Factors controlling resource allocation in mountain birch

Perspectives in Plant Ecology, Evolution and Systematics

Vol. 5/4, pp. 231–249 © Urban & Fischer Verlag, 2003 http://www.urbanfischer.de/journals/ppees

Factors controlling resource allocation in mountain birch Pekka Kaitaniemi & Kai Ruohomäki Section of Ecology, Department of Biology, and Kevo Subarctic Research Institute, University of Turku, Turku, Finland Received: 9 October 2002 · Revised version accepted: 19 January 2003

Abstract We present a comprehensive analysis of factors affecting resource allocation and crown formation in a subarctic birch tree, Betula pubescens ssp. czerepanovii (Orlova) HämetAhti. Using biomass measurements and digitized data on tree architecture, we investigated several hypotheses on various factors that may modify plant growth. We also analyzed the extent to which different mechanisms operate at different scales, ranging from individual shoots to the whole branches or trees. Different factors affected allocation at different levels of organization. Stem age had a minor effect, suggesting that similar control mechanisms operate at all stages of development. Fates of individual shoots were affected by their local growing conditions as indicated, for example, by the dependence of long shoot production on light. Buds formed in the current long shoots were likely to become new long shoots. In the innermost crown parts, radial growth had priority compared to long shoot production. Elongation of individual long shoots was controlled by two conflicting factors. Long distance from the roots suppressed growth, probably indicating costs associated with resource transportation, whereas a high level of light augmented growth. In contrast, growth of entire branches was not so clearly related to the availability of resources, but showed limitation due to allometric scaling. This set a relationship between the maximum long shoot number and the overall branch size, and may indicate allometric constraints to the way a tree is constructed. Strict allometric relationships existed also between other structural traits of mountain birch, most of them similar at all levels of branching hierarchy. However, despite the upper level restrictions set by allometry, source-sink interactions and localized responses of individual shoots operated as local processes that directed allocation towards the most favourable positions. This may be a mechanism for achieving efficient tree architecture in terms of resource intake and costs of transportation. Key words: allometry, apical control, plant architecture, resource allocation, source-sink interactions

Introduction Formation of a tree crown is a process governed by many and often intermingled factors. Depending on conditions experienced during the past growth, final

crown shape may vary greatly within even an individual species. However, despite great plasticity in the final shape, it is possible that rather simple design principles and control mechanisms underlie the contrasting crown architectures (Hallé et al. 1978; West

Corresponding author: Pekka Kaitaniemi, Hyytiälä Forestry Field Station, University of Helsinki, Hyytiäläntie 124, 35500 Korkeakoski, Finland; e-mail: [email protected]

1433-8319/03/5/04-231 $ 15.00/0

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et al. 1999a). Especially in trees, the modular functional organization permits semiautonomous and localized responses of structural parts to their environment (Sprugel et al. 1991; Room et al. 1994). This enables plastic growth where the final architecture may be determined by the most favourable local growth responses based on individual meristems constantly tracking their environment (Hutchings & de Kroon 1994; Ballaré 1999). However, the scale of control for various growth responses may, hypothetically, range from the level of whole tree to the level of individual small-scale modules, such as single meristems (Tuomi & Vuorisalo 1989). The scale of control is largely unknown for many growth responses in trees, because few studies have attempted to simultaneously consider a mature tree both as a whole entity and as a population of semiautonomous modules organized in three-dimensional space. Experimental studies often concentrate on tree saplings (Naumburg et al. 2001), or some parts of the tree crown only (Henriksson 2001), ignoring the responses in other parts. Descriptive analyses of tree architecture (Sabatier & Barthélémy 1999), analyses of bud populations (Lehtilä et al. 1994), and measurements of growth or biomass compartments of whole trees (Sterck & Bongers 2001), in turn, ignore most of the information on the three-dimensional arrangement of structures, which is crucial for light interception, for instance. Some studies have divided the canopy into small compartments to gain more accuracy (Sumida & Komiyama 1997), but since these are artificial divisions, there is a risk of failing to detect properly the modules responding to the environment. The modern analysis of tree growth employs methods for recording the exact three-dimensional structure of plants and their compartments with a digitizer (Sinoquet et al. 1997; Godin et al. 1999). Recording the topology and coordinates of plant structures allows easy calculation of various distance measures, lengths, angles, growth directions, numbers and locations of different structure types. Such information can be used for studying hypotheses about the factors controlling plant growth, such as interactions between sources and sinks (Marcelis 1996), apical control (Wilson 2000), allometry (West et al. 1999a), biomechanics (Niklas 1994), light interception (Takenaka 1994), gravimorphism (Wareing & Nasr 1961), and exposition of reproductive structures (Schoen & Ashman 1995). However, considering all these potentially confounded factors in an experimental study would be a truly challenging task. In this paper, we have taken an alternative approach and utilize information-theoretic methods to identify the simplest set of growth rules for describing

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growth and biomass allocation in a subarctic birch species, mountain birch [Betula pubescens ssp. czerepanovii (Orlova) Hämet-Ahti]. Biomass measurements and digitized data on tree structure form the basis for investigating the agreement between the observed allocation patterns and some of the central hypotheses on factors controlling tree growth. Due to its small size, mountain birch is a convenient study object with an easy access to the canopy of mature trees as well (Fig. 1).

Fig. 1. Mountain birch at the time of bud burst in spring. Growth takes place via elongation of long-shoot internodes that produce successive single leaves with axillary buds. In autumn, the terminal bud of a long shoot often dies or transforms into a dormant male catkin (small figure on the right), which matures in spring. In old trees, the majority of leaves are in monopodial short shoots, which usually bear three leaves, and do not elongate more than a couple of millimetres a year. The apical bud in a short shoot includes primordia for leaves flushing in the following year and, in reproductive short shoots, also for usually one female catkin (small figure on the left). Short shoots also retain the capacity to convert to a long shoot. All short-shoot leaves and the basal leaves of new long shoots burst simultaneously in the spring. New long shoots continue production of new leaves and buds during the summer. Some of the buds may remain dormant for long periods and produce leaves only after a catastrophic event (Lehtonen & Heikkinen 1995).

Factors controlling resource allocation in mountain birch

The information-theoretic analysis of measurements is based on the principle of parsimony and seeks, from among the set of candidate models formulated a priori, the model that best describes the structural information present in the data with the loss of information minimized (Anderson et al. 2000). While the approach may not separate the effects of confounded variables from each other, it does give a scaled ranking for alternatives, and that way suggests a suitable simplification of a study system with many imaginable factors involved. Our study operates with variables largely measurable by a digitizer, i.e. by collecting information from the outside of the tree, or with variables that can be easily derived from the digitized data. Such architectural variables indirectly estimate the physiological allocation processes inside a tree (Kaitaniemi 2000). Table 1 lists the main allocation variables and explanatory variables investigated in the study. The ex-

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planatory variables relate to the different hypotheses explained in the next section. Most of the allocation variables relate to the size and number of long shoots produced (Fig. 1), because these were the traits best addressable with the set of data collected. Like other birches, mountain birch has two types of leaf-bearing shoots, long shoots and short shoots (Macdonald & Mothershill 1983; Macdonald et al. 1984). Short shoot length was not included in the allocation variables because, in mountain birch, elongation of short shoots takes place in almost a constant manner (Fig. 1; see Material and Methods). The occurrence of shoot death was included since it involves reallocation of nutrients from the dying leaves. Some attention was paid to radial growth and reproduction as well, but the data did not allow as comprehensive treatment as with variables in Table 1. In some places, we have complemented our measurements by compiling and analyzing data available in the literature.

Table 1. Combinations of explanatory and allocation variables examined. All tree traits refer to the current-year (y) measurements whereas some explanatory variables were measured also one (y–1) or two (y–2) years before. Stem age was used a classification variable. Long shoot production and shoot death are binary variables, i.e. a bud either produces a long shoot or not, or a shoot dies or not. Explanatory variable

(a) Light environment 1. PARb (b) Transportation network 2. Distance from roots 3. Branching order 4. Distance to nearest shoot - above - below 5. Short shoot length

Allocation variable ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– Long shoot Long shoot Shoot Branch-specific length (y) production (y) death (y) long shoot growtha (y)

y, y–1

y–1

y

y, y–1

y y

y–1

y y

y y

y y y

(c) Apical control 6. Mean distance to long shoots above

y

(d) Gravimorphism 7. Angle to vertical

y

(e) Source-sink interactions 8. Total long shoot length 9. Predicted radial growth

y, y–1

y–1, y–2

(f) Developmental stage 10. Reproduction 11. Stem age

y, y–1 y

y

(g) Allometry 12. Stem/branch diameter a b

y–1

y

y–1

y–1

y

y y

Number and length as separate variables Photosynthetically active radiation

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Hypotheses investigated Light environment For plants, light is both an essential resource and one of the central control mechanisms affecting morphogenesis (Ballaré 1999). Accordingly, plants are supposed to have many adaptations for efficient light capture (Pearcy & Yang 1998), for example, by sensing their light environment (Huber-Sannwald et al. 1996). In trees, too, it has been clearly demonstrated that the amount of light intercepted affects growth (Messier & Nikinmaa 2000). Availability of light is also a central mechanism affecting the death of tree shoots and branches. Probability of death is high, if a branch cannot assimilate enough to cover its own maintenance costs (Sprugel et al. 1991; Henriksson 2001). However, it may not be so obvious when and where the effects of light take place in different plant species. For example, apical control (Wilson 2000), intra-tree competition (Sachs et al. 1993), allometric limitations (Niklas 1994) and preformation of buds (Kaitaniemi et al. 1999) may all interact with light, restricting the extent of responses presently available. Obviously, these possibilities need to be considered to uncover the full effects of light. We assumed photosynthetically active radiation (PAR) to potentially affect all the allocation variables examined (Table 1a). Elongation and production of individual long shoots may depend on the favourability of local growth conditions as affected by the amount of PAR received. The total amount of growth in a branch may also depend on PAR, if the other shoots contribute to elongation by providing photosynthates similar to long shoot leaves themselves. In the analyses of long shoot growth, the contribution of previous year PAR was also considered (Table 1a), because in mountain birch both the amount of elongation and determination of shoot types may partly depend on the resource status of the previous year. Thermal sum of the previous summer, a variable correlated with the amount of sunshine and PAR (Nöjd & Hari 2001), positively correlates with the current-year long shoot length (Haukioja et al. 1985). On the other hand, both previous-year and current-year defoliation of long shoots, i.e. reduction of photosynthesizing leaf area, reduce long shoot length (Ruohomäki et al. 1997). Preformation of buds, in turn, mediates the effects of the resource status experienced during the preceding summer, as suggested by reduced long shoot production a year after defoliation (Kaitaniemi et al. 1999). Therefore, in all cases, the values the variables had in the previous summer were used to explain current long shoot production (Table 1a).

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Transportation network A short transportation distance should be favoured to reduce the potential costs of transportation. In plants, transportation is two-way between roots and shoots, and so plants should be efficiently designed to simultaneously harvest and transport resources by structures both below- and above-ground. At least in terms of length, a tree-like transportation network is often the most efficient one compared to other designs (Banavar et al. 1999). At the same time, a tree canopy should be efficient in light capture and competition, as well as resist mechanical forces (Niklas 1994). We considered the distance from roots as an architectural trait best describing the efficiency of the vascular transport system (Table 1b). Accordingly, it was hypothesized that long shoots may gain more length, if the transportation distance from roots is short (Sterck & Bongers 2001). Similarly, the probability of long shoot production may be highest if a shoot is located in a microenvironmentally favourable position with also a short transport distance (Maillette 1987). On the other hand, long distance from roots may increase the risk of death of individual shoots (Buck-Sorlin & Bell 1998). All these are features that may explain ontogenetic differences in the amount of growth between young and old trees (Reed 1927). Another important demand for trees is the maintenance of efficient transpiration by leaves. Efficient hydraulic conductance is crucial for water transport, and several potential adaptations have been suggested to aid in this process (Zimmermann 1983). One is the lower conductivity of branches compared to the terminal, especially at the branching points. This is said to give, under unfavourable conditions, hydraulic preference to the main axes, thereby reducing the flow of nutrients into branches and, supposedly, reducing their growth and increasing their risk of death (Zimmermann 1978). We investigated the potential importance of these hydraulic features by including the branching order (Bell 1991) as an explanatory variable for long shoot length and the probability of shoot death (Table 1b). Efficient transpiration is also central for tree functioning, and demands the collective action of leaves (Hubbard et al. 1999). Costs of transpiration may become high, if few shoots are located along a route to a remote shoot or branch, and may thus increase the probability of shoot death. On the other hand, reduced number of neighbours may, as well, reduce the amount of competition between shoots (Heuvelink 1997), or have implications to the microclimate of shoots (Drouet & Bonhomme 1999). We examined the effect on the probability of shoot death of distance to both roots and to the nearest neighbouring shoots (Table 1b), which are variables that also reflect the amount of

Factors controlling resource allocation in mountain birch

leaves along a transport pathway. Distance was measured from the points of attachment to the branch. A similar logic applies to the use of short shoot length as an explanatory variable (Table 1b). The short shoots of mountain birch elongate a couple of millimetres a year and, with time, their leaves may be located quite far from the stem. However, very old short shoots are rare, which may reflect some disadvantages associated with being isolated from the stem, potentially related to the transportation distance. We measured short shoot length as the distance from its base to the tip of the shoot.

Apical control Plants have evolved control mechanisms to ensure efficient growth form in a given environment. Apical dominance or apical control is one of the most studied of such mechanisms (Cline 1997). Apical control can be defined as “the regulation of the primary and secondary growth of proleptic lateral branches, both young and old, that have grown from a bud following a single period of dormancy” (Wilson 2000). Inhibition of lateral growth may be beneficial for a plant under strict competition when it quickly has to elongate to better capture light (Aarssen 1995). Accordingly, young stems could be expected to show stronger apical control because they experience stronger competition for light than the already established old stems. Experimental evidence suggests that apical control is highest in the actively growing parts (Novoplansky 1996). A hormonal gradient also seems to be involved, such that the control weakens as the distance to an active growing point increases (Rinne et al. 1993). Therefore, to assess the strength of apical control exerted by growing parts, we calculated for each shoot its average distance to the current long shoots located in the more distal parts (Table 1c). This measure indicated both the position and the distance of shoots in relation to the current long shoots and was used to predict both the probability of long shoot formation and the final length of long shoots in the more basal parts of branches. To examine apical control at different developmental stages, we used stem age as an additional explanatory variable (Table 1f).

Gravimorphism Gravimorphism is a term describing the effect of shoot angle on shoot growth (Wareing & Nasr 1961). Tree shoots usually grow more if their angle to the vertical is small. Thus, in addition to apical control, this is a mechanism that may restrict the lateral spread of a tree crown. To assess the contribution of gravimor-

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phism, we calculated the angle between the vertical and the direction of growth for each long shoot, and examined this as a variable potentially contributing to long shoot length (Table 1d).

Source-sink interactions Within plants, there is a constant interplay between sources, i.e. structures that provide the plant with nutrients or photosynthates, and sinks, i.e. structures that import nutrients and photosynthates for their own growth or storage (Marcelis 1996). To some extent, both sources and sinks may control allocation. Resource supply from sources may control formation of new sinks (Kaitaniemi et al. 1999) whereas the presence and activity of sinks may control the activity of sources (Wibbe & Blanke 1995). For example, decreased demand for resources may decrease photosynthesis. Apical control may also be confounded with sink activity, i.e. strongest sinks exhibit strongest apical control (Stoll & Schmid 1998). A common view is that sinks compete for resources with each other. Sink strength, the relative activity of a sink compared to other sinks, determines the competitive ability of a sink to draw resources for its growth (Minchin & Thorpe 1996). In mountain birch, defoliation experiments suggest that individual shoots are largely independent in their growth responses (Ruohomäki et al. 1997). However, defoliation responses may only reflect differences in the availability of photosynthates and, therefore, it was reasonable to use sink strength to study the possibility of competition for mineral nutrients as well. Since we were not able to quantify sink strength directly, without physiological measurements on sink activity during growth, we used the observed realized strength, such as the final length of long shoots, as an approximation. For testing some hypotheses, this was justified. First, we tested whether proportionally more growth occurs in branches that invested more biomass in long shoots in the previous year, i.e. had the highest sink activity during the time of shoot formation (Table 1e). Second, we tested a hypothesis confounded with apical control that the length of a given long shoot could be larger the farther away the competitors are, i.e. the greater the distance to other long shoots is (Table 1c). Third, we tested whether the scarcity of strong sinks (long shoots) affected the probability of shoot death, for example, via poor resource flow within the branch (Table 1e). During a certain stage of development, long shoots may also act as a source of photosynthates but even then they are likely to act as sinks for mineral nutrients. Mineral nutrients are subject to competition because they are limiting growth in our study area (Karlsson & Nordell 1996; Ruohomäki et al. 1996).

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Radial growth of the stem may form a sink competing with elongation. The more there is foliage to support, the higher the demand for radial growth is. Therefore, we also considered the local ‘need’ for radial growth (predicted radial growth) as an explanatory variable for the formation and length of long shoots (Table 1e). The predicted radial growth was empirically determined from the data by using an allometric relationship that described the dependence of branch diameter on the amount of foliage. The amount of diameter growth required to support the annual increase in foliage was then calculated on the basis of the foliage produced by long shoots during the previous year. Accordingly, the predicted radial growth also indicated the cumulative size of the long shoots above a given point.

Developmental stage During maturation and after attaining a certain size, trees switch from pure vegetative growth to the reproductive phase. This may, in addition to other size- and age-related effects, reduce allocation to growth in favour of reproduction (Silvertown & Dodd 1999). However, only few catkins were present in the experimental trees during the study years and hence possibilities for directly investigating the effect of reproduction on growth were limited. We relied on observations that 1998 was a year of high reproductive output in the study area in general (Selås et al. 2001), as recorded also in a tree-line garden close to our study area (S. Neuvonen, unpubl. data). Because young stems do not produce female catkins, it was plausible to compare differences in the growth between young and old stems before, during and after the reproductive peak (Table 1f). The contribution of other and unspecified differences in resource allocation between developmental stages was explored using stem age as an explanatory variable (Table 1f).

Allometric scaling of structure Theoretical studies by West et al. (1999a, b) have provided a mechanistic explanation to the allometric scaling laws often empirically detected in plants and other organisms (Niklas 1994). Their explanation is based on the assumption that natural selection has maximized both metabolic capacity, by maximizing the scaling of exchange surface areas (such as leaves in canopy), and internal efficiency, by minimizing the scaling of transport distances and times (such as branching and structure of tree stems). From the allometric scaling principles, several predictions concerning the structural and physiological traits of plants can be predicted, for example, as functions of radius or mass of plant branches (West et al. 1999a).

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These predictions serve as a high-level explanation for structural tree traits, aggregating traits of structural entities. Accordingly, in addition to the variables listed in Table 1, we investigated the possibility that allometric scaling may be a central factor controlling the structure and volumetric growth of mountain birch at the scale of whole trees or branches (Table 1g). Quantifying deviations from the theoretical allometric relationships assessed the relative importance of factors other than allometric rules. For example, potential differences in allometric scaling between young and old stems could indicate ontogenetic changes in allocation patterns and consequent allometric relationships. The closely similar pipe model theory (Shinozaki et al. 1964; West et al. 1999a) was not separately addressed because it relies on related, but more constrained, relationships between the sapwood area and the amount of growth and foliage in a tree. Although the values listed by West et al. (1999a) do not directly predict the fates of individual shoots, we also examined this by considering the amount of radial growth, as determined by allometric relationships, as an explanatory variable at the level of individual shoot positions within branches (Table 1e).

Genes and environment Except for light interception and annual temperature sums, other environmental variables were not measured. The genetic background of the experimental trees was also unknown. Potentially, there existed a large amount of genetic variation between tree individuals because mountain birch is an introgressive hybrid between B. pubescens ssp. pubescens and B. nana (Elkington 1968; Vaarama & Valanne 1973), and may to varying degrees express different traits of either parent species (Karlsson et al. 2000). Therefore, to obtain an estimate of the potential joint contribution of genetic background and microenvironment on the control of mountain birch growth, we also included the term ‘tree’ as an explanatory variable in the data analyses to estimate the variation between individual trees and to quantify its contribution to the overall model fit. The term ‘year’ was also used in the analyses to account for the contribution of weather and other annual variation in growth conditions.

Material and methods Study site and tree species The study was conducted at a 50-ha area of a forest located 200 m a.s.l. on Puksalskaidi hill, in the vicinity of the Kevo Subarctic Research Station (69º 45′ N,

Factors controlling resource allocation in mountain birch

27º 01′ E). For the study, we selected 45 free-standing mountain birch trees (Fig. 1) growing in a sparse mixed forest with Scots pine (Pinus sylvestris L.). Freestanding trees were used to minimize competition, shading and other potential interactions between trees. The experimental trees usually had one old main stem (1.5–2.5 m high) and a small number of young basal sprouts (0.5–1 m high), which made them resemble more the monocormic than the polycormic form of mountain birch (Vaarama & Valanne 1973). The height of the old stems was about half of the maximum birch height observed in the study area. One actively growing young sprout, when available, and one old stem were selected for each tree. This enabled us to compare the effect of stem age in genotypically identical individuals of a single clone, growing in the same microclimatic and nutritional conditions. Of the 45 trees, 24 had a basal sprout used in the experiment. Based on their crown size and on the number of petiole scars in the oldest short shoots, the old stems were estimated to be 20–50 years old and the young stems to be 2–5 years old.

Measurements and data The 3D structure of trees was digitized in summer 1999 using a Polhemus FASTRAK equipped with a stylus and a LONGRANGER transmitter (Polhemus Inc., Colchester, VT, USA). The stylus was used to record the coordinates for the points at the base of each visible shoot, at the base of branching points and at the tip of each shoot where the primordial bud for the next-year growth is located. A branch was defined as any side shoot growing from the main shoot and having at least two buds capable of producing leaf-bearing shoots. The coordinates were captured with Pol95 software (INRA, Clermont-Ferrand, France) running on a portable computer. Simultaneously, a spreadsheet program was used to take records on the type and age of shoots, and on the topological connections between shoots. The shoots were recorded as ‘dead’, ‘dormant’, ‘short shoot’, ‘long shoot’, and ‘with catkin’ or ‘without catkin’. Using the petiole scars in short shoots, we determined the age of youngest shoots two years backwards, allowing us to simultaneously obtain growth data for three years 1997–1999. However, death of shoots was recorded only in 1999 and 2000 when direct observations were possible. Death of individual shoots or branches often takes place in late summer just before the autumn senescence. Because leaves on the dying shoots are the first ones to turn yellow, they were easily recognizable at this stage. The topological positions of long shoots produced in 2000 were recorded by hand, and their lengths were measured with a ruler. This was sufficient to link them

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to the positions of their mother shoots digitized in 1999. During digitizing, the trees were surrounded with a wind shelter to achieve the typical 1-cm field accuracy in determining the coordinates (Thanisawanyangkura et al. 1997). To measure biomass allocation to leaves, the number, weight and area of full-grown leaves was measured from samples taken from shoots at different parts of young and old stems of each tree. These measurements were used to estimate the leaf number, weight and area for all shoots in each tree. The estimated values were then used for calculation of PAR, biomass and the number of leaves. We clipped mature short shoot leaves from 2–3 basal and apical short shoots aged >5 years (less in young stems), as well as from long shoots and two-yearold and one-year-old short shoots. The leaves were weighed fresh and scanned for area measurements. Dry weight was measured after two days drying in a 60 ºC oven. Shoot-specific leaf number, which is nearly constant within mountain birch individuals, was determined by visually inspecting shoots of different ages. To estimate the biomass of structures other than leaves, we destructively sampled 12 stems, both young and old, that belonged to six trees in the immediate neighbourhood of the study trees. The dry mass and volume of 2–7 stem pieces (including bark), representing parts with different diameter, age, canopy position and branching order, were determined from both young and old stems of each tree. Using these data, the wood densities were estimated for the woody parts of short shoots, long shoots, and the older parts of branches. Leaves, petioles and primordial buds for the next year were oven-dried and weighed separately. The parameters obtained were then used to estimate the biomass of different compartments for the experimental trees (Table 2). Measurements of diameter and length of branch segments were used to estimate branch volume and, further, branch biomass in the experimental trees. Depending on tree size, branch diameter was measured from 10–25 points representing different parts of the main stem, as well as branches with different age and branching order. For the remaining parts, branch diameter was interpolated. In the data analyses involving diameter, we used only the actual measured branch diameters.

Table 2. Parameters for calculating the biomass of structures in experimental trees. All weights are in dry weight; 95% confidence limits given in parentheses.

Petiole weight (mg) Bud weight (mg) Branch density (g cm–3) Short shoot spur density (g cm–3)

Long shoot

Short shoot

2.36 (2.08–2.64) 4.27 (3.47–5.05) 0.60 (0.54–0.66) –

3.86 (2.99–4.72) 8.29 (6.74–9.85) 0.57 (0.55–0.59) 0.60 (0.56–0.64)

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To obtain various distance and length measures, and to count the numbers and types of different structures present above or below a certain shoot in a stem, the algorithm described in Kaitaniemi & Honkanen (1996) was modified to calculate and collect positionspecific information for each shoot. To do this, the topology of each stem was represented as a data structure tree (Cormen et al. 1990) where shoot-specific data, originating from digitizing and biomass measurements, were attributed to each node of the tree to be used in the calculations.

Light interception The relative amount of PAR intercepted was estimated for each leaf with calculations made with the LIGNUM modelling system (Perttunen et al. 1998). The three dimensional structures of the digitized trees were reconstructed in the program and the amount of PAR was then calculated for each leaf. The sky was divided into 64 sectors and the amount of radiation coming from each sector was calculated assuming a standard overcast sky (Perttunen et al. 1998). Leaves were simulated as partially filled (82%) disks. Leaf number was set according to shoot age for all shoots with known age. All other leaf-bearing shoots were assumed to have a number of leaves typical for the old short shoots of a tree. However, the shoot-specific leaf number was set randomly if it showed clear variability within a tree. For example, when two-year-old shoots equally often had either two or three leaves, which was typical in many trees, a random choice was made between these values for each two-year-old shoot. The angle of leaves with respect to the horizontal direction was set as a random number between –30º and 30º for each leaf. This estimates the variation observed in angles in the field. The estimated PAR-values were verified with measurements using PAR quantum sensors (type QS, Delta-T Devices Ltd, Cambridge, UK). During each measurement, two sensors were mounted in a horizontal position as close as possible to the reference shoots located at two different parts of a tree crown. A control sensor was placed on an open area close to the tree, and the amount of PAR was calculated in relation to the control value. Two to six ten-minute PAR measurements were made on 13 stems, using both basal and apical shoots to obtain a representative sample of light conditions inside the tree canopy. The measurements were conducted under uniformly overcast sky, which gives a good estimate of the actual availability of PAR (Gendron et al. 1998).

models were used as an analysis tool for categorical responses describing the probability of long shoot formation and shoot death. These variables were investigated with separate models because of their minor overlap, i.e. shoot death usually occurred in a different part of the tree canopy than long shoot growth. Stepwise selection was used as method for choosing the final explanatory variables and their interactions. Linearity of logits was confirmed with Box-Tidwell transformation. The analyses were conducted with the procedures LOGISTIC and GENMOD in the SAS System (SAS Institute Inc., Cary, NC, USA). Binomial distribution gave the best fit with the data, even though the values of model deviance indicated some underdispersion, probably due to the low number of events (changes in bud status) with respect to the number of trials (total number of buds). For continuous variables, we used both linear and nonlinear regression models (SAS procedures REG, NLIN and GLM). Data plots and correlation analyses were used to detect potential interactions, and to assess collinearity between variables. Spearman rank correlation was constantly used in the analyses where some variables had non-normal distributions. We used the measures of percent of variance explained (R2) and the Bayesian Information Criterion (BIC) as the principal methods for comparing the explanatory power of models with alternative but nested sets of variables. BIC was chosen as the criterion because it favours simpler models than Akaike’s Information Criterion or a test of log-likelihood ratio when the sample size is large (Zucchini 2000), as was the case in the analyses of shoot-specific data. In general, the analyses were based on tree-, branch- or shoot-specific values depending on the level of response variables explained. Tests of significance for individual variables were mainly used to indicate the statistical significance in relation to other ones during the stepwise selection of variables, and they may not present true statistical significance due to the repeated measurements made on the same tree individuals. Because we were most interested in detecting the patterns predicted by the well-identified explanatory variables (Table 1), the contribution of unspecified differences caused by year, stem age or tree individual was considered only at the last step of model fitting, by quantifying the subsequent change in the fit after their inclusion.

Results

Data analyses

Light interception

The general rationale of statistical analyses was to detect the set of explanatory variables best explaining the values of allocation variables (Table 1). Logistic regression

The simulated values of PAR interception were clearly correlated with the measured ones (r = 0.58, P < 0.0001, N = 58), and provided a reasonable indi-

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cation of the radiation level for the individual shoots within the mountain birch canopy (Fig. 2). At low PAR values < 0.5, the simulated values seemed to be slightly higher than the measured ones, which may indicate the effect of surrounding vegetation. Although the trees had no nearby neighbours, the surrounding trees may have affected the PAR received by shoots closer to the ground.

Long shoot length Long shoot length was typically less than twenty centimetres but showed a great deal of variation not explicable by the variables examined (R2 < 0.16). However, a graphical examination of data revealed that both low current-year availability of PAR (Fig. 3) and a

Fig. 2. Correspondence between the simulated and measured values of photosynthetically active radiation (PAR) in mountain birch. Values represent the relative amount of PAR received by individual shoots in different parts of tree canopies under uniform overcast sky; the 1:1 line is shown as well.

Fig. 3. Dependence of the length of individual long shoots on the availability of photosynthetically active radiation (PAR). The function for the maximum is the same in all years, and covers at least 95% of the points each year.

Table 3. Spearman correlation coefficients in the 1999 data between the shoot-specific values of the variables listed in Table 1. Depending on the presence of missing or incalculable values, N ranged roughly from 16,000 to 31, 000.

PAR (y–1) Root distance (y) Mean dist. to long shoots (y) Branch diameter (y) Predicted radial growth (y) Predicted radial growth (y–1) Predicted radial growth (y–2) Angle to vertical (y) Short shoot length (y) Dist. to nearest shoot above (y) Dist. to nearest shoot below (y)

PAR (y)

PAR (y–1)

Root dist. (y)

0.83 0.14 –0.10 –0.30 –0.01 –0.11 –0.01 0.08 –0.27 0.07 0.06

0.13 –0.03 –0.25 0.15 –0.06 –0.01 0.09 –0.32 0.05 –0.01

–0.05 –0.10 –0.08 –0.09 –0.05 –0.03 –0.00 –0.08 –0.06

Mean dist. Branch to long diameter shoots (y) (y)

Pred. radial growth (y)

Pred. radial growth (y–1)

Pred. radial growth (y–2)

0.67 0.61 0.48 0.07 –0.01 0.15 0.34 0.06

0.34 0.06 0.02 –0.07 0.15 0.01

0.07 –0.01 0.05 0.17 0.03

–0.01 0.02 0.04 0.02

0.58 0.58 0.06 –0.04 0.36 0.44 0.07

Angle to vertical (y)

–0.01 –0.00 –0.00

Short shoot length (y)

Dist. to nearest shoot above (y)

0.28 –0.12

0.09

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long distance from roots set a maximum that restricted long shoot elongation (Fig. 4). We summarized these effects with functions that confined at least 95% of the points each year (Figs. 3, 4). It was evident that PAR and root distance had an independent effect on long shoot length because PAR is highest in the apical part of the crown where distance from the roots is greatest. This independent relationship was also suggested by only a weak correlation between current-year PAR and root distance (Table 3), indicating that long distance from roots alone does not predict PAR due to the occurrence of self-shading. In addition, there was a substantial effect of tree on long shoot length (increasing R2 by 0.09), but stem age had a minor contribution (increasing R2 by 0.03). Including all the estimable interactions between the explanatory variables and the terms year, tree and stem age did not improve the model fit considerably as R2 remained below 0.35. This suggests that largely similar mechanisms were affecting long shoot elongation in all trees and stems during all years. Figures 3 and 4 also indicate differences in the long shoot length between years. The term year alone explained a fourth of the variation (R2 = 0.25). The average length was highest in 1997, declining towards 2000 (Fig. 5). This may partially indicate the joint action of root distance and year. As the trees grow, the distance of branch tips from roots increases and may

contribute to reduced long shoot length although it is unlikely to explain the observed rapid decline of long shoot lengths. The term year, in turn, includes yearspecific weather conditions as an important component. In mountain birch, the thermal sum of the previous summer correlates positively with the current long shoot length (r = 0.43, P = 0.02, Fig. 6). In our data, the years 1997 and 2000 seemed to be extremes compared to the overall variation (Fig. 6), the year 1997 mainly due to the plentiful growth of young stems (Fig. 5). Because some of the effects of the factor year became expressed with a delay, we examined whether PAR acts in a similar way. We selected a subset of shoots having at least 0.3-unit difference in PAR between successive years and plotted the long shoot length against their PAR values. In this subset, the current-year PAR seemed to explain the maximum length as it produced a pattern very similar to Fig. 3, whereas previous-year PAR did not produce a clear pattern (data not shown). According to our simulations, the average amount of PAR received by shoots in a tree remained the same over the four years, ranging from 0.73 to 0.75, suggesting that there was no marked increase in the treelevel self-shading due to tree growth. There was also a strong correlation between the PAR values simulated for successive years (Table 3).

Fig. 4. Dependence of the length of individual long shoots on the distance of shoots from roots. The function for the maximum is the same in all years and covers at least 95% of the points each year.

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Factors controlling resource allocation in mountain birch

As year 1998 was noted as a masting year in mountain birch, we used an ANOVA with stem-specific means to test for the interaction between the factors stem age and year, potentially indicating the effects of reproduction on growth of old stems, which were mature enough to reproduce. There was a significant interaction (F 3, 64 = 10.2, P < 0.0001), caused mainly by the proportionally greater elongation of young stems in 1997 and weaker in 2000. The 1997 result suggests that the factors leading to plentiful long shoot growth in 1997 may have been the same that enabled a reproductive peak in old stems in 1998.

Long shoot production Several factors contributed significantly to the probability of an existing shoot (either long or short shoot) to produce a new long shoot (Table 4). PAR clearly had the greatest impact, positively related to the probability of long shoot production. Shoots located far from the current long shoots and in the basal stem parts that required a large amount of radial growth were not likely to produce new long shoots (Table 4). Because the correlations between the variables were weak (Table 3), the effects were largely independent from each other. The model with all the explanatory variables and their interactions showed a poorer fit (BIC = 26,052) than the final model in Table 4 (BIC = 25,989). However, factors not covered by the variables examined may have controlled long shoot production as well. There was a large amount of overlap in the values of ex-

Fig. 5. Year to year changes in long shoot growth of mountain birch. Year 1998 was a masting year. Average length with 95% confidence limits shown separately for young and old stems.

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planatory variables in the categories of shoots remaining short shoots and shoots producing long shoots (Table 4). This implies that a large number of short shoots remained unchanged despite explanatory variables reaching values that favoured long shoot production. The overall model fit was further improved by adding the terms tree (BIC = 25,543) or year (BIC = 25,626). Including the interactions with tree did not improve the model fit (BIC = 26,014), whereas interactions with year resulted in a considerable improvement (BIC = 25,016). This is likely due to the term year reflecting the effect of unmeasured weather factors. If weather does not favour growth, long shoot production is likely to decrease, and especially the

Table 4. Variables affecting the production of new long shoots according to a logistic regression model. Parameter

Model statistics ––––––––––––––––––––––2––––– Estimate χ (SE)

Intercept

–6.43 (0.11)

3336a

PAR (y)

5.12 (0.13)

1525a

0.8 (0.1)

0.7 (0.1)

a

0.1 (0.2) 1.9 (7.2)

0.2 (0.4) 5.7 (12.0)

b

Pred. radial growth (y–1) –1.61 (0.08) Mean dist. to long shoots (y)c –0.02 (0.003)

395 47a

Averages (SD) –––––––––––––––––––––––––– New long Short shoot shoot

a

df = 1, P < 0.0001 In millimetres c In centimetres b

Fig. 6. Relationship between the long shoot length and the previous year thermal sum (dd2, degree-days above the base of 2 °C). Data compiled from several studies.

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predictor of the number of buds produced in mountain birch (Fig. 7). This indicates the role of long shoots in production of both new assimilative shoots and in replacement of dead shoots. Furthermore, in mountain birch, the age-structure and number of buds together determine the amount of foliage available, because both the number and the area of leaves increase as the shoots become older (Table 5). In long shoots, the number of leaves follows the number of buds produced because each bud is subtended by a single leaf. In addition to these, two to three basal leaves are grown depending on the age of the mother bud. The buds of the basal leaves usually die or remain dormant.

Shoot death Fig. 7. Relationship between long shoot length and the production of new buds capable of forming leaf-bearing shoots (additional buds may remain dormant or die). The figure shows stem-specific averages for each year; the function fitted to the data depicts the relationship.

shoots in the unfavourable positions may be less likely to produce new long shoots. Stem age did not contribute to the explanatory power (BIC = 25,992), and adding its interactions resulted in a minor improvement of the model fit (BIC = 25,950), suggesting that control of growth was basically similar in young and old stems. The improvement was mainly due to the term stem age × mean distance to long shoots, which together with stem age and without other interactions gave BIC = 25,938. This reflects the fact that the internodes between the individual buds were longest in the young stems which produce the longest long shoots and proportionally less buds (Fig. 7), resulting in longer mean distances (7.8 cm in young vs. 5.3 cm in old stems). Indeed, the spatial arrangement and the number of new buds produced is an essential component of shoot production. In birches, long shoots are responsible for bud production, and long shoot length was also a good

Shoot age, as indicated by shoot length, and average distance to long shoots were the factors affecting the probability of shoot death (Table 6). The model with only these factors had a better fit (BIC = 3729) than the model with all the estimable interactions (BIC = 4182), or intermediate models. Again, there remained a large overlap in the values of explanatory variables, indicating that unstudied factors were involved in shoot death (Table 6). There were no tree-specific differences in the mechanisms affecting shoot death, as indicated by the lack of improvement in the model fit with the inclusion of the term tree and its interactions (BIC = 4323). The effect of stem age and its interactions was also absent (BIC = 3767). However, there were too few dying shoots in the young stems to warrant a reliable conclusion.

Branch-specific growth In a regression analysis, branch diameter (regression coefficient b = 0.73, P < 0.0001) and the total length of previous year long shoots (b = 0.12, P < 0.0001) additively influenced the total length of new long shoots in a branch (R2 = 0.34), and were also positively correlated with each other (r = 0.52). Inclusion of all continu-

Table 5. Number and area of leaves in the shoots and stems with different age and position (SD in parentheses).

Table 6. Variables affecting shoot death according to a logistic regression model.

Shoot type

Parameter

Model statistics –––––––––––––––––––––––––––– Estimate (SE) χ2

Intercept Short shoot length (y)b Mean dist. to long shoots (y)b

–4.1 (0.1) 0.40 (0.04) –0.02 (0.004)

Young stem –––––––––––––––––––––––––––– Number Area (mm2)

Olda basal short shoot 3.0 (0.2) Oldb apical short shoot – Two-year-old short shoot 2.2 (0.5) One-year-old short shoot 2.0 (0.1) a b

871 (169) – 776 (202) 654 (152)

Old stem ––––––––––––––––––––––––––––– Number Area (mm2) 3.1 (0.3) 3.1 (0.3) 2.5 (0.5) 2.0 (0.2)

885 (190) 854 (221) 726 (167) 596 (156)

More than five years in old stems, less in young stems. Not present in young stems.

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a b

df = 1, P < 0.0001 In centimetres

1737a 113a 36a

Averages (SD) ––––––––––––––––––––––––––– Dying Alive

2.3 (1.3) 6.4 (15)

1.8 (1.1) 9.3 (16)

Factors controlling resource allocation in mountain birch

ous explanatory variables and all possible interactions produced R2 = 0.57, but the increase in the explanatory power could not be attributed to any individual effect. Obviously, it merely reflected the large increase in the number of model parameters. When the classification factors ‘tree’ and ‘stem age’ were included (GLM model), the effect of tree was considerable as it alone increased R2 by 0.22. Including interactions with tree resulted in R2 = 0.94, but then the model was almost saturated. Stem age and its interactions increased R2 only by 0.02 suggesting, again, related control mechanisms in both young and old stems. Additional examination of data revealed that the observed relationship between the branch diameter, the total length of previous-year long shoots, and the total length of current long shoots was mainly caused by an effect of branch diameter on long shoot number. We collected data from the literature and plotted the total short shoot number of a branch, a variable associated with branch diameter (see below) and frequently reported in the literature, against the total long shoot number of a branch. This indicated the presence of a maximum number of long shoots that a branch with a given short shoot number could produce (Fig. 8). A lot of variation remained below the maximum (Fig. 8). The scaling exponent for the function illustrating the maximum was 0.75 while the exponent 4/3 based on the theoretically assumed relationship between the leaf number and branch mass (West et al. 1999a) seemed to produce a too steep increase. However, it is not that obvious what the true exponent

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should be, because new long shoots increase simultaneously both the mass and the leaf number of a branch. Unfortunately, usually neither the mass nor the leaf number of long shoots in Fig. 8 was available. A further literature search revealed that, similar to long shoot length, part of the variation might be explained by the contribution of previous-year thermal sum on long shoot production. The correlation had a similar magnitude (r = 0.4) with that in Fig. 6, but was not significant due to the lower number of points available (n = 9). However, the observed positive relationship between the thermal sum and long shoot production is in line with defoliation studies suggesting that the current-year resource status may affect long shoot production next year (Ruohomäki et al. 1997; Kaitaniemi et al. 1999). Measurements of radial growth suffered from a large measurement error (including negative growth) due to the small amount of growth and difficulties in taking repeated measurements at exactly the same branch positions. However, the accuracy was sufficient to demonstrate that the amount of radial growth was positively related to the total number of long shoots produced in the previous year, and located above the measurement point (the corresponding regression being radial growth (cm) = 0.12 + 0.003 long shoot number, P < 0.0001 for the regression coefficient, R2 = 0.2). This gives justification to the use of the predicted radial growth as an explanatory variable in the analyses (Table 1). There was a much weaker relationship with the buds produced by the current-year

Fig. 8. Relationship between the short shoot number and the number of long shoots produced in mountain birch branches or stems with variable size. A function to estimate the maximum is also shown. Data from several studies compiled and plotted on a logarithmic scale. In some cases, long shoot number is below one, because the value is based on the average of several branches.

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long shoots (R2 = 0.01, P = 0.1), suggesting that radial growth follows the increase in the shoot number with a one-year delay. Predicted radial growth did not show strong correlation with any other variables (Table 3).

Allometry and biomass allocation In general, there was a close correspondence between the theoretical (Table 1 in West et al. 1999a) and the observed allometric relationships. The height of young and old stems followed almost the same scaling with respect to the tree biomass and basal diameter (Fig. 9). A branch-level analysis, in turn, indicated that the basal diameter of a branch followed the same scaling relation with respect to branch biomass at all branching orders and at both stem age classes (Fig. 10). However, relating branch-specific shoot number to branch biomass or branch diameter revealed that the rate of change (scaling coefficient) was different between the main stem and branches, although the scaling relation remained almost the same and relatively close to the theoretical prediction (Fig. 10). A likely explanation is the shedding of dead branches from the main stem, which reduces the rate of increase in shoot number.

Fig. 9. Allometric scaling relationships between biomass, basal diameter and the height of mountain birch stems drawn on a logarithmic scale. Data for young and old stems plotted separately. Curves fitted to the data use either observational or theoretical scaling exponents (R2 given for both).

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Discussion Long shoot growth Different mechanisms were found to control allocation at different scales of mountain birch organization. The fates of individual shoots were affected by their local growing conditions as indicated, for example, by the significant effect of PAR. Growth of whole branches, in turn, was not related to the overall amount of PAR received but showed limitation with respect to branch size. This may not be an active control mechanism but rather indicates allometric constraints to the way a tree crown is constructed (West et al. 1999a, b). Clear allometric relationships were present between many structural traits of mountain birch. Accordingly, long shoot growth may not exceed a certain maximum within a branch, even though all the shoots were located in favourable conditions. In the same way, initiation of new long shoots was, to some extent, decoupled from the factors affecting long shoot length. Production of long shoots seemed to be constrained by a hierarchy among buds whereas elongation was more clearly related to the availability of resources. A bud already located in the apex and well exposed to light, i.e. usually a bud in a long shoot, was likely to continue growth as a long shoot as illustrated by the positive effect of PAR. On the other hand, a bud located far from the current long shoots was less likely to become a new long shoot, which disagrees with the idea that apical control weakens with increased distance from the actively growing parts. However, the effect of distance was weak and may be associated with the other factor suppressing long shoot production, i.e. the need for excessive radial growth in the inner parts of crown, which may also be related to possible hormonal effects (Wilson 2000). Altogether, occurrence of such control mechanisms suggests that mountain birch operates as a partially integrated individual, although localized responses even at a shoot level do also exist (Haukioja et al. 1990; Ruohomäki et al. 1997; Henriksson et al. 1999). However, the probability of long shoot production was not a simple function of the explanatory variables, because there was a large overlap in their values for the shoots producing or not producing a long shoot. This indicates that bud fate may be decided by subtle differences in the conditions experienced by individual buds, such as interaction between bud size and the strength of apical control during the time of bud type determination (Novoplansky 1996; Berleth & Sachs 2001). A balance between several genetically determined developmental pathways may also be involved in the process (Maloof et al. 2001), and, in mountain birch, bud for-

Factors controlling resource allocation in mountain birch

mation is probably subject to great variability due to introgressive hybridization (Elkington 1968; Vaarama & Valanne 1973). Buds situated in the currently best conditions may actually gain an advantage, not the ones that meet some minimum criteria (Novoplansky et al.1989; Sachs et al. 1993). In the field, many tangled factors are probably operating during the preformation of buds and explain the large differences between trees. Mountain birch buds seem to be sensitive especially to localized defoli-

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ation (Haukioja et al. 1990; Ruohomäki et al. 1997; Henriksson et al. 1999), suggesting that tree growth and architecture can be modified by even a slight amount of herbivory. In a broader scale, there may be different growth responses depending on the ecotype and the environment of mountain birch individuals (Verwijst 1988; Weih & Karlsson 1999). However, despite the considerable amount of unexplained variation, the information we extracted was sufficient for constructing realistic structural growth rules for a

Fig. 10. Allometric scaling relationships between biomass, diameter and the shoot number of mountain birch branches drawn on a logarithmic scale. The plots show data for young and old stems and different branching orders, as indicated by the numbers in the legend (zero is the main stem). Curves fitted to the data use either observational or theoretical scaling exponents (R2 given for both).

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model that describes the three-dimensional growth of mountain birch (Renton et al. 2003; M. Renton et al., unpubl. results). The length of individual long shoots was controlled by two conflicting factors. Long distance from the roots suppressed growth whereas a high current-year amount of PAR, as in the branch apices, augmented it. In addition, the thermal sum of the previous year had a large contribution to the long shoot length in general, indicating the effects of temperature on both resource capture from the soil (Karlsson & Nordell 1996) and the availability of PAR (Nöjd & Hari 2001). Obviously, long shoot elongation was affected by both current- and previous-year resource status, as has also been reported for other spring-flushing trees (Kozlowski & Clausen 1966; Kimura et al. 1998). Current-year PAR seemed to be responsible for most of the photosynthates required in long shoot growth, as indicated also by the results of Henriksson (2001). We are not aware of other field studies simultaneously quantifying the light environment and the growth of individual tree shoots. However, some studies report a clear dependence between the growth and architectural position of shoots and, similar to our results, suggest that light alone may not provide a sufficient explanation to the amount of growth (Goulet et al. 2000). Usually these studies consider shoot position in terms of branching order, and have demonstrated that the higher the order the lower the amount of growth is (Sabatier & Barthélémy 1999; Buck-Sorlin & Bell 2000; Goulet et al. 2000; Suzuki 2000). Hydraulic architecture of branches has been invoked as an explanation (Zimmermann 1983). Our results show that it is the root distance rather than branching order that is limiting growth, although these variables were weakly positively correlated (r = 0.22). However, root distance was a better predictor of growth than branching order was. Besides hydraulic architecture, there exist many physiological mechanisms potentially controlling elongation and hence limiting tree height (Becker et al. 2000), i.e. the maximum distance of growing parts from the roots. We suggest that, in whole-plant studies, these can all be embraced under the terms transportation distance and costs of transportation. These notions can then be used to evaluate the various costs and benefits associated with the form and construction of transport tissue (cf. Banavar et al. 1999). In different plant species, various life-history traits and growth strategies are presumably reflected in the way the transportation network is constructed (King 1990; Enquist et al. 1999; Becker et al. 2000). In addition, environmental factors, such as high winds and snow load in the mountain birch, are likely to modify the realized architecture of a plant in its habitat.

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Shoot death Shoots located in unfavourable positions should be removed from the transportation network, because their maintenance becomes costly. Indeed, our results suggested that isolated short shoots with a long distance to the supporting branch were most likely to die. On the other hand, shoots with close long shoot neighbours were most likely to persist, perhaps due to improved resource flow in the branch. Again, due to large overlap in the values, these variables alone were far from being decisive for shoot death. There was no clear link between shoot death and the branching order as reported, for example, in Quercus with active shedding of leafy branches (Buck-Sorlin & Bell 1998, 2000). However, mountain birch loses its shoots and branches passively without the formation of an abscission layer, which is a process probably controlled by different factors than the active shedding, and may relate to differences in the growth strategy of trees. Contrary to expectations (Sprugel et al. 1991), the amount of PAR was not important for shoot death, suggesting that PAR was not severely limiting in the freestanding trees studied. However, since we used the relative instead of actual amount of PAR, we were not able to detect the critical limit triggering shoot death. PAR may have had a contribution, as suggested by the negative correlation between PAR and short shoot length.

Developmental stage In general, stem age had a minor effect on the allocation variables examined, which suggests that similar control mechanisms operate during both stages of development. The only obvious differences were the slightly higher long shoot length in young stems and the lower rate of shoot number increase with respect to the size of main stem in old stems. In 1997, a year with high thermal sum and hence with favourable growth conditions, the young stems allocated photosynthates to elongation whereas the old stems obviously stored the excess resources for the use in catkin production next year. For example, production of male catkins by the long shoots of old stems can reduce their elongation (Karlsson et al. 1996; Henriksson & Ruohomäki 2000); otherwise the generally larger long shoot length in young stems may reflect shorter transportation distance from the roots. Differences in the scaling function between the stem size and shoot number, in turn, reflect the higher mortality rate and abscission of whole branches from the old stems. At the level of higher-order branches there were no scaling differences, suggesting that essentially similar control mechanisms prevail in both age classes.

Factors controlling resource allocation in mountain birch

Allometry and source-sink interactions In general, the structural traits of mountain birch showed allometric scaling that was in close correspondence with the theoretical predictions (West et al. 1999a). The fit was good at all branching orders, suggesting that allometry largely predicts the traits of whole branches (see also Sveinbjörnsson 1987). Related to the maintenance of allometric relations, the local amount of current radial growth partially restricted the production of new long shoots. This implies, for example, that even if a basal short shoot could otherwise turn into a new long shoot, a large number of long shoots present in the apical parts of a branch would indirectly prevent this via an increased demand for radial growth. If radial growth creates a strong sink, a short shoot may experience scarcity of resources that, similar to the effects of defoliation (Ruohomäki et al. 1997), suppresses its ability to become a long shoot. Another indication of the potential role of sink activity was the positive effect of the previous long shoot growth on the current long shoot growth. A trivial explanation for this would be that large branches produce many long shoots each year. However, in our data, stem diameter already reflected the branch size, and hence the presence of long shoots seemed to have an additive effect. This is in line with previous results showing that branches located in favourable conditions may increase their resource intake at the expense of more inferior branches (Honkanen & Haukioja 1995; Henriksson 2001), indicating that an active sink may gain a proportionally higher amount of resources. On the other hand, since the long shoots may also act as a big source of photosynthates they may that way enhance the growth potential of the branch they are located in, for example, by providing resources for the buds they produce. Thus, even if a tree maintains constant allometric scaling at an upper level of hierarchy, growth may be directed within certain limits, such as the observed relation between the maximum long shoot number and branch size, towards the individual shoots located at the most favourable positions (Sachs et al. 1993; Marcelis 1996).

Conclusions Our study indicated a number of key factors and mechanisms that controlled growth and resource allocation in mountain birch. It appeared that somewhat different mechanisms operated at different scales, i.e. there were localized responses controlled at the level of individual shoots whereas the growth of whole branches followed allometric constraints. However, there was also a clear link between these seemingly unconnected processes. The increase in the amount of shoots and foliage within a branch was connected to

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the increased demand of radial growth, which, in turn, acted to suppress further formation of new long shoots. This is a mechanism by which source-sink interactions may maintain allometry. The interplay between the localized growth responses and the allometric constraints provides a simple construction principle for tree crowns and may be a mechanism by which a tree can achieve the most efficient fractal architecture in terms of resource intake and costs of transportation (West et al. 1999b). However, comparative analyses with other tree species, with trees with more pronounced size variation, with tree individuals interacting with each other, and experimental manipulations will be needed to assess the generality of the factors and mechanisms we distinguished to be important at the level of detail measurable from the outside of trees. Acknowledgements. We are grateful to Henrik Heinilä, Tiina Kaitaniemi, Piia Juntunen, Jarno Kaapu, Sanna Laakso, Mikko Paajanen, Paula Salminen and Harri Vehviläinen for their assistance in the field and laboratory. Hervé Sinoquet kindly provided the Pol95 software for digitizing. The work would not have been possible without the contribution of the Lignum-team, particularly Mika Lehtonen, Jari Perttunen and Risto Sievänen. Gerhard Buck-Sorlin, Peter Gleissner, Kyösti Lempa and two anonymous referees gave valuable comments on the manuscript. Academy of Finland financed the study (grants number 44141 and 80706).

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