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Keywords:

  • forest growth;
  • individual based model;
  • intrinsic and extrinsic growth limitation;
  • neighbourhood competition;
  • production decline;
  • self-thinning

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  • 1
    In growing forest stands, above-ground net primary production peaks early in stand development and then declines. The causes for this decline are not yet well understood, but hypotheses include physiological and ecophysiological effects, as well as changes in stand structure due to local competition among neighbouring trees.
  • 2
    The majority of existing studies address mono-causal explanations of this decline. Here we study the combined effects of intrinsic growth limitation of individual trees, growth limitation due to neighbourhood competition, and self-thinning.
  • 3
    We use an individual-based model to analyse forest wood production of a mangrove species described by a sigmoidal growth function, and two hypothetical species with exponential or linear growth. The model reproduces a decline for all species investigated, even when individual growth rates did not become limited.
  • 4
    We conclude that individual, sigmoidal growth curves are sufficient but not necessary to explain the production decline in natural forests where neighbourhood competition is appreciably active.
  • 5
    We show that the causes for production decline change during forest development. Whereas growth reduction through neighbourhood competition is the main process at the beginning, imbalanced wood loss dominates the later stage of the decline.

Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Age-related studies reveal that the above-ground net primary production of forests declines after the full canopy leaf area has been attained (Gower et al. 1996 among others). There is ongoing debate among ecologists about the causes for this well-known phenomenon.

Each of the following physiological explanations has been proposed as the dominant cause of the decline: changing imbalance between photosynthesis and respiration (Kira & Shidei 1967); a decrease in stomatal conductance caused by hydraulic constraints (Gower et al. 1996; Ryan & Yoder 1997); and changes in allocation (Linder & Axelsson 1982). Nutrient limitation increasing with forest maturation has also been discussed as a potential mechanism (Vitousek et al. 1989; Gower et al. 1996), although Ryan et al. (1997) argue that this is not well supported as a generalization. Binkley et al. (2002) proposed tree-to-tree competition leading to growing differences in the efficiency of resource use between dominant and non-dominant trees.

On the other hand, Gower et al. (1996) and particularly Weiner & Thomas (2001) argue that all these explanations should be considered in combination rather than separately. Weiner & Thomas (2001) furthermore claim that the age-related decline of production is size-related and simply a logical and thus inevitable consequence of the sigmoidal growth curves of individual trees. Here we intend to go beyond the logical argument of Weiner & Thomas and explicitly model how both the growth limitation of individual trees (i.e. sigmoidal growth functions) and competition among neighbouring trees affect the age-related production decline.

Several models already exist that describe growth and production in virtual stands (e.g. Prentice et al. 1993; West 1993; Murty et al. 1996; Mäkelä 1997; Valentine et al. 1997; Courbaud 2000; Ditzer et al. 2000; Mäkeläet al. 2000). However, these models are geared more to physiological processes and biomass partitioning within the trees than to neighbourhood competition (but see Bartelink 2000). They either describe ‘averaged’ individuals (West 1993; Murty et al. 1996; Mäkelä 1997; Valentine et al. 1997; Courbaud 2000; Mäkeläet al. 2000) or describe individual trees but not their specific spatial location (Prentice et al. 1993; Ditzer et al. 2000), or describe individual trees and their stem position but do not consider the distances between the trees (Mäkeläet al. 2000).

To describe neighbourhood competition appropriately, the model structure should meet the following criteria (Stoll & Weiner 2000): each tree should have an explicit spatial location, a basal area where no other individual can exist, and a zone of influence where it influences, and is influenced by, neighbouring trees. Furthermore, the number, size and location of neighbouring trees should be taken into account to quantify the competition pressure acting on the focal tree.

An individual-based, spatially explicit model that fulfils these criteria is the KiWi model (Berger & Hildenbrandt 2000). Originally developed to study mangrove forest dynamics, KiWi has also been used to address theoretical issues of self-thinning trajectories and dynamics of size-distributions in even-aged stands (Berger et al. 2002; Berger & Hildenbrandt 2003), asymmetric competition (Bauer et al. 2004), and cyclic population dynamics in perennials (Bauer et al. 2002). KiWi concentrates on a tree's spatial configuration and the resulting neighbourhood competition. Growth is described phenomenologically by using an individual growth function, instead of deducing it from physiological mechanisms like the above-mentioned models. This makes KiWi suitable for testing the argument of Weiner & Thomas (2001) in a spatially explicit context. We ask whether the age-related decline at stand level is observed only if individual trees show sigmoidal growth curves. In accordance with the stand level hypothesis of Binkley et al. (2002), we also ask whether growth depression due to neighbourhood competition could be strong enough to induce a production decline even if the trees were not limited in their growth by other factors. In simulation experiments designed to address these questions, KiWi is parameterized for the mangrove species Rhizophora mangle, and two hypothetical species characterized by a constant and a linearly increasing growth rate, respectively.

Methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

The KiWi model represents a tree by its stem position and a circular zone-of-influence on which a scalar field-of-neighbourhood (FON) describes the influence on potential neighbours (Fig. 1). Trees interact if their FONs overlap. The radius R of the zone-of-influence depends on the stem diameter of the tree R = a*(stem radius)b (Fig. 1). The values of a and b are chosen according to earlier calibrations of the model for R. mangle (Berger & Hildenbrandt 2000; Berger & Hildenbrandt 2003); the same values are used for the two hypothetical species described below. The field-of-neighbourhood is scaled between 1 (within the stem) and Fmin = 0.1 (at the boundary). Between the stem and boundary, the FON decreases exponentially. For a focal tree at a given time, the FONs of all neighbouring trees, i.e. those that overlap the focal tree's zone-of-influence, are additively superposed to determine a correction factor by which the potential current growth rate, which occurs without competition, is reduced (for details see Berger & Hildenbrandt 2000; Bauer et al. 2002; Bauer et al. 2004):

image

Figure 1. the KiWi model describes an individual by its ‘field-of-neighbourhood’ (FON). FON(r) defines the area within which an individual influences, and is influenced by, its neighbours, as well as its competition strength. The radius R of the FON increases with tree size. The FONs of neighbouring trees overlap. The sum F(x, y) marks the competition exerted by all existing individuals at the position (x, y).

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  • Growth rate  =  Growth ratepotential * CorrectionFactor
  • with CorrectionFactor  =  1 − f(FON)

The functions used to describe the potential growth rate (increment in stem diameter at breast height, d.b.h.) are as follows:

1 The mangrove (R. mangle) is described by a non-linear growth rate, which is widely used in gap models of forests (Shugart 1984):

  • image(eqn 1)

where G, b2, b3 are growth parameters, dbhmax is the maximum stem diameter, H is the tree height (see equation 4), and Hmax is the maximum tree height (see Fig. 2a, Chen & Twilley 1998, and Table 1 for parameterization).

image

Figure 2. (a) Growth curves of individual trees for hypothetical species with constant and linearly increasing growth rates and the mangrove species Rhizophora mangle. (b) Stem wood production of mono-specific forests consisting of the species described in (a). Each curve represents an average from 10 simulations. The square markers emphasize the period of production decline.

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Table 1.  Species-specific parameters of R. mangle obtained from Chen & Twilley (1998) and Berger & Hildenbrandt (2000), respectively. The average weight was used to calculate the stem wood production based on the annual volume increment
DescriptionParameterValueReference
Maximum stem diameter (eqn 1)d.b.h.max100 cmChen & Twilley (1998)
Maximum height (eqn 1)Hmax4000 cmChen & Twilley (1998)
Growth parameter (eqns 1 & 4), used also for hypothetical species (eqn 4)b277.3Chen & Twilley (1998)
Growth parameter (eqns 1 & 4), used also for hypothetical species (eqn 4)b30.396Chen & Twilley (1998)
Growth parameter (eqn 1)G267Chen & Twilley (1998)
  1077*http://www2.fpl.fs.fed.us
Average dry weight (eqn 5)Average weight10−3 tm−3 
Threshold mortalityΔd.b.h.crit0.3Assumed
FON parametera7.113Berger & Hildenbrandt (2000)
FON parameterb0.654Berger & Hildenbrandt (2000)
FON parameterFmin0.1Berger & Hildenbrandt (2000)

2 For theoretical considerations about the impact of the shape of the growth curve, a hypothetical tree species is defined that has a constant growth rate:

  • image(eqn 2)

3 A second hypothetical tree species is characterized by a linearly increasing growth rate in time:

  • image(eqn 3)

Thus in the hypothetical cases, there is no growth limitation due to tree age or tree size (Fig. 2a). The height of the trees is calculated according to Shugart (1984):

  • image(eqn 4)

For all three species the parameters b2 and b3 are those given for R. mangle in Table 1. The time increment Δt in all simulations is 1 year.

Mortality is assumed to be growth dependent (Kikuzawa 1993; Pedersen 1998; Berger & Hildenbrandt 2000; Keane et al. 2001). If the mean of the growth rates within a certain period falls below a critical value of Δdbhcrit the tree dies (see Table 1).

During the simulations, the fate of each tree was logged. Each tree's stem volume was geometrically approximated as a cylinder given by d.b.h. and tree height. Given the average weight of the wood (Table 1), the net stem wood production per year (SWP) was calculated with the total stem volume increment ΔVtotal as:

  • image(eqn 5)

In the same way, the gross stem wood loss of the stand was calculated by considering the stem wood volume of all trees that died in a certain year. In the following, we use stem wood production as a rough approximation for the above-ground net primary production, when regarding production decline.

We simulated monospecific forests of each species (R. mangle, constant and linearly increasing growth rates, respectively). Based on field observations at the Bragança peninsula in north Brazil (M. Adams et al., unpublished data), initially 10 000 trees are randomly distributed in a 1-ha empty plot. The initial d.b.h. of the trees is 1 cm. Each year, 100 new saplings are randomly released. They can establish only at locations that are weakly overlapped by FONs of established trees (F(x,y) < 0.5; Fig. 1). Thus, saplings tend to become established at forest gaps and under crown boundaries.

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

All stands, including hypothetical ones, show a stem wood production decline (Fig. 2b). Forests consisting of hypothetical trees with linearly increasing growth rates show highest stem wood production and the most pronounced decline. On the other hand, the declines observed for R. mangle forests and forests consisting of trees with constant intrinsic growth rates are almost similar. As individuals of the hypothetical species can only be hindered in their growth by neighbourhood competition, the shape of the stem wood production curves show the importance of competition for the decline. For a further demonstration of competition's impact on stem wood production of R. mangle forests, we carried out the following simulation experiment: we increased the competition of the individuals by increasing the FON parameter a (see Berger & Hildenbrandt 2003 for details). This scenario results in a lower maximum stem wood production and reduced absolute decline (Fig. 3).

image

Figure 3. Temporal course of stem wood production for different competition strengths (quantified by FON parameter a) among individuals.

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We look for the relation between decline and self-thinning by analysing the biomass-density trajectories of the stands (Fig. 4). Stem wood production starts to decline (square markers in Figs 2b and 4) at the end of the linear segment of the biomass-density trajectories, thus well after the onset of self-thinning. The d.b.h. size distribution is then rather narrow (Fig. 5a) and both stem wood production and loss is balanced and can mainly be attributed to the group of trees with d.b.h. of around 40–50 cm (Fig. 5b). In contrast, the d.b.h. size distribution is significantly wider at the end of the decline (Fig. 5c). The largest trees have then achieved a d.b.h. of about 90 cm but the majority of trees have stem diameters smaller than 20 cm, indicating rejuvenation. While all d.b.h. size classes contribute to the gross stem wood production, the massive wood loss caused by the death of the largest trees is not compensated (Fig. 5d). At this stage, the trees contributing most to the stem wood loss also belong to size classes with high mortality (Fig. 6). This is not the case at the beginning of the decline where size classes suffering the lowest mortality contribute most to the wood loss of the forest (compare Fig. 5b with Fig. 6).

image

Figure 4. Biomass-density trajectories of the forests investigated. Square markers correspond to those in Fig. 2(b) and show the period of production decline. Biomass was calculated as biomass = mean volume × average dry weight (Table 1).

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image

Figure 5. Each marker drawn in the left subplots represents the actual stem diameter (d.b.h.) and stem wood production (SWP) of an individual tree existing in the plot when total SWP is maximal (a) and at the end of the decline (c) (SWPmin s. Fig. 2b). The right subplots show the corresponding SWP and stem wood loss summarized for d.b.h. size classes at maximum (b) and minimum (d) SWP.

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image

Figure 6. Mortality of stem diameter (d.b.h.) size classes during 250 years for the simulated Rhizophora mangle forests and for real stands of the Norway spruce (after Monserud & Sterba 1999).

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Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Despite numerous investigations, there is still no consensus about the mechanisms that determine the age-related decline in wood production observed in plantations and in natural forests. The existing hypotheses can be subdivided into three groups: (i) (eco-) physiological constraints, (ii) natural resource limitations, and (iii) stand structure differentiation due to neighbourhood competition. A common feature of most of these hypotheses is that they focus on details of the mechanisms proposed. In contrast, Weiner & Thomas (2001) go beyond specific details and argue that the decline in production is not age related but size related, that the decline is inevitable because the growth of any organism will eventually be constrained, and that the search for a single physiological explanation is inappropriate because the proximate causes of growth limitation vary among tree species and forest ecosystems.

Like Weiner & Thomas (2001) we do not refer to specific mechanistic theories but simply focus on factors that reduce growth and, in turn, trees’ wood production. For this, our model assumes only a growth limitation of individual trees, so we cannot ask about the physiological mechanisms that might cause growth limitation resulting in a sigmoidal growth curve. However, many semi-mechanistic models do not deduce growth limitation from first principles either, but impose this limitation more or less by certain assumptions, e.g.: a forced reduction of projected crown area by a correction factor (Ditzer et al. 2000); a maximum leaf area density (West 1993); self-limitation of crown height (Mäkelä 1997); or a predefined reduction of photosynthesis of larger trees being indirectly proportional to crown height (Mäkelä 1997). As these features also lead to sigmoidal growth curves of individual growing trees, our phenomenological description is reasonable and adequate for the purpose of this study. In addition to an intrinsic growth limitation of individual trees, our model includes growth reduction due to local competition among neighbouring trees and mortality induced by growth suppression (self-thinning). It should be noted that our results do not depend on the details of the KiWi model but can be expected in general for all models describing neighbourhood competition explicitly.

Weiner & Thomas (2001) argue that sigmoidal growth of individual trees is a sufficient condition for a production decline. Our results show that it is not a necessary condition. The decline also occurred in hypothetical forests where individuals have constant or linearly increasing growth rates in which growth reduction and mortality was only caused by neighbourhood competition. This and the observation that individuals’ competition strength determines maximal achievable stem wood production and absolute decline (Fig. 3), suggest that competition among trees is likely to contribute to production declines observed in nature. The differences in the temporal pattern of stem wood production for R. mangle and the hypothetical species show nevertheless that intrinsic growth reduction may have an important impact on the course of decline. Thus, physiological hypotheses about the decline in production are of interest.

We studied the effects of neighbourhood competition considering self-thinning and natural recruitment, which has not been done before in studies of age-related production decline. Ryan et al. (1997) already recommended such a study but found that there were hardly any empirical data sets combining self-thinning, recruitment and production decline. Our finding is that decline starts after self-thinning. This confirms also the argument that stem wood loss is balanced by gross stem wood production during the self-thinning process (e.g. Shugart 1984; Pretzsch et al. 2002).

In our model the cohort of largest trees dominates wood production and wood loss when decline starts. At this time, wood production becomes more and more reduced due to neighbourhood competition, whereas mortality of the most productive d.b.h. size classes is low. Later on, stem wood loss becomes substantial. The death of large trees creates forest gaps, allowing the establishment of numerous saplings. Consequently, the size variability (seen as d.b.h. variability) increases, and smaller trees also contribute significantly to forest production but increasingly fail to compensate for the stem wood loss. This result seems to contradict Ryan et al. (1997), who state that mortality is not frequent enough and thus cannot contribute significantly to the decline. In our model this statement is valid at the beginning of decline, but not at later stages. Low tree mortality is observed in all size classes except the smallest (d.b.h. < 5 cm) and largest (d.b.h. > 70 cm, Fig. 6). The U-shape of this mortality distribution corresponds qualitatively to those of empirical time series (Monserud & Sterba 1999) and other modelling studies (Keane et al. 2001).

Our results are related to the stand-structure hypothesis of Binkley et al. (2002), in which changes in stand structure allow dominant trees to sustain high rates of growth by increasing their acquisition of resources, whereas smaller, non-dominant trees grow more slowly as a result of their more limited acquisition of resources and use the resources acquired less efficiently than dominant ones. Binkley et al. (2002) assume that growth by dominant trees cannot compensate for this lower efficiency and therefore overall stand production decreases. Our model does not address the resource use, so we cannot validate this part of the stand-structure hypothesis. In our study size differences increase while decline occurs, so differences in resource use efficiency may become increasingly important during this process. The causes for growth decline may vary not only among tree species and forest ecosystems (Weiner & Thomas 2001) but may also change during forest development.

Our results emphasize the need for investigations of changes in forest structure that accompany production decline. Most studies describe potential mechanisms in detail, but lack information about the structure and configuration of the forest under consideration. Such information will help us distinguish among alternative hypotheses.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

We are grateful to Jacob Weiner for discussions on the topic and his encouraging help. We thank furthermore Dan Binkley and two anonymous reviewers for helpful comments on an earlier version of this manuscript. This study is a result of cooperation between the Center of Tropical Marine Ecology (ZMT), Bremen, Germany, and the Universidade Federal do Pará and the Museum Paraense Emil’o Goeldi (MPEG), both Belém, Brazil, under the Governmental Agreement on Cooperation in the Field of Scientific Research and Technological Development between Germany and Brazil financed by the German Ministry of Education, Science, Research and Technology (BMBF) (MADAM, Mangrove Dynamics and Management, Project number: 03F0154A), and the Conselho Nacional de Pesquisa e Tecnologia (CNPq). This is MADAM contribution number 83.

References

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
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