Introduction

Natural disturbances are discrete events in time that disrupt the structure of an ecosystem, community, or population, and change resource availability or the physical environment (White and Pickett 1985; Turner 2010). In forest ecosystems, major agents of disturbance are wildfire, wind, and insects, among others. Disturbance processes are of growing importance for forest landscape dynamics, as disturbance damage is increasing in many ecosystems as a result of climatic and anthropogenic changes (Seidl et al. 2011). In addition, disturbances are expected to further increase in the future in forest ecosystems (Williams et al. 2001; Westerling et al. 2006; Seidl et al. 2009, 2014; Tian et al. 2014), which makes understanding the causes and consequences of disturbances an increasingly central issue for ecosystem management (Dale et al. 2001; Mori 2011).

Disturbances influence a wide range of ecosystem functions and services in forest ecosystems (Thom and Seidl 2015). And while our understanding of short-term disturbance impacts on individual parameters of ecosystems is increasing, the long-term effects of disturbances and their complex interactions at the ecosystem level are still incompletely understood. This can be illustrated in the context of ecosystem productivity, where both direct effects of disturbance as well as indirect effects (e.g., disturbance-mediated changes in diversity, which in turn affect productivity) exist. With regard to direct effects previous studies showed that disturbances initially affect forest landscapes negatively. A disturbance-induced loss in leaf area results in reduced carbon uptake and ecosystem productivity (Lindroth et al. 2009; Peters et al. 2013). Furthermore, the structural damage caused by disturbances, e.g., through the breakage of branches and roots in a storm event, can lead to a reduction in tree growth (Busby et al. 2008; Seidl and Blennow 2012). Soil losses often associated with disturbances result in additional negative effects on forest productivity (Nave et al. 2011; Mayer et al. 2014). Yet, most forest ecosystems are remarkably resilient to the impacts of natural disturbances, and productivity usually recovers within a relatively short time frame (of typically years to a few decades) after disturbance (Gough et al. 2013; Peters et al. 2013; Taylor et al. 2014).

However, disturbance is also a strong driver of diversity in forest ecosystems, which can exert an indirect influence on landscape productivity. The most prominent hypothesis of how disturbances shape diversity is the intermediate disturbance hypothesis (IDH; Connell 1978). The IDH predicts that species richness is maximized at intermediate levels of disturbance, because competitively dominant species exclude other species at low levels of disturbance, whereas at high disturbance levels only the most resistant species subsist. However, studies testing the prediction of the IDH have reported inconclusive results on the relationship between disturbance and diversity (Mackey and Currie 2001; Shea et al. 2004; Hughes et al. 2007). Consequently, a debate on the validity of the IDH is currently ongoing in the literature (Fox 2013; Huston 2014), yet the general influence of disturbance on diversity is widely acknowledged.

Diversity, in turn, is assumed to contribute positively to ecosystem functioning and productivity (Tilman et al. 1996; Kondoh 2001; Thompson et al. 2009; Zhang et al. 2012; Scherer-Lorenzen 2014). Three main mechanisms have been suggested to explain the observed higher growth performance of species-rich forests compared to monocultures: niche complementarity, selection effect and ecological insurance (Scherer-Lorenzen 2014). Niche complementarity occurs when more diverse forests are better able to exploit limited resources due to different and complementary traits of species (Morin et al. 2011; Lasky et al. 2014). The selection effect results from an increased likelihood of including a highly productive species in the species pool, which is optimally able to utilize site resources in forests of higher diversity (Morin et al. 2011). And finally, ecological insurance recognizes that species-rich forests are more likely to contain species that can cope with perturbations (Lebourgeois et al. 2013; Perot et al. 2013; Morin et al. 2014; Silva Pedro et al. 2015).

Disturbances can thus influence productivity not only directly but also indirectly via their effect on diversity. We here focus on the latter effect, and hypothesize that disturbances increase tree species diversity, and that such an increased diversity facilitates landscape productivity. Testing this hypothesis is challenging because of the intricacies in the relationships between disturbance, diversity, and productivity. For instance, the contradictory findings from studies analyzing the disturbance—diversity relationship may be a result of the variety of mechanisms that are subsumed under the “umbrella” of disturbance (Shea et al. 2004; Dornelas 2010; Turner et al. 2012). In order to obtain a clear process-based understanding of the effect of disturbances on diversity it is essential to disentangle the roles of different disturbance regime attributes such as duration (Roxburgh et al. 2004), timing (Miller et al. 2012b), spatial and temporal autocorrelation (Elkin and Possingham 2008; Garrison et al. 2012), disturbance type, spatial extent, frequency, and severity (Shea et al. 2004; Miller et al. 2012a). Furthermore, while the majority of previous studies demonstrated a positive effect of diversity on forest productivity (see Zhang et al. 2012 for a recent review), some have also found negative (e.g., Moser and Hansen 2006; Nguyen et al. 2012; Potter and Woodall 2014) or non-significant relationships (Vilà et al. 2005). These inconsistent findings may arise from differences in soil fertility and climate (Scherer-Lorenzen 2014), but also from studying different successional stages and spatiotemporal scales (e.g., Thompson et al. 2009; Paquette and Messier 2011; Zhang et al. 2012; Lasky et al. 2014). The majority of existing studies consider relatively short temporal and spatial scales (where direct effects might dominate) (see Scherer-Lorenzen 2014; Thom and Seidl 2015 for reviews), and often disregard later stages of successional development and the contribution of diversity beyond the local scale.

Here, our objectives were to investigate how different disturbances regimes (i.e., differing in disturbance type, damage and frequency) influence tree species diversity, and how this diversity effect relates to productivity in a temperate forest landscape in Central Europe. As disturbances are key processes shaping ecological systems across several scales (Turner 2010), and as the importance of diversity beyond the local scale is increasingly recognized (Pasari et al. 2013), we explicitly considered within- and between-stand diversity in our analysis. Using simulation modeling allowed us to take a long-term perspective on disturbance–diversity–productivity relationships, and to consider how successional development in forest landscapes is modulating these relationships. Within this framework our specific objectives were (i) to study the effect of disturbance on tree species diversity at different spatial scales (α and β diversity), and (ii) to analyze how a disturbance-mediated variation in tree species diversity affects forest productivity.

Methods

iLand

We used the individual-based forest Landscape and disturbance model iLand (Seidl et al. 2012a) to analyze the relationship between disturbance, diversity, and productivity at different spatial scales. iLand was developed to dynamically simulate the interactions between forest vegetation processes (i.e., growth, mortality, and regeneration), environmental drivers (e.g., climate, nutrient and water availability), and disturbance regimes (e.g., large-scale mortality agents such as wind storms and wildfires) at the landscape scale (Seidl et al. 2012a). Individual trees are dynamically competing for resources (i.e., light, water, nutrients) and adapting to their environment in the model (Seidl et al. 2012a). Tree regeneration is spatially explicit on the landscape, and is determined by the availability and distribution of seeds, light, and a favorable climatic environment (Seidl et al. 2012b). Primary production is derived at the stand-level (i.e., for regular cells of 100 × 100 m horizontal resolution in this study) using a light-use efficiency approach (Landsberg and Waring 1997), where scalar modifiers are used to account for the effects of environmental limitations on utilizable radiation at daily time steps. Within stands, individual tree competition for resources is accounted for by an approach based on ecological field theory (at a horizontal resolution of 2 × 2 m), in which a trees local competitive effect is characterized by a size- and species-specific influence pattern (Seidl et al. 2012a). Allocation of carbohydrates to tree compartments is based on empirical allometric ratios (Duursma et al. 2007) and accounts for dynamic adaptation of trees to their biotic and abiotic environment. Tree mortality depends on a species’ maximum longevity as well as on an individual’s carbon balance. Furthermore, mortality can result from disturbance events or management. A more detailed description of the model can be found in Seidl et al. (2012a, b) and online at http://iLand.boku.ac.at, where also the model code and executable are available under an open source license.

iLand has been successfully evaluated for simulations in diverse, multi-species forest ecosystems over extensive environmental gradients in western North America and central Europe (Seidl et al. 2012a). It was also successfully applied to investigate the relative contributions of structural and species diversity to ecosystem productivity and C storage previously (Seidl et al. 2012b). Recently, Silva Pedro et al. (2015) used the model to investigate how tree species richness modulates the effect of disturbances on the forest C cycle.

Study landscape and simulations

Our study was conducted at Hainich National Park, one of the largest unmanaged deciduous forest ecosystems in Central Europe. Hainich is located in the German federal state of Thuringia (N51.1°, E10.5°) and consists of approximately 5000 hectares of old-growth and uneven-aged forests (i.e., 67 % of the total park area). The natural vegetation is mainly characterized by beech forest types (Galio odorati (Asperulo)-Fagion) as well as oak-hornbeam forest types (Carpinion betuli) (Bohn et al. 2004). In a previous study, iLand was successfully tested against independent data from the Hainich ecosystem, documenting its ability to reproduce expected values of dendrometry and growth, as well as trajectories of long-term forest dynamics and composition (see Silva Pedro et al. 2015 for details).

Here, we were particularly interested in how disturbance-mediated variation in tree species diversity influences forest productivity. In order to isolate the disturbance effect we controlled for environmental heterogeneity in simulating a generic 2500 hectare landscape in which all factors other than the study variables (disturbance regime and available species pool—see below) were fixed. All simulations were started from bare ground and spatially homogeneous site conditions were assumed. We selected a moderately fertile site from study plots implemented at Hainich National Park (Baeten et al. 2013). Site conditions are characterized by an effective soil depth of 100 cm, a clay-loamy soil texture (resulting in a water holding capacity of 180 mm), and 70 kg ha−1 year−1 of plant-available nitrogen. Information on daily climate (i.e., temperature, precipitation, radiation, and vapor deficit) was extracted from a gridded European database (25 km horizontal resolution) representing the period 1961–1990 (Déqué et al. 2011). The selected climate is characterized by a mean annual precipitation sum of 627 mm and a mean annual temperature of 7.5 °C.

To address a wide variety of disturbance impacts we studied four disturbance types which varied in their type of impact and damage level. In two disturbance scenarios severity (i.e., the tree mortality occurring within a disturbance perimeter) varied with tree size: Under the bottom-up scenario (“bottom-up”), saplings (≤10 cm diameter at breast height (dbh)) were completely eliminated within a disturbance perimeter, whereas large trees (≥30 cm dbh) survived the disturbance event. An inverse pattern was assumed in the top-down disturbance scenario (“top-down”), where large trees (≥30 cm dbh) were removed within the disturbance perimeter while saplings (≤10 cm dbh) were assumed to survive. Between these two threshold diameters the mortality probability of individual trees changed linearly with dbh, i.e., decreasing from 10 to 30 cm in the bottom-up scenario and increasing in the top-down scenario. The two threshold diameters were chosen to approximately represent the onset of the stem exclusion and mature stages of stand development, respectively. The top-down disturbance scenario thus loosely resembles disturbance agents such as wind, which predominately affect mature trees while leaving younger cohorts widely unaffected, while the bottom-up scenario corresponds to the impact of a low severity fire regime, only killing individuals with thin bark and their live crown close to the ground.

In addition to these two size-related disturbance scenarios we simulated two high-severity disturbance scenarios which removed all trees within the perimeter of a disturbance event. The complete disturbance scenario (“complete”) eliminated all trees regardless of their taxon, whereas the species-specific scenario (“species-specific”) removed all European beech (Fagus sylvatica L.) trees in a disturbance event. While the former scenario represents the highest possible severity for a given disturbance size and frequency, the latter scenario is related to disturbance agents such as pathogens or insects which can cause major damage but usually are host-specific (e.g., many phytophthora and bark beetle species) (Tomiczek et al. 2006; Boyd et al. 2013). Beech was targeted in this scenario as it is the dominant tree species in our study area. For each of these four disturbance scenarios, an identical disturbance rotation period (DRP) of 300 years (i.e., the average time needed to disturb an area of the size of the study landscape) was assumed, corresponding approximately to historic disturbance frequencies in central Europe (Thom et al. 2013). In order to also investigate increased disturbance on the landscape, we simulated an intensified disturbance regime with a DRP of 150 years for the top-down and complete disturbance types. This intensified DRP corresponds to expectations of disturbance changes under climate change for Europe in the coming decades (e.g., Seidl et al. 2014).

The same disturbance size distribution was assumed for all combinations of disturbance type and rotation period. We used a negative exponential distribution to model disturbance size (see, for example, Wimberly et al. 2000), parameterized for a mean disturbed area of 25 ha (i.e., 1/100th of the simulated landscape extent). For every disturbance event, its size was drawn randomly from this distribution, and its position randomly determined in the landscape. A circular disturbance footprint was assumed, and the 5000 × 5000 m hypothetical landscape was implemented as a toroid to control for edge effects with regard to disturbance impact.

We hypothesized that disturbance effects on diversity are contingent on the available species pool on the landscape, as species-rich systems also have higher response diversity to disturbance (Mori et al. 2013). To further explore how the available species pool of a system modulates the disturbance-diversity relationship, we set up a factorial design studying all disturbance scenarios over a gradient of richness levels. In order to include a variety of life-history traits and responses towards disturbance we selected major tree species from all seral stages of natural forest development at Hainich (Bohn et al. 2004), i.e., Betula pendula Roth, Populus tremula L. (both pioneer species), Acer pseudoplatanus L., Fraxinus excelsior L. (both intermediate species), Fagus sylvatica L., and Quercus petraea (Mattuschka) Liebl. (both old-growth species), resulting in 63 unique combinations of species (N) in six richness levels (n = 1 to 6) (i.e., N = 26 − 1).

Simulations were started from bare ground and species were introduced in the simulation with a low constant background probability for seeds (Pseed = 0.01) uniformly distributed over the simulation area. Sensitivity tests for different Pseed values showed no significant differences in the results (data not shown). Simulations were run for 500 years in order to compare the outcomes at different successional stages of forest development. For each of the six disturbance scenarios (i.e., four disturbance types and two DRP) and each of the 63 species combinations, we ran 10 replicates in order to account for the stochasticity in the simulations. As a reference run we furthermore included an undisturbed scenario for all species combinations. In total, 1,921,500 simulation years of the 2500 ha landscape were available for analysis.

Analysis

First, we aimed at understanding how disturbances affect tree species diversity within and between stands (here defined as 100 m × 100 m cells of a grid overlaying the continuous forest landscape), i.e., at the level of alpha (α) and beta (β) diversity, respectively. To quantify and compare disturbance impact across scenarios we for every run calculated the annual disturbance percentage as the relative standing timber volume damaged by disturbance on average every year. We chose Shannon index (H′) (Shannon and Weaver 1949; Jost 2007) as the indicator of species diversity, since it not only accounts for species richness but considers the relative abundances of species (i.e., species evenness). Species richness alone can be a relatively insensitive metric as it doesn’t account for shifts in evenness that can strongly affect ecosystem functioning (Gaston and Fuller 2008). For a more intuitive interpretation of our results, we report the exponential of the Shannon index [exp (H′)] in our analysis, which equals tree species richness if all species shares are equal (Jost 2007). Within each simulation and 100-year time step we used the proportion of basal area of each species to calculate the Shannon index of the landscape, obtaining gamma diversity (γ) α diversity was derived as the exponential of the weighted average of the Shannon index in all 100 m cells on the landscape (i.e., using the contribution of each cell to landscape-level basal area as weights). Subsequently, β diversity was estimated from α and γ diversity using Whittaker’s multiplicative law (γ = α × β) (Jost 2007), thus representing the effective number of distinct communities on the landscape. The diversity levels of α and β were calculated as averages for 100-year periods over the 500-year simulation period.

To quantify the impact of disturbance on diversity we calculated the ratio between a disturbed simulation and the respective undisturbed simulation with the same species combination for both alpha and beta diversity components (αr and βr). Values lower than one indicate a disturbance-induced reduction of diversity, while values higher than one correspond to simulations where disturbance increases diversity. We used ordinary least squares regression to statistically analyze the effect of disturbance damage on the response variables αr and βr. This analysis was conducted separately for each disturbance type and DRP as well as richness level, in order to compare the effects of the different simulated disturbance scenarios on αr and βr. Finally, analysis of variance was used to determine the relative contributions of richness level, disturbance damage, and disturbance type on αr and βr. Since exploratory analyses suggested functionally different behavior over time all statistical analyses were conducted separately for 100-year time periods. In the discussion of the results we focus predominately on the first and last period of our 500-year study period, which we henceforward referred to as early and late seral stages, respectively. The assumptions of normality and homoscedasticity required for regression analysis were found to be satisfactorily met, and standard transformations of independent variables did not improved regression diagnostics.

Subsequently, we explored how α and β diversity over all richness levels and disturbance scenarios contribute to the productivity of the simulated forest landscapes. We selected mean annual increment (MAI, m3 ha−1 year−1) as proxy of forest productivity, as it is closely related to the ecosystem service of timber production and thus of high managerial importance. MAI was estimated from the total growth of each species computed at the stand level (i.e., for each 100 m × 100 m cell) for each 100 year period. For each simulation and time step, the total growth of each species was aggregated over the landscape and averaged to derive the response variable for the analysis. To quantify the effect of tree species diversity on MAI, the net diversity effects (DE, m3 ha−1 year−1) was calculated according to Loreau and Hector (2001). DE was derived as the difference between the simulated MAI of a multi-species forest (MAIO) and that of corresponding monospecific landscapes (MAIE) under the null hypothesis that there is no complementarity effect or selection effect (Loreau and Hector 2001):

$${\text{DE }} = {\text{ MAI}}_{\text{O}} {-}{\text{ MAI}}_{\text{E}}$$
(1)

MAIE was derived as a weighted average from simulations of monospecific landscapes of the respective species, using the species’ basal area shares of the corresponding multi-species forest as weights. DE values higher than zero correspond to simulations where mixed forests show a higher productivity than the one expected from their monospecific counterparts, while DE values below zero represent a negative effect of species diversity on productivity. We subsequently partitioned a positive DE (also referred to as overyielding) into transgressive overyielding and non-transgressive overyielding (Kirwan et al. 2009). Transgressive overyielding occurs when mixtures show higher productivity than the single most productive monoculture, while non-transgressive overyielding refers to mixtures with higher productivity than the average of the monoculture productivities, but lower than the most productive single-species landscape (Kirwan et al. 2009). Furthermore, in order to understand the mechanisms behind the observed net diversity effects on forest productivity, we partitioned DE into complementary (CE; m3 ha−1 year−1) and selection (SE; m3 ha−1 year−1) effects following the approach suggested by Loreau and Hector (2001). CE was calculated as:

$${\text{CE}} = n \times \overline{{\Delta {\text{RMAI}}_{i} }} \times \overline{M_{i}}$$
(2)

where n is the number of tree species in the mixture and Mi is the productivity of species i in the monospecific landscape. ∆RMAIi is the deviation from expected relative productivity of species i in the mixture:

$$\Delta {\text{RMAI}}_{\text{i}} = {\text{RMAI}}_{\text{Oi}} - {\text{RMAI}}_{\text{Ei}}$$
(3)

where RMAIOi is the observed relative productivity of species i in the mixture derived from the ratio of the observed productivity of species i in the mixture to its productivity in the monospecific landscape:

$${\text{RMAI}}_{\text{Oi}} = {\text{MAI}}_{\text{Oi}} /{\text{M}}_{\text{i}}$$
(4)

RMAIEi is the expected relative yield of species i in the multi-species forest, here defined as the averaged species basal area shares in each 100-year analysis periods in the simulated mixtures.

SE was derived from the covariance between the productivity of species in the monospecific landscape and their change in relative productivity in the mixture:

$${\text{SE}} = n \times {\text{cov}}(\Delta {\text{RMAI}}_{\text{i}} ,\;{\text{M}}_{\text{i}} ).$$
(5)

We conducted ordinary least square regression and analysis of variance for each 100-year analysis period to determine how the independent variables α and β influenced the dependent variables DE, CE, and SE through successional development. To further elucidate the relative contribution of α and β diversity we not only used their respective absolute levels directly in the analysis but also standardized them by subtracting the mean and dividing by the standard deviation, in order to adjust for possible design-related disparity in the ranges of α and β.

Acknowledging the wide variety of β diversity metrics in the literature (Legendre and De Cáceres 2013; Barwell et al. 2015), we furthermore investigated the sensitivity of our findings to a distinctly different approach to estimating β diversity. To that end we selected the total variance of community data approach of Legendre and De Cáceres (2013), which estimates β diversity independently from α and γ. This alternative β diversity (hence referred to βL-D) was determined by considering the species proportions of basal area in all 100 m cells of the landscape as community data, and applying Chord transformation to the raw abundance data [see Legendre and De Cáceres (2013) for details]. We averaged βL-D over each 100-year analysis period and compared results obtained by both β diversity indices in order to further corroborate the robustness of our findings. All statistical analyses were performed in the R language and environment for statistical computing (R Core Team 2013).

Results

Disturbance effect on diversity

We found an overall positive effect of disturbance on diversity, both with regard to α and β diversity, and regardless of the seral stage of the landscape. Our simulations showed that increasing disturbance damage generally boosts α diversity, especially for species-rich landscapes (Fig. 1). Over all disturbance scenarios, the positive effect of disturbance damage on α diversity was on average 5.5-fold greater for landscapes containing all six species compared to landscapes consisting of only two species, illustrating a strong positive interaction between the size of the species pool and disturbance level.

Fig. 1
figure 1

The effect of disturbance damage on the variation of alpha (αr; top panels) and beta (βr; bottom panels) diversity relative to undisturbed simulations. Results are for the late-seral system (simulation years 401–500) and different tree species pools on the landscape (n = 2–6). Both investigated DRPs of 300 and 150 years are shown, with disturbance damage expressed as the mean annual disturbance percentage relative to the total standing volume (vol% year−1). α diversity was estimated as the exponential of the weighted average of the Shannon index [exp(H′)] in all 100 m cells on the landscape, while β diversity was obtained by employing Whittaker’s multiplicative law (Jost 2007). Lines indicate linear regressions for each disturbance type and richness level using disturbance damage as independent variable. (Color figure online)

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The effect of disturbance damage on diversity was found to be strongly contingent also on the type of the disturbance (Fig. 1). In other words, at the same damage percentage, diversity effects varied distinctly between disturbance scenarios. Over all richness levels, the positive effect of disturbances on α diversity was strongest in the complete disturbance scenario (i.e., the most severe disturbance type), followed by the species-specific, top-down and bottom-up disturbance types [Fig. 1, Tables A1 and A2 in the Electronic Supplementary Material (ESM)]. For the late-seral landscape, the mean α diversity over all richness levels of the complete disturbance regime (effective severity: 100 %) increased by 30.2 % compared to undisturbed simulations, whereas α diversity of the bottom-up disturbance regime (average effective severity of 12.8 %) increased by only 2.7 %. For the late-seral landscape (i.e., in the last 100 years of the 500 year simulation period), the disturbance-induced variation in α was mostly explained by disturbance type, followed by damage level, richness level, and their respective interaction (Table 1). Furthermore, our results indicate a weakening of the positive relationship between disturbance damage and α diversity with a doubling of disturbance frequency (see Table A2 in the ESM). For the complete disturbance scenario, for instance, the positive effect of disturbance damage on α diversity under a DRP of 300 years decreased by between 16.8 and 90.1 % in a DRP scenario of 150 years.

Table 1 Amount of variance in alpha and beta diversity (αr and βr) explained by disturbance damage, disturbance type and richness level (disturbance rotation period of 300 years)
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We found similar positive patterns for the effect of disturbance on β diversity, although the effect strength was generally weaker for between-stand diversity compared to within-stand diversity (Table A2). Disturbances always increased β diversity in the landscape (Fig. 1) and—similar to α diversity—the positive effect of disturbance damage was higher for landscapes with a larger species pool and higher disturbance severity (Supplementary Table A2). For an increase in disturbance damage by +0.1 % year−1, α diversity increased by between +1.6 and +6.0 %, while β diversity responded with a change of between +0.1 and +1.6 % (richness level n = 6, last 100 years of the simulation) (Fig. 1; Supplementary Table A2). Disturbance type had the highest relative contribution to the increase in β diversity, while also damage level, richness level, and their respective interaction had a significant effect (Table 1).

For the early-seral landscape (i.e., the first century of the study period), the effects of disturbance on diversity were less pronounced compared to the late-seral systems (Table A1 in the ESM). Over all richness levels and disturbance scenarios, disturbance increased α diversity by between 0.3 and 6.8 %, while for β diversity this increase was between 0.5 and 8.3 %. Similar to the late-seral stage, positive disturbance effects were stronger for species-rich landscapes and high severity disturbance types. However, in the early stage of forest succession, species richness level had the highest relative contribution to the increase of α diversity, indicating that diversity in early-seral systems is more strongly contingent on the available species pool on the landscape than on disturbance effects. Overall, between 4.4 and 65.3 % of the variation in diversity was explained by disturbance (Table 1).

Diversity-productivity relationships

Both main design variables of our study—disturbance impact and richness of the landscape species pool—influenced productivity positively. Yet their influence changed over time, with the disturbance effect increasing with successional development (Fig. 2). Furthermore, both factors interacted, with the highest productivity levels observed for species-rich and highly disturbed landscapes. Subsequently, we thus analyzed how diversity drives landscape productivity. We observed a strong positive net diversity effect on forest productivity over the 500-year simulation period in our simulations, i.e., diverse forests generally showed higher MAI than their monoculture counterparts. For the early stage of succession, 90.5 % of our simulations showed a higher productivity in multi-species forests compared to the respective monospecific forests (Table 2). However, from these simulations, only 11.9 % achieved a higher productivity than the most productive monoculture (i.e., transgressive overyielding; Table 2). A similar albeit slightly weaker pattern was found for the late-seral landscape, with the majority of mixtures (70.1 %) showing positive net diversity effects but only 6.3 % resulting in transgressive overyielding (Table 2).

Fig. 2
figure 2

Net diversity effect on productivity (DE, m3 ha−1 year−1) as a function of disturbance damage and species richness on the landscape for both a early and b late successional stages (i.e., the first and last centuries of the 500 year simulation period) over all disturbance scenarios. DE is the difference between the productivity of a multi-species forest and the species share-weighted average of the corresponding monospecific forests (Loreau and Hector 2001). Species richness corresponds to the available tree species pool on the landscape. Ribbons were derived by fitting local polynomial regressions. (Color figure online)

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Table 2 Effect and attribution of tree species diversity on landscape productivity
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We found that both α and β diversity had significant positive effects on DE (Fig. 3; Table 3). An increase in diversity by a Shannon exponent of one increased net diversity effects on productivity by +0.32 m3 ha−1 year−1 (α diversity) and +1.62 m3 ha−1 year−1 (β diversity) in the early-seral system. In the late-seral stage of forest development, a diversity increase by the same amount resulted in a productivity response of +0.17 m3 ha−1 year−1 (α diversity) and +1.66 m3 ha−1 year−1 (β diversity), respectively. The relationship between productivity and diversity was generally stronger for α diversity (i.e., with a higher portion of the variance explained by within-stand than between-stand diversity). However, β diversity showed higher effects (i.e., slopes of the regression) compared to α diversity (Table 3). Similar results on the importance of β diversity were also obtained using a different indicator of between-stand diversity (Supplementary Table A4; Fig. S1). Yet, if accounting for the range disparity in α and β diversity by standardizing them, this relationship reversed for the early-seral system (Table A3 in the ESM).

Fig. 3
figure 3

Net diversity effect on productivity as a function of alpha (α) and beta (β) diversity for both early (green) and late (gray) successional stages over all disturbance scenarios. Marginal boxplots display the distribution of the data over DE, α and β diversity. (Color figure online)

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Table 3 Influence of alpha (α) and beta (β) diversity on the net diversity effect on productivity (DE), as well as on the selection (SE) and complementarity (CE) effects contributing to DE
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Mechanisms driving the net diversity effect on productivity

Both CE and SE ranged from negative to positive values. In the early-seral stage, CE were positive in 90.5 % of the simulations, while SE were positive in 55.8 % of the simulations (Table 2). Furthermore, we found that CE were stronger than SE in 87.0 % of the simulations, i.e., CE was the primary mechanism behind diversity effects and generally stronger than SE. Positive SE were found to be generally less prevalent after several hundred years of forest dynamics (Table 2). Subsequently, we also investigated how α and β diversity components relate to the CE and SE as the underlying mechanisms of diversity effects. Increasing diversity at both spatial scales in general increased CE and decreased SE in our simulations (Table 3). This illustrates that positive diversity–productivity effects are mainly driven by complementarity resource use between tree species in our study, and are not only related to within—but also to between-stand diversity.

Analyzed at the level of species groups we found that particularly a mixture of species that are well able to quickly respond to disturbances (i.e., pioneer species) and those that are able to dominate the community in the long term (i.e., intermediate to old-growth species) resulted in positive productivity responses (Fig. 4). This effect is particularly evident in the early-seral stage, in which landscapes holding species from all three different species groups (i.e., pioneer, intermediate and old-growth tree species) showed the highest mean DE. Interestingly, there is a significant increase in DE also in all runs where pioneer species co-occur with intermediate or old-growth species. However, the positive influence of species with different life-history traits was less distinct in old-growth systems compared to the early-seral systems (Fig. 4).

Fig. 4
figure 4

Net diversity effect on productivity in simulations containing combinations of species with different life-history strategies in a early- and b late-seral stages of forest succession. P Pioneer species (here: Betula pendula Roth and/or Populus tremula L.), I intermediate species (here: Acer pseudoplatanus L. and/or Fraxinus excelsior L.), O old-growth species (here: Fagus sylvatica L. and/or Quercus petraea (Mattuschka) Liebl.)

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Discussion

Here we have investigated how disturbances affect diversity at different spatial scales in a temperate forest landscape, finding that disturbances generally boost both α and β diversity. In particular, we observed a positive relationship between disturbance damage and tree species diversity. However, we also found a decreasing diversity benefit of increasing disturbance frequency, which may suggest a unimodal relationship between disturbance and diversity beyond the range of studied disturbance levels. This is supported by the fact that for productive sites as the one studied here the diversity optimum is expected to be found at higher disturbance levels compared to less productive sites (Huston 1994; Kondoh 2001).

We found that besides the commonly studied disturbance attributes such as disturbance frequency or severity (Shea et al. 2004), also the type of disturbance strongly influences the relationship between disturbance and diversity. In addition, and in line with the findings of Miller et al. (2012a), we could show that species life-history traits and the species pool available at the landscape highly modulate the disturbance-diversity relationship. However, it has to be noted that our study did not investigate other important disturbance aspects such as the interactive effects of disturbance frequency and spatial extent, which can influence competitive outcomes and thus species diversity (Miller et al. 2012a). In searching for generality in disturbance–diversity relationships it is thus not only important to consider diversity responses at different spatial scales (Svensson et al. 2012), but also to aim for a more comprehensive and process-oriented characterization of the disturbance regime (Miller et al. 2011).

Furthermore, our detailed analysis of the disturbance–diversity relationships over time scales of forest succession revealed important insights with regard to the differences between early- and late-seral systems. While in early-seral systems the increase of α diversity was less pronounced and mainly driven by the species pool available on the landscape, in late-seral systems positive effects were more strongly dependent on disturbance type. Generally, in later stages of successional development, superior competitive species dominate the ecosystem and strongly limit the relative abundance of other species, i.e., competitive exclusion occurs (e.g., Paquette and Messier 2011; Lasky et al. 2014). Disturbances here act as a disruption of the exclusion processes, freeing up resources for other species and, consequently, increasing structural and species diversity (e.g., Franklin et al. 2002; Shea et al. 2004). The stronger response of late-seral systems compared to early-seral systems also illustrates that disturbances have a long-lasting legacy on the compositional dynamics of forest landscapes, and that the spatiotemporally heterogeneous impact of disturbances on diversity accumulates over time. Furthermore, we found that not only α but also β diversity—a diversity dimension much less studied to date—responded positively to disturbance. It has to be noted, however, that we did not include extreme disturbance scenarios in our analysis here, but rather restricted disturbance frequencies to current observations and predictions for the coming decades. Here our analysis suggests that at least for productive sites in temperate forests the tree species diversity impact of the disturbance changes expected for the future (e.g., Seidl et al. 2014) might overall be positive.

We subsequently investigated the link between diversity and forest productivity at different spatial scales. Our results document that disturbances are responsible for between 4.4 and 65.3 % of diversity on the landscape (Table 1), and that both α and β diversity contribute to enhanced productivity in forest landscapes. We found that species-rich landscapes were generally more productive than the weighted average of their respective monoculture counterparts, but that only a small number of diverse landscapes achieved greater productivity than their single most productive species. These findings are in congruence with an earlier study on diversity–productivity relationships in temperate forest ecosystems (Pretzsch and Schütze 2009). Moreover, diversity effects on forest productivity remained positive over time, indicating a persistent pattern of diversity-related productivity gains over successional development (Morin et al. 2011). However, our analysis indicates that the processes contributing to this persistence over time might change with succession, with the role of disturbance gaining in importance over that of the species pool on the landscape (cf. Fig. 2). We furthermore found the positive productivity response to be mainly a result of a complementarity effect prevailing through the forest successional development. However, in contrast to previous studies we did not observe a saturating effect of increasing diversity on productivity (e.g., Morin et al. 2011; Paquette and Messier 2011), possibly due to the relative low number of species included in our simulations, and their orthogonal selection aiming for complementarity in their life-history strategies. Also the relatively weak selection effect found in our analysis can be partly explained by the restricted species pool considered in the simulations.

In extension to many previous studies we here not only focused on α diversity but also included β diversity in our analysis. While we here found between-stand diversity to have an even larger effect on productivity than within-stand diversity, a recent study focusing on perennial grasslands reported a greater importance of α compared to β diversity (Pasari et al. 2013). The same was recently reported for tropical forests, where the positive influence of diversity on productivity was found to decrease with increasing level of scale (Chisholm et al. 2013). However, both of these studies did not explicitly consider disturbances in their analyses, and might thus underestimate the role of β diversity in the context of responding to and recovering from disturbances (Mori et al. 2013; Silva Pedro et al. 2015). Also the choice of β diversity metric might influence results and limit comparability between studies. Yet we here found that β diversity based on Whittaker’s multiplicative approach (Jost 2007) and β diversity measured as the total variance of the community (Legendre and De Cáceres 2013) showed similar results, demonstrating the robustness of our findings. Nevertheless, when controlling for the diverging ranges of α and β diversity in our analysis the relative advantage of β diversity compared to α diversity was diminished, indicating that methodological considerations might indeed complicate a comparison across studies. Future analyses should thus lay an increased focus on landscape-level diversity and its influence on ecosystem functioning. Other factors contributing to β diversity, such as spatial heterogeneity in topography and biophysical conditions (e.g., climate, soil) across the landscape should also be considered for a comprehensive assessment of the effect of landscape-level heterogeneity on ecosystem functions and services (Seidl et al. 2012b; Turner et al. 2012).

Conclusion

Our study highlights that not only local (α) but also landscape-level diversity (β) affect forest productivity positively, and that successional dynamics strongly modulate these relationships in temperate forest landscapes. Disturbances enhanced diversity in our study system (even under elevated disturbance frequencies), a mechanism that counters losses in productivity e.g., through a disturbance-induced reduction in leaf area. This underlines the importance of considering disturbance, succession and scale more explicitly to deeper understand the links between diversity and forest productivity.

Our results are also of considerable relevance for ecosystem management as they document that disturbance effects are not limited to negative impacts on ecosystems and their productivity (Lindroth et al. 2009; Peters et al. 2013; Silva Pedro et al. 2015), but that a disturbance-induced increase in diversity can also foster productivity. An important take-home message for management in this regard is that we found positive disturbance responses to be strongly contingent on the species pool available on the landscape. In particular, adding a pioneer species to a species pool of intermediate or old-growth species strongly facilitated a diversity-related increase in productivity. This effect was found to be especially pronounced in early stages of forest succession, i.e., here simulated as structurally simple systems that are in many regards not unlike managed forests. These are important insights in particular for temperate forest ecosystems in Central Europe, where century-long management practice has favored a limited number of highly productive coniferous species (Spiecker et al. 2004). We conclude that, rather than homogenizing disturbed areas in striving for a swift recovery to a narrow set of target species, forest managers should incorporate the diversity created by disturbances into stand development and retain early-seral species on the landscape. Fostering response diversity and harnessing the positive effects of disturbance might be a way forward to dealing with a climate-mediated increase in future disturbance damage in ecosystem management.