Tree species richness enhances stand productivity while stand structure can have opposite effects, based on forest inventory data from Germany and the United States of America

Material

Methods

Statistical analysis

When applying our models, the full model versions always yielded the lowest AIC, and so, were chosen as the final models. To interpret the GAM results, two-dimensional heat maps were used and the effect of each variable was isolated while all other variables were set to their mean values. When testing each variable by varying its value from the minimum to the maximum, its isolated effects on the dependent variable were observed.

QI: How is forest productivity influenced by tree species richness and tree size heterogeneity?

Germany

Location

The effect of location covered by the interaction term for longitude and latitude showed mostly a strong positive effect of latitude on stand productivity. Our model showed that stand productivity increased from ~10 m³∙ha⁻¹∙yr.⁻¹ to ~13 m³∙ha⁻¹∙yr.⁻¹ along the range of 47.33° N up to 54.92° N (Fig. 1b), indicating that productivity was increasing toward the northern part of Germany (Fig. 2a).

Stand density and tree size

SDI clearly explains part of the variation in stand productivity. An increase in SDI up to 2000 stems∙ha⁻¹ (where most of the data was represented) made productivity rise from 7 to 17 m³∙ha⁻¹∙yr.⁻¹ (Fig. 1e). Tree size (dq) had only a small negative effect (Fig. 2c). For an increase in dq from 0 to 100 cm, the effect on stand productivity explains a variation of ~ 3 m³∙ha⁻¹∙yr.⁻¹ in productivity (Fig. 1f).

Species richness and structure

For up to two different species, stand productivity decreased with increasing tree species richness from about 14 to about 12 m³∙ha⁻¹∙yr.⁻¹, which means that inventory plots with two species on average had a ~2 m³∙ha⁻¹∙yr.⁻¹ lower stand productivity than did monocultures. For more than three tree species the trend was the opposite and stand productivity increased again up to ~ 16 m³∙ha⁻¹∙yr.⁻¹ for stands with eight tree species (Figs. 1g and 2d).

Since the mean number of tree species in the German plots was two, stands with a high number of species were represented only by a small sample size. The effect of structural heterogeneity was negative. With a mean CVd of ~0.32 and most of the data occurring around this value, the valid part of the model still describes a negative effect of structure on stand productivity by ~2 m³∙ha⁻¹∙yr.⁻¹ along the range of CVd from 0 to ~1.0, covering most of the data (Figs. 1h and 2d).

The least productive combination was a low number of tree species with a high tree size heterogeneity. Additional tree species could partly mitigate the negative effect of tree size heterogeneity on stand productivity.

USA

Location

Most of the productivity in our model was determined by location and climatic conditions, which together explained up to ~4 m³∙ha⁻¹∙yr.⁻¹ of the variation among the plots. From the western part (−124.7° E) to the most eastern part of the conterminous USA (−67° E), productivity increased from ~5 to more than 6 m³∙ha⁻¹∙yr.⁻¹ (Fig. 3a). Latitude explained a drop of more than 1.5 m³∙ha⁻¹∙yr.⁻¹ in productivity from the most southern part (25.07° N) to the most northern part (49.35° N) (Fig. 3b). Productivity was, therefore, highest in the southeastern part of the US (Fig. 4a).

Stand density and tree size

Tree size had a small but positive effect and explained about 0.2 m³∙ha⁻¹∙yr.⁻¹ of the variation in stand productivity (Fig. 3f). Stand density had a small positive influence on stand productivity up to an SDI of ~500. For an SDI > 500, the effect was contrary (Fig. 3e). Figure 4c shows the combination of both effects.

Species richness and structure

The number of species showed a small but positive effect on stand productivity for up to 10 different tree species. For more than 10 species the relationship between species richness and stand productivity was found to be negative (Fig. 3g). Tree size heterogeneity dq had a slightly positive influence on stand productivity (Fig. 3h). As most of the variation was already by location and climatic influence, the effects of tree species richness and tree size heterogeneity were small but still evident. The combination of both effects is shown in Fig. 4c.

QII: How is forest productivity influenced by precipitation and temperature?

Germany

Location

Neither longitude nor latitude had any large effect on tree size heterogeneity, meaning that stand structure was rather homogeneous from south to north. Only toward the most northern part of Germany did tree size heterogeneity show a slight increase (Figs. 5a, b and 6a).

Climate

Annual precipitation and mean annual temperature had small positive effects on tree size heterogeneity CVd. Increasing precipitation from ~600 to 1400 mm∙yr.⁻¹ showed an increase in CVd from ~0.35 to 0.4 (Fig. 5c). CVd was increasing from 0.26 to 0.3 along a range of a mean annual temperatures from 0 °C up to 10 °C (Fig. 5d). In Germany, the analyzed forest inventory plots were more heterogeneous in tree size at warm and wet sites (Fig. 6b).

Stand density and tree size

SDI only showed a positive effect on tree size heterogeneity up to an SDI of ~500 (Fig. 5e). With increasing tree size dq from 10 to 80 cm, tree size heterogeneity decreased from ~0.45 to ~0.2 (Fig. 5f), indicating that stands with larger trees on average were less heterogeneous in tree size. Forest stands with a combination of a high SDI and a lower dq showed the highest tree size heterogeneity (Fig. 6c).

Tree species richness

The number of species was clearly positively related to stand heterogeneity CVd, which increased from 0.3 up to 0.6 along a range of species richness of 2 to ~7 species per plot (Fig. 5g). For more than ~8 tree species, species richness had a negative effect on tree size heterogeneity. The graphical representation of species richness R as a single variable shows its effect on CVd on the y-axis (Fig. 6d).

USA

Location

Structural heterogeneity increased from the eastern part to the western parts of the USA with a coefficient of variation (CVd) of 0.4 to about 0.6 (Fig. 7a). The effect of location on a north-south gradient had a lower effect on tree size heterogeneity, showing the highest tree size heterogeneity between 35° N and 40° N (Fig. 7b). On sample plots that were more northerly, stand structure was less heterogeneous. The overall variation explained by location is shown in Fig. 8a.

Climate

The effect of climate was not very pronounced but a slightly lowering effect of annual precipitation on structure was found (Fig. 7c). Mean annual temperature did not show any clear effect on tree size heterogeneity CVd (Fig. 7d). The combination of precipitation and temperature highlights the strong role of precipitation as a driver of tree size heterogeneity (Fig. 8b). Thus, structural heterogeneity was highest at sites with low precipitation.

Stand density and tree size

Stand density and tree size heterogeneity CVd were positively correlated. CVd increased from ~0.30 to ~0.7 for an increase in SDI along a range from 0 up to 5000 (Figs. 7e and 8c). Tree size had a slightly negative effect on CVd (Figs. 7f and 8c).

Species richness

The number of tree species had a vital effect on tree size heterogeneity. An increase in tree species richness from 1 to 20 led to a more heterogeneous stand structure CVd, increasing from ~0.4 to ~0.6 (Fig. 7g). The single effect of species richness R on CVd is presented on the y-axis (Fig. 8d).

The results of using the GAMs are presented in Tables 3 and 4. They show the intercept a of the model function, its standard error, the significance of each model, and the R-square (adjusted). Based on AIC, the full versions of the models were selected.

		USA
	Term	Intercept a	Std. error	Sig.	R-sq. (adj)
QI/QII	f 1 (Lon × Lat)	6.22	0.00	***	0.90
	f 2 (Precip × Temp)			***
	f 3 (R × CVd)			***
	f 4 (SDI × dq)			***
QIII	f 1 (Lon × Lat)	0.44	0.00	***	0.37
	f 2 (Precip × Temp)			***
	f 3 (SDI × R)			***

Lon longitude, Lat latitude, Precip annual precipitation, Temp mean annual temperature, R species richness, CVd coefficient of variation of diameter, SDI stand density index, dq quadratic mean diameter (cm). Sig. Significance values: 0 ‘***’, 0.001 ‘**’, 0.01 ‘*’, 0.05

		Germany
	Term	Intercept a	Std. error	Sig.	R-sq. (adj)
QI/QII	f1 (Lon × Lat)	12.24	0.04	***	0.19
	f2 (Precip × Temp)			***
	f3 (R × CVd)			***
	f4 (SDI × dq)			***
QIII	f1 (Lon × Lat)	0.32	0.00	***	0.29
	f2 (Precip × Temp)			***
	f3 (SDI × R)			***

Lon longitude, Lat latitude, Precip annual precipitation, Temp mean annual temperature, R species richness, CVd coefficient of variation of diameter, SDI stand density index, dq quadratic mean diameter (cm). Sig. Significance values: 0 ‘***’, 0.001 ‘**’, 0.01 ‘*’, 0.05

Stand productivity

Tree size heterogeneity did not have a stronger positive effect on stand productivity than did tree species richness (QI), which was found to influence stand productivity, as well as tree size heterogeneity, in both the German and US inventory plots. In Germany, structure had a negative effect on stand productivity, whereas, in the USA, structurally more diverse stands were slightly more productive.

In the German inventory plots, we found the lowest stand productivity in the case of two tree species. Comparing monocultures to the two-species mixed stands showed lower productivity for the two-species plots, as explained by others (Binkley 1984; Chen and Klinka 2003), possibly due to the more efficient use of resources by the highly productive monocultures. For more than two tree species, a positive biodiversity–productivity relationship appeared. For the US data set, there was a similar trend seen of increasing productivity with increasing tree species richness. Despite the findings of Binkley (1984) and Chen and Klinka (2003), the US inventory plots having up to 10 different tree species showed an increase in productivity. The positive relationship of tree species richness with stand productivity found in US and German inventory plots with more than two tree species matches the positive biodiversity–productivity relationships described by Kelty (2006), Gamfeldt et al. (2013), Vilà et al. (2013), Pretzsch et al. (2015), Liang et al. (2016) and Pretzsch et al. (2017).

We wanted to test the interaction of tree species richness and structure in particular. Silva Pedro et al. (2017) found that species composition and stand structure are strongly connected, and that their combination could quite influence forest productivity. In the case of a lower productivity due to a lower crown cover in mixed-species stands, a more heterogeneous stand structure could mitigate the potential loss. In our case, as most of the variation in productivity among the sample plots was already explained by location and climate, for the US inventory plots, effects of species and structure were very small but still present. This finding matched those by Bohn and Huth (2017), who had discovered a positive correlation between structure and productivity. Potential benefits of a higher structural heterogeneity, which leads to overyielding can result from more efficient use of resources through multiple forest layers and a better exploitation of niches. However, contrary results were found for the German inventory plots. The negative effect of structure on stand productivity was strongest on stands with about two to four tree species. Mitigated by tree species richness, mono-specific stands and stands with more than four tree species experienced weaker negative effects of structure. Similar trends were also found by Bourdier et al. (2016), who show that tree size heterogeneity would also decrease productivity, depending on the shade-tolerance of the tree species. Also, Luu et al. (2013) and Soares et al. (2016) reported a negative effect of tree size heterogeneity on stand productivity.

Stand productivity can also be negatively or positively correlated with stand density (Uhl et al. 2015). Stand density and tree size were, therefore, considered in our model. In the German plots, productivity was positively correlated with stand density, whereas the effect of tree size was very small. In the US plots, the influence of stand density on productivity was less clear and tree size did not show any effect. A lower mean stand density and lower productivity in the US plots compared to a higher stand density and a higher stand productivity in the German plots is in line with findings of higher yields in mixed stands resulting from a higher stand density (Pretzsch and Biber 2016).

Explaining the opposite effects of structure on stand productivity in Germany and the USA, we hypothesize that the two countries are located along a gradient concerning latitude, annual precipitation, temperature, and also productivity, and structure. Possibly, the inventory plots from the two inventories are at different development stages with consequently different structure-productivity relationships. Tree size heterogeneity, here CVd, in the German inventory plots (0.32) was already lower than in the US plots (0.44), and stand productivity was higher in Germany (12.24) than in the USA (6.22). Precipitation and temperature were lower in Germany (842 mm, 8.3 °C) than in the USA (1056 mm, 11.6 °C). This would mean that Germany is located at the northern end of the gradient and adjacent to the USA. The lower number of tree species and temperatures in the German plots can lead to a lower structure while highly productive even-aged monoculture-type forest stands are still present with combined high productivity and low tree size heterogeneity. The forest stands in Germany are much longer and more intensively shaped by even-aged management (Paillet et al. 2010; Schall et al. 2017), while in the USA structural heterogeneity is still higher due to disturbances and climatic shifts (Oliver 1980; Dolanc et al. 2014; McIntyre et al. 2015).

Climate

Apart from the location which already explains a large part of the variation in stand productivity, climate played a major role. We found that a warm and dry climate can especially decrease stand productivity (QII) but only with regard to precipitation, which was a strong predictor of stand productivity, as the latter is restricted by lower annual precipitation. This trend has also been described by others (Toledo et al. 2011; Żywiec et al. 2017). We found that for both countries, there is an optimum amount of annual precipitation beyond which additional units of precipitation were rather counter-productive. In Germany this effect could come from large quantities of precipitation, especially in the mountain areas and along the coastline, with counter-productive effects due to a shorter vegetation period in the mountainous areas and strong winds along the coast (Friend and Woodward 1990; Pretzsch et al. 2015). In the USA, we also saw a similar pattern where the Pacific Coast was generally lower in forest productivity than was the Atlantic Coast, despite the Pacific’s greater annual precipitation. Regardless of the differences in biomes and other underlying silvicultural and environmental factors, our findings of an optimum beyond which additional annual precipitation could not lead to a higher stand productivity supported the saturation effect inherent in the biodiversity–productivity relationship (Liang et al. 2015). Mean annual temperature’s effect on stand productivity in Germany was opposite to those in the USA. Trees in the German inventory plots were benefiting from the warmer climate, whereas in the US plots, higher temperatures in combination with a low amount of precipitation were leading to lower growth rates. We speculate that the effects of temperature in the US could come from a less flexible situation of inventory plots, which are situated in regions where temperature cannot increase productivity anymore because trees, e.g., tropical trees, are already growing at their optimum temperature. Any additional temperature would be rather counter-productive (Way and Oren 2010). In Germany, trees are rather growing on sites below their temperature optimum, so a higher mean annual temperature consequently can lead to higher growth rates as compared to colder sites. Our speculation is supported by the acceleration of growth due to effects of the climate changes found in Europe (Pretzsch et al. 2014), as well as in boreal Canada (Wu et al. 2014), but not in the USA (Silva et al. 2010). Especially if higher temperatures occur in combination with higher amounts of precipitation, the effect on growth can be positive (Gustafson et al. 2017). Moreover, species traits, species composition, forest structure (Bohn and Huth 2017) and forest type (Vilà et al. 2013) determine how forest productivity is influenced by climate and could have shaped the relationships found in our study.

Stand structure

Finally, we also tested if water scarcity or low temperatures could enhance structural heterogeneity through the limitation of growth (QIII). Stand structure quantified by tree size heterogeneity was found to be highest in German plots with a high annual precipitation and high temperatures, and in US plots with low and intermediate amounts of annual precipitation.

Water limitation may foster the growth of small trees at the expense of their taller neighbors and reduce the size-asymmetry of competition. This phenomenon may be due to tall trees’ being more exposed to the sun in sites with low water availability, especially during dry years. The tall trees close their stomata earlier and cannot make longer use of their preferential access to light. In contrast, under warm and dry conditions, the small trees in contrast may be less affected by or may even benefit from the reduced water consumption of their taller neighbors. So, the growth partitioning between the trees in stands on water-limited sites may favor the smaller members of the population, keeping them in the play, thereby fostering the diameter variation and structural heterogeneity (Pretzsch et al. 2012).

In both the German and the US plots, with more species, more structural heterogeneity was found. This effect could potentially result from the different allometry and functions of tree species, so that niches could be filled with a certain species, thereby creating more stand structure. Also, stand density was positively correlated with structure. These trends are well described in the European and Anglo-American literature (Zeide 2001; Pretzsch 2005).

Considering that species richness fosters structural heterogeneity and structure, which, in turn can increase stand productivity even more, the combination of tree species richness and structure would be recommended while keeping in mind that other ecosystem services also benefit from species richness and structure, e.g., stability and the distribution of risk. Furthermore, a characterization of forest stands by species can still result in different outputs (all ecosystem goods and services) depending on regional peculiarities or the genetic variation of each species (Boyden et al. 2008). Higher productivity in mixed stands could be related to the species’ traits more than to tree diversity in general (Jacob et al. 2010). Forming groups of species according to their functional traits rather than their taxonomy could, therefore, be useful. Analyzing the effect of species richness on stand productivity, as done in this study, could then potentially yield much clearer results, as the effects may not be hidden by intra-specific variation in traits.

Methods

Applying GAM models to large data sets, as performed in our study, will automatically lead to high significance values, which mean that the interpretation of p-values should be completed by analyzing the single effects of each variable. The size of the effect of each independent variable on the dependent variable must still be tested to estimate if the effect is only a slight trend. The major problem in our analysis was the use of different methods to obtain productivity values for each plot in Germany and the US. Conducting large inventories such as the one in the USA is an expensive endeavor and not all sample plots can be measured regularly. If productivity on inventory plots is calculated only for the ones measured more often and interpolated to all the other inventory plots, very different plots can become assigned to the similar productivity value. The variation in productivity as a dependent variable may then not be large enough to be explained by variables other than location or climate. Considering that the effects of species richness and structure on productivity in our model can only be very small, we can still take them seriously and interpret their trends. The US inventory data can be expected to comprise a comparable high degree of inexplicable variation due to the method of estimating and interpolating productivity.

Including successional stages through stand age would have been useful as well but no reliable data was available as the stand ages given in the inventories were roughly estimated without considering the different ages of the different layers. Therefore, we used SDI and tree size to cover the potential effects of development stages. Assuming that a higher stand density results from a higher number of smaller trees that yield higher relative growth rates and a lower stand density can be explained by fewer larger trees with a lower relative growth (Caspersen et al. 2011), our model promotes the choice of SDI as a substitute for the lack of information on stand age. Analyzing the relationship of structure, species mixing and productivity along the developmental stages in terms of stand age could be a worthwhile study for the future.