Mechanistic scaling of twig allometry and crown architecture in Scots pine: implications for moose browse availability

Mechanistic scaling of twig allometry and crown architecture in Scots pine: implications for moose browse availability | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 9 March 2026 V1 Latest version Share on Mechanistic scaling of twig allometry and crown architecture in Scots pine: implications for moose browse availability Authors : Christer Kalén 0000-0003-0621-095X [email protected] , Astrid Bornfeldt Persson , and Märtha Wallgren Authors Info & Affiliations https://doi.org/10.22541/au.177305800.04431555/v1 147 views 73 downloads Contents Abstract Introduction Method Statistical analysis Estimation of vertically accessible shoot biomass for moose browsing RESULTS Crown-level distribution of total shoot length and biomass Available moose forage DISCUSSION Conclusions Appendix A1 MATHEMATICAL CROWN MODEL References Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Balancing moose (Alces alces) populations with forest production objectives remains a major challenge in Swedish boreal forestry. Browsing damage is commonly assessed using empirical indices, while the underlying availability of browsable shoot biomass is rarely quantified mechanistically. We developed a mechanistic, data-driven model of browse availability in young Scots pine (Pinus sylvestris) by linking shoot-level allometry, crown architecture, and tree height development. Empirical data were collected from nine unbrowsed trees, for which current-year shoots were measured by branch whorl, including shoot length, shoot number, and wet/dry biomass ratio. Shoot scaling with crown position was analysed to quantify crown allometry and distribution. Crown architecture was coupled with a height–age growth model to simulate vertical crown development and estimate shoot biomass accessible to moose browsing within a defined browsing height for moose. Simulations were conducted across site productivity classes and scaled to the stand level. Shoot biomass, length and diameter increased with tree height and declined exponentially with distance from the apex with 50%, 33% and 13% per whorl, respectively. At the crown level, both total shoot length and biomass followed unimodal distributions, peaking near the vertical midpoint of the crown. Simulations showed that browse availability increased rapidly with tree growth, peaked at tree heights around 3.5 m (15–25 years depending on site productivity), and subsequently declined. Peak shoot biomass ranged from 330 to 450 g per tree, with high-productivity sites yielding up to 35% more biomass. When scaled to stands ≤2.5 m in height at 2,000 stems ha⁻¹, simulated browse availability was 100–200 kg ha⁻¹. These results show that crown architecture in young Scots pine follows consistent scaling rules that can be expressed as functions of tree height and crown position. The model provides a mechanistic connection between tree growth and herbivore-accessible forage and implications for management is discussed. Abstract Balancing moose ( Alces alces ) populations with forest production remains a major challenge in Swedish forestry. Browsing damage is commonly assessed using empirical indices, while the underlying availability of browsable shoot biomass is rarely quantified mechanistically. We developed a mechanistic, data-driven model of browse availability in young Scots pine ( Pinus sylvestris ) by linking shoot-level allometry, crown architecture, and tree height development. Empirical data were collected from nine unbrowsed trees, for which current-year shoots were measured by branch whorl, including shoot length, shoot number, and wet/dry biomass ratio. Shoot scaling with whorl position was analysed to quantify crown allometry and distribution. Crown architecture was coupled with a height–age growth model to simulate vertical crown development and estimate shoot biomass accessible to moose browsing within a defined browsing height for moose. Simulations were conducted across site productivity classes and scaled to the stand level. Individual shoot biomass, length and diameter increased with tree height and declined exponentially with distance from the apex with 50%, 33% and 13% per whorl, respectively. The vertical distribution of total shoot length and shoot biomass among whorls was unimodal, with peaks occurring close to crown midpoint. Simulations showed that browse availability peaked at tree heights around 3.5 m (15–25 years depending on site productivity), and subsequently declined. Peak shoot biomass ranged from 330 to 450 g dry weight per tree, with high-productivity sites yielding up to 35% more biomass. When scaled to stands ≤2.5 m in height at 2,000 stems ha⁻¹, simulated browse availability was 100–200 kg dry weight ha⁻¹. These results show that crown architecture in young Scots pine follows consistent scaling rules that can be expressed as functions of tree height and whorl position. The model provides a mechanistic connection between tree growth and herbivore-accessible forage and implications for management are discussed. Key words: Pinus sylvestris, Alces alces, browsing damage, food availability Introduction Forage availability for moose ( Alces alces ) varies strongly among forest types and stand development stages, with young forests providing substantially higher browse availability than older forests or non-forest land (Bergqvist et al. 2018, Giguere et al. 2025). Moose distribution and browsing intensity appear to follow an ideal free distribution driven by forage availability at the landscape scale. Therefore, moose and other large herbivores exert a strong influence on forest regeneration with consequences for boreal forest ecosystems, structure, growth and plant species composition (Gill 1992; Danell et al. 2006, Bergquist et al. 2009). In Sweden, this interaction is particularly pronounced due to the long-standing coexistence of intensive forest management and the management of a dense population of moose. For several decades, Swedish forest and wildlife management have aimed to maintain a balanced relationship between moose population size and the level of browsing damage inflicted on commercial forests, especially in young stands of Scots pine ( Pinus sylvestris , from here on pine) (Sandström et al. 2013; Dressel et al. 2020). A national management objective in Sweden is that no more than 5 % of young pine trees should incur browsing damage annually (Naturvårdsverket 2018). However, this target has proven difficult to achieve (Franklin et al. 2026), despite a recent decline in the moose population (Kalén et al. 2022), which nevertheless remains one of the largest viable populations globally (Kramer & Kalén 2026). It is acknowledged today that browsing damages is not determined solely by herbivore abundance, but also by the spatial and temporal availability of forage within the forest landscape (Pfeffer et al. 2020; Pfeffer et al. 2022). Therefore, a proposed strategy to mitigate browsing damage is not only to regulate the density of moose and other cervids, but to also increase the amount of pine in the forested landscape, thereby diluting browsing pressure across a larger number of trees (Naturvårdsverket 2018). This approach assumes, besides stable population levels of cervids, that increasing pine availability leads to a proportional increase in accessible forage, reducing repeated browsing on individual trees. The assumption is validated by several empirical studies showing that browsing intensity is influenced by many landscape features such as tree species composition, availability of young forests apart from merely the composition and density of cervids (Bergqvist et al. 2014, Pfeffer et al. 2020, Pfeffer et al. 2022, Franklin et al. 2026). A key challenge in predicting forage availability for moose is scaling from individual shoots to the reachable portion of the crown, and further to entire stands and landscapes. Moose conducts a species-selective feeding behavior (Månsson et al. 2007) where twigs from trees constitute bulk feed during winter (Spitzer et al. 2020). The accessibility of these shoots is strongly constrained by tree height and vertical crown structure (Faber and Lavsund 1999, Kalén 2006). Consequently, browse availability depends not only on stand age and density, but also on allometric relationships governing shoot length, shoot biomass, shoot number, and crown rise over time (Kalén and Bergquist 2004; Osada 2011; Bergqvist et al. 2018; Repola et al. 2024). Although allometric relationships for Scots pine are well documented (e.g. Socha and Wezyk 2007), crown-level organization for young pines and its implications for herbivore accessibility remain less understood (but see Kalén and Bergquist 2004). Existing approaches often rely on empirical damage indices or coarse stand descriptors, rather than explicit representations of shoot production and crown architecture. Recent studies have highlighted the need for mechanistic frameworks that link plant architecture, biomass allocation, and herbivore foraging constraints across scales (Nichols et al. 2015; Pfeffer et al. 2020; Pfeffer et al. 2022). Apical dominance suppresses lateral bud outgrowth through hormonal signaling from the shoot apex (Cline 1997). In Scots pine, crown structure is further regulated by apical control, whereby dominant shoots hierarchically influence subordinate branches (Wilson 2000), and by light availability, which constrains branch growth and survival. In this study, we quantify the allometric relationship between shoot length and shoot biomass across crown positions, a pattern partly reflecting the effects of crown structure. Building on this physiological basis, we develop a mechanistic, data-driven model of crown architecture in young Scots pine that links shoot traits to tree height and whorl position in crown, and thereby predicts how browseable biomass varies with stand age and density. Specifically, we sought to: • Quantify allometric relationship between shoot length and biomass across whorl positions within the crown. • Describe the vertical distribution of shoot length, biomass, and shoot number within the crown using simple, biologically interpretable functions. • Develop a dynamic representation of crown development based on discrete annual height increments and a fixed maximum number of living branch whorls. • Estimate total browsable shoot biomass per tree and per hectare by explicitly accounting for crown rise and a maximum browsing height. • Provide a quantitative framework for predicting how stand age, site index, and tree density influence forage availability for moose in managed pine forests. Method Fieldwork was conducted in Salsta, Uppsala County, in southeastern Sweden. The landscape is flat and low-lying, with most of the area situated below 35 m a.s.l. The regional climate is cool-temperate, with mean July and January temperatures of approximately 16 °C and −4 °C, respectively, and an annual precipitation of 450–600 mm (SMHI 2023). The mean annual number of days with snow cover is approximately 100–125 based on the 1961–1990 climate normal period. The data collection was based on nine unbrowsed Scots pine trees originating from the same stand. Trees were sampled during the dormant season in winter 2024/2025 to avoid effects of ongoing shoot growth. For each tree, total height was recorded. All current-year shoots were measured for each branch whorl, with whorls numbered consecutively from the apex downwards. For each whorl, the number of shoots was recorded and individual shoot length and fresh mass were measured after cutting each shoot at its base, allowing calculation of total shoot length and total shoot biomass per whorl. Shoots were sorted by tree and branch whorl and placed in separate bags. All samples were oven-dried at 50 °C for 72 h, after which dry mass was determined. Mean dry mass per current-year shoot was calculated for each whorl. In total, 1857 shoots were recorded from the nine sampled trees. Average features for the nine trees are summarized in Table 1. Table 1. Summary of structural and shoot-level characteristics of the nine Scots pine trees included in the study. 1 0.33 3 68 15 46 8 0.39 0.20 2 0.56 6 119 49 179 35 0.44 0.32 3 0.94 6 160 59 242 80 0.45 0.60 4 1.01 5 220 124 627 190 0.47 0.73 5 1.51 5 216 196 946 212 0.51 0.56 6 1.53 6 290 90 671 163 0.50 0.86 7 2.10 6 340 197 1451 473 0.50 1.19 8 2.43 6 332 307 1844 694 0.52 1.16 9 3.34 8 530 820 8056 1722 0.37 0.86 Statistical analysis Shoot length was analysed in relation to position within the crown, expressed as branch whorl number counted from the apex, starting with 0 (Figure 1). Figure 1. Scots pine grows in a distinct pattern in which several lateral shoots emerge from the same point, forming—at least in young trees—clearly distinguishable annual whorls. Because multiple shoots usually occur within the same branch whorl, shoot length was averaged within each tree × whorl combination prior to analysis. This yielded a single representative value per whorl and tree, avoiding pseudoreplication while preserving the nodal structure of crown development. Based on principles of apical dominance, apical control, and light limitation, shoot length and shoot biomass were assumed to decline multiplicatively with increasing distance from the apex. Under this assumption, a constant proportional change between whorls implies linearity on the logarithmic scale. Shoot length was therefore analysed on a log scale, and the change between consecutive whorls was defined as: \begin{equation} d_{i,g}={log(L}_{i,g+1})-{log(L}_{i,g})\nonumber \\ \end{equation} where L i,g denotes mean shoot length of tree i at branch whorl g . A constant, d i,g across whorls indicates a stationary hierarchical and light-mediated regulation of shoot growth. The mean magnitude of the decline rate between whorls was estimated using a linear model with an intercept only: \begin{equation} d_{i,g}=\beta_{0}+\epsilon_{i,g}\nonumber \\ \end{equation} where β 0 represents the average log-reduction in shoot length per branch whorl. To evaluate whether the strength of the vertical growth regulation varied among trees, tree identity was included as a random intercept in a linear mixed-effects formulation: \begin{equation} d_{i,g}=\beta_{0}+b_{i}+\ \epsilon_{i,g}\nonumber \\ \end{equation} where b i is a tree-specific random effect. Models were fitted using restricted maximum likelihood (REML). To assess whether decline rate changed systematically with crown depth, branch whorl number was added as a fixed effect: \begin{equation} d_{i,g}=\beta_{0}+\beta_{1}g+b_{i}+\ \epsilon_{i,g}\nonumber \\ \end{equation} A slope parameter β 1 not different from zero indicates that the proportional reduction in shoot length is constant along the crown. While individual shoot length was analysed using explicit statistical models to characterise the underlying nodal growth process, total shoot length and shoot biomass represent aggregated outcomes of shoot length and shoot number. To confirm that these aggregated quantities exhibited systematic variation with crown position, total shoot length and shoot biomass per branch whorl were additionally analysed using linear mixed-effects models with branch whorl number as a fixed effect and tree identity as a random intercept. These analyses were intended to characterise variability and uncertainty rather than to infer additional biological processes. To formally characterise crown-level patterns, total shoot length and total shoot biomass per branch whorl were analysed using linear mixed-effects models with relative crown depth as a predictor. Both quadratic and sinusoidal functional forms were evaluated, and model support was assessed using Akaike’s Information Criterion (AIC). Tree identity was included as a random intercept to account for repeated measures. Shoot biomass per branch whorl was calculated as the sum of dry mass of all current-year shoots within each whorl. Mean dry mass per shoot was used when estimating total biomass at the whorl level, with adjustments applied for brush formations in browsed trees as described above. The distributions of total shoot length and shoot biomass were analysed descriptively as functions of branch whorl number. Because these quantities are directly derived from observed shoot-level data, no additional statistical models were fitted. Instead, their patterns were interpreted in relation to the nodal scaling of shoot length identified in the vertical growth regulation analysis. Estimation of vertically accessible shoot biomass for moose browsing To estimate the amount of shoot biomass accessible to moose browsing, crown-level shoot data were linked to vertical tree development using a height–age model for Scots pine. As existing height models for pine are unreliable in the height range 0–4 m, annual height growth was modeled as a function of current tree height using cross-sectional data. Growth was described by a linear height–growth relationship, dH/dt = β 0 + β 1 H , from which height development was derived by integration, yielding H ( t )=(β 0 /β 1 )( e β1 t -1). The model is valid within the observed height range and assumes a stationary growth relationship. Annual height increment was calculated as Δ H=H(t)-H(t-1) , and interpreted as the length of the leader shoot at year t . The vertical position of each annual shoot cohort was then determined relative to current tree height by cumulative subtraction of annual height increments. To examine the effect of site productivity, separate parameterizations of the height growth function were used to represent three site index classes (SI 100 = 18, 22, and 26). For each site index, 50 Monte Carlo simulations were run with stochastic variation in height development (±10%), and mean trajectories were used for analysis. Observed shoot biomass and shoot number per branch whorl were associated with annual shoot cohorts based on crown position. For each year, shoot biomass located within the vertical browsing zone accessible to moose (defined here as 0–2.5 m above ground) was identified and summed to obtain the total amount of browsable shoot biomass per tree. This procedure was applied across all ages represented in the height-growth model, yielding annual estimates of shoot biomass accessible to browsing. Stand-level forage availability was subsequently calculated by scaling tree-level estimates by stem density. The height-growth model and the crown architecture analysis serve distinct roles in this framework: the former provides vertical placement of crown components in absolute height units, while the latter describes the distribution of shoot length, shoot number, and biomass along the crown. No assumptions were made regarding historical constancy of within-crown scaling parameters; all vertical positioning was derived explicitly from the height-growth model. Two alternative functions were tested to estimate annual shoot biomass: one based on tree height and one based on annual leader shoot length. The two formulations were used to examine their respective effects on the trajectory of available forage biomass. The mathematical model is described further in Appendix A1. All analyses were conducted in R (version 2023.12.1 Build 402). Linear mixed-effects models were fitted using the lme4 package. Model adequacy was evaluated using residual diagnostics, and inference focused on parameter estimates and their ecological interpretation rather than on formal hypothesis testing. RESULTS Scaling shoot length and biomass with crown position Mean shoot length increased with tree height and declined systematically with increasing branch whorl number counted from the apex (Figure 2). When analysed on a logarithmic scale, the change in shoot length between consecutive whorls showed a consistent negative value, indicating a multiplicative reduction in shoot size with increasing distance from the apex. Across all trees and whorls, the mean log-transformed difference in shoot length between adjacent whorls was −0.40 (SE = 0.04), corresponding to an average proportional reduction of approximately 33% per whorl (reduction factor ≈ 0.67). The variation in log-differences among observations was moderate (residual standard deviation ≈ 0.27) and reflected local deviations rather than systematic departures from the overall trend. Including tree identity as a random intercept did not explain additional variation, indicating that the strength of vertical growth regulation was highly consistent across the sampled trees. Adding branch whorl number as a fixed effect yielded no evidence of a systematic change in vertical growth regulation with crown depth. Applying the same statistical model on shoot biomass resulted also in a consistent manner with log-transformed difference of -0.69 (SE = 0.05), corresponding to 50% reduction per whorl. This pattern provides strong support for an exponential attenuation of shoot growth along the crown (Figure 3). Figure 2. The relationship between tree height and mean shot length is dependent on the branch whorl. 0 = top shoot, 1 = first whorl of shoots below the top shoot, and so on. Figure 3. Observed shoot length and biomass declines exponentially with increasing whorl position in the crown. Points show observed values (●=length, ●=biomass) normalized to the top shoot (whorl 0), and the lines (dashed=length, solid=biomass) represents the fitted exponential model Y w =Y 0 exp(-kw), where w denotes whorl position and k the rate of exponential decline. Shoot relative radius (dotted line) was estimated from biomass and length. Crown-level distribution of total shoot length and biomass When aggregated to the crown level, both total shoot length and total shoot biomass per whorl exhibited pronounced unimodal distributions along the crown. Expressed as relative crown depth, total shoot length per whorl was best described by a quadratic function with an increasing shoot length towards intermediate crown positions followed by a decline towards the crown base. Both a quadratic and a sinusoidal function provided adequate descriptions of this pattern although the sinusoidal alternative provided a poorer fit (ΔAIC ≈ 12). For total shoot biomass, a quadratic mixed-effects model again outperformed the sinusoidal alternative (ΔAIC ≈ 9), with peak biomass located close to the crown midpoint. However, the distributions differed slightly: total shoot length per whorl was slightly biased toward the lower crown, whereas total shoot biomass per whorl was biased toward the upper crown (calculations made from table in appendix A1). Although absolute values differed among trees, the functional shape of both total shoot length and biomass distributions was consistent across individuals, as reflected by shared fixed-effect responses and tree-specific random intercepts. Available moose forage Simulated trajectories of available browse biomass showed an initial exponential increase to a distinct maximum, followed by a rapid decline to zero. Maximum availability occurred when trees are 3,5 meters in height, approximately 15–25 years old, depending on site index, with peak values ranging from 330 to 450 g of shoot biomass. When shoot biomass was estimated as a function of tree height, similar maximum biomass levels were reached but at different ages among the simulated site indices. In contrast, when shoot biomass was modeled as a function of annual leader shoot length, both a temporal shift in the age of maximum availability and differences in peak biomass were observed, with trees growing on sites corresponding to SI = 26 producing up to 35% more available biomass than those on sites corresponding to SI = 18 (Figure 4 & Figure 5). Figure 4. Simulated available browse biomass for an individual pine tree growing under three site index classes (SI = 18, 22, and 26). Left panels show results when shoot biomass was estimated as a function of tree height, whereas right panels show results when shoot biomass was estimated as a function of annual leader shoot length. Figure 5. When the height limit for available browse biomass was set to 2.5 m, maximum availability occurred at a tree height of approximately 3.5 m. Total available biomass was similar across simulated site indices when shoot biomass was estimated as a function of tree height, whereas a more pronounced site index effect was observed when shoot biomass was estimated as a function of annual leader shoot length. Scaling browse availability to forestry provides an estimate of the potential availability of pine shoots up to the defined height limit (2.5 m). Assuming a pine density of 2,000 stems ha⁻¹, the average browse availability in young pine forests (0–6 m in height) is estimated at 100–200 kg ha⁻¹, depending on site productivity. DISCUSSION A unified structural organization of the crown This study demonstrates that crown architecture in Scots pine trees is governed by a small set of simple, continuous functions linking shoot size, shoot number, and biomass allocation across the crown. Rather than being uniformly distributed, growth investment is concentrated in the upper half of the crown, where both individual shoot length and biomass reach their maximum. Previous work has shown that branch and needle biomass in young Scots pine is strongly structured by position in the crown and tree size (Xiao and Ceulemans 2004), which aligns with the height-dependent patterns in available twig biomass observed in this study. Shoot length declined exponentially with increasing distance from the apex, with an average proportional reduction of 33% per branch whorl, and with little variation among trees. This pattern provides strong empirical support for vertical growth regulation as a dominant organizing principle of crown architecture in young pine, and indicates that shoot growth along the crown can be described as a stationary multiplicative process rather than as a sequence of discrete, depth-dependent growth regimes. The absence of detectable variation in the strength of vertical growth regulation among trees or with crown depth suggests that this scaling relationship is robust to local differences in growth conditions and tree size within the studied range. Importantly, this regularity implies that crown structure can be predicted from a small set of parameters linked to leader growth, providing a parsimonious foundation for mechanistic models of crown development, biomass allocation, and, ultimately, herbivore-accessible forage. The parabolic distribution observed for both total shoot length and biomass suggests a balance between apical control and lower-crown limitation. Near the apex, apical dominance suppresses lateral development, while in the lower crown increasing shading and tissue age likely constrain shoot production and elongation (Cline 1997, Wilson 2000). The crown’s intermediate section thus represent the maximum zone for lateral growth due to a combination of branching strategy and apical dominance. Crown length in Scoth pine is regulated by light availability within the stand, which in turn is strongly influenced by stand density and competition among neighbouring trees (Saarinen et al. 2022). In the present study, crown length was implicitly constrained by the number of living branch whorls. Empirically, the number of whorls with living shoots observed in the data never exceeded eight, indicating that crown depth is structurally limited even under varying growth conditions. Because explicit stand density information was not available for the present dataset, crown length was not modelled as a continuous function of light or competition. Instead, a simple and biologically reasonable assumption was adopted for the dynamic simulations: the number of living branch whorls was allowed to increase with age but constrained to a maximum of six. This approach captures the essential effect of crown rise and self-pruning while avoiding overparameterisation and the introduction of poorly constrained stand-level processes. Importantly, this assumption affects only the vertical extent of the crown, not the internal allocation patterns within the crown. The relative distributions of shoot length, shoot biomass, and shoot number across the crown remain invariant, consistent with the empirical results. Shoot number as a derived, not independent, trait Shoot length, shoot diameter, and also shoot number are important traits for a feeding herbivore such as the moose (Shipley 2010). Our results indicate that the number of shoots within the crown can be derived from more fundamental properties: total shoot length and mean shoot length. This suggests that shoot number is an emergent outcome of growth allocation rather than a primary control variable. Scaling from leader growth to crown architecture A key result is the strong linkage between leader length, tree height, and crown structure. Because leader length in young trees scales linearly with tree height, and shoot length throughout the crown scales proportionally with leader length, overall crown architecture can be described as a function of height growth alone. This provides a powerful framework for predicting crown structure across trees of different sizes and site productivity levels, and suggests that variation in crown form primarily reflects differences in overall growth potential rather than fundamentally different architectural rules. Many studies puts forward that tree diameter or more specifically sapwood area is a better determinant of total biomass production of shoots, needles/or leaf biomass than tree height (Shinosaki et al. 1964, Kalén and Bergquist 2004 and Konôpka et al. 2023). Including stem diameter at the base (D 0 ) in future surveys would therefore be useful to link top-shoot length to growth. Such approach would enable a sounder biological model linking stem basal area to total shoot production and leader length, from where the other attributes (distribution of nr of shoots, shoot length and biomass) can be estimated by the model presented in this paper. Linking crown architecture to herbivore accessibility Building on the structural crown model, we further explored how crown architecture translates into herbivore-accessible forage at the stand level. The extension of the crown architecture model to estimate browseable shoot biomass provides a mechanistic link between tree growth, crown structure, and herbivore accessibility. By explicitly incorporating a maximum browsing height, the model translates relative crown position into absolute height above ground, allowing the identification of the crown fraction that is physically accessible to browsing herbivores such as moose. Declining accessibility with increasing tree height is consistent with observations of reduced browsing in taller stands (Faber and Lavsund 1999; Bergqvist et al. 2018) and highlights height growth as an indirect defense against herbivory. The assumption of a fixed maximum browsing height represents a simplification, as browsing height may vary with snow depth, animal size, and seasonal conditions. However, the use of a constant threshold allows transparent comparison across stand ages and densities and avoids introducing poorly constrained behavioural parameters. Importantly, this assumption affects only the accessible fraction of the crown and does not alter the internal allocation patterns within the crown, which are empirically derived and remain invariant. Implications for crown modeling and forest dynamics The simplicity and internal consistency of the derived functions make them well suited for inclusion in process-based or structural forest models. By linking shoot number, shoot length, and biomass to a common positional axis and to tree height, the model offers a mechanistic bridge between individual shoot growth and whole-tree structure. Implication for management In Sweden, the national policy target for balancing moose density and browsing damage on Scots pine is set at 5% annual damage. Damage is defined as leader shoot browsing, stem breakage, or bark damage in forest stands with an average height of 1–4 m, of which the majority (~75%) is attributable to leader shoot browsing (Bergqvist et al. 2001). At the stand level, the relationship between browsing pressure and leader shoot damage is non-linear (Wallgren et al. 2024; Franklin et al. 2026), but under low to moderate browsing intensities an approximately linear relationship can be assumed (Wallgren et al. 2024). This allows the results of the present study to be interpreted in a management context. Using Västerbotten County, Sweden, as an illustrative example, data from the National Browsing Inventory (Älgbetesinventeringen) show an average Scots pine density of 1,360 stems ha⁻¹ in stands 1–4 m tall, with a mean site index (SI₁₀₀) of 15. Based on the model presented here, the corresponding amount of available dry twig biomass is approximately 200 kg ha⁻¹. Applying the 5% damage threshold implies that only browsing while remaining within policy targets. Scots pine constitutes approximately 30% of the moose diet when averaged across seasons (Spitzer 2019). Assuming a daily intake of 5 kg dry matter per moose, this translates to a carrying capacity of roughly six moose-days per hectare before the browsing damage threshold is exceeded. However, pellet group counts from the National Browsing Inventory during 2022–2025 indicate that young pine stands in Västerbotten experienced 7–11 moose-days ha⁻¹, depending on assumptions regarding daily pellet group production. This level of browsing pressure exceeds the theoretical threshold derived here and is consistent with the observed proportion of annually damaged pines of approximately 10% during the same period. Together, these results suggest that current moose use of young pine stands in northern Sweden is sufficient to exceed nationally defined damage targets, even under conservative assumptions regarding diet composition and intake rates. Model limits and further research Spatially explicit estimates of cervid forage availability, such as those provided by national-scale models integrating National Forest Inventory data and remote sensing (Graf et al. 2025), offer valuable tools for linking browsing damage assessments with habitat management. Combining such forage maps with empirical data on twig biomass availability for moose across different stand heights could improve predictions of browsing risk and support targeted mitigation strategies. The model for pine twig allometry presented in this paper has the important limitation of not including browsing history. It is well known that browsing will cause a number of long-term impact on the tree itself through risk of mortality and growth response (Wallgren et al. 2014) and at stand level (Petterson et al. 2010). The model would benefit from including response to browsing in both short and long term. The figures presented on available browse biomass is should therefore be considered as a potential upper limit. Conclusions • Shoot length declined exponentially with increasing distance from the apex, with an average proportional reduction of approximately 33% per branch whorl, and with little variation among trees. • Yearly shoot production and total shoot length follows a unimodal distribution over the crown whorls in Scots pine • Biomass available to moose is concentrated in stands below six meters in average height with a peak at 3.5 meters • The potential available browse biomass in Scots pine stands with 2000 stems ha⁻¹ amount to 100-200 kg ha⁻¹ when averaging annual production until the average heigh reaches 6 meters. • The number of moose days spent in young forest stands in Sweden indicate why the national target of five per cent annual damaged pines is exceeded. Appendix A1 Table A1. Fixed-effect estimates (± SE) from quadratic mixed-effects models describing the unimodal distribution of total shoot length and shoot biomass per branch whorl along relative crown depth ( x rel =0 at crown apex and x rel =1 at crown base). Shoot length -51.7 (120.2) 1637 (402.2) -1541.8 (386.3) Shoot biomass 11.59 (10.35 ) 133.10 (30.37 ) -147.78 (29.17 ) Appendix A2 MATHEMATICAL CROWN MODEL In the model, crown architecture is governed by a small set of independent components: (i) a growth-driven scaling term linked to leader elongation, (ii) an exponential decline in mean shoot length with increasing distance from the apex, (iii) a unimodal distribution of biomass within the crown, and (iv) a structural constraint on crown length represented by a fixed maximum number of living branch whorls. Let x ∈[0,1] = relative crown position (0 = top, 1 = crown base) H = tree height L 0 = k 0 H = leader length g = Whorl number (0,1,2,…) W =Total number of worls W max =Maximum number of whorls with annual twig biomass α, β = constants Annual leader shoot length L 0 is derived from successive height increments:\(L_{0}\left(t\right)=Height\left(t\right)-Height(t-1)\) (A1) The crown is represented by a fixed maximum number of living branch whorls W max . At tree age t , whorls are indexed as w = 0, 1, …, W max − 1, where w = 0 denotes the uppermost whorl. Relative crown position is defined as:\(x_{w}=\frac{w+0.5}{W_{\max}+1},\ \ \ w=0,1,2,\ldots,W_{\max}\)(A2) Biomass vertical distribution over the crown follows a symmetric function:\(\omega_{w}=x_{w}(1-x_{w})\) normalized so that Σω w = 1. (A3) Total shoot biomass per tree is estimated using one of two alternative allometric models: a) as a function of length of leader shoot (cm):\(B_{\text{tot}}\left(L_{0}\right)=e^{-\alpha}\times L_{0}^{\beta}\),\(\alpha=3.82,\ \beta=2.64\) (A4) b) as a function of tree height (cm):\(B_{\text{tot}}\left(H\right)=e^{-\alpha}\times H^{\beta}\),\(\alpha=6.49,\ \beta=2.24\) (A5) Biomass assigned to whorl w is given by:\(B_{w}=B_{\text{tot}}\omega_{w}\) (A6) The height position of each whorl is obtained from the height growth curve as h w = H(t − w) . Available shoot biomass is defined as the sum of biomass located below the browsing height limit H lim :\(B_{a}(t)=\sum{B_{w}\text{\ for\ all\ w\ such\ that\ }h_{w}\leq H_{\lim}}\)(A7) Number of shoots Average shoot length at whorl w can be estimated as a function of leader shoot length L 0 : \(\overline{L}\left(L_{0},w\right)=L_{0}e^{-\alpha w}\),\(\alpha=0.44\) (A8) Biomass (g dw) for an individual shoot can be calculated using one of two alternative models a) \(B\left(L_{w},w\right)=e^{-\alpha_{1}-\beta_{1}w}\times L_{w}^{-\alpha_{2}-\beta_{2}w}\) (A9) \(\alpha_{1}=2.3326,\)\(\beta_{1}=0.005264,\ \text{\ \ α}_{2}=1.4583,\)\(\beta_{2}=0.11931\) \(b)\ \ B\left(L_{w}\right)=\alpha L_{w}^{\beta}\),\(\alpha=0.0487,\ \beta=\)1.396 (A10) The maximum number of whorls ( W max ) was set to 6. References 1. Bergquist, J., Löf, M., Örlander, G. 2009. Effects of roe deer browsing and site preparation on performance of planted broadleaved and conifer seedlings when using temporary fences. 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Crossref Google Scholar Information & Authors Information Version history V1 Version 1 09 March 2026 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords alces alces browsing damage crown allometry food availability pinus sylvestris Authors Affiliations Christer Kalén 0000-0003-0621-095X [email protected] Swedish Forest Agency View all articles by this author Astrid Bornfeldt Persson Swedish University of Agricultural Sciences View all articles by this author Märtha Wallgren Skogforsk View all articles by this author Metrics & Citations Metrics Article Usage 147 views 73 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Christer Kalén, Astrid Bornfeldt Persson, Märtha Wallgren. Mechanistic scaling of twig allometry and crown architecture in Scots pine: implications for moose browse availability. Authorea . 09 March 2026. 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