Individual Tree Structure and Growth in Mixed Compared with Monospecific Stands

Pretzsch, Hans

doi:10.1007/978-3-662-54553-9_6

Hans Pretzsch⁴

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7 Citations

Abstract

This chapter focuses on the shape, growth, and productivity of individual trees growing in inter- versus intraspecific environments. The individual tree senses and responds to the prevailing environmental conditions. The properties of the individuals determine the forest stand dynamics as individuals of different species interact with each other. Therefore, the level of the individual tree is most suitable for understanding competition, competition reduction through complementarity, and facilitation, which can result in the differences between structure dynamics and productivity of mixed compared with monospecific stands. The chapter shows how species mixing can modify the size development, persistence, and productivity of individual trees in mixed stands compared with members of the same species in neighbouring monospecific stands. Many of the beneficial tree mixing reactions result from complementary crown and root shape, spatially or temporally complementary resource exploitation, redistribution of resources, or modification of growth allocation and allometry introduced in this chapter.

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Growth and Structure in Mixed-Species Stands Compared with Monocultures: Review and Perspectives

Effect of tree species mixing on the size structure, density, and yield of forest stands

Article 15 October 2015

Characterization of the structure, dynamics, and productivity of mixed-species stands: review and perspectives

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Size growth and persistence are key requirements for a tree to compete and maximise fitness under the selective pressure in a forest stand. This chapter shows how species mixing can modify the size development, persistence, and productivity of individual trees in mixed stands compared with members of the same species in neighbouring monospecific stands. Living in association, both in intra- and interspecific neighbourhoods, entails pros and cons in comparison to solitary growth. An individual tree may be facilitated physically, e.g. by neighbours as they protect against storm breakage (von Lüpke and Spellmann 1997, 1999), sun scorch of bark (Assmann 1970), or snow sliding (Kuoch 1972; Mayer and Ott 1991, pp. 194–197; Strobel 1995). However, the meaning of neighbourhood is ambivalent, as it also entails competition when there are insufficient resources for all (Connell 1990). The interplay between facilitation and competition determines intraspecific and particularly interspecific coexistence (Larocque et al. 2013).

Mixing effects can be studied at various levels of organisation, e.g. at organ, individual, stand, or landscape level. Given that the individual tree forms the basic unit in forest stand ecology, this chapter focusses on the shape, growth, and productivity of individual trees growing in inter- versus intraspecific environments. The individual tree senses and responds to the prevailing environmental conditions. The properties of the individuals determine the forest stand dynamics as individuals of different species interact with each other (Smith and Smith 2009, p. 13). Therefore, the level of the individual tree is most suitable for understanding competition, competition reduction through complementarity, and facilitation, which can result in the differences between structure dynamics and productivity of mixed compared with monospecific stands discussed in Chaps. 4 and 5.

Understanding of the interspecific interactions between tree species can be improved through generalisation of the hologenome theory (Zilber-Rosenberg and Rosenberg 2008). According to this theory, a holobiont in a strict sense is a host organism in interaction with all associated microorganisms. More generally, all regular organisms which closely interact with each other (e.g. trees in mixed-species stands) can be perceived as holobiont-like systems and may also be studied as entities rather than focussing on the individual organisms (Matyssek and Lüttge 2012).

Tree species mixing may change the environmental conditions and thereby the physiology, morphology, and stand structure. As a result, the tree and stand growth also undergo changes. Because of the strong interaction between structural patterns and processes, the structure and morphology may reflect the results of mixing effects which are much more difficult to measure than the underlying physiological processes. To quantify mixing effects in this chapter, we compare the individuals’ behaviour in terms of tree shape and growth in mixed versus monospecific stands. We use the trees’ structure and growth in a monospecific stand as a reference for quantifying tree behaviour in neighbouring mixed stands.

Reaction patterns of shape, allometry, growth, and productivity at the individual tree level as presented in this chapter may contribute to understanding mixing effects. Further insight into the underlying mechanisms require analyses of the change in supply, capture, or use efficiency of resources in poly- versus monocultures (Binkley et al. 2004; Richards et al. 2010) as introduced in Chap. 3. We will set the growth of individual trees in relation to their required growing area (equivalent to tree stand area) and, in this way, link the tree level with the stand level and size distribution level (Chaps. 4 and 5).

6.1 Principles of Individual Tree Ontogeny

To explain inter- and intraspecific interactions between trees such as competition, competition reduction, and facilitation as well as their net effect on the growth of individual trees in mixed and monospecific stands, plant biology mostly starts with the ontogeny of a solitarily growing tree. The schematic Fig. 6.1a shows the unimodal course of the stem volume increment, ivs, and the s-shaped curve of stem volume, abbreviated to vs. These curves represent the characteristic individual tree ontogeny and were originally derived theoretically from basic relationships between tree assimilation and respiration (von Bertalanffy 1951). However, many works (e.g. Ryan and Yoder 1997; Yoder et al. 1994) show that it is rather nutrient limitation, genetic changes in meristem tissue, and hydraulic limitations that are behind the characteristic unimodal course of the stem volume increment, ivs, and the s-shaped curve of stem volume (see Boxes 6.1 and 6.2).

Box 6.1 Characteristics of a Tree’s Crown Morphology, Crown Extension, and Growing Area

Description and analysis of tree structure, growth, and growth efficiency in this chapter are mainly based on the tree variables shown in Box Fig. 6.1-1. To compare tree morphology in mixed versus monospecific stands, the following ratios between tree organ sizes are frequently used:

h/d = the h–d ratio using h (m) and stem diameter at breast height (cm) addresses tree stability.
cd/d = the cd–d ratio with crown diameter (m) and stem diameter (cm) addresses the crown extension.
d _r/d _s = d _r–d _s ratio with diameter of the main root, d _r, and stem diameter at breast height, d _s, quantifies the root-stem relationship. When based on increment cores from stem and main roots, this relationship provides insight into the allocation principle between stem and main root (Fig. 6.18).
cpa/sa = this ratio between crown projection area, cpa, and tree stand area, sa, is a measure for the interlocking of neighbouring crowns.

Most relationships between tree organ sizes change non-isometrically with tree size, i.e. when organ size x increases, organ y does not enlarge linearly (y = a + α × x) but according to the allometry equation (y = a × x ^α) with α ≠ 1. This means that the above ratios between organs, e.g. h/d or cd/d, show an ontogenetic drift with increasing size (see Box 6.3).

Raw density of wood (RDW) of species in boreal and temporal forests ranges mainly between 350 and 650 kg m⁻³ (Pretzsch 2009, p 67). RDW can be used to transform stem volume, vs, to stem mass, ms (ms = vs × RDW).

Box 6.2 The Rules by Kleiber (1947) and Rubner (1931) for Explaining the Ontogeny and the Growth and Yield Curves of Individual Trees

According to these rules, the unimodal course of the net growth (Fig. 6.1a) results from the difference between the anabolistic term (A = a × v ^3/4) as minuend and the catabolistic term (R = b × v ¹) as subtrahend (NG = a × v ^3/4 − b × v ¹). The variable A represents the gross assimilation, R the respiration, and NG the net growth of the tree. For the anabolistic term, the rule by Kleiber (1947) assumes that A scales with 3/4 over plant mass or volume. According to Rubner’s rule (1931), respiration increases linearly with mass or volume (plant mass ∝ plant volume). These two underlying allometric relationships are shown together in Box Fig. 6.2-1a and reflect that the net growth (grey area between the curves) is low for small trees, high for medium-sized trees, and low again for giants. This in turn reveals that plant size is a conflicting trait. It entails both supremacy over smaller neighbours and also low growth due to high expense for respiration. Intra- and interspecific interactions can affect both A and R and thus modify the trees’ development. Box Figure 6.2-1b shows the characteristic unimodal curve of the net growth, ivs, over tree volume, vs, which results from that in Box Fig. 6.2-1a. Starting with the unimodal ivs–vs relationship in Box Fig. 6.2-1b and assuming an initial stem volume for plant age 1 (e.g. v ₁ = 0.001 m³), the course of volume increment, ivs, and the achieved volume, vs, can be derived (Box Fig. 6.2-1c). The development of ivs over age is the unimodal growth curve; the sigmoid development of vs over age results from integration of ivs.

While the shown unimodal course of the stem volume increment, ivs, and the s-shaped curve of stem volume, abbreviated to vs, are a good basis and reference for analysing any external effects such as intra- and interspecific competition and facilitation on tree growth, their causal explanation has been improved. Ryan and Waring (1992) showed that respiration of older and taller trees generally declines as growth declines (i.e. R < < b × v ¹) because more than half of the respiration is growth respiration. Even maintenance respiration of big trees typically goes down (Yoder et al. 1994). Many works (e.g. Ryan and Yoder 1997) show that it is rather nutrient limitation, genetic changes in meristem tissue, and hydraulic limitations that are behind the characteristic unimodal course of the stem volume increment, ivs, and the s-shaped curve of stem volume. Although it is temptingly simple, the theoretical explanation of individual tree ontogeny by von Bertalanffy (1951) based on the rules by Kleiber (1947) and Rubner (1931) is increasingly called into question by empirical findings.

Figure 6.1a represents the growth through ‘the plant’s eye view’, i.e. the development of growth and size. The production ecology represented by the ‘forester’s eye view’ asks for the growth and volume per growing area, i.e. for the productivity. To transition from tree growth to tree growth per growing area, we apply the allometric relationship between stem volume and tree growing area (sa ∝ vs^1/2) which is shown in Fig. 6.1b (West et al. 2009). By dividing the increment, ivs, and volume, vs, by the required growing area, we get the growth per unit area (productivity ivs/sa) and standing volume per unit area (standing stock vs/sa) of the tree (Fig. 6.1c).

Note that the transition from tree growth to tree productivity is based on growing area, sa, and not crown projection area, cpa. Unless cpa = sa, crown area productivity (ivs/cpa) differs from growing area productivity (ivs/sa) (Gspaltl et al. 2012). Particularly in mixed stands, cpa is often larger than sa as illustrated in Fig. 6.1b. In this case, ivs/cpa << ivs/sa, i.e. upscaling from tree to area level based on crown projection area underestimates tree productivity. The transition from tree growth to tree growth per area means that the time point of culmination and inflexion shifts towards younger tree ages as the required stand area of a tree increases with size (compare broken vertical lines in Fig. 6.1c and a).

The depicted unimodal and s-shaped development courses of a solitary tree in terms of growth per plant and growth per unit area (Fig. 6.1a and c) form the reference for the subsequent introduction to the effects of competition and facilitation.

6.2 Interaction Between Trees in Inter- Versus Intraspecific Environments

Suppose that of three equally sized trees established on similar sites, one tree grows solitarily, one in medium, and the third in maximum density with neighbours of the same species (Fig. 6.2a, trees 1–3). When we choose the solitary tree (tree 1) as a reference and set its growth rate to 1.0, what will the growth rate of the trees growing in medium and high stand density be and what does this depend on? On the one hand, the individual growing area becomes smaller from trees 1 to 3 so that the competition for resources (water, light, nutrients) increases. Helms (1998, p 34) defined competition as ‘… the extent to which each organism maximizes fitness by both appropriating contested resources from a pool not sufficient for all, and adapting to the environment altered by all participants…’. However, living in association with neighbours may also have advantages over solitary growth. For example, neighbours may protect against windthrow (Knoke and Hahn 2007; Griess and Knoke 2011), improve the soil conditions (Augusto et al. 2002; Heinsdorf 1999), or prevent nearest neighbours from sun scorch of bark or drought (Assmann 1970; Pretzsch et al. 2012b). The latter abiotic or biotic improvement of the neighbours’ living conditions is called facilitation (Vandermeer 1992). Vandermeer (1992, p. 9) defined facilitation as ‘… the process in which two individual plants or two populations of plants interact in such a way that at least one exerts a positive effect on the other. Double facilitation is equivalent to mutualism’. In Fig. 6.2a, the trees’ growth rates (indicated by the white envelopes of trees 1–3) when growing in solitary conditions and in medium and high density reflect the net effect of competition and facilitation on tree growth. In relation to the growth of the solitary tree 1, the interaction between competition and facilitation results in a net facilitation under medium density (Fig. 6.2a, envelope tree 2 > envelope tree 1) and a net competition effect (Fig. 6.2a, envelope tree 3 < envelope tree 1) in the case of high density.

Analysing, understanding, modelling, and prognosticating monocultures often entail a thorough consideration of the effect of competition between neighbouring trees but mostly ignores facilitation. A plant may be facilitated by its neighbour through improvement of environmental factors (non-resource) or resource supply or a combination of both. Examples for improvement of environmental factors are slowing down the wind speed and avoidance of storm breakage, shading and avoidance of sunburn, providing a barrier against spread of insects, suppression of forest floor vegetation and competing weeds, and protection against snowslides or browsing. This kind of facilitation does not entail direct costs in terms of resources for the benefactor. In contrast, when facilitation is based on an improved resource supply, the benefactor may lose resources while the beneficiary gains.

Competition and facilitation act simultaneously. It is difficult to separate them. In field experiments in monospecific stands, the net effect of the interaction between facilitation and competition on tree structure and growth rather than their particular effects is accessible through measurement. To simplify matters, the interplay between competition and facilitation is first illustrated for monospecific stand conditions. In Fig. 6.3 we set the growth in solitary conditions as the reference (1.0-line) and show three basic patterns of how facilitation and competition can modify this solitary growth. Remember that in terms of absolute growth, a solitary tree follows the trajectories shown in Fig. 6.1 and that we ask here how neighbourhood might modify this generic trajectory.

Figure 6.3a assumes that competition only increases from low to high stand densities and that facilitation also only increases with density. Given that in this theoretical case, the balance between the negative effect of competition and the positive effect of facilitation on growth is always positive, we consider net facilitation (facilitation only minus competition only) over the whole range of stand densities. Figure 6.3b represents the opposite case where competition only always has the upper hand and net competition prevails over the whole range of stand densities. These two reaction patterns with net facilitation or rather net competition over the whole range of densities tend to be exceptions. Figure 6.3c represents the most frequently observed reaction pattern, where net facilitation dominates under low densities and net competition is predominant in dense stands. In sparsely stocked stands, competition is still low enough to be compensated or even overcompensated by facilitation. Such low density conditions, where facilitation may have the upper hand, are frequently observed in grassland ecosystems which are too poor for the development of closed forests (Callaway and Walker 1997; Canham et al. 1994, 2004). But they are less relevant in forest ecosystems (Forrester 2013). As stand density increases, growth mostly declines, can hardly be balanced by facilitation, and causes mostly net competition. However, this consideration highlights that although not easy to detect and to separate from competition, facilitation may also play a role in forest stands with high stand density. The facilitative effect of medium density compared with high density or solitary growth can be revealed by Nelder trials (Nelder 1962) where the tree growth can only be at optimum between the extremes (Uhl et al. 2015).

The combined effect of competition and facilitation becomes even more complex in mixed stands where trees differ in terms of traits and niches. Suppose the above trees in solitary and medium- and high-density constellations grow in mixed as opposed to monospecific stands (Fig. 6.2b, trees 4–6). In this example, 50% of the neighbours belong to a second species, i.e. competition and facilitation become interspecific and modified compared with monospecific stand conditions.

Reduced competition and an even stronger facilitation caused by species mixing might result in an even more obvious growth maximum under medium stand density (tree 5, envelope tree 5 >> envelope tree 4) compared with growth rates under solitary conditions or growth rates under maximum density.

Figure 6.4a indicates this shift in the growth-density relationship due to a reduction in competition (e.g. by spatial or temporal niche complementarity) and an increase in facilitation (e.g. tapping nutrients in deep soil layers which are favourable for species 1) through admixture of trees of species 2. Such a reaction pattern can cause a widening of the density range with net facilitation (horizontal arrow). In other words, the range where net competition has the upper hand narrows. For mixed-species stands as in monospecific stands, a net competition which is normal for trees growing in medium or high stand density does not exclude the effect of facilitation. In both cases, competition merely has the upper hand over facilitation. The relationship between the net tree growth in mixture and in monoculture (vertical arrows in Fig. 6.4a) reflects the mixing effect in terms of tree growth.

Facilitation effects are widely held to be strong under harsh environmental conditions and weaker under favourable conditions (Brooker et al. 2008; Callaway and Walker 1997). Accordingly, the density range with net facilitation may increase as site quality decreases (see Fig. 6.4b curves referred to as +, ±, −). Note that it is also possible for the net curve to remain the same although its components change in the case that the positive and negative changes in competition and facilitation cancel each other out.

While in plant ecology the net effect of competition and facilitation is mostly related to solitary plant growth (Callaway and Walker 1997; Belsky and Canham 1994; Forrester 2013), in closed forests we are interested in the mixing effects under mean or high stand density. In field experiments in monospecific stands, the net effect of the interaction between facilitation and competition rather than their specific effects are accessible through measurement. To complicate the situation, measurements of solitary plant or tree growth which are required as a reference are scarcely available, except from very rare experiments like the outer Nelder circles (Nelder 1962; Uhl et al. 2015) or spacing and thinning experiments, which include plots with open-growing trees. So, in most cases only growth of medium to high density plants is measured, and it is difficult to quantify whether net facilitation or competition has the upper hand because of the lack of reference measurements. The same restriction applies for quantification of net facilitation or net competition in mixed stands in relation to solitary plant growth (according to the definition of facilitation and competition). However, what can instead be easily detected in field experiments is the change in the net curve from monospecific to mixed stands (see upwards shift of the net curves in the centre of Fig. 6.4a and b marked with vertical arrows).

The relationship between the tree growth in mixed versus monospecific stands indicates the net mixing effect in closed stands. Of special interest is to what extent mixing increases or reduces net competition of trees in closed stands rather than whether the growth-density relationship shows net facilitation or net competition of a solitary tree. The former would mean an increase or decrease in productivity of the species in mixed versus monospecific stands. This practically relevant effect is represented by the relationship between mixed and monospecific stand performance in the right branch or even at the right end of the net growth-density relationship in Fig. 6.4.

6.3 Basic Feedback Loop Between Growth, Structure, and Local Environment in Forest Stands

The tree–tree interaction illustrated by an example in the previous section can be conceptualised by the basic feedback loop between functioning, structure, environment, and functioning in forest stands (Fig. 6.5). In order to explain the emergence of intra- and interspecific interactions between neighbouring trees, a distinction between their functioning (e.g. germination, growth, defence, flowering, fruiting, senescence), their structure formation (e.g. body size, crown and root extension, crown space filling with foliage), and environment (resource supply, e.g. water, nutrient, or CO₂ supply) and environmental factors (e.g. temperature, salinity, browsing) is helpful.

The conceptual model in Fig. 6.5 clarifies essential plant–plant interactions in monospecific and mixed-species communities. Trees interact with their environment in two ways, via structure and functioning (Hari 1985). The feedback between functioning and environment (FE loop) can be very rapid and temporary, e.g. defence substances are exuded quickly after or nearly simultaneously to the injury or pathogen attack and are reduced after stress release (within-stand environment versus external environmental drivers). Reduction of atmospheric CO₂ concentration or soil water supply by roots and crowns of fast-reacting neighbours can immediately reduce photosynthesis or growth of slower-reacting trees.

The feedback between functioning, structure, and environment (FSE loop), in contrast, is slow and accumulative. The functioning changes the structure (e.g. tree size and structure) and, via tree and stand structures, the trees’ environment. The crown structure, for instance, determines where the water and mineral nutrients from the crown periphery drip to and to what extent neighbours are shaded. The pattern of water drip and shading determines where the roots and crowns of neighbours grow and where they forage. This in turn determines their morphological structure. Trees develop and maintain their root, stem, and crown structure for decades and affect and adapt to their surroundings rather permanently.

The feedback between environment, growth, and structure may be relatively clear in monospecific stands where the species apply similar tricks and traits when appropriating contested resources, adapting to the environment, and modifying the stand structure. In mixed stands with two species as shown in Fig. 6.5, or with even more species, interactions and their effects on growth, structure, and environment may be more varied. Mixed-species modify their environment to their own benefit, e.g. by overtopping the neighbouring crowns or penetrating neighbouring roots in order to improve access to contested resources and acclimation to the environment altered by their neighbours. The principle feedback remains the same when neighbours belong to different species; however, their tricks and traits to modify their environment may be different, so that a broader range of reaction patterns, structures, and changes to the environment may occur.

The subsequent analyses of tree structure and tree growth in mixed versus monospecific stands address the two key elements of the feedback loop. Long-term experiments provide retrospective information on growth and structure but rarely time series on environmental variables such as light profile, nutrient supply, or water uptake of trees in mixed versus monospecific stands. Therefore, the effect of mixing on the local environment is less known and understood than the effect on structure and growth. However, future approaches will close this knowledge gap to enhance understanding of the feedback and underlying mechanism as a whole (Binkley et al. 2004; Pretzsch et al. 2015).

6.4 Growth and Yield at the Tree Level

Any changes to the local environmental conditions in mixed stands compared with monospecific stands primarily determine tree functioning in terms of growth (Fig. 6.5). This section will deal with these growth responses to mixing. Reduction or increase of the growth rate due to mixing can modify the tree and stand structure. In addition, the local environment may considerably modify the growth allocation in terms of tree morphology and thereby the tree and stand structure. Such structural changes which have a feedback effect on the local environment will be the subject of Sect. 6.5.

6.4.1 Dominant Rather Than Open-Grown Trees as Reference

Grassland plant ecology mostly uses solitarily growing plants as a reference for detecting facilitation or competition effects (Canham et al. 1994, 2004; Forrester 2014). When association with neighbours increases plant growth above the level of solitary plants, this indicates facilitation. When the opposite occurs, this serves as evidence of competition. Using open-grown trees as a reference for mixing effects such as facilitation or competition reduction is barely feasible given that these are rare in woodlands and, when situated in distant open land, are mostly incomparable in terms of site characteristics.

In Fig. 6.6 we therefore use dominant trees (d) in monocultures as a reference instead of open-grown trees (o). The former have lower growth rates than open-grown trees, but long-term experiments in monocultures provide a sound database for predicting the potential growth of dominant trees in forest stands in dependence on the site conditions. In the following, we use the unimodal diameter growth-tree diameter curve expected for dominant trees in monocultures as a reference for revealing the competition and species admixture effect. For derivation of the species-specific unimodal potential diameter growth-diameter relationships, see Pretzsch and Biber (2010). Following the approach from Sect. 6.2, we use this potential curve (the curve for dominant trees in monospecific stands) as the 1.0-line to show any mixing effects. Of main interest is how stand density and mixing proportion lead growth away from this baseline.

6.4.2 Evidence of Facilitation and Competition Effects at the Tree Level

Figure 6.7 shows exemplarily for even-aged mixtures of Norway spruce/European beech, European beech/sessile oak, and Scots pine/Norway spruce how mixing can modify the individual tree diameter growth under ceteris paribus conditions, i.e. when all effects (tree size, stand density, or site conditions) except for species composition are statistically eliminated. The analysis is based on long-term mixing experimental plots in Bavaria (Pretzsch 2009). Established in the 1930s, they mostly include reference plots in monospecific stands, provide individual tree data (tree position, tree size, growth rate) of several thousand trees in mixed and neighbouring monospecific stands, and thus provide information about mixing effects on tree growth.

The underlying model for the reaction patterns shown in Fig. 6.7 considers that growth of trees in mixed and monospecific stands may simply differ because of different size. Given space restrictions it is introduced here only briefly: the size effect is taken into consideration by the unimodal relationship between growth and size in monospecific stands (Fig. 6.6). This unimodal curve expected for dominant trees in monospecific stands is used as a reference to reveal the effects of species mixing and local stand density. Of main interest is how mixing proportion and stand density lead growth away from the baseline (1.0-line). Competition was quantified in the model using the local stand density index, i.e. the number of trees, n_i, within a defined radius around each tree scaled up to a hectare (N _i = n _i/(r _i ² × π)) and converted to the SDI_i = N _i × (25/d _q)^−1.605 according to Reineke (1933). This total SDI was split into two components, the part containing the species equal to the species 1 (= species of the centre tree) and the rest. The mixing portion was therefore the ratio between the SDI portion of trees differing from the species of the centre tree and the total SDI. So a mixing portion of mix = 0 signifies a monoculture composed of species equal to the centre tree, whereas mix = 0.25 indicates that within the circle of radius r around the centre tree, 25% of trees are unequal to species 1. We considered two-species stands, so that mix = 0.25 or 0.50 means an admixture of 25 or 50%, respectively, of trees of species 2 in the vicinity of species 1. To show the tree reaction patterns at the tree level, we applied a model which considers the size effect on growth (id–d relationship) and the stand density effect (id-SDI relationship) so that the effect of inter- versus intraspecific environments on growth under ceteris paribus conditions can be eliminated. The model was fitted with individual tree data from N. spruce (n = 10,160), E. beech (n = 13,861), pine (n = 2052), and oak (n = 4960) growing in monospecific and mixed stands.

In all tree associations shown in Fig. 6.7, stand density reduces tree growth; the reduction is very strong in the case of beech and rather small in the cases of oak and pine. Even more variable is the mixing reaction between the species combinations investigated. In mixture of Norway spruce and European beech (Fig. 6.7a, b), both species show a reduction in competition and increase in growth compared with the monospecific stand (black solid line). Norway spruce benefits moderately from beeches in the neighbourhood (Fig. 6.7a), while European beech benefits strongly from Norway spruce (Fig. 6.7b). In the mixture with sessile oak, European beech again benefits considerably (Fig. 6.7c), while tree growth of oak is hardly affected (not shown). Scots pine is the beneficiary in the mixture with Norway spruce (Fig. 6.7d), and the benefit gained by Scots pine is partly at the expense of Norway spruce (not shown). Of the species considered, European beech experiences the strongest growth reduction through increased stand density index (SDI) but also the greatest benefit through admixture of other species like Norway spruce and sessile oak. The results suggest that mixing reactions vary depending on both the particular species investigated and the species which is added in its vicinity.

Important is the finding that the positive mixing effects in terms of growth are modified by stand density. The mixing effects are present to various extents all along the density range. However, they can be at maximum in sparsely stocked stands and decrease with increasing stand density (from left to right in Fig. 6.7). Under low density, facilitation and competition can raise the growth above the potential for dominant trees in monospecific stands (1.0-line), i.e. the net effect of mixing can be positive. Of course, at the latest when density gets very close to zero, there is no longer any facilitation or competition caused by trees. In dense stands, the increase from monoculture to 25% and 50% is still relevant, but the positive mixing effect cannot overcompensate the negative effects of density on tree growth, so the combined effect of mixing and density on tree growth is negative.

6.4.3 Basic Growth Reaction Patterns in Intra- Versus Interspecific Neighbourhoods

The last section showed that—depending on the mixing portion and the degree of stand density—living in association can increase or decrease the growth rate. This means that the unimodal course of individual tree growth is modulated depending on the prevailing local environmental neighbourhood conditions of the tree. Figure 6.8 is a schematic representation showing that facilitation and competition in inter- and intraspecific neighbourhoods can modify the volume growth in manifold ways. In contrast to an open-grown tree (o), dominant trees (d) in forest stands grow permanently under net competition. For the dominant tree (d) in Fig. 6.8a we assume a constant reduction in the solitary tree growth by 35% due to a sequestration of resources by neighbours. The trajectories of dominant trees (d) are more suitable as a reference for indicating mixing effects than are open-grown trees (o) (see Sect. 6.4.1). However, in Fig. 6.8b–e we include both open-grown and dominant trees as references.

Figure 6.8b shows how permanent facilitation, e.g. through wide spacing, can increase the growth of an individual tree (bold line) permanently above that of the solitarily open-grown tree (o). In this case, the balance between the respective positive and negative effects on the growth of competing and facilitating neighbours is positive. Trees growing in group structure in the alpine zone compete for light, but their neighbours also protect them against snow and wind so that they frequently benefit from being associated and can grow more than solitary trees. Forest management makes use of such a permanent facilitation by planting trees in groups or clusters known as ‘Rotten’ in the alpine zone (Strobel 1995) or ‘Nester’ in the lowlands (Saha et al. 2012).

The pattern in Fig. 6.8c (bold line) occurs frequently when a dominant tree benefits from neighbours of a different species through competition reduction (e.g. the effect of a rather translucent species) or facilitation (e.g. the effect of an atmospheric nitrogen fixing species or hydraulic water redistribution). In this case, the growth of a dominant tree might be accelerated permanently, and its superiority may extend over the whole tree age.

The net effect of competition and facilitation may vary over time. Figure 6.8d (bold line) shows a frequently observed acceleration in growth through facilitation in the early state, followed by a reduction in the advanced state of plant development. So, tree growth exceeds the reference (d) in the early phase and falls behind in the late development phase. For example, in mixture with beech, larch growth can be accelerated in the juvenile state through competition reduction, whereas it can be slowed down by European beech in the mature phase due to the increasing height, crown extension, and overshading effects. This means an earlier culmination of volume growth due to the rather solitary conditions of an early-successional species when combined with a late-successional species.

Figure 6.8e (bold line) shows the opposite case. Neighbouring trees might reduce the growth level compared with dominant trees and delay the time of culmination. Suppression of Norway spruce by Scots pine is a common example of this growth response pattern in species mixing (Wiedemann 1951; Christmann 1939).

6.5 Crown Size and Morphology in Mixed Compared with Monospecific Stands

6.5.1 Interspecific Variation in Crown Shape and Size

Tree species can differ considerably in crown shape and size (Fig. 6.9). The allometric equation in logarithmic (ln(y) = a + α × ln(x)) or untransformed version (y = e ^a × x ^α) can be used to compare different species regarding their crown size and scaling of the crown to tree size (Niklas 2004). Factor a represents a multiplicative effect of species on the crown expansion. Species-specific differences of exponent α signify an exponential difference in the dynamic of the crown expansion with increasing size (Box 6.3).

To show the interspecific variation in tree growing area, we used the dataset compiled by Pretzsch and Dieler (2012) which includes 126 yield tables of 52 species, of which 30 are of angiosperm and 22 of gymnosperm taxonomy. Species included the genera Abies, Acer, Alnus, Betula, Carpinus, Castanea, Cunninghamia, Eucalyptus, Fagus, Fraxinus, Juglans, Larix, Nothofagus, Picea, Pinus, Populus, Prunus, Pseudotsuga, Quercus, Robinia, Shorea, Thuja, and Tilia. From these yield tables, we derived among others the mean tree diameter, \( \overline{d} \), and tree stand area, \( \overline{sa} \). The dataset includes only yield tables with self-thinning conditions or light and moderate thinning regimes where crown cross-section area, \( \overline{cpa} \), is scaled proportionally to tree stand area, \( \overline{sa} \), (\( \overline{cpa}\cong \overline{sa} \)). Note that light and moderate thinning permanently maintain a stand’s canopy in a structure in which the tree crowns touch each other but barely overlap (Verein Deutscher Forstlicher Versuchsanstalten 1873, 1902).

Figure 6.10a shows the considerable variation in the allometry between stand area and tree diameter; the intercepts amount to a = − 1.96, − 3.57, 2.47 (mean, min, max) and the slopes to α = 1.47, 0.14, 2.33 (mean, min, max). According to Fig. 6.10, angiosperms (ln(sa) = − 1.33 + 1.36 × ln(d)) need on average more growing area than gymnosperms (ln(sa) = − 2.03 + 1.52 × ln(d)). Angiosperms with a tree diameter of d = 25 cm, for example, occupy on average sa = 19.51 m², while gymnosperms occupy just sa = 16.90 m², i.e. significantly (p < 0.05) less tree stand area. The fact that species can differ in the intercept of their allometric crown relationship is represented, e.g. in yield tables, by species-specific tree numbers per ha at a given stand age (Assmann and Franz 1965) and by species-specific levels of the self-thinning lines (Pretzsch 2006).

The species-specific growing space requirement is relevant for calculation of the mixing proportions, stand density, and quantification of mixing effects on growth. If the species-specific growing space requirements are not considered and the calculation of the mixing proportions is simply based on mean tree stand area or tree numbers, this can result in flawed diagnoses of overyielding at the stand level and especially at the species level (see Chap. 4, Box 4).

Note that in this section the relationships between crown width and stem diameter are represented by the allometric relationship between crown projection area, cpa, and stem diameter at breast height, d, in logarithmic (ln(cpa) = a + α × ln(d)) or untransformed (cpa = e ^a × d ^α) version. When crown diameter, cd, or crown radius, cr, is required, they can be calculated as follows: \( cd=2\times \sqrt{cpa/\uppi} \) and \( cr=\sqrt{cpa/\uppi} \), respectively.

6.5.2 Intraspecific Variation in Crown Size

The crown size and shape of a tree are strongly determined by the local environment in the stand that has prevailed in the past and is now present. While maximum crown extension is achieved under solitary growing conditions, crown width decreases from open-grown (o) to dominant (d) and suppressed trees (s) (Fig. 6.11a). Stand density and competition can considerably modify the crown allometry, e.g. the cd–d relationship (Fig. 6.11b). The extent to which a tree may vary in crown extension in different environments is a crucial requirement for its success in coping with crowding.

In the following, we use 2346 crown projection area measurements of beech crowns in monospecific stands with spacing and thinning ranging from solitary growing conditions to moderate thinning and self-thinning, to illustrate the intraspecific variation (Fig. 6.12) (see Pretzsch 2014). The stand age ranges from 57 to 207 years; the surveys come from the experiments Arnstein 638, Gerolzhofen 627, Fabrikschleichach 15, Hain 27, Starnberg 91, Waldbrunn 105/106, and Zwiesel 111 in Bavaria in the years 1980–2004. Regressions for the upper 95% quantile (cpa = 3.03 × d ^0.92), the group of moderately and heavily thinned stands (cpa = 1.05 × d ^1.01) and the slightly and unthinned plots (cpa = 0.21 × d ^1.36) describe the broad variation (Fig. 6.12, upper, middle, and lower regression line). According to these allometric equations, a beech with 25 cm stem diameter occupies 58 m² when growing without lateral restriction, 27 m² under medium stand density, and 16 m² when growing in close to self-thinning conditions. This plasticity equips beech with high competitive strength in intra- and interspecific environments.

In terms of a species’ acclimation to intra- and interspecific competition, the maximum and minimum of its crown extension are of special interest as these indicate the range of plasticity. Figure 6.13a shows exemplarily for maple the upper (95%) and lower (5%) quantile of the cpa–d allometry in addition to the mean relationship. The ranking of species in terms of their 95% quantile is different. Species such as lime tree and silver birch lose when ranked in terms of their 95% quantile, whereas rather plastic species such as beech and silver fir win in this ranking. This emphasises that deriving crown behaviour for solitary conditions from average behaviour in closed stands, especially from monocultures, is questionable. For example, beech, elm, maple, and silver fir profit considerably in crown expansion when released from competition in monospecific or mixed stands.

Figure 6.14 illustrates that crown plasticity can differ considerably between tree species. The data comes from crown measurements on long-term experimental plots in Germany and covers a broad range of tree ages and densities, in monospecific and mixed stands (Pretzsch et al. 2015; Pretzsch 2014). Based on the 95% and 5% quantile of the cpa–d allometry (Fig. 6.14, upper and lower lines), the following relative measure, CPL, for tree crown plasticity can be derived. Based on the lower quantile line (\( {cpa}_{5\%}={a}_{5\%}\times {25}^{\alpha_{5\%}} \)) and the upper one (\( {cpa}_{95\%}={a}_{95\%}\times {25}^{\alpha_{95\%}} \)), and using a reference stem diameter of 25 cm (where stand density in monolayered stands is rather high or even at maximum), CPL is formulated as follows: \( CPL={cpa}_{95\%,25}/{cpa}_{5\%,25}=\left({a}_{95\%}/{a}_{5\%}\right)\times {25}^{\alpha_{95\%}-{\alpha}_{5\%}} \). For a tree with a reference diameter of 25 cm, CPL indicates how wide a crown can range in solitary conditions in relation to maximum restriction. By setting the 95% in relation to the 5% width, any species-specific differences in shape and form (e.g. that beech crowns are a priori wider than spruces) are eliminated. CPL only indicates the relative potential for expansion which is of particular importance for competing in mixture.

Analyses of CPL values for various tree species in Europe revealed a maximum value for European beech of CPL = 5.1, i.e. upper crown area is more than fivefold compared to its lower crown area under strong competition. With respect to CPL, the species represented in Fig. 6.14 are ranked as follows: beech (CPL = 5.1) > silver fir (4.7) > oak (4.5) > spruce (4.2) > maple (4.0) > pine (3.7). Out of the set of 14 species represented in Fig. 6.13b and c, beech (5.1) has the highest value, whereas alder (2.8) and birch (2.6) have the lowest.

6.5.3 Modification of Tree Allometry in Interspecific Local Environments

6.5.3.1 Shift in Crown Allometry in Interspecific Compared with Intraspecific Environments

Species mixing can considerably reduce a tree’s competition and increase its lateral crown expansion even when the stand density in mixture equals that in monoculture (Dieler and Pretzsch 2013). Of special relevance for stand dynamics, growing area efficiency and stand productivity are the behaviours of the lateral and vertical crown extension in mixed versus monospecific stands. This determinates both a tree’s growth and its space occupation and competition pressure on its neighbours.

We use data from Bavarian long-term experiments in monospecific and mixed stands of Norway spruce and European beech (Pretzsch and Schütze 2009) to scrutinise any shift in morphology caused by intra- versus interspecific competition. Figure 6.15 shows that the lateral and vertical crown extension of (a) Norway spruce and (b) European beech is higher in mixed than in monospecific stands.

Scaling between cpa and d is mostly considerably steeper as predicted by West et al. (2009) for the allometrically ideal plant (α _cpa, d = 4/3 in cpa ∝ d ^4/3). It is shallower in mixed than in monospecific stands but lies at a higher level in mixture (Fig. 6.15a). With increasing size, the collectives become more similar in this regard, i.e. in young and middle-aged stands, the species profit from interspecific competition but in mature stands, where crowns are less restricted, crown extensions become similar. According to allometric theory (Enquist et al. 2009; West et al. 2009), scaling between hcb and d should be hcb ∝ d ^2/3. That applies to neither of the species investigated here; the exponents are mostly lower. The intercepts of trees in mixed stands differ considerably from those in monospecific stands; crowns are significantly longer in mixed compared with monospecific stands. The h–d allometry, in contrast, is only slightly modified by species mixing, and the observed scaling is close to h ∝ d ^2/3 as predicted by the allometric theory. Stem taper may be different in mixed versus monospecific stands; however, the h–d relationships are similar. Note that by comparing the species’ behaviour based on their scaling size, differences are eliminated. This contrasts with less indicative and questionable comparisons based on ratios (see Box 6.3).

Box 6.3 Allometric Relationship Between Tree Dimensions, Ratios, and Ontogenetic Drift

As an example for size relationships between tree organs, Box Fig. 6.3-1 shows the allometric relationship between tree diameter, d in (cm), and crown diameter, cd in (m). It is linear at the ln–ln scale (Box Fig. 6.3-1a) and degressive with α _cd, d < 1.0 at the logarithmic scale (Box Fig. 6.3-1b).

The allometric theory assumes cd ∝ d ^2/3 (Enquist et al. 1998; West et al. 2009); however, our empirical evaluation based on crown measurement of n = 3974 Norway spruces yielded ln(cd) = − 1.24(±0, 018) + 0.75(±0.006) × ln(d), i.e. cd = 0.289 × d ^3/4 with α _cd, d = 0.75. The OLR regression was based on the ln-transformed values, according to Niklas (1994, p 331) RMA slope is α _RMA = α _OLS/r _y, x with r _y, x = r _cd, d = 0.95 as correlation coefficient between cd and d. In this case, α _RMA = 0.75/0.95=0.79 deviated even more from the slope for the allometrically ideal plant predicted by allometric theory (α _RMA = 2/3 = 0.66).

From cd = 0.289 × d ^3/4, it follows that cd/d ∝ d ^−1/4, i.e. the ratio decreases with tree size. Assmann (1970, p 112) used this ratio to compare crown morphology within and between different species. The non-isometric cd–d relationship shows that the ratio changes simply with size due to the ontogenetic drift of the tree size proportions. That means that comparison can be misleading when trees in mixed and monospecific stands differ in size. As the ratio decreases with size (Box 6.3), any size differences between the compared trees in mixed versus monospecific stands should be eliminated before comparison (see Sect. 6.7.2).

In this case, the observed cd/d ratio of the trees in mixture can be extrapolated to the size of neighbouring monocultures by cd/d ^′ = cd/d × (d _p/d _m)^−1/4. After this transformation, the adjusted observed ratio (cd/d ^′) can be compared with the observation in neighbouring monocultures.

Analysis of cpa–d allometry of beech in monocultures compared with beech in mixture with Norway spruce, European larch, common ash, and sessile oak shows striking differences (Fig. 6.16). This analysis is based on densely stocked stands with no or only light thinning. Mixing matters even when the stand density is at maximum. Obviously a neighbouring European beech restricts the crown of a beech more than any other of the analysed species. For a beech with stem diameter 25 cm, the allometric equation shown in Fig. 6.16 (be) predicts a crown projection area of cpa = 17 m². Beeches with the same stem diameter achieve cpa = 25 m² when mixed with ash, and 27, 37, or even 45 m² when mixed with spruce, larch, or oak, respectively. The ranking of neighbours regarding the effect on crown restriction is beech > ash > spruce > larch > oak. For European beech, mixing with each of the other species means ‘competition reduction’ in terms of crown extension in the sense of Kelty (1992) and Vandermeer (1992). In other words, a neighbouring Norway spruce, sessile oak, or Scots pine means a relief in crown restriction compared with a neighbouring beech. This is in accordance with findings by Pretzsch and Biber (2005) and Zeide (1985) that self-thinning is the highest in beech monocultures and much lower in monocultures of the other three species, with the ranking European beech > Norway spruce > Scots pine > sessile oak.

While allometric scaling theory predicts cpa ∝ d ^4/3 (i.e. α = 1.33) for the allometrically ideal plant, the allometric exponent is at a maximum α = 1.54 in beech monocultures and ranges between α = 0.76 (be, (ash)) and α = 1.21 depending on the species composition of the neighbours.

6.5.3.2 Root Morphology and Root-Shoot Allometry

According to the optimal partitioning theory (McCarthy and Enquist 2007), the shape of the tree crown, root system, and the relationship between these depend highly on the resource supply of the plant. Part of the large variation in the root-shoot relationship of plants can be explained by this theory. It predicts that the limitation of a resource leads to the promotion of growth of the plant organ responsible for supplying that critical resource (Comeau and Kimmins 1989; Keyes and Grier 1981).

In Fig. 6.17, four examples indicate the behaviour of the root-shoot ratio. In the first example, where light, water, and nutrient conditions are favourable (Fig. 6.17a), the tree develops a root-shoot ratio of 10:90. Under adequate light conditions, but with a water or nutrient deficiency (Fig. 6.17b), the tree invests more in root growth, especially fine roots. Thus, the root-shoot ratio increases in favour of roots to 45:55. With an adequate water and nutrient supply combined with critical light conditions, e.g. on nutrient-rich soils or for understorey trees (Fig. 6.17c), shoot growth is enhanced so that the tree root-shoot ratio may become 30:70. In the case of rich soils, trees in the upperstorey tend to allocate growth resources to extensive crown development, whereas trees in the understorey often invest in height growth to escape the shade (Oliver and Larson 1996). If light, water, and nutrient supply is limited (Fig. 6.17d), the root-shoot ratio may resemble the example in Fig. 6.17a of 10:90.

Changes in the partitioning between root and shoot growth can indicate a modification of environmental conditions through mixing as shown for the rather easily accessible crown growth. Intraspecific variation in root morphology due to species mixing, however, is more difficult to measure. Analysis of root-shoot allometry based on tree-ring analyses at increment cores from stem and coarse roots can reveal how the root-shoot relationships depend on site conditions (Pretzsch et al. 2012a, b) and silvicultural treatment (Pretzsch et al. 2014). For the methodology see Box 6.4. Figure 6.18 shows results of combined increment boring of coarse roots and stem at breast height applied in mixed spruce/beech stands versus monospecific spruce stands.

At both sample sites in the prealpine lowlands in Bavaria (SON 814 and ARN 815), the mixture with beech causes a significantly shallower root-shoot allometry of spruce compared with neighbouring monospecific stands. In the size range of 20–50 cm stem diameter, which is well backed with sample trees (right sections of the regression lines), spruces in mixture have a significantly lower root-stem growth than in monospecific stands. Coarse root growth is more sluggish in growth reaction than the resource-capturing fine roots. However, as in the case of the crown structure, coarse roots indicate the long-term dynamics as they represent the holding fixture and connecting pipes for fine roots. A cause of the repartitioning from root to stem growth in mixed stands may be a better supply of below-ground resources in mixed versus monospecific stands (Rothe 1997; Rothe and Binkley 2001) which triggers crown expansion to remedy above-ground resource limitation. Spatial niche separation between spruce roots in the upper soil horizon and beech roots in the deeper layer may be an additional reason (Rothe 1997; Wiedemann 1942, 1951). Decrease in root diameter growth entails shorter root length and a smaller influence zone of a tree. This may indicate a reduced investment in mechanical stabilisation and a decrease in the tree’s growing area in mixed versus monospecific stands (see Sect. 6.6).

Box 6.4 Analysing the Allometric Relationship Between Coarse Root and Stem Growth of Trees in Mixed Versus Monospecific Stands

To analyse the allometric relationship between coarse root and stem growth increment, cores can be sampled from both stem at breast height and coarse roots in close distance from the stem axis (Pretzsch et al. 2014; Nikolova et al. 2011). For each trunk, two increment cores may be sampled from the cardinal direction north and east (Box Fig. 6.4-1, left). In addition, the trees’ two to three biggest coarse roots can be sampled. Because of their rather elliptical cross section, two increment cores may be taken from each root at a 45° angle from the vertical line. To enable the sampling, the selected roots need to be partly excavated (Box Fig. 6.4-1, right).

Based on tree-ring analysis, the diameter development of coarse roots may be plotted over the stem diameter development for each tree in a double-logarithmic scale. The grey trajectories in the background of Box Fig. 6.4-2 show such root-shoot allometries exemplarily for European beech and Douglas-fir grown in monospecific and mixed-species stands (Thurm et al. 2016).

The regression analysis of the individual coarse root diameter-stem diameter trajectories revealed that both European beech and Douglas-fir have reduced coarse root growth in mixed compared with monospecific stands (Box Fig. 6.4-2c versus a and f versus d). In both monocultures (Box Fig. 6.4-2a and d), the allometric relationship between coarse root growth and stem diameter growth is the steepest, i.e. the investment in roots compared with stem is maximal.

Certainly, the selected coarse roots represent just a small portion of the trees’ whole root system, and their development is more sluggish and persistent than that of the ephemeral fine roots. But analogously to the stem which indicates the development of the crown and leaf area, the coarse root diameter reflects the activity of the whole root, since the coarse roots ultimately provide the basic structure and pipe system for the fine roots. So, the coarse root growth might be used as an integrative and non-specific indicator for the root system as a whole.

6.5.4 From Pattern to Process of Crown Expansion in Interspecific Neighbourhoods

6.5.4.1 Dynamics of Lateral Crown Expansion in Inter- Versus Intraspecific Environments

The change in intraspecific crown morphology in mixed versus monospecific stands becomes even more obvious by analysing successive crown maps of monospecific and mixed stands (Pretzsch 1992, 2009). Based on long-term plots with first crown measurements in the 1950s and successive measurements every 10–20 years, a 3D model delivers distances between neighbouring crowns (Fig. 6.19). The successive eight-radius crown measurements (Box 6.5) provide lateral crown growth for all eight directions. This enables derivation of functions for predicting lateral crown growth in dependence on the distance to neighbouring crowns in the respective directions (Fig. 6.20).

The functions describe the relative changes in crown radii of Norway spruce and European beech in relation to the crown distance to neighbours. A relative increment of crown radius of 1.0 means that a tree can expand its crown radius without lateral restriction and achieve the potential crown radial increment. A relative increment of 0.0 or less, by contrast, means stagnation and degeneration of the crown.

The curves in Fig. 6.20 show the decline in crown radial increment as the central tree crown becomes increasingly interlocked with neighbouring crowns as well as in the crown distance at which a crown dieback commences (below the dotted 0-line). Based on these distance-dependent crown growth functions, the crown cross-sectional development at a trial plot can be simulated for each individual tree in relation to its neighbourhood. Figure 6.21 shows the crown map for a 20 m × 20 m section of the experimental trial plot ZWI 111/3 in 1954, the year the simulation run starts based on the crown measurements in this year. The crown development of Norway spruce and European beech, at this time 60 and 80 years old, respectively, was simulated for a 50-year period at 5-year intervals. The interim results at times t = 10 years, t = 30 years, and t = 50 years (Fig. 6.21b, c, and d) show how the crowns expand and respond to increasing restriction by developing oval and eccentric crown shapes. To develop the crown perimeter, the eight crown radii are connected by a cubic spline (Pretzsch 2009).

The simulations and underlying functions (Fig. 6.20) reveal the following species-specific competition behaviour: when a Norway spruce grows towards another Norway spruce, the decrease in radial increment after an overlap of 1.0 m is almost linear. Yet, if it grows towards a European beech, a decrease in radial increment of the crown occurs much later. Effectively, this leads to a tighter interlocking of a Norway spruce crown with neighbouring European beech than with neighbouring Norway spruce (Pretzsch 2014). Similarly, the crown interlocking for a European beech growing towards a Norway spruce is also tighter than for European beech in monocultures. This finding confirms the species-specific behaviour of beech shown in Fig. 6.16. For Norway spruce and European beech, a reduction in lateral crown expansion of more than 5% only occurs when crowns interlock by 1.0–2.0 m, and the crowns recede only after the crowns overlap by 2.0–3.0 m. Thus, the crown growth dynamics of Norway spruce and European beech differ considerably from, e.g. the response of the light-demanding species European larch, which shows a clear reduction in the growth of side branches once the distances from branches to the neighbouring crown fall below 40 cm (Schütz 1989).

6.5.4.2 Variability of Crown Projection Area in Inter- Versus Intraspecific Environments

Solitary trees achieve wide and, apart from a slight tendency towards ovality due to one-sided solar irradiation in northern or southern latitudes, rather circular crowns. The symmetry of their crowns indicates unimpeded lateral expansion or at least all-round homogeneous restriction by, for example, water, light, or nutrients (Møller and Swaddle 1997). When coping with crowding, crowns may adapt their lateral extension to their prevailing neighbourhood conditions and increasingly lose the symmetry typical for solitary growth. Species with higher crown plasticity can to some extent overcome their restriction by occupying emerging niches, penetrating neighbouring crowns, or even edging out neighbours. The eccentric crown expansion and crown asymmetry which enables occupation of additional space by directional lateral crown expansion should be distinguished from degeneration-caused asymmetry through die-off and mechanical abrasion of branches and crown parts due to overwhelming competition.

Box 6.5 Measures for the Variability of Lateral Crown Expansion of Individual Trees in Intra- and Interspecific Environments

The following measures of crown plasticity are based on common crown maps with eight-radius crown projection areas as shown in Box Fig. 6.5-1. The graph shows exemplarily a 400 m² sized section of the 80-year-old triplet Freising 813/2 of Norway spruce, European beech, and a mixture of both species close to Freising in southern Bavaria. The crown projection areas (in m² per crown) and their shape (divergence from circle) can be compared between mixed and neighbouring monocultures to reveal inter- versus intraspecific crown variability.

The following three measures address different aspects of the variability of lateral crown expansion (see Box Fig. 6.5-2):

The ratio cpa/sa between crown projection area, cpa, and stand area of an individual tree, sa, indicates the degree of crown engagement. A value of cpa/sa = 1 would indicate identity of cpa and sa. High values (cpa/sa > 1) indicate wide crown expansion reaching beyond the trees’ sa. Small cpa/sa values indicate a tree’s suppression and crown recession (see Box Fig. 6.5-2 from left to right).

The ratio between the shortest and longest of the eight crown radii, r _min/r _max, indicates the crown rotundity. In Box Fig. 6.5-2 the rotundity decreases (from left to right) with stand density due to growing competitive pressure.

Crown eccentricity, \( ecc=\sqrt{{\left({x}_s-{x}_g\right)}^2+{\left({y}_s-{y}_g\right)}^2}/{d}_{1.3} \), is based on the Cartesian coordinates of the stem position, x _s and y _s, and on the coordinates of the centre of gravity, x _g and y _g, of the crown, calculated on the basis of the coordinates of the corner points of the crown projection area (\( {x}_g={\sum}_{i=1}^8{x}_i/8 \), \( {y}_g={\sum}_{i=1}^8{y}_i/8 \)). Division of the distance \( \sqrt{{\left({x}_s-{x}_g\right)}^2+{\left({y}_s-{y}_g\right)}^2} \) by the stem diameter, d _1.3, eliminates size effects and makes different trees and species comparable. A measure of, for example, ecc = 0, 2.0, and 10.2 means that the gravity centre of the crown is perpendicular above the tree position (ecc = 0), twice (ecc = 2), or even more than ten times (ecc = 10) the stem diameter deviating from the tree position (see Box Fig. 6.5-2 left to right). Note that in Box Fig. 6.5-2 the trees’ centres of gravity are represented by circles and the trees’ stem foot positions by the origin of the coordinate system.

In the following, crown maps of monocultures and mixed stands of Norway spruce and European beech and sessile oak and European beech on long-term plots in Germany with eight-radius crown measurements are used to illustrate the differences between crown dynamics in intra- and interspecific environments. In order to quantify the variability of crown structures in those stands, the measures introduced in Box 6.5 will be applied.

Using the ratios, the crown engagement, rotundity, and eccentricity can be compared between mixed and neighbouring pure stands. The cpa/sa ratios in Table 6.1 reflect that, except for beech when mixed with oak, all three species can significantly expand their crowns laterally far beyond their stand area when growing in mixed compared with pure stands.

Table 6.1 Lateral crown expansion of individual trees in even-aged mixed versus pure forest stands of Norway spruce and European beech (above) and sessile oak and European beech (below)

Full size table

The ratio r _min/r _max reveals that, compared with the other species, beech crown projection areas are mostly less circular, i.e. more jagged. Mixing significantly increases the rotundity in the case of spruce (p < 0.001), decreases the rotundity of beech (p < 0.001), and leaves the rotundity of the crowns of sessile oak unaffected.

The ecc values are the highest for beech, especially when growing in mixed stands. Values of ecc = 5.7 to 7.4 indicate that beeches have plastic crowns for resource capture even distant from their stem position. The measures show that crown morphology can significantly shift from intra- to interspecific competition and trigger the space occupation of the combined species in a species-specific way. Mixing increases the crown eccentricity of both beech (p < 0.001) and oak (p < 0.001) but fosters the centricity in the case of Norway spruce (p < 0.001).

6.5.4.3 Species Mixing and Inner Crown Properties

Species mixing can obviously modify the fractal dimension of the crown surface area and leaf area from a lower space filling (Euclidian scaling) towards higher space filling of the crown volume (fractal scaling) (Pretzsch and Dieler 2012). Tree crowns as described by Oldemann (1990), Purves et al. (2007) and Roloff (2001) lie somewhere along the continuum between the borderline cases of an umbrella-like crown with the majority of the leaf surface area allocated close to the convex hull (surface dimension n = 2) and a broom-like crown with leaf surface area distributed all over the crown space (surface dimension n = 3) (Zeide 1998).

Terrestrial laser scanning and subsequent skeletonisation of tree crowns based on the voxel patterns revealed significantly different inner crown structures in mixed versus monospecific stands of Norway spruce and European beech (Bayer et al. 2013). An example of the procedure from compilation of point clouds to derivation of inner crown properties is shown in Fig. 6.22a–d.

Although similar in stem diameter and tree height, beeches growing in mixture with spruce can have significantly more branches of first order and—because of stronger ramification—nearly twice the number of second and third order branches compared with those in monocultures (Bayer et al. 2013). The branch bending can be higher and the branch angle flatter. Also, the sum of branch length and the crown volumes can be higher in mixed compared with monospecific stands. The schematic representation in Fig. 6.23 accentuates the broom-like crown shape of beeches when growing in intraspecific interaction (left) with most of the leaf area allocated close to the top of the convex hull. In interspecific environments, the crowns are rather bouquet-like (right) with the leaves reaching deeper into the crown volume (Arz 2013; Bayer et al. 2013).

6.6 From Tree Morphology to Space Occupation

All individuals in monocultures—particularly when they are relatively homogeneous in genetics and size—use similar strategies to compete for the growing space in a stand and for the same resources when these are not sufficient for all. When their demands and abilities are relatively similar (Fig. 6.24a), the function and structure of all competitors vary within a small range. Theoretically, this leads to a hexagonal pattern of tree distribution. Given that all are equipped with rather similar tricks and traits, neighbouring trees are in a stalemate rather than outwitting each other. That is why many species, when growing in monocultures, have tree crown projection areas that are rather similar to growing area. Their crowns barely interlock and 5–10% of the stand area is not covered by crowns at all (see Chap. 5, Fig. 5.19 and Table 5.6).

Compared with monocultures, the trees’ elbowroom in mixed stands can be wider. If the crown shapes of the combined species complement each other (Fig. 6.24b), the trees might simply have more space to occupy without mechanical abrasion or penetration of the neighbours’ crowns, while mixtures with similar crown shapes (Fig. 6.24c) cause less competition reduction. Beyond these differences in species-specific structure, the species-specific strategies for space occupation through, e.g. crown penetration due to different light compensation points and lateral expansion due to change in branch angle may result in competition release and wider crown expansion than in monoculture of one species and crown restriction and regression compared with the monospecific stands for the other species.

6.6.1 Crown Projection Area, Tree Stand Area, and Degree of Crown Engagement

Regarding the crown as a tool for resource sequestration, any crown and root plasticity may be relevant for tree and stand productivity. Suppose that if species combined in mixture retained the same morphology as they have in monoculture, the mixing effect may simply be additive. Any crown structures emerging in mixture, e.g. a plastic acclimation or complementarity of spatial niches, may cause higher resource capture and multiplicative mixing effects such as overyielding or underyielding in mixed versus monospecific stands.

The crown projection area, cpa, of a tree of a given size indicates its reach for resource acquisition, light interception, and shading of neighbours. In contrast, the tree stand area, sa, represents its available growing area. So the ratio between cpa and sa, introduced as the degree of crown engagement in Box 6.5 indicates how wide crowns reach beyond their growing area, fill the canopy space, and forage for light in their local environment.

Table 6.1 shows exemplarily for monospecific and mixed stands of spruce, beech, and oak that the cpa/sa ratio is mostly close to cpa/sa = 1.0 in monocultures, i.e. the tree crown area is similar to its growing area. In mixture, trees can overcome the lateral crown restriction by expanding and interlocking more closely. In total, the cpa/sa value increases by 24 and 39%, respectively, when spruce and beech are mixed, and by 12 and 54%, respectively, when beech and oak grow in mixture (see Table 6.1, cpa/sa values). This increase in the crown expansion beyond growing area can be coupled with a reduction in the mean growing area per tree in mixed versus monospecific stands (Sect. 6.4).

Figure 6.25a is a schematic representation showing that in monocultures crown projection area is rather similar to stand area, whereas in mixed stands the crowns often exceed the tree stand area. Due to the higher stand density in mixed compared with monospecific stands, the mean tree stand area decreases (see Chap. 4, Sect. 4.3.2). So, in mixed stands the cpa-d allometry can shift upwards and the sa-d allometry downwards, and the cpa/sa relationship, i.e. the crown engagement, often rises in mixed compared with monospecific stands (see cpa_m/sa_m > cpa_p/sa_p in Fig. 6.25b).

Tree size is an ambiguous trait. As trees become larger, they tend to gain more privileged access to resources, occupy more space, and have a greater repression effect on neighbours. However, size can also mean higher maintenance costs and susceptibility to windthrow, drought, or bark beetle attacks. When trees expand far beyond their stand area by spreading their crowns without much additional investment in tree diameter or tree mass, this can mean a higher resource acquisition without the drawbacks of higher resource investment. Section 6.6 will show that this can increase the growth per stand area and thereby the tree and stand productivity.

6.6.2 Dynamics of Canopy Gap Occupation

Crown plasticity is species specific. We quantified it by CPL in Sect. 6.5.2 and saw that, for instance, CPL of beech >> CPL of Scots pine. A species’ crown plasticity is relevant for its persistence and continuous extension in closed stands; it enables crown competition through penetration or even edging out of neighbouring crowns in the course of stand development. But plasticity also means a strong capacity for first access to unoccupied space in the early stand phase or spontaneous occupation of gaps caused by mortality or thinning. During stand development, various kinds of disturbances (e.g. tree mortality due to competition, storm damage, bark beetle attacks, and thinnings) may cause openings in the canopy and gaps in the root space. The quicker and wider a species’ crown extension, the greater the benefit it gains from erratic gaps. At the stand level, plastic crowns which can quickly occupy gaps can mean continuous cover of the ground and high resilience of productivity in the case of disturbances.

The following rough estimation underlines the relevance of gap occupation for interspecific competition and stand productivity. The roughly 3% annual rate of tree loss due to mortality or thinning means a gap area of 300 m² per hectare and year. A continuation of the drop-out process of trees over a 100-year rotation period can cause a transient gap area of about 30,000 m², i.e. 3.0 ha. In other words, a stand’s given growing area is repeatedly contested by neighbours, occupied by trees, released after mortality or thinning, and finally captured by the most competitive neighbours. Starting with some thousand (when planted) or million trees (when naturally regenerated), capture and recapture of growing area due to competition ultimately leave just a few hundred trees per hectare in the mature stand. Again and again trees drop out and release space for the remaining neighbours, which can occupy it faster and more completely the more plastic their crowns are.

Particularly in more or less monolayered stands, this ongoing mortality and subsequent closure through crown extension causes a continuous opening up of the canopy. Crown size and accordingly gap size increases with tree age. As larger gaps need more time to be recaptured and closed by neighbours and because older trees’ lateral shoot growth is rather slow, the crown re-coverage becomes more sluggish with increasing stand age. The ongoing gap dynamics are probably one additional reason why even in unthinned monolayered monocultures, 5–15% of the stand area remains uncovered by crowns (Chap. 5, Table 5.6). In temperate forests, where individual tree growth is mainly light limited, gaps are closed more rapidly through crown extension above ground than through tree root extension below ground (Bauhus 2009). Species with higher crown plasticity can achieve more additional canopy space through faster and more extensive gap occupation equivalent with additional resource capture and competitive strength. Particularly gaps caused abruptly by thinning favour those species capable of wide and fast crown extension. Additional growing space caused by mortality emerges more continuously and is more gradually occupied by neighbours already in advance of a tree’s death.

Time series of TLidar measurements before and after gap cuttings (2006, 2008, 2010, and 2012) in monospecific and mixed stands of Norway spruce and European beech reveal the species-specific strategies for occupying crown gaps caused by thinning (Bayer et al. unpublished). Figure 6.26 illustrates the initial gap size (non-black areas in the centre), the gap filling till 2008 (dark grey) and 2012 (light grey), and the still uncovered area in 2012 (white). The progressing occupation of gap area (in m²) is much slower in the monospecific spruce stand (left) compared with beech (middle). This finding corresponds with the much lower growth resilience to stand density reduction through thinning of spruce compared with beech (Pretzsch 2005b). The gap in the mixed stand of spruce and beech is closed relatively quickly; again beech contributes much more than spruce. On average, the area occupation in the 6-year period of spring 2006 to spring 2012 amounts to 0.8 m² year⁻¹ for spruce and 2.8 m² year⁻¹ for beech.

Figure 6.27a quantifies the dynamic of gap closure for the canopy cover of the ground. While spruce in the monospecific stand (sp) closes about 5 m² during the 6-year period (2006–2012), beech (be) and the mixed stand (sp, be) close more than 15 m², i.e. about three times this area. Figure 6.27b reveals the contribution of both species to closing the gap in the mixed stand in terms of their sum of crown area which has grown into the gap since 2006. Again, beech (17.5 m²) is superior to spruce (10 m²), and large portions of the canopy covered area are multilayered (hatched area). The high multiple crown coverage in mixed stands indicates the complementary use of light by spruce and beech.

TLidar reveals that beech is superior in terms of both the absolute area occupation and the velocity of gap occupation. This continuous contest for space occupation is rather unspectacular, but in view of the above-stated total area of about 3 ha during a rotation, it is highly relevant for a species’ survival and spread. Efficient space occupation does not necessarily mean superior productivity but signifies an increase in dominance and persistence through restraining, penetrating, and suppressing the other species in a kind of permanent guerrilla warfare. Even in stands without active silvicultural interference, this contest for space and resources can gradually change the mixing proportion in favour of those species which are best equipped for continuous gap dynamics.

A superior crown plasticity and gap occupation of species such as European beech, maritime pine (Pinus pinaster Ait.), or lenga (Nothofagus pumilio [Poepp. U. Endl.] Krasser), respectively, is probably one essential reason for their dominance in Central European, Mediterranean, and South American forest ecosystems.

6.7 Efficiency of Tree Crown Area and Tree Growing Area

Productivity means growth per time and unit area and indicates how efficiently a tree uses a given growing area for volume or biomass growth. So far we have compared tree morphology and growth in mixed stands versus monocultures without any relation to the required growing area. The following transmission to growth per tree stand area yields tree and stand productivity.

Dividing the annual volume increment of a tree (m³ year⁻¹) by its crown projection area or stand area (m²) (see Box 6.6) yields a measure of the tree’s area use efficiency in terms of volume growth. In this case, area is used as a surrogate variable for the tree’s resource supply.

Note that indices which set the growth in relation to the consumption of light, water, or nitrogen and water follow the same concept and are much more informative because they are directly related to the resources. Although they reflect the efficiency of light, water, and nutrient use, they are still rarely available for trees in mixed and monospecific stands.

Efficiency parameters based on growing area or growing space were frequently used to compare the performance of trees of different sizes or social classes in the stand, at different ages, or in different environments (Gspaltl et al. 2012; Pretzsch and Schütze 2009; Sterba et al. 1993; Sterba and Amateis 1998). When calculated for trees in mixed stands and neighbouring monospecific stands, efficiency parameters can contribute to quantifying and understanding the emergence of mixing effects.

Box 6.6 Crown Projection Area, cpa, and Stand Area, sa, of Trees

The crown projection area of a tree, cpa, results from projection of four or eight crowns. In Box Fig. 6.6-1a, the crown projection area is represented by a circle with the mean crown radius circle with a radius \( {\overline{r}}_q \), which corresponds to the quadratic mean of four or eight radial measurements r ₁, … r _n. The growing area—also called stand area—of a tree, sa, is a substitute for its resource supply (Box Fig. 6.6-1a). It results from dividing the whole-stand area (e.g. the plot area of 1 ha) by the number of living stocking trees. The sum of the tree stand areas of all trees is the stand area (\( \mathrm{AA}={\sum}_{i=1}^n{sa}_i \)). The simplest method for obtaining the mean stand area, \( \overline{sa}=\mathrm{AA}/n \), is to divide the stand area by the number of trees, n. Other methods such as the circle segment method by Alemdag (1978), the rastering methods by Faber (1981, 1983) and Nagel (1985), and the growing area polygons by Brown (1965), Jack (1968), Fraser (1977), and Pelz (1978) make additional assumptions about the trees such as their diameter, crown size, or growth rate in order to partition the total stand area between them (see Pretzsch (2009)).

The cpa/sa relationship can become greater in mixed stands and the degree of crown closure and therefore the crown closure and the sum of crown projection areas higher than in monocultures (Box Fig. 6.6-2). Wider crown extension may result in denser canopy space filling and higher tree growth per unit area.

6.7.1 Ratios for Comparing Tree Growth in Mixed Versus Monospecific Stands

The ratios presented in Table 6.2 are useful for analysing efficiency of growth at the tree level and for the transition from growth per tree to growth per stand unit area (Box 6.6). The ratios can be quantified for trees in monospecific and mixed stands. Comparing these can reveal, for example, whether overyielding results from higher stand density, higher growth rate per tree, or from a combination of both.

Table 6.2 Efficiency ratios for characterising individual tree growth in relation to tree size, crown projection area, and tree stand area

Full size table

The ratios E _cpa/v and E _iv/cpa indicate the efficiency of the crown in terms of crown space occupation and exploitation without considering the required tree stand area, sa, i.e. they reflect aspects of plant ecology. E _cpa/v (m² m⁻³) indicates how much crown area a tree occupies per unit of tree volume. E _iv/cpa (cdm year⁻¹ m⁻²) reflects the growth efficiency of the tree’s crown projection area. The ratios E _cpa/sa, E _iv/sa, and E _v/sa relate the structure and growth of the tree to its required growing space. They thereby enable the transition from tree growth to tree productivity. E _cpa/sa (m² m⁻²) reflects the degree of crown extension beyond the tree stand area and is equivalent to the degree of crown engagement. E _iv/sa (cdm year⁻¹ m⁻²) represents the efficiency of stand area in terms of tree volume growth (m³ year⁻¹) per tree stand area (m²) and is equivalent to the tree productivity. E _v/sa (m³ m⁻²) indicates the stand density in terms of tree volume per tree growing area (Pretzsch and Schütze 2005). We use the above ratios to compare tree development in mixed versus monospecific stands. The ratio rE _iv/csa = E _iv/cpa, m/E _iv/cpa, p represents how trees perform with regard to crown growth efficiency in mixed versus monospecific stands. Most of the ratios change with tree size and require allometric adjustment before being applied to compare trees in mixed versus monospecific stands when there are differences in tree size, e.g. in tree diameter or tree volume (Dirnberger and Sterba 2014).

6.7.2 Elimination of the Size Effect from Efficiency Parameters

Efficiency ratios such as E _iv/cpa or E _iv/sa are useful for comparing tree growth in mixed versus monospecific stands. However, these ratios change with tree size. If the size of trees in mixed and monospecific stands differs, such size-dependent changes in the efficiency parameters should be eliminated. Allometric theory (Enquist et al. 1998; West et al. 2009) and empirically derived allometric exponents (Pretzsch and Dieler 2012) are available for such corrections. If these are not undertaken, then mixing effects might be confounded with size effects as shown in the following example.

Supposing that Norway spruce volume increment, iv, scales with an exponent of α _iv, v = 0.42 and cpa with α _csa, v = 0.62 to total plant volume, then the efficiency of crown area, E _iv, csa = iv/csa scales with α _iv/cpa, v = − 0.20 to plant volume (as iv ∝ v ^0.42 and cpa ∝ v ^0.62 E _iv, cpa = iv/cpa ∝ v ^{0.42 − 0.62} ∝ v ^−0.20) as shown in Fig. 6.28 at (a) linear and (b) double-logarithmic scale. Suppose a tree of volume v _m = 1.0 m³ growing in the mixed stand has a crown area efficiency of E _iv/cpa, m = 1.25 cdm year⁻¹ m⁻² and should be compared with a tree of volume v _p = 3.0 m³ and crown area efficiency of E _iv/cpa, p = 1.20 cdm year⁻¹ m⁻² in the neighbouring monocultures. The relative efficiency of the tree in the mixed stand is then rE _iv/cpa = E _iv/cpa, m/E _iv/cpa, p = 1.25/1.20 = 1.04, which is equivalent to a 4% increase through mixing. In this case it is obvious that the size growth of the tree (or a mean tree) in the mixed stand is behind the monoculture (v _m < < v _p), and part of its superiority is related to its younger allometric state. If we apply α _iv/cpa, v = − 0.20 and estimate which E ^′ _{iv, cpa, m} the tree in the mixed stand would have if it was the same size as the reference tree in the monoculture (v _p = 3.0 m³), we get E ^′ _iv/cpa, m = (iv_m/cpa_m) × (v _p/v _m)^−0.20 in the example E ^′ _iv/cpa, m = (1.25) × (3/1)^−0.20 = 1.00 and the relative efficiency calculated on the basis of \( r{E}_{iv/cpa}^{\prime }={E}_{iv/cpa,m}^{\prime }/{E}_{iv/cpa,p}=1.00/1.20=0.83 \). In other words, the real mixing effect is −17% as opposed to +4%; the different sizes create the illusion of a positive mixing effect.

In such cases, one should either refrain from comparison at the tree level or eliminate the size effects as shown. Based on the uncorrected mixing effect rE _iv, cpa = 1.04 and the ‘real’ mixing effect rE ^′ _iv, cpa = 0.83, we can calculate the size effect S = rE _iv, cpa/rE ^′ _iv, cpa = 1.04/0.83 = 1.25. The observed uncorrected mixing effect rE _iv, csa = 0.83 × 1.25 = 1.04 can be split into a real negative mixing effect (rE ^′ _iv, cpa = 0.83) and a positive size effect (S = 1.25). Part of the size effect might have been caused in the past by mixing but should not be confounded with present mixing effects.

For the allometric adjustment in this chapter, the following exponents for Norway spruce and European beech, α_iv/v, v = − 0.58, − 0.41, α_cpa/v, v = − 0.38, − 0.31, α_iv/cpa, v = − 0.20, − 0.10, and α_sa/v, v = − 0.38, − 0.31, were specially derived from trees on long-term experiments. See Pretzsch and Dieler (2012) for empirically derived allometric scaling relationships of other tree species or Enquist et al. (1998, 2009), and West et al. (2009) for general scaling exponents of allometrically ideal plants.

6.7.3 Transition from Tree Growth to Tree Productivity in Mixed Versus Monospecific Stands: An Example

The transition from growth of the individual tree to the productivity of the mean tree and the stand productivity of mixed versus monospecific stands is illustrated for the age series NOR 811, FRE 813, and SON 814 of monospecific and mixed forest stands of Norway spruce and European beech in southern Germany. The age series provide triplets of neighbouring plots which are different in terms of species composition (spruce monoculture, mixed spruce/beech, beech monoculture) and relatively similar in all other characteristics such as site conditions, stand age, silvicultural treatment, etc. The 12 triplets of plots cover 36–161-year-old stands with dominant height of 25–44 m at age 100, standing volume stock of 55–1.041 m³ ha⁻¹, and current annual volume growth of 2–32 m³ ha⁻¹ year⁻¹. The relatively even-aged and monolayered monospecific and mixed stands are fully stocked, unthinned, or only slightly thinned and represent good to optimal site conditions for both spruce and beech. For more details about the plots, see Pretzsch and Schütze (2009) and Pretzsch et al. (2010).

As the considered stands are more or less even aged and the size characteristics are normally distributed, this is the easiest way to explain the transition from the tree level to the stand level. In these stands, the mean tree is a good representative of the respective cohort. In order to demonstrate how mixing can modify the growth and growth efficiency at the individual tree level, we calculated the mean ratios cpa/v, iv/cpa, cpa/sa, iv/sa, and v/sa introduced in Table 6.2 for all plots of the 12 triplets. The mean ratios between the mean tree volume in mixed versus monospecific stands of v _m/v _r = 0.85 for beech and v _m/v _r = 1.04 for spruce indicate that beech is 15% smaller and spruce 4% larger in mixed stands versus the neighbouring monoculture of the same triplet. The effects of these size differences were eliminated through allometric adjustment; the adjusted ratios are marked by a stroke (e.g. E ^′ mixed).

E _cpa/v in Table 6.3 reflects that with a given tree volume, v, trees in mixed stands develop a wider crown than those in monospecific stands. The table shows an increase of 18% for spruce and 45% for beech. Beech is already superior to spruce in terms of crown extension in monospecific stands (26.44/11.83 = 2.2) but even more so in mixed stands (38.33/13.96 = 2.8). On average, both species benefit from mixture in E _cpa/v, which indicates that the benefit of one species is not at the expense of the other but rather that their strategies are complementary. The E _iv/cpavalues indicate that mixing reduces the crown area efficiency. This reduction amounts to 4% for the rather vertically expanding spruce and 20% for laterally expanding beech. In contrast to E _cpa/v, the crown efficiency E _iv/cpais about twofold for spruce compared with beech. Mixing increases the crown engagement E _cpa/sa in spruce by just 6% (E ^′ _cpa/sa, m/E _cpa/sa, p = 1.06) but in beech by 69% (E ^′ _cpa/sa, m/E _cpa/sa, p = 1.69). In both mixed and monospecific stands of beech, the crown engagement E _csa/sa is superior to spruce. Mixing hardly changes the stand area efficiency E _iv/sa (= productivity) of spruce (E ^′ _iv/sa, m/E _iv/sa, p = 1.01) but increases that of beech by 15% (E ^′ _iv/sa, m/E _iv/sa, p = 1.15). So, productivity of spruce is generally higher in both monospecific and mixed stands, but beech benefits more from mixing than spruce. Note that especially for beech, efficiency measures based on crown area (E _iv/cpa) may indicate a negative mixing effect. However, due to the multiple crown coverage of beech as indicated by its high E _cpa/sa values, it can achieve an overyielding in inter- as opposed to intraspecific environments. The wider extension and denser interlocking of beech crowns enables a 13% higher stand density of beech in mixed stands as indicated by E _v/sa ratios of E ^′ _v/sa, m = 0.06 compared with E ^′ _v/sa, p = 0.05 in monoculture.

Table 6.3 Refined analysis and allometric adjustment of tree growing space efficiency and productivity of (a) Norway spruce and (b) European beech growing in mixed and monospecific stands

Full size table

6.7.4 Crown Engagement cpa/sa as Link Between Tree and Stand Level Evaluation

For linking tree to stand level evaluation, the overlap and interlocking of crowns is crucial. From E _iv/sa = iv/sa, E _iv/csa = iv/csa, and E _sa/csa = sa/csa, it follows that E _iv/sa = E _iv/csa × E _csa/sa. The latter equation conceptualises individual tree productivity as a product of individual tree crown efficiency and crown engagement. Consider further that the mixing effects in terms of crown efficiency and crown engagement can be expressed as rE _iv/csa = E _iv/csa, m/E _iv/csa, p and rE _cpa/sa = E _cpa/sa, m/E _cpa/sa, p, respectively. The relative productivity of trees in mixed versus monospecific stands is then rE _iv/sa = rE _iv/cpa × rE _cpa/sa, i.e. the relative effect of mixing on productivity is the product of the effect of mixing on crown efficiency and crown engagement.

Figure 6.29 illustrates the efficiency ratios for the 12 triplets in monospecific and mixed stands of Norway spruce and European beech introduced in the previous section (see also Table 6.3). In Fig. 6.29a the mean crown efficiency of beech in mixture is plotted over the efficiency in neighbouring monocultures. Observations close to the 1.0-line would indicate equality of efficiency. Points above or below this bisectoral line indicate a plus or minus, respectively, as compared with monospecific stands. In the case of beech, crown efficiency is reduced through mixing, but crown expansion increased to such an extent that productivity is 10–20% higher in mixed compared with neighbouring monospecific stands (Fig. 6.29a, from left to right). For Norway spruce, the reactions to mixing are similar but less pronounced (Fig. 6.29b, from left to right). When coping with interspecific competition, both species benefit to a different extent from a release of lateral crown restriction. Their wider crown spread and overlap can overcompensate the reduction of crown efficiency and result in a higher tree and stand productivity. Fully stocked mixed stands can differ slightly from monocultures in terms of the ground cover ratio, but the main difference is their higher sum of crown area due to two- to fourfold crown overlaps (see also Sect. 5.7.2). As crown maps are rare and crown areas difficult to measure, the multiple coverage was often neglected and counted only once in analyses (e.g. Assmann 1970, p. 105), but this seems to be crucial for over-/underyielding and should be considered more thoroughly in future.

Figure 6.30 illustrates the complementarity of Norway spruce and European beech in terms of space occupation with a section of the mixed stand SON 814/8 (age 80, survey 2004) which is one of the 12 triplets (spruce monoculture, spruce/beech mixed, beech monoculture) used for this example analysis. While spruce tends to expand vertically, beech fills the canopy space through lateral expansion and can increase the stand density.

6.8 Overview of Some Main Causes and Effects of Tree Species Mixing on Individual Tree Growth

Many of the beneficial tree mixing reactions introduced in this chapter result from complementary crown and root shape, spatially or temporally complementary resource exploitation, redistribution of resources, or modification of growth allocation and allometry. This section summarises the main causes and effects of tree species mixing on individual tree growth. There are many more causes of beneficial mixing effects, such as mechanical stabilisation, reduction of crown shyness, mechanical abrasion of parts of the crown by wind and storm, barrier building against biotic and abiotic disturbances, holobiontic interactions via mycorrhizal networks, or common use of root channels for exploitation of deeper soil layers. As the effects of these are so difficult to disentangle, the following overview of cause and effect is still rather phenomenological, qualitative, and mostly restricted to two-species mixtures. Many ongoing research projects strive to generalise and better quantify the effects and to extend the research to mixtures with more than two species.

6.8.1 Complementary Exploitation of Crown and Root Space

Any changes in tree crown morphology and canopy structure in interspecific versus intraspecific environments suggest a modification of the trees’ space occupation, resource capture, and productivity. Of special interest is a wider crown extension as this indicates a competition reduction and an increase in light interception and may also contribute to overyielding of mixed compared with monospecific stands (Chap. 4). Changes in crown structure and allometry underline that the mixing effect goes beyond a merely additive effect where the species’ behaviour in terms of structure and growth remains similar to that in the monoculture (Fig. 6.31a–c).

In temperate forests where tree growth is primarily limited by light, canopy space filling may be denser and light interception higher in mixed than in monospecific stands. Especially when their crown shapes are complementary, the crown expansion may be wider (Fig. 6.31d), the tree packing density higher (Fig. 6.31e), or both reactions may be combined (Fig. 6.31f). Similar complementarity with regard to their root morphology may increase the benefit of inter- compared with intraspecific neighbourhoods.

Because of the complementarity in crown shape (e.g. a combination of ▼-shaped with ▲-shaped crowns) and resource demand (e.g. combination of light-demanding and shade-tolerant species), tree crowns may expand more widely in inter- compared with intraspecific environments. On top of that, mixing can change inner crown properties such as branch length, branch angle, number of branches, and their straightness. The cpa/sa relationship can become greater in mixed stands (Fig. 6.32b) and the degree of crown closure—and therefore the crown closure and the sum of crown projection areas—may be higher than in monocultures (Fig. 6.32a). Larger crowns and denser canopy space filling can increase the tree and stand growth.

Analogously, a complementary root morphology may benefit inter- compared with intraspecific neighbourhoods in the root space.

6.8.2 Hydraulic Lift and Hydraulic Redistribution

Especially in dry years and on dry sites where water is the limiting factor, processes in the root space become decisive for tree growth and survival. However, outcomes under drought conditions may turn into benefits for some of the associates. One such phenomenon is the well-described ‘hydraulic lift’ or ‘hydraulic redistribution’ of water in woody plants, particularly observable in arid conditions, through deeply extending root systems (Fig. 6.33a), which release water at night into surface-near soil horizons of low water potential (Fig. 6.33b) as described in detail by Caldwell and Richards (1989) and Prieto et al. (2012). Once released, such water represents an external storage capacitance for the deep-rooting plant, but concomitantly enables survival of neighbouring shallow-rooting plants as the profiteers. The resulting benefit is not an active support provided by the deep-rooting plant, but occurs indirectly as an emergent feature of the specific species association under a specific site scenario. In such a case, competition turns into facilitation, which denotes an indirectly mediated, functional emergence between neighbouring plants. One or several of the associates may benefit with regards to water availability and growth.

6.8.3 Increased Availability of Mineral Nutrient Supply Through Deep-Rooting or Atmospheric N₂ Fixation

In mixed stands one tree species may benefit from another species which can exploit mineral nutrients in deeper root layers (Fig. 6.34a) or can fix atmospheric N₂ (Fig. 6.34a). In both cases, mineral nutrients are procured by a benefactor species and partly transferred to the other through litter fall. Thus, the additional nutrients are socialised among the neighbouring trees of the benefactor independently of their species. An additional benefit may come from root channels abandoned by one species and used by the other for penetrating compacted soil layers and reaching resources in deeper and otherwise inaccessible soil layers (Bauhus and Messier 1999; Gaiser 1952; Puhe 2003; Stone and Kalisz 1991).

6.8.4 Temporal Complementarity of Niches, Resource Use, and Growth

Many studies show clear differences in the course of growth between the species across their lifetimes (Assmann 1970, p 45) but also within a single year (Pretzsch 2005a; Rötzer et al. under review; Schober 1950/51). This asynchrony in growth entails a temporal diversification in resource uptake which can release stress.

For instance, Norway spruce may profit from a released competition for water in early spring when European beech is still leafless and lives from the reserves of the previous year (Fig. 6.35). In this period, photosynthesis and growth of spruce may profit from higher temperatures and light supply till beech sprouts in April/May. Afterwards, European beech may profit from the mixture in relation to the monospecific stand as the admixed Norway spruces have shallower roots. During the main growing season, scattered European beeches in the mixture with Norway spruce may have greater water availability than in monocultures of beech as the interspecific competition with neighbouring spruces is lower than the intraspecific competition with beech (Rötzer et al. under review). This may explain why beeches in interspecific environments grow much better than those beside beeches, especially in drought years (Goisser et al. 2016; Rötzer et al. under review).

Analogously, temporal diversification of space occupation during stand development may relax resource competition. It occurs, for example, in species assemblages of shade-tolerant and shade-intolerant, shallow- and deep-rooting, and early- and late-successional tree species. For given site conditions, species 1 and 2 in Fig. 6.36 may access resources in different spaces or at different times.

6.8.5 Modification of Growth Partitioning and Allometry of Trees in Inter- Versus Intraspecific Neighbourhoods

In order to acclimatise to an interspecific neighbourhood, trees species may change their growth partitioning in mixed-species stands compared with monospecific stands. Most of the comparisons between the productivity of mixed and pure stands are based on stem volume production (Liang et al. 2016; Pretzsch et al. 2015). Comparison based on total biomass production may produce different results, as tree species mixing can change stem-crown allometry (Bayer et al. 2013), root-shoot relationship (Thurm et al. 2016), and also tree-ring width and wood density (Zeller 2016) as illustrated in Fig. 6.37.

An increase in crown in relation to stem size in mixed-species stands as reported by Dieler and Pretzsch (2013) and Pretzsch (2014) would mean that the overyielding would be even higher when calculated for the total above-ground volume of mixed versus pure stands. However, the decrease of root in relation to shoot growth as reported by Thurm et al. (2016) and reported in Sect. 6.5.3 as well as the decrease of wood density revealed by Zeller (2016) would lower the overyielding of mixed versus pure stands when calculated for the total biomass growth. Ongoing works on within-tree growth partitioning in mixed versus pure stands will clarify how mixed stand productivity compares with that in pure stands when calculated for the stem volume productivity, which is of primary interest for forestry. They will also clarify how mixed stand productivity compares with pure stands based on their total biomass production, which is relevant for ecosystem understanding and carbon balance.

The presented tree properties emerging when growing in interspecific in contrast to intraspecific neighbourhoods go beyond an acceleration or reduction of growth velocity, i.e. a quicker tree and stand development. Rather, they can change the trees’ structure and space requirement. The presented tree properties emerging in interspecific in contrast to intraspecific competition indicate complementarity in use of above- and below-ground resources.

Beyond the increased productivity, the wider extension of tree crowns and multiple crown overlap in mixture can increase the growth resilience after disturbances, as gaps are smaller or can be closed more quickly. Properties emerging in mixed but not in monospecific stands such as increase in crown size, change in the crowns’ space filling pattern, reduction in growing area requirement, and increase in tree productivity are crucial for appropriate estimation of maximum density, silvicultural treatment, and dynamic modelling of mixed-species stands. Because of their size, firm position, and longevity, trees are the founder species in ecosystems and determine the living conditions of many ecosystem characteristics, functions, and services. So, the effects of mixing on tree and furthermore on stand structure have far-reaching effects on most ecosystem properties.

6. Take-Home Messages

1.
Interspecific difference in tree size causes well-known additive mixing effects such as higher or lower tree numbers per unit area in mixed versus monospecific stands due to different growing space requirements. Interspecific functional and structural complementarity (light-demanding vs. shade-tolerant, early- vs. late-successional, shallow vs. deep-rooting, deciduous vs. evergreen species) may cause multiplicative mixing effects such as multiple crown layering, denser canopy space filling, and eventually overyielding.
2.
The feedback between environment, growth, and structure enables a structural acclimation of trees to their local environment. Their size and longevity improve the capacity to increasingly acclimate morphologically with progressing stand development. Mixing can foster the variability of both the local environment and the tree structure and growth.
3.
Species mixing can trigger emergent properties of individual tree structure and growth which may result in an increase in resource capture and overyielding of mixed compared with monospecific stands.
4.
Depending on the net effect of competition and facilitation by neighbours, the unimodal increment curve of individual trees can be modified in different ways; e.g. its level can be raised or lowered and its rhythm can be accelerated or slowed down.
5.
Due to the complementarity of species and a reduction of competition, crowns may expand more widely in length and width in interspecific compared with intraspecific environments.
6.
Mixing can generate allometric relationships, crown projection areas, and inner crown properties which differ significantly from respective properties in monospecific stands.
7.
Wider crown extension and multiple crown overlap in mixed stands may indicate a more complete canopy space filling and light capture. Wider reach of the crowns combined with lower growing space requirements can increase the tree productivity in mixed versus monospecific stands by 10–20%.
8.
By relating the achieved tree growth to growing area instead of plant or crown size, we proceed from plant biology to production ecology.
9.
Tree characteristics change non-linearly with tree size. Therefore, comparison of structure or growth of trees in mixed versus monospecific stands should consider and eliminate any size differences between trees in mixed and monospecific stands.
10.
The beneficial tree mixing reactions introduced in this chapter result mainly from complementary crown and root shape, spatially or temporally complementary resource exploitation, redistribution of resources, or modification of growth allocation and allometry.

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Chair for Forest Growth and Yield Science, Faculty of Forest Science and Resource Management, Technical University of Munich, Hans-Carl-von-Carlowitz-Platz 2, 85354, Freising, Germany
Hans Pretzsch

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Faculty of Forest Science and Resource Management, Chair for Forest Growth and Yield Science, Technical University of Munich, Freising, Germany
Hans Pretzsch
Swiss Federal Institute for Forest, Snow and Landscape Research WSL, Birmensdorf, Switzerland
David I. Forrester
Institute of Forest Sciences, Chair of Silviculture, University of Freiburg, Freiburg, Germany
Jürgen Bauhus

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Pretzsch, H. (2017). Individual Tree Structure and Growth in Mixed Compared with Monospecific Stands. In: Pretzsch, H., Forrester, D., Bauhus, J. (eds) Mixed-Species Forests. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54553-9_6

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Individual Tree Structure and Growth in Mixed Compared with Monospecific Stands

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Growth and Structure in Mixed-Species Stands Compared with Monocultures: Review and Perspectives

Effect of tree species mixing on the size structure, density, and yield of forest stands

Characterization of the structure, dynamics, and productivity of mixed-species stands: review and perspectives

Keywords

6.1 Principles of Individual Tree Ontogeny

Box 6.1 Characteristics of a Tree’s Crown Morphology, Crown Extension, and Growing Area

Box 6.2 The Rules by Kleiber (1947) and Rubner (1931) for Explaining the Ontogeny and the Growth and Yield Curves of Individual Trees

6.2 Interaction Between Trees in Inter- Versus Intraspecific Environments

6.3 Basic Feedback Loop Between Growth, Structure, and Local Environment in Forest Stands

6.4 Growth and Yield at the Tree Level

6.4.1 Dominant Rather Than Open-Grown Trees as Reference

6.4.2 Evidence of Facilitation and Competition Effects at the Tree Level

6.4.3 Basic Growth Reaction Patterns in Intra- Versus Interspecific Neighbourhoods

6.5 Crown Size and Morphology in Mixed Compared with Monospecific Stands

6.5.1 Interspecific Variation in Crown Shape and Size

6.5.2 Intraspecific Variation in Crown Size

6.5.3 Modification of Tree Allometry in Interspecific Local Environments

6.5.3.1 Shift in Crown Allometry in Interspecific Compared with Intraspecific Environments

Box 6.3 Allometric Relationship Between Tree Dimensions, Ratios, and Ontogenetic Drift

6.5.3.2 Root Morphology and Root-Shoot Allometry

Box 6.4 Analysing the Allometric Relationship Between Coarse Root and Stem Growth of Trees in Mixed Versus Monospecific Stands

6.5.4 From Pattern to Process of Crown Expansion in Interspecific Neighbourhoods

6.5.4.1 Dynamics of Lateral Crown Expansion in Inter- Versus Intraspecific Environments

6.5.4.2 Variability of Crown Projection Area in Inter- Versus Intraspecific Environments

Box 6.5 Measures for the Variability of Lateral Crown Expansion of Individual Trees in Intra- and Interspecific Environments

6.5.4.3 Species Mixing and Inner Crown Properties

6.6 From Tree Morphology to Space Occupation

6.6.1 Crown Projection Area, Tree Stand Area, and Degree of Crown Engagement

6.6.2 Dynamics of Canopy Gap Occupation

6.7 Efficiency of Tree Crown Area and Tree Growing Area

Box 6.6 Crown Projection Area, cpa, and Stand Area, sa, of Trees

6.7.1 Ratios for Comparing Tree Growth in Mixed Versus Monospecific Stands

6.7.2 Elimination of the Size Effect from Efficiency Parameters

6.7.3 Transition from Tree Growth to Tree Productivity in Mixed Versus Monospecific Stands: An Example

6.7.4 Crown Engagement cpa/sa as Link Between Tree and Stand Level Evaluation

6.8 Overview of Some Main Causes and Effects of Tree Species Mixing on Individual Tree Growth

6.8.1 Complementary Exploitation of Crown and Root Space

6.8.2 Hydraulic Lift and Hydraulic Redistribution

6.8.3 Increased Availability of Mineral Nutrient Supply Through Deep-Rooting or Atmospheric N2 Fixation

6.8.4 Temporal Complementarity of Niches, Resource Use, and Growth

6.8.5 Modification of Growth Partitioning and Allometry of Trees in Inter- Versus Intraspecific Neighbourhoods

6. Take-Home Messages

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6.8.3 Increased Availability of Mineral Nutrient Supply Through Deep-Rooting or Atmospheric N₂ Fixation