 3). The difference between the maximum and minimum annual browsing levels of oak, fir, spruce, and beech was 20%, 19%, 6%, and 9%, respectively (Table 1). These differences together with Moran's I (browsing level) clearly show that browsing is a highly variable process both in time and in space. While this is well-known in plant-herbivore ecology (Beguin et al., 2016;Bernes et al., 2018;Sinclair & Krebs, 2002;Sokal & Oden, 1978a), our study is the first to show evidence that the browsing level of four major European tree species (fir, spruce, oak, and beech) is characterized by a significant short-distance auto-correlation. The fact that Moran's I of the browsing level and sapling density was more likely to be significant for a neighborhood distance of 100 m suggests that processes responsible for this spatial pattern were themselves characterized a by short-distance spatial autocorrelation (Sokal & Oden, 1978b). The observed spatial pattern can be explained by four different responses (Sokal & Oden, 1978b): (1) to an environmental gradient (Model I): (2) to habitat patches that are heterogeneous among themselves but internally homogenous (Model II); (3) to the isolation caused by distance (Model III); and (4) to differences in historical factors (Model IV).
We suggest that the observed auto-correlation of the sapling density is best explained by a combination of Model II, III, and IV.
As for the observed spatial auto-correlation of the browsing level,  Figure S4] and 0.28 km 2 [ Figure S2] for spruce in 2005) might reflect not only the sapling density but also the selection process of roe deer within their home range, as the home range size varies between 0.2 and 0.6 km 2 (Lovari et al., 2017;Morellet et al., 2013;Richard et al., 2014) and is smaller in forest areas (Lovari et al., 2017). If this was the case, then the analysis of datasets of browsed and unbrowsed trees using a grid size of 50 m or 25 m would be informative. Although definitively identifying the drivers of the spatial auto-correlation in both the regeneration and the browsing level will be challenging, our findings highlight the importance of accounting for spatial patterns in plant-herbivore ecology. In addition, the application of indicator variables based on browsed trees (cf. Chevrier et al., 2012;Maublanc, Bideau, Launay, Monthuir, & Gerard, 2016;Morellet et al., 2007;Pierson & De Calesta, 2015) should account for the spatial pattern in sapling density. It should also be noted that although forest inventories in Austria, Germany, and Switzerland are conducted using a grid size of 100 × 200 m or 100 × 100 m (Kupferschmid, 2018;Nothdurft et al., 2009;Ohse et al., 2017), the distance between the sample units used to obtain information on browsed trees is frequently <100 m (Ammer, 1996;Moser et al., 2006;Kuijper et al., 2009;Champagne et al., 2018) or ≤200 m (Heinze et al., 2011;Heuze, Schnitzler, & Klein, 2005;Kuijper, Jedrzejewska, et al., 2010;Morellet & Boscardin, 2001;Ohse et al., 2017;Partl, Szinovatz, Reimoser, & Schweiger-Adler, 2002).
Thus, we suggest that every study using data on browsed trees should first investigate the existence and strength of spatial auto-correlation. If the variable of interest is used as a target variable for any regression model or correlation analysis, then appropriate statistical methods should be applied (cf. Dormann et al., 2007).
Otherwise, the assumption of independence of most standard statistical procedures will be violated and type I and II error rates might increase Legendre, 1993). Our study can be understood as a first step in a systematic investigation of short-distance spatial autocorrelation phenomena in plant-herbivore ecology.
The insights obtained from those investigations will likely have important consequences for the design of forest inventories and the management practices derived from their results.

ACK N OWLED G M ENTS
We thank W. Ran for editorial support during the preparation of previous drafts of this manuscript and two anonymous reviewers and the associate editor for constructive comments. Open access funding enabled and organized by Projekt DEAL.

CO N FLI C T O F I NTE R E S T
Rudi Suchant and Robert Hagen disclosed no conflict of interests.  Figures 2, 3 and S2-S4 were archived in Dryad (https://doi.org/10.5061/dryad.4xgxd 256m). Data of forest inventories (raw data shown in Figure 1) will not be made publicly available as data contain sensitive information (human subject data in time and space) about timber production in the federal state of Baden-Württemberg.