Insights in forest structural diversity indicators with machine learning: what is indicated?

Indicator choice is a crucial step in biodiversity assessments. Forest inventories have the potential to overcome data deficits for biodiversity monitoring on large spatial scales which is fundamental to reach biodiversity policy targets. Structural diversity indicators were taken from information theory to describe forest spatial heterogeneity. Their indicative value for forest stand variables is largely unknown. This case study explores these indicator–indicandum relationships in a lowland, European beech (Fagus sylvatica) dominated forest in Austria, Central Europe. We employed five indicators as surrogates for structural diversity which is an important part of forest biodiversity i.e., Clark & Evans-, Shannon, Stand Density, Diameter Differentiation Index, and Crown Competition factor. The indicators are evaluated by machine learning, to detect statistic inter-correlation in an indicator set and the relationship to twenty explanatory stand variables and five variable groups on a landscape scale. Using the R packages randomForest, VSURF, and randomForest Explainer, 1555 sample plots are considered in fifteen models. The model outcome is decisively impacted by the type and number of explanatory variables tested. Relationships to interval-scaled, common stand characteristics can be assessed most effectively. Variables of ‘stand age & density’ are disproportionally indicated by our indicator set while other forest stand characteristics relevant to biodiversity are neglected. Within the indicator set, pronounced inter-correlation is detected. The Shannon Index indicates the overall highest, the Stand Density Index the lowest number of stand characteristics. Machine learning proves to be a useful tool to overcome knowledge gaps and provides additional insights in indicator–indicandum relationships of structural diversity indicators.


Introduction
The rapid rate of biodiversity loss is an emerging public concern. There is high scientific evidence for a positive relationship between the loss of biodiversity and the decline of forest ecosystem services (Hooper et al. 2005;Balvanera et al. 2006;Isbell et al. 2011;Mace et al. 2012;Gamfeldt et al. 2013). Biodiversity loss threatens the provision of ecosystem services at an accelerating rate and erodes the foundation of humanity (IPBES 2019).
The main drivers of extinction and decline are of anthropogenic origin (Sala et al. 2000;Newbold et al. 2015). Forest degradation, fragmentation, and loss as side effects of human economic activities already caused severe biodiversity losses (Newbold et al. 2015;FAO 2020). Globally, extinction rates are being one hundred to one thousand times greater than the natural baselines (Ceballos et al. 2010(Ceballos et al. , 2015. This trend is expected to continue globally (Keenan et al. 2015;Newbold et al. 2015).
Acknowledging the importance of biodiversity, numerous measures in policy, public, and sciences have been taken to halt biodiversity loss. Major global initiatives are the Convention on Biological Diversity (est. 1992), the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (est. 2012), and the Sustainable Development Goals (est. 2016). At the European level, the Ministerial Conference on the Protection of Forests in Europe (est. 1990), the Streamlining European Biodiversity Indicators Initiative (est. 2005), the EU Biodiversity Strategy (est. 2011), and the European Green Deal (est. 2019) were initiated. About 14.4 billion USD was spent globally from 1992 to 2003 to halt biodiversity loss (Waldron et al. 2017). Although, the rate of biodiversity decline was below the expected decline, strategic aims to control biodiversity loss are never met (CBD 2014;Tittensor et al. 2014).
One of the reasons for environmental policy implementation gaps may be the lack of effective biodiversity monitoring systems (Pereira et al. 2012;CBD 2018;Ette and Geburek 2021). Biodiversity indicators play a crucial role in assessing biodiversity and were established in large numbers (Lindenmayer et al. 2000;Larsson et al. 2001;Chirici et al. 2011). Nonetheless, biodiversity indicators are still criticized for poor indicator-indicandum relationships (Ferris and Humphrey 1999;Margules et al. 2002;Duelli and Obrist 2003;Gao et al. 2015). Following the definition of Heink and Kowarik (2010) an indicator is of major relevance for a given issue, e.g., assessment of a certain impact on conservation policy, while an indicandum is the phenomenon indicated.
Indicators for biodiversity are considered to be more useful the more precise the correlation between indicator and indicandum is known (Heink and Kowarik 2010). Scientists, policymakers, and forest managers are facing severe knowledge gaps while having to decide which and how to choose and aggregate biodiversity indicators (Yoccoz et al. 2001;McElhinny et al. 2005;Katzner et al. 2007;Jones et al. 2011). On large spatial and temporal scales, the availability of reliable data sets is another limiting factor for biodiversity monitoring (Purvis and Hector 2000;Heym et al. 2021). Therefore, there is no forest biodiversity monitoring approach internationally established or accepted yet (CBD 2018).
Due to a lack of consistent correlations, indicator species concepts have not been successful (Margules et al. 2002;Duelli and Obrist 2003). Structural diversity indicators reflect potential habitat variability, niche differentiation, structural complexity (Heym et al. 2021), and sources of forest biodiversity (McElhinny et al. 2005) e.g., for umbrella species (Müller et al. 2009) and bird species (MacArthur and MacArthur 1961). There 1 3 is broad scientific evidence for positive relationships between measures of forest structural variety and elements of biodiversity (Begon et al. 1996;McNally et al. 2001;Motz et al. 2010).
Forest inventories have a potential to overcome data deficits on large scales Corona et al. 2011;Storch et al. 2018). Major advantages of inventory-based biodiversity assessments are the repeated measurements which reflect temporal changes (Heym et al. 2021) with low additional costs (Corona et al. 2003(Corona et al. , 2011 for a high number of attributes, forest types, sample sizes, and scales (Storch et al. 2018;Heym et al. 2021). In the long term, changes in biodiversity can even be related to forest management practices (Storch et al. 2018) which makes it highly reasonable to choose indicators based on forest inventory data. Handling knowledge gaps in choice and aggregation of biodiversity indicators by machine learning approaches has already been explored in permanent grassland and freshwater ecosystems (Gallardo et al. 2011;Plantureux et al. 2011).
Our case study examines the potential of this approach for forest ecosystems. In line with Noss (1990), andMcElhinny et al. (2005), it focusses on tree species composition and forest structure in a surrogate approach (Olsgard et al. 2003). Scientifically well-established metrics of structural diversity relevant to forest biodiversity are applied. Although the relationship to the indicandum may not be fully understood yet, we will refer to these metrics as 'indicators' in the following.
Our goal is to promote the applicability of forest inventory-based diversity indicators by precising indicator-indicandum relationships through machine learning. Following Pretzsch (2002), the comprehensive indicator set considers horizontal distribution, tree species diversity, Stand Density and stand differentiation. Machine learning is applied to forest inventory data on a landscape scale in an unmanaged, lowland, European beech (Fagus sylvatica L.) dominated forest in Austria to answer the following research questions: (1) Which levels of structural diversity can be found in the unmanaged core areas of the Biosphere Reserve Vienna Woods (BR)? (2) Which stand characteristics are indicated by single structural diversity indicators? (3) Which stand characteristics are indicated or neglected by a comprehensive indicator set? (4) How strong is the intercorrelation in an indicator set?
The hypotheses of this study are that (1) machine learning as an integral part of artificial intelligence is an effective way to gain new insights in indicator-indicandum relationships in forests and (2) some stand characteristics relevant to forest biodiversity are indicated disproportionally in comprehensive indicator sets (in sense of Pretzsch 2002), while others are neglected.

Study area
The case study focuses on the core areas of the Biosphere Reserve Vienna Woods in East Austria, Central Europe (48° 5′ N, 15° 54′ E). The BR Vienna Woods has an area size of 105.000 ha and was established in 2005. The study area is located in the transition zone between the Vienna Basin and the Northern Limestone Alps. The 37 core areas (5.400 ha) under strict nature protection and without forest management are scattered across the Biosphere Reserve (Fig. 1, ESM1) Due to beneficial climatic conditions along the Vienna Thermal Line, the landscape was intensely used for centuries for transportation, settlement, agriculture, and forest management (Schachinger 1934). Historical forest management was favoring oak, black pine, and wild fruit tree species targeting firewood, game, resin, wild fruits, and acorns (Schachinger 1934). The centrally located climate station in "Brunn im Gebirge" shows the highest average monthly precipitation in July (99 mm) and the lowest in February (41 mm). Mean monthly temperatures range between − 0.1 °C in January and + 20.8 °C in July (Fig. 1). Hydrographic examinations in the Biosphere Reserve show, that annual precipitation amount can diverge up to three times on small spatial scales (EHYD 2021). The Eastern parts of the BR are under Pannonian climate, while the North-Western parts are dominated by Atlantic climate. From a geological point of view, the area under survey can decisively be distinguished in flysch and limestone bedrock. Due to heterogeneity in terms of soil, bedrock, precipitation, and topography, the BR Vienna Woods is ecologically highly diverse. About a quarter of the 125 forest types of Austria (Mucina et al. 1993) occur in the BR.

Core area monitoring
The core area monitoring of the BR Vienna Woods consists of 1555 permanent sample plots in the 37 unmanaged core areas. Since 2007, updated field data is available in a 10 year interval. Depending on the core area size, variable grid spacing guarantees a recording accuracy of ± 10% of the living standing volume. For more details, please see the field work manual (Posch et al. 2008

Tree species and growing stock volume
Sample trees were collected using angle count sampling (synonym: relascope sampling, Bitterlich sampling) with basal area factor z = 4m 2 ha −1 (Bitterlich 1984). Angle count sampling, which is commonly used in large scale forest inventories (e.g., Gabler and Schadauer 2007), is a variable radius sampling technique, with inclusion probabilities proportional to the trees' basal area. Trees are recorded according to the relation of stem diameter and distance to a central inventory point (Heym et al. 2021). Tree diameter at breast height (dbh) at 1.3 m above ground was measured for all trees in the angle count sample using a caliper. Additionally, tree height of every basal area median tree was measured per tree species and sample plot. In any case of tree top break, tree heights were additionally measured. Heights of all other trees in the sample were estimated using the basal area median tree heights and unified height curves of the Austrian National Forest Inventory (Gabler and Schadauer 2007).

Nearest neighboring tree and forest spatial structure
For each tree in the angle count sample, horizontal distance to the nearest neighboring tree was measured and recorded together with tree species and dbh of the nearest neighbor. A diameter threshold of ≥ 10 cm was applied.

Standing and lying dead wood
To estimate standing dead wood volumes, tree height and dbh of all standing dead wood within the angle count sampling (Bitterlich 1984) was measured. In addition, lying deadwood was recorded using fixed radius circular sample plots (horizontal radius r = 8 m) with 20 cm diameter threshold. Depending on diameter at the midpoint (dm), two different cubing tables were used to calculate the individual wood volume for objects of (i) 20 cm < dm ≤ 50 cm (vol 20−50 cm dm ) and (ii) dm > 50 cm (vol >50 cm dm ) . These single cubations were added up per sample point in both categories, yielding the total volume of lying deadwood with dm > 20 cm ( vol >20 cm dm ). The total volume of lying dead wood with dm > 5 cm ( vol >5 cm dm ) was deviated from this value by applying a bridging function (Eq. 1) for natural, beech dominated forests following Christensen et al. (2005):

Natural regeneration
At each sample point, young trees between 10 and 130 cm height were recorded on an area of 12.5 m 2 . The last year's browsing damage on leading shoots by ungulates was documented binary (browsed/not browsed).

Soil monitoring
Information about soils in the core areas is available from the BR Vienna Woods soil monitoring which was completed in 2012. Soil samples were analyzed in the laboratory by the Austrian Federal Research Centre for Forests. Every fourth sample plot of the core area monitoring was inventoried. At those 422 sample plots, bedrock, geological unit (flysch and limestone forest), soil type, humus type, and soil water balance were surveyed.

Structural diversity indicators
For a reliable assessment of structural diversity and biodiversity, it is necessary to consider comprehensive indicator sets (Pretzsch 2002;LaRue et al. 2019). This case study uses a surrogate approach (Olsgard et al. 2003). In order to assess structural forest diversity, five structural diversity indicators (Table 1)  The Clark & Evans-Index (C & E) describes the aggregation of horizontal tree distribution which is calculated by the quotient of the observed to the expected distance between neighboring trees assuming Poisson distribution (Clark and Evans 1954). The Shannon Index (H´) indicates the diversity of tree species and their relative abundances in a species mixture (Shannon and Weaver 1949). The Stand Density Index (SDI) displays the allometric relationship between quadratic mean diameter and stem density (Reineke 1933;Pretzsch 2002). The Crown Competition factor (CCF) as a second Stand Density indication is a relative measure of competitive pressure in crown space describing the ratio of area size and crown canopy area (Krajicek et al. 1961). The Diameter Differentiation Index (Diff) reveals distance-dependent structural diversity and quantifies the heterogeneity of plant stands (Füldner 1995). The choice of indicators relevant to biodiversity needs to be legitimated (Heink and Kowarik 2010). Scientific evidence for the expected relation between the structural diversity metric (indicator) and certain aspects of forest biodiversity (indicandum) in order to establish a comprehensive biodiversity indicator set is provided in Table 2.

Explanatory variables
We apply machine learning on forest inventory data to gain new insights in indicator-indicandum relationships. Twenty stand characteristics are reviewed as potential explanatory variables in ten random forests models. These variables can be grouped into five categories: (i) 'age & density', (ii) 'vertical structure', (iii) 'forest site', (iv) 'game impact', and (v) 'soil & bedrock' (Table 3). The explanatory variables tested were chosen from monitoring data available and based on literature reviews (e.g., McElhinny et al. 2005;Gao et al. 2015;Storch et al. 2018). In this case study, species distribution maps (bats, birds, amphibians, snails, insects, higher plants, mosses, lichens, and fungi)  Clark and Evans (1954) Species diversity

Shannon Index
Shannon and Weaver (1949) Stand Density Reineke (1933) Crown Competition factor Krajicek et al. (1961) Stand differentiation Diameter Differentiation Index Füldner (1995) 1 3 in the BR core areas, as well as forest age classes, tree species browsed, fraying & bark peeling effects, and tree structural foursome were not considered.

Random forest models
Random forest models are composed from regression trees and are trained to predict the values of five structural diversity indicators. We are using the statistical language R (R Core Team 2020) with the packages randomForest (Breiman 2001(Breiman , 2002, VSURF (Geneuer Table 2 Scientific evidence for a comprehensive indicator set in a surrogate approach

Structural diversity indicators Scientific evidence
Clark & Evans-Index Greater structural spatial diversity increases resource partitioning among species (Kohyama 1993;Yachi and Loreau 2007;Álvarez-Yépiz et al. 2017;Atkins et al. 2018) The variation of tree spacing provides an indication of the size and distribution of gaps (Neumann and Starlinger 2001) and thus indirectly on processes such as mortality, ingrowth, and competition (Svensson and Jeglum 2001) Shannon Index Tree species abundance can be used as a proxy for habitat quality or biotope trees (Heym et al. 2021) and related microhabitats (Larrieu et al. 2014) or habitat types (Kovac et al. 2020); e.g., saproxylic beetles, bryophytes, lichens, fungi, and arthropods (Uliczka and Angelstam 1999;Brändle and Brandl 2001;Berglund et al. 2009; Ulyshen 2011) There is high scientific evidence for a positive relation between tree species diversity and the number of bird (Baguette et al. 1994;Fisher and Goldney 1998), ground beetle (Fahy and Gormally 1998;Davis et al. 2000;Magura et al. 2000), arthropod (Chey et al. 1997) and ground vegetation species (Fahy and Gormally 1998;Humphrey et al. 2002) Tree species richness is a proxy for the number of niche spaces filled by different tree species (Turnbull et al. 2016) Stand Density Index The SDI can be used as a proxy for spatial distribution of resource availability in biodiversity assessments (Heym et al. 2021 ) In a meta-study, tree canopy cover could be related negatively to spider species richness in Europe (Gao et al. 2015) Contrary to the SDI, the CCF can delivers reliable outcomes in uneven aged stands (Sterba 1987) Diameter Differentiation Index Variation of tree dimension can be used as a proxy for habitat quality or biotope trees (Heym et al. 2021) and related macro-and microhabitats (Larrieu et al. 2014), e.g., saproxylic beetles, and lichens (Berglund et al. 2009; Uliczka and Angelstam 1999) Large tree diameters indicate high potential for tree related habitats (Hilmo et al. 2009;Nascimbene et al. 2008) 1 3 et al. 2015) and randomForest explainer (Ishwaran et al. 2010). In total, 15 random forest models are trained, three for each diversity indicator. The first random forest models consider 15 explanatory variables (Table 2) of the categories 1-4 (i.e., age & density, vertical structure, forest site, and game impact) per diversity indicator. These models are trained based on data of 1555 permanent sample plots. The second random forest models consider 20 explanatory variables (Table 2) of the categories 1-5 per diversity indicator. These models are trained based on 1555 permanent sample plots. The third random forest models characterize the interrelation between the five structural diversity indicators within the comprehensive indicator set. These models are trained based on data of 422 permanent sample plots including soil monitoring information.
Every random forest is composed of 500 regression trees. For every regression tree, a training set is drawn using bootstrap aggregating (bagging). The decision tree is built by rule-based splitting of the bagging sample into subsets, maximizing the variance between the subsets (Venables and Ripley 2002). At each split in the learning process, a random subset of explanatory variables is used (Ho 1998). The splitting process is repeated recursively on each derived subset, until (i) the subset has identical values with the target variable or (ii) the splitting does no longer add value to the prediction (Quinlan 1986). The mean value of the target variable within a final subset (leaf of a decision tree) is used as the conditional prediction of the target variable for a corresponding combination of explanatory variables (Venables and Ripley 2002).

Variable importance
The importance of every explanatory variable j is assessed by two measures, the percentual increase of the mean squared error (Geneuer et al. 2015;Zhu et al. 2015) and the average minimal depth (Ishwaran et al. 2010). To compute the mean squared error (%IncMSE), the out-of-bag error for every variable j is recorded during the fitting process and averaged over the random forest. Then, the estimated values of j are randomly permutated in the outof-bag data and dropped down every fitted tree. A higher mean squared error (%IncMSE) indicates higher variable importance and higher explanatory power of the variable. Slightly negatively %IncMSE values may arise in case the mean squared error of the original predictor variable exceeds %IncMSE of permuted values. 1 3 To compute the average minimal depth (AvgMinDepth), the level on which variable j is used on average to split the decision tree for the first time is assessed. Averaging MinDepth over 500 decision trees yields the average minimal depth (AvgMinDepth) in our case study. Lower AvgMinDepth values indicate higher variable importance and higher explanatory power of the variable.

Variable selection
A two-step variable selection procedure implemented in the R package VSURF (Geneuer et al. 2015) is used. VSURF strengthens the models by preselecting a subset of explanatory variables with sufficient explanatory power and removing variables with little or no explanatory power in advance. For details, please see Geneuer et al. (2015).

Levels of structural diversity in the unmanaged core areas
In line with Bitterlich (1984), Lappi and Bailey (1987), Sterba (2008) we aggregated indicator scores on the core area level (Table 4) which is particularly important using angle count method data (Storch et al. 2018).

Indicator-indicandum relationships of forest structural diversity indicators in lowland, European beech forests
Variable importance of explanatory variables is measured by two metrics, %IncMSE and AvgMinDepth. In the text, variables are ordered by the %IncMSE values because differences are more pronounced with this indication. Figures 2, 3, 4, 5, and 6 additionally display AvgMinDepth to gain insights in variable importance distribution among the 500 decision trees. For stand variable abbreviations, please refer to Table 3.

Indicator-Indicandum relationships of aa comprehensive forest biodiversity indicator set
The variable category neglected by the indicator set are 'game impact' and 'soil & bedrock' (Fig. 7). Partially reflected are the categories 'forest site' and 'vertical structure'. Variables of the category 'age & density' are overrepresented. There are no major differences between first and second model results. However, variable importance decreases on average about − 23% in the second models compared to the first ones which consider a lower number of explanatory variables. Testing fifteen instead of twenty explanatory variables affects the sum of explanatory power between + 9%IncMSE (SDI) and + 33%IncMSE (H′). Using randomForest to gain insight in indicandum-indicator relationships, a pronounced sensitivity to the number of explanatory variables tested could be found.
Explanatory variables indicated best by the indicator set in the first and second models are stem basal area (BA = 154.43%IncMSE), stem density (N = 117.61%IncMSE), standing stock volume (V = 101.34%IncMSE), quadratic mean diameter (qmd = 81.02%IncMSE), and dominant tree species (dom spec = 71.22). 17 of 20 explanatory variables under study are at least once indicated in the ten models. The three stand variables overall neglected by the indicators set are coarse woody debris < 25 mm MDM (cwd < 25 mm), proportion of regeneration with browsing damage (bd), and humus type (humus).

Intercorrelation within a comprehensive indicator set
The five structural indicators are highly interrelated (Fig. 8). Overall, SDI shows highest statistical relation to other diversity indicators and can also be well predicted by them. Moreover, Adding CCF to a model considerably raises it's explanatory power. Contrary, C & E displays very low statistic relation to other structural diversity indicators. Overall highest correlation can be found between SDI and CCF (33.2-34.8%IncMSE). Strong correlations within indicator sets may arise due to description of the same structural aspect (e.g., Stand Density) and by sharing direct elements (e.g., tree diameter and stem density) in the formula.

Model approach
Comparing the use of a machine learning approach (random Forests) to gain additional insights into indicator-indicandum relationships and intercorrelation within indicator sets in comparison to e.g., linear regression with forward selection, we see following main advantage for ecological science: (i) no assumptions about linear relationships are needed, (ii) a possible collinearity of variables does not affect model predictions negatively and (iii) stable prediction results in terms of the Out-Of-Bag error. The disadvantages of random Forests are that (i) outcomes are more challenging to interpret, (ii) direction of statistic relation is unknown, and (iii) collinearity might affect %IncMSE, are clearly outweighed in our case study. The package random Forest explainer proved to be a useful tool to interpret the model outcomes.
Validity of most indicators used is weakly scientifically supported (Gao et al. 2015). A biodiversity indicator is found to be more useful the more precise the correlation with the indicandum is known (Heink and Kowarik 2010). Yet, indicator-indicandum relationships are poorly understood and tested across habitat and scales (Gao et al. 2015). Our case study shows, how random Forest can be applied for the indicator validation urgently needed on large spatial scales (Ferris and Humphrey 1999;Gao et al. 2015) considering intercorrelated data and indicators sets.

The Clark & Evans-Index (C & E)
Actual C & E levels in the unmanaged core areas of the BR Vienna Woods range between 0.76 ('Anninger') and 1.25 ('Latisberg'). In the core area 'Anninger', trees are evenly arranged, while stem distribution in 'Latisberg' already evolved towards a more clustered spatial structure. Comparable C&E levels to 'Latisberg' were found in a 53-year-old pure European beech stand in Germany (Pommerening 2002). Older stands tend to have lower stem numbers and clumped structure, while young stands are often found to be evenly arranged (Pretzsch 2002;Dieler 2013). Even if mean stand age only differs about 20 years between two core areas, 'Latisberg' displays twice the amount of living stock volume and half the number of trees per hectare. In line with Pretzsch (2002) and Dieler (2013), this points towards a more mature successional state of 'Latisberg' which is indicated by C & E.
In unmanaged forests, structural complexity, and diversity significantly increase with stand age, denoted by enhanced levels of lying and standing deadwood and natural regeneration (Pretzsch 2002). In line with the findings of Pretzsch (2002) all these variables (cwd, swd, regen) are very well indicated by C & E in our case study. C & E indicates the variable category 'vertical structure' very well. Moreover, our results underline a profonde indication of the category 'age & density'.
C & E was found to indicate horizontal distribution as a proxy for resource partitioning of light use among species (Kohyama 1993;Yachi and Loreau 2007;Álvarez-Yépiz et al. 2017;Atkins et al. 2018), the size and distribution of gaps (Neumann and Starlinger 2001) and processes such as mortality, ingrowth, and competition (Svensson and Jeglum 2001). Therefore, it is highly plausible that the variable indicated best by C& E in our case study is 'stem density'. C & E shows particularly low statistical relation to other structural diversity indicators.

The Shannon Index (H′)
Shannon Index levels varies between 0.04 ('Übelaugraben') and 0.79 ('Finsterer Gang'). Comparable Index levels were described for pure European beech forest (H′ = 0.09) and oak-beech mixed forest (H′ = 0.62) in Germany (Pommerening 2002). Rare species increase H′ disproportionately, while common species affect it under proportionately (Pretzsch 2002). Overall, the Shannon Index indicates the highest number of variables. Moreover, the category 'vertical structure' and the variable 'dominant tree species' are predicted best by the Shannon Index. This is supported by scientific literature in which the Shannon Index is expected to indicate tree species abundance and diversity and is considered as a proxy for the number of niche spaces filled by different tree species (Turnbull et al. 2016), habitat quality or biotope trees (Heym et al. 2021), diversity of microhabitats (Larrieu et al. 2014), and habitat types (Kovac et al. 2020) for a variegation of taxonomic groups.
Of the five diversity indicators surveyed in this study, H′ indicates variables of 'soil & bedrock' best (s. s., soil type, flysch or limestone Vienna Woods, and soil moisture). These variables are interdependent, have major impact on plant communities, and underline the geological peculiarity of the study area. The distinction between flysch and limestone Vienna Woods has crucial implications for the soil types, their chemical composition and water balance, as well as the diversity of occurring animal and plant species (BFW 2011). In the flysch parts of the Vienna Woods, heavy, nutrient-rich, deep soils have developed. These soils are characterized by advantageous water supply and high specific water storage capacity (Leitgeb et al. 2012). Species diversity monitoring in the BR Vienna Woods detects few vascular plant species in high abundances in those areas (BR Vienna Woods Management 2021a). In the limestone parts of the study area, dry, nutrient-poor, and shallow soils are common (BFW 2011). Specific water storage capacity and water supply of these soils is much lower and promote drought tolerance species (Leitgeb et al. 2012). Species diversity monitoring indicates species-rich herbaceous vegetation in low abundances (BR Vienna Woods Management 2021a) making the model outcomes highly reasonable.

The Stand Density Index (SDI)
Of all indicators, the variables 'basal area', 'living wood volume', 'quadratic mean diameter', and 'Stand Density' are indicated best by SDI. The Stand Density Index reflects the lowest number of explanatory variables, all belonging to the category 'age & density', in very high accuracy. In our study, pronounced correlations with other indicators, especially with CCF, are found. Besides directly sharing the element 'Stand Density' in their formula, CCF and SDI describe the same forest structural aspect. The SDI is a proxy for spatial distribution of resource availability (Heym et al. 2021) and No correlation between SDI and 'dominant tree species' is detected in the case study, even if e.g., tree mortality with increasing Stand Density was found to be strongly tree species dependent (Liang et al. 2007). This indicates that (1) the broadleaved species observed have similar maximum densities in terms of stem numbers and basal areas or (2) species dependent mortality does not yet play a major role in the core areas of the BR Vienna Woods.
Additionally, occurrence of 'clastic bedrock', on which nutrient-poor soils establish (NW-FVA 2008), is indicated by SDI. Our study shows how canopy competition in the BR Vienna Woods could be a proxy for soil nutrient supply. These findings are in line with Schmidt et al. (2002) and Podrázský et al. (2014), who proved that soil base supply is the most important factor explaining herbaceous species diversity in temperate beech and Douglas fir forests. Greater overlap of crowns indicates a greater use of niche space for light in the canopy (Williams et al. 2017), and limits light transmission to the ground. In future studies, it would hence be interesting to test if ground vegetation diversity or quantity can be indicated by SDI in European beech dominated forests.

The Crown Competition factor (CCF)
The ranking of the core areas deviates between Stand Density assessment with SDI and CCF. Actual CCF levels in the core areas of the BR Vienna Woods range between 225.60 ('Johannserkogel II') and 471.75 ('Übelaugraben'). CCF can be applied to uneven-aged mixed forests (Sterba 2008). Difficulties with CCF can arise with the assessment of pure stands of the very shade-tolerant and large-crowned European beech, for which Sdino (1996) described maximum CCF levels of > 2000. Variables well indicated by CCF are 'stem basal area', 'quadratic mean diameter', and 'dominant tree species'. The indication of 'dominant tree species' by the CCF is in line with Sdino (1996) and Liang et al. (2007) and may occur due to the species-wise crown diameter being considered in the CCF formula.
Moreover, CCF indicates the variables 'altitude' and 'aspect' well. The Vienna Woods contains both, hall-shaped, low understory beech stands and south-exposed hilltops, where European beech (Fagus sylvatica) is already water-limited. On those sites, red pine and oak forest communities with rich understory occur (BR Vienna Woods Management 2021b), making this result highly plausible.

The Diameter Differentiation Index (Diff)
The Diameter Differentiation Index is the only indicator to mirror game impact and an overall high number of variables. Closest intercorrelation of Diff is found with CCF and SDI, both of which Diff shares one element (qmd) in the formula with, respectively. Actual Diameter Differentiation Index levels in the core areas of the BR Vienna Woods range between 0.22 ('Hengstlberg') and 0.40 ('Johannserkogel I'). Diameter heterogeneity in unmanaged stands is created by natural disturbance regimes which are decisive for most forest structural legacies. Natural disturbance regimes of European beech forests contain frequent, small-scale, low intensity as well as rare, large-scale, high intensity disturbance events (Leibundgut 1982;Mayer 1984;Tabaku 1999;Meyer et al. 2003).
Species diversity monitoring in the BR Vienna Woods shows that occurrence probabilities for bat, snail, relict beetle, and old-growth forest bird species increase in the core areas compared to the managed parts. The Diameter Differentiation Index seems to mirror plenty of the crucial habitat structures and quality for those guilds best (e.g., altitude, aspect, micro-and meso-relief, natural regeneration and standing dead wood). Deadwood input often relates with the natural disturbance regimes (Christensen et al. 2005). The outcomes line up with findings of Winter and Möller (2008) who showed that the Diff can be an important indicator of microhabitats in forest stands.

Indicative value of a comprehensive biodiversity indicator set
The variable category 'age & density' is overrepresented by the comprehensive indicator set. Partially reflected are the categories 'forest site' and 'vertical structure'. The categories neglected are 'game impact' and 'soil & bedrock'. Using random Forest to gain new insights in indicandum-indicator relationships, pronounced sensitivity to the number of explanatory variables tested could be found. Variables reflected best by the indicator set are 'stem basal area', 'stem density', 'standing stock volume', and 'quadratic mean diameter'. Contrary, stand characteristics like 'coarse woody debris > 25 MDM', 'tree browsing', and 'humus type' are neglected in all models. Scientifically, there is broad consensus for the 1 3 relevance of humus type (e.g., Schäfer and Schauermann 1990;Hooper et al. 2000;Ponge 2003;Salmon et al. 2006Salmon et al. , 2008, tree browsing (e.g., Gill 1992;Pastor et al. 1997;Reimoser et al. 2003) and large coarse woody debris (Kappes & Topp 2004;Müller et al. 2007;Rondeux and Sanchez 2010;Brin et al. 2011;Lassauce et al. 2011) for forest biodiversity.
In line with LaRue et al. (2019), our study shows that aspects of forest structure indeed are intercorrelated and neither ecologically nor statistically independent. Furthermore, we agree with these authors that structural niche space or ecosystem structure and function cannot be understood by one metric. Indicators which measure either more or less than they are supposed to, i.e., construct-irrelevant variance or construct underrepresentation may bias the qualitative connection between evidence and interpretation (Heink and Kowarik 2010).
Due to unavailable indicator values (e.g., bark diversity, hollow trees, forest communities, litter dry weight, litter decomposition, perennial species richness, tree age, and undisturbed reference areas) or different scales it was not possible to compare our indicator set with the performance of other aggregated biodiversity indicators (Parkes et al. 2003;McElhinny et al. 2006;Geburek et al. 2010;Storch et al. 2018;Heym et al. 2021). However, there is partial agreement in choice of elements of biodiversity studied in McElhinny et al. (2006) and Storch et al. (2018) like quadratic mean diameter, natural regeneration, standing and lying deadwood, stem basal area. Compared to Heym et al. (2021) partly identical structural diversity indicators are chosen (e.g., Shannon Index, SDI).
Handling knowledge gaps in biodiversity monitoring by machine learning approaches has already been explored in permanent grassland and freshwater ecosystems (Gallardo et al. 2011;Plantureux et al. 2011). In line with these authors, our case study underlines the large potential of machine learning for testing indicative value of single indicators and comprehensive forest biodiversity indicator sets. Moreover, machine learning could advance biodiversity indicator choice.

Summary and conclusion
In this publication, a machine learning approach to provide novel insights in indicator-indicandum relationships of biodiversity indicators and comprehensive indicator sets is presented. The indicators tested are parameters of forest spatial and structural heterogeneity. We surveyed a comprehensive indicator set of Clark & Evans-, Shannon, Stand Density, Diameter Differentiation Index, and Crown Competition factor with randomForest and examine their indicative value for twenty explanatory stand variables.
Biodiversity indicators are sometimes criticized for displaying poor indicator-indicandum relationships (Ferris and Humphrey 1999;Margules et al. 2002;Duelli and Obrist 2003;Gao et al. 2015). Machine learning proves to be a useful tool to overcome these knowledge gaps and provides additional insights in indicator-indicandum relationships. This scientific work deepens understanding of statistic properties of forest-inventory based biodiversity indicators and comprehensive indicator sets.
Examining 37 unmanaged core areas in the Vienna Woods, following scientific questions are answered: Which levels of structural diversity can be found in the unmanaged core areas of the Biosphere Reserve Vienna Woods? (2) Which stand characteristics are indicated by single structural diversity indicators? (3) Which stand characteristics are indicated or neglected by a comprehensive indicator set? (4) How strong is the intercorrelation in an indicator set?
Indicator choice is the most crucial step in biodiversity assessments. In our study, the Shannon Index is found to be most useful to indicate the variable category 'soil & bedrock' and 'vertical structure'. Variables of 'age & density' are best considered using the Stand Density Index which indicates a low number of stand variables in very high accuracy. CCF indicates the variables of 'forest site' best and altogether displays closest relation to all variables studied. The Diameter Differentiation Index is the only indicator to mirror 'game impact' and might reflect natural disturbance regimes well. Overall, the Shannon Index indicates highest, the Stand Density Index lowest number of forest stand characteristics.
Strong correlations between indicators may arise due to indication of the same forest structural aspect in indicator sets and/or by sharing direct elements in the formula. To rise reliability of biodiversity assessments, both should most possibly be avoided. Some stand characteristics (e.g., variable category 'age & density') relevant to biodiversity are indicated disproportionally in the comprehensive indicator set, while other important ones (e.g., 'coarse woody debris < 25 MDM', 'tree browsing', and 'humus type') are neglected.
More ecological studies are needed to explore indicator-indicandum relationships in detail. Machine learning as integral part of artificial intelligence may be a novel, effective and entire objective way to gain new insights into indicator-indicandum relationships on variable scales. The prediction outcome is decisively impacted by type and number of explanatory variables tested. The smaller the number of input variables, the more parsimonious is the model. Preselecting variables with regression algorithms is highly recommended. Random Forest models assumes interval scaled variables. Therefore, the impact of interval-scaled, common features on biodiversity can effectively be evaluated with machine learning. Nonetheless, relevance of qualitative variables and rare events may be underestimated. The methodology described in this study might be more suitable to review quantitative (measurable) than qualitative (observed) variables.
Our goal was to contribute to the use of inventory-based structural diversity indicators in forests by precising indicator-indicandum relationships through machine learning. This case study shows, how random forest models can be applied for the indicator validation on large spatial scales, considering intercorrelated data and comprehensive sets of structural diversity indicators. It might be a useful tool to create novel biodiversity indicator sets. Our findings support the great potential of random Forest in the context of forest biodiversity assessments and indicator choice.
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