Height growth patterns of genetically improved Scots pine and silver birch

Abstract

The breeding of forest tree species in the Baltic region has notably contributed to wood production for the bioeconomy. Growth modelling is used for long-term estimates of forest development. However, usually based on data from unimproved stands, they may underestimate the growth of improved trees. Accordingly, it is important to identify and integrate the altered stand dynamics associated with improved planting stock into existing growth models to accurately capture the resulting gains or, alternatively, develop new functions specifically designed for improved trees. We used the generalized algebraic difference approach to model and analyze height growth patterns of Scots pine and silver birch with different genetic improvement levels (improved forest reproductive material categories ‘qualified’ and ‘tested’). Modelling was based on 14 260 and 55 926 height–age series from open-pollinated progeny trials in Latvia and Lithuania with an age range of 3–46 and 5–22 years for pine and birch, respectively. Dynamic generalized algebraic difference approach forms of commonly applied height growth functions with forest reproductive material-category-specific sets of coefficients were tested. The dynamic form of the Chapman–Richards and King–Prodan equations had the best fit for Scots pine and silver birch, respectively. The expected height growth of the category ‘tested’ was slightly better than the one for ‘qualified’, with more distinct differences in silver birch. The model with forest reproductive material-category-specific coefficients reflected the actual growth of improved trees; however, such application is limited to sites with medium and high site indices, where improved planting stock is typically used. We recommend the model for young stands up to the age of 20 and 40 years for pine and birch, respectively, considering the empirical data cover on which the functions are based. A unified dynamic height model with the same functional form but category-specific parameterization for different improvement levels allows a practical applicability and effective communication amongst diverse users, thereby promoting the utilization of the model amongst forest owners and managers who possess information regarding the origin of planting stock.

Introduction

Forests are a major natural resource in the Baltic region, and the forestry sector is a vital contributor to the bioeconomy on a pan-European scale along with the forestry sectors of the Nordic countries (Hetemäki 2020; Klauss 2020; Girdziušas et al. 2021). The forest sector is a significant contributor to the gross domestic product (GDP), providing employment in timber harvesting, processing, and transport. Forest products are also major exporting goods of the region, providing a valuable source of income. Namely, the GDP share of the forest sector in the Baltic States reaches 2.4%–4.0%, which is several times higher than the European average (0.72%) (Olschewski et al. 2020). Given the growing demand for roundwood as an alternative to fossil raw materials, sustainable management of forests aims to simultaneously increase timber production and forest carbon sinks (Hetemäki 2020) to maximize its potential in the region’s bioeconomy.

In the Baltic region, Scots pine (Pinus sylvestris L.) is a dominant coniferous tree species with high economic importance for the sawn softwood market, whilst silver birch (Betula pendula Roth) is a dominating broadleaved species serving as raw material for plywood industry (Klauss 2020; Girdziušas et al. 2021). Considering the commercial importance of these species, breeding programmes have been conducted since the middle of the 20th century aiming to improve growth, quality, and resistance to biotic and abiotic risks (Jansons et al. 2006; Krakau et al. 2013; Gailis et al. 2020b). Regional tree breeding programmes are estimated to achieve 10%–30% of genetic gains in growth, resulting in profitability from increased production of high-quality timber (Jansons et al. 2011; Ruotsalainen 2014; Jansson et al. 2017; Gailis et al. 2020a). In 2021, 99.5% of the 23.9 million and 37% of the 5.4 million nursery seedlings of Scots pine and silver birch, respectively, in Latvia (LV) were grown from improved seed orchards’ seeds (State Forest Service 2022). Considering the substantial share of improved seeds (for both sawing and planting) in Scots pine regeneration, as well as purposeful afforestation of marginal agricultural land over the last decades with improved birch seedlings aiming for high-quality plywood (Liepins and Rieksts-Riekstins 2013), the estimated noteworthy gains in growth need to be better reflected in forest management planning.

Growth and yield models are common tools to predict forest development, plan silvicultural activities, or evaluate different management scenarios (Ahtikoski et al. 2012). However, existing growth models for the Baltic region are usually based on empirical data from unimproved trees collected several decades ago (Gould et al. 2008; Kuehne et al. 2022). Hence, concerns about incorrect predictions for improved material have been raised, which highlights a need to incorporate and reflect the enhanced growth of improved trees in growth models (Rehfeldt et al. 1991; Egbäck et al. 2017; Deng et al. 2020). Such growth models, which are calibrated or modified to account for altered dynamics for improved nursery stock, in the Baltic region are still lacking.

Given the available data from extensive genetic field trials of the main coniferous and broadleaved tree species Scots pine and silver birch, respectively, in the Baltic region, we aim to model height growth of genetically improved trees as a reliable proxy for areal production (Burkhart et al. 2012; Manso et al. 2021; Kuehne et al. 2022) with further potential to be implemented in growth simulator systems. We model the growth of the two categories of improved forest reproductive material (FRM)—‘tested’ and ‘qualified’, assigned to phenotypically selected material with or without determined superiority by comparative testing, respectively (Gömöry et al. 2021). The category ‘qualified’ represents first-generation seed orchard material with estimated genetic gains of 10%–15% for growth compared to unimproved trees, whilst predicted gains reach ~20%–25% for the best genetically superior material (corresponding to 1.5-generation seed orchards) based on genetic field test findings (category ‘tested’) (Ruotsalainen 2014; Jansson et al. 2017). Therefore, the main objective of the study was to develop dynamic single tree height models for improved Scots pine and silver birch in the Baltic region to predict height growth and analyze differences in height growth patterns of different genetic improvement levels.

Methods

Study material

The study was carried out in the Baltic region—including data from LV and Lithuania (LT)—situated on the eastern European plain next to the Baltic Sea between ca. 55° and 58°N and 21° and 28°E (Fig. 1). Both are typical lowland countries with plains and low hilly elevations, with the highest peaks reaching 311.6 and 293.8 m above sea level in LV and LT, respectively. The region is located in the northern part of the temperate climate zone, with a distinct western–eastern gradient of continentality from a milder sea climate in the west to a more continental inland climate in the east (Laiviņš and Melecis 2003; Galvonaitė et al. 2013). The average mean annual air temperature in LV is 6.4°C ranging from +5.7°C to +7.5°C (from the inland to the coastal regions). The mean monthly temperature varies from −3.1°C to +17.8°C in February and July, respectively. The mean annual precipitation is 685.6 mm, reaching ca. 850 mm in coastal and upland regions. July and August are the wettest months (75.7–76.8 mm), whilst April is the driest (35.8 mm) (Latvian Environment, Geology and Meteorology Centre 2020). In LT, the average annual temperature is 7.4°C. The warmest month is July (18.3°C), whilst the coldest is January (−2.9°C). The average annual precipitation sum is 695 mm, the most of which falls in July (84 mm) and the least in April (37 mm) (Lithuanian Hydrometeorological Service 2021).

Figure 1

Location of progeny trials in Latvia and Lithuania (denoted with black dots and triangles) with available tree height measurements for model calibration and validation.

The study comprises tree height data from 11 remeasured progeny trials of Scots pine and silver birch (Fig. 1). Such trials are controlled experiments in tree breeding, where the offspring of phenotypically selected trees (plus trees) are planted and observed to comparatively evaluate their growth and characteristics, aiding in the selection of superior trees (genotypes) for further breeding and seed production. In total, 14 260 and 55 926 height–age series were used for pine and birch, respectively (Fig. 2). The available data covers ages from 8 to 42 years with height–age series consisting of two to seven height measurements for a single tree (Supplementary Tables S1 and S2). In total, the trials comprised progenies from 638 and 1048 families (an offspring from each plus tree forms a separate family) of Scots pine and silver birch, respectively (Supplementary Table S3). Experimental design for the families comprised single-tree plots in 10−93 replications (silver birch trials Taurene and Ukri) and 10–100-tree block plots in three to eight replications. The trials were established using 1–2-year-old seedlings at sites suitable for the particular species, with initial planting densities typically used in practice (from 2 × 1 to 2.5 × 2.5 m for Scots pine and silver birch, respectively). Scots pine was planted on relatively poor, sandy soil corresponding to the Vacciniosa forest type (Buss 1997). Silver birch trials in Latvia were planted on silty dry soils in former agricultural lands with mesotrophic conditions. In Lithuania, the birch trials were characterized by heavy-textured eutrophic soils of normal moisture (Šiaulių), eutrophic drained histosols (Dubravos), and light-textured eutrophic gleyic soils with temporarily over moisture (Šilutės).

Figure 2

Height–age series from progeny trials of Scots pine (a, n = 14 260) and silver birch (b, n = 55 926).

For the modelling purposes, 10% of families (standard selection intensity in tree breeding) with the highest mean height were assigned as the FRM category ‘tested’ in each trial, representing the best genetically superior material demonstrated by comparative testing, whilst the other 90% of families were assigned as the category ‘qualified’. The latter genetic improvement level characterizes first-generation seed orchards with phenotypically selected individuals and estimated genetic gains of 10%–15%, but the tested material is predicted to provide gains of 20%–25% (Ruotsalainen 2014; Jansson et al. 2017). In the present study, the functions for each of the species are built specifically for the improved trees and are not compared to unimproved FRM due to the lack of control plots with basic local seed sources without phenotypic selection.

Modelling approach

We used the generalized algebraic difference approach (GADA) to model base-age-invariant individual tree height growth for each species separately (Cieszewski and Bailey 2000; Cieszewski and Strub 2007). We consider five different polymorphic dynamic site equations previously derived from base equations to model height growth (Table 1).

Table 1

Tested generalized algebraic difference models (GADA) fitted to height time series and their corresponding base models with the solutions. a₁, a₂, and a₃ are parameters in the base model; b₁, b₂, and b₃ are parameters in the GADA models; h₀ and h are heights (m) at age t₀ and t₁ (years); X₀ is the solution for X with initial values of height (h₀) and age (t₀).

Designation	Base model	Site parameter	Solution for X	Dynamic equation	Reference
M1	King–Prodan |$h=\frac{t^{a_1}}{a_2+{a}_3{t}^{a_1}}$|	|${a}_2={b}_2+{b}_3X$|   |${a}_3=X$|	|${X}_0=\frac{\frac{t_0^{b_1}}{h_0-{b}_2}}{b_3+{t}_0^{b_1}}$|	|$h=\frac{t_1^{b_1}}{b_2+{b}_3{X}_0+{X}_0{t}_1^{b_1}}$|	Krumland and Eng (2005)
M2	Hossfeld |$h=\frac{a_1}{1+{a}_2{t}^{-{a}_3}}$|	|${a}_1={b}_1+X$|   |${a}_2={b}_2X$|	|${X}_0=\frac{h_0-{b}_1}{1-{b}_2{h}_0{t}_0^{-{b}_3}}$|	|$h=\frac{b_1+{X}_0}{1+{b}_2{X}_0{t}_1^{-{b}_3}}$|	Cieszewski (2002)
M3	Hossfeld IV |$h=\frac{a_2{t}^{a_3}}{t^{a_3}+{a}_1}$|	|${a}_1=\frac{b_1}{X}$|   |${a}_2={b}_2+X$|   |${a}_3={b}_3$|	|${X}_0={h}_0-{b}_1+\sqrt{{\left({h}_0-{b}_1\right)}^2+\frac{2{h}_0\exp \left({b}_2\right)}{t_0^{b_3}}}$|	|$h={h}_0\frac{t^{b_3}\left({t}_0^{b_3}{X}_0+\exp \left({b}_2\right)\right)}{t_0^{b_3}\left({t}^{b_3}{X}_0+\exp \left({b}_2\right)\right)}$|	Cieszewski (2001)
M4	Chapman–Richards |$h={a}_1{\left(1-\exp \left(-{a}_2t\right)\right)}^{a_3}$|	|${a}_1=\exp (x)$|   |${a}_3={b}_2+\frac{b_3}{X}$|	|${X}_0=\frac{1}{2}\Big(\left(\ln{h}_0-{b}_2{F}_0\right)+\sqrt{{\left(\ln{h}_0-{b}_2{F}_0\right)}^2-4{b}_3{F}_0\Big)}$|⁠) |${F}_0=\ln \left(1-\exp \left(-{b}_1{t}_0\right)\right)$|	|$h={h}_0{\left(\frac{1-\exp \left(-{b}_1t\right)}{1-\exp \left(-{b}_1{t}_0\right)}\right)}^{b_2+\frac{b_3}{X_0}}$|	Cieszewski (2004)
M5	Lundqvist |$h=a\ \exp \left(-b{t}^{-c}\right)$|	|$a=\exp (X)$|   |$b={b}_1+\frac{b_2}{X}$|	|${X}_0=\frac{1}{2}\left({b}_1{t}_0^{-c}+\ln{h}_0+{F}_0\right)$|   |${F}_0=\sqrt{{\left({b}_1{t}_0^{-c}+\ln{h}_0\right)}^2+4{b}_2{t}_0^{-c}}$|	|$h=\exp \left({X}_0\right)\exp \left(-\left({b}_1+\left(\frac{b_2}{X_0}\right)\right){t}^{-c}\right)$|	Cieszewski (2004)

The GADA models after solving the base equation for unobservable theoretical site variable X (Cieszewski and Bailey 2000) has the following general implicit form:

$$ \begin{equation} {h}_{ij}=f\left({h}_{0 ij},{t}_{0 ij},{t}_{ij},\boldsymbol{\mathrm{\beta}}, {\boldsymbol{\mathrm{\alpha}}}_{\boldsymbol{j}}\right)+{\mathrm{\varepsilon}}_{ij} \end{equation} $$

(1)

where h_ij is the observed height at age t_ij for tree i within FRM category j, h_0ij is the height for tree i at a reference age t_0ij, β is the parameter vector affected by the fixed effect α_j associated with FRM category j, and ε_ij is the error term representing unobserved factors and random noise. For each species, we estimated the model parameters by applying all possible combinations of the fixed effect of the FRM category on the model coefficients b₁, b₂, and b₃ (Supplementary Table S4):

$$ \begin{equation} {h}_{ij}=f\left({h}_{0 ij},{t}_{0 ij},{t}_{ij},{\mathrm{\alpha}}_{j1}\cdot{b}_{1j},{\mathrm{\alpha}}_{j2}\cdot{b}_{2j},{\mathrm{\alpha}}_{j3}\cdot{b}_{3j},\right)+{\mathrm{\varepsilon}}_{ij} \end{equation} $$

(2)

where α₁, α₂, and α₃ are fixed effects associated with FRM category j that affects the corresponding parameters b_1j, b_2j, and b_3j. The chosen nonlinear-fixed-effects (NFE) approach demonstrates the desirable characteristics associated with logical behaviour of growth models (Cieszewski and Strub 2018).

In the model specification, the fixed effect was incorporated using the dummy variable approach. Separate fixed effects were estimated for each level (‘qualified’ or ‘tested’) of the FRM category, allowing the estimation of group-specific effects on the corresponding model parameters. The model parameters were estimated with nonlinear least-square regression using the function gnls of the R package nlme (Pinheiro et al. 2021). Due to multiple measurements from each tree, we applied a first-order autoregressive AR (1) error structure to account for temporal autocorrelation (Supplementary Fig. S1) (Box et al. 1994). We modelled different variances for different FRM category levels within each trial using a variance function (Pinheiro and Bates 2000).

Statistical analysis

We tested five different GADA functions with all possible (n = 7) combinations of forest reproductive material category (‘qualified’ and ‘tested’) specific coefficients b₁, b₂, and b₃ (in total, 35 functions for each Scots pine and silver birch, Supplementary Table S4). The best-fit model for each species was selected using the likelihood ratio test, Akaike’s information criterion (AIC), and Bayesian information criterion (BIC) (Supplementary Table S4). The fitted models were evaluated using the aggregated difference (AD, similar to mean residual), aggregated absolute value differences (AAD), and the root mean squared difference (RMSD) (Salas-Eljatib et al. 2010):

$$\begin{equation} \mathrm{AD}=\frac{\sum_{i=1}^n\left({y}_i-{\hat{y}}_i\right)}{n} \end{equation}$$

(3)

$$\begin{equation} \mathrm{AAD}=\frac{\sum_{i=1}^n\left|{y}_i-{\hat{y}}_i\right|}{n} \end{equation}$$

(4)

$$ \begin{equation} \mathrm{RMSD}=\sqrt{\frac{\sum_{i=1}^n\left|{y}_i-{\hat{y}}_i\right|}{n}} \end{equation} $$

(5)

where n is the number of observations and |${y}_i$|⁠, |${\overline{y}}_i$|⁠, and |${\hat{y}}_i$| are the observed, average, and predicted height values, respectively. We did a graphical analysis of trends in residuals plotted against predicted tree height and drawn height–age curves overlaid on the measured height data. For testing the predictive accuracy of the final fitted models, we split the datasets into calibration and validation data (70% and 30%, respectively). The prediction statistics included mean prediction error (MPE; calculated similarly to AD), ADD, and RMSD. The likelihood ratio test was used to test the significance of the fixed effect. For graphical inspection of model growth curves for different site quality (height classes) plotted against observed height series, we selected a reference age of 10 years, which is a common time when evaluations of progeny trials are done. Average realized genetic gains in height (%) of category ‘tested’ over ‘qualified’ was estimated at this reference age and used when plotting category-specific curves. All modelling and data analysis were conducted in R, v 4.0.3 (R Core Team 2020).

Results

All tested models showed good fit statistics with statistically significant coefficients (P < .001) and rather small differences between them for both species, except for an insignificant parameter b₂ in the GADA form of the Hossfeld equation for silver birch regardless of the category-specific combinations (Supplementary Table S4). For Scots pine, the GADA model derived from the Chapman–Richards base equation with FRM category-specific parameters b₁ and b₂ showed the smallest AIC, BIC, and highest log likelihood and was therefore chosen for further analyses. For silver birch, the GADA form derived from the King–Prodan base equation with all FRM category-specific parameters b₁, b₂, and b₃ exhibited the most favourable fit statistics (Table 2 and Supplementary Table S4).

Table 2

Estimated coefficients with standard errors (SE) and confidence intervals (CI) of the final best-fit models for Scots pine and silver birch, and their fit and prediction statistics [N—number of observations; _r (%) = denotes respective relative error]

		Scots pine			Silver birch
	Category	Estimate (SE)	2.5% CI	97.5% CI	Estimate (SE)	2.5% CI	97.5% CI
b1	Tested	0.047*** (0.001)	0.045	0.049	3.157*** (0.021)	3.115	3.199
	Qualified	0.048*** (0.000)	0.047	0.049	3.017*** (0.007)	3.002	3.032
b2	Tested	−21.209*** (1.390)	−23.935	−18.484	−1474.788*** (243.673)	−1952.393	−997.182
	Qualified	−21.514*** (1.410)	−24.277	−18.751	−831.973*** (37.543)	−905.557	−758.388
b3	Tested	78.910*** (4.690)	69.716	88.104	37 960.938*** (5777.893)	26 636.124	49 285.751
	Qualified				21 082.885*** (848.442)	19 419.917	22 745.853
Fit statistics
n		9988			39 135
AIC		17 555.7			143 393.2
RMSD (m) RMSDr (%)		1.079 10.363			1.346 9.590
AD (m) ADr (%) AAD (m) AADr (%)		0.041 0.394 0.695 6.678			0.221 1.573 1.023 7.288
Prediction statistics
n		4272			16 791
RMSD (m) RMSDr (%)		1.185 11.245			1.360 9.697
MPE (m) MPEr (%) AAD (m) AADr (%)		0.044 0.421 0.742 7.041			0.221 1.576 1.030 7.342

^*P < .05.

^**P < .01.

^***P < .001.

The final selected models fitted the data with high accuracy—AAD was 0.695 and 1.023 m for Scots pine and silver birch, respectively, with corresponding relative values of 6.7% and 7.3%. The AD and RMSD were higher for silver birch (AD = 0.221 m, RMSD = 1.346 m) than for Scots pine (AD = 0.041 m, RMSD = 1.079 m). Relative values AD_r were small (0.4%–1.6%), yet RMSD_r was ca. 10% for both species (Table 2). The distribution of the residuals over predicted height were scattered around zero without distinct trends for both species, yet slight increase in variance with increasing height for Scots pine (Fig. 3). A slight underestimation was observed for the highest trees (around ca. 23 m) of Scots pine, whilst the model for silver birch somewhat underestimated the growth of trees of ca. 7–12-m height.

Figure 3

Residuals of fitting (first column) and validation (second column) data against final best-fit models for Scots pine (upper panels) and silver birch (lower panels) with trendline, its regression equation, and R-square value. Grey crosses denote the residuals; black circles with vertical lines show the means of the residuals in 10 classes with a 95% confidence interval of the class mean.

Predictions statistics also indicated sufficient fit of both models (AAD = 0.742 m, AAD_r = 7.0%, RMSD = 1.185 m, RMSD_r = 11.3%, MPE = 0.044 m, MPE_r = 0.4% for Scots pine; AAD = 1.030 m, AAD_r = 7.3%, RMSD = 1.360 m, RMSD_r = 9.7%, MPE = 0.221 m, MPE_r = 1.6% for silver birch) to the validation datasets (Table 2) with similar slight tendencies of underestimation for model fitting dataset described above (Fig. 3).

When comparing the growth curves of the two species studied, silver birch showed faster early height growth than Scots pine. The most productive birch reached a height of 23 m after 22 years, whilst the same height for the fastest-growing Scots pine took ~35 years with a flatter growth trajectory (Fig. 4). Within the range of available data, we observed more distinct differences in growth patterns for different height classes for silver birch compared to Scots pine That is, with higher productivity, the increase in birch height growth was more rapid compared to trees growing in poorer site conditions, whilst the height curves for different height classes of Scots pine were more parallel.

Figure 4

Expected height growth of the final best-fit models (solid black and dark grey dashed lines for the improved forest reproductive material categories ‘tested’ and ‘qualified’, respectively) for Scots pine (a) and silver birch (b). The growth curves represent different height classes at the base age of 10 years.

The graphical inspection of the height growth curves confirmed the statistically estimated differences in model parameters for the distinct FRM categories ‘qualified’ and ‘tested’ (Table 2, Fig. 4). For both species, differences between the FRM categories tended to somewhat increase with the age. At the base age of 10 years, the height of the category ‘tested’ was on average 7.5% and 10.8% higher for Scots pine and silver birch, respectively, comparing to the ‘qualified’ material. Still, growth patterns for different categories varied between the species. For Scots pine, differences in category-specific growth indices appeared to increase with increasing site productivity, whilst being rather similar for birch in different site indices.

Discussion

We built dynamic models for height growth of genetically improved trees of Scots pine and silver birch in the Baltic region. These species have undergone considerable productivity and quality gains due to a relatively long breeding history. The use of the base age invariant polymorphic GADA model form (Cieszewski and Bailey 2000) in combination with FRM category-specific coefficients allowed a successful modelling of tree height growth, considering genetic improvements, across different site qualities, even with rather short time series data (Cieszewski and Strub 2007; Sharma et al. 2011, 2017; Kimberley et al. 2015). For the studied datasets of improved progenies, GADA models derived from the Chapman–Richards (for Scots pine) and King–Prodan (for silver birch) base equations showed the best statistical fit (Supplementary Table S4, Table 2, Fig. 4). The AR(1) error structure successfully accounted for temporal autocorrelation in final fit models for both species (Supplementary Fig. S1). Although residuals for silver birch model showed homogenous variance, applied variance structure did not fully remove heteroscedasticity in the final fit function for Scots pine leaving a slight trend of increasing variance for higher trees (Fig. 3). Still, overall good model fit statistics suggest that the presence of such heteroscedasticity would not undermine the validity of the nonlinear model (Louangrath 2013).

Nevertheless, all tested equations equally satisfied the criterion of biologically realistic trajectories (Nunes et al. 2011) for the covered age range. Historically, both final fitted types of base height–age equations have been recognized and frequently used (Zeide 1993). Furthermore, the dynamic derivatives have been commonly reported to have good fit for height, dominant height, or diameter predictions (Nunes et al. 2011; Sharma et al. 2011, 2017, 2019; Kahriman et al. 2018; Manso et al. 2021).

We calibrated completely new functions based on empirical data from progeny trials intended to predict height growth of improved Scots pine and silver birch. Although considered to be the best and most accurate approach (Weiskittel et al. 2011; Sabatia and Burkhart 2013), calibration of the model parameters has been commonly reported to have limited use due to the lack of costly and time-consuming repeated measurements of improved trees (Sabatia and Burkhart 2013; Joo et al. 2020; Manso et al. 2022). Thus, relatively simple modifications of existing models originally intended for unimproved trees—adjustment of site index (e.g. Nance and Wells 1981; Buford and Burkhart 1987) and application of genetic multipliers (e.g. Carson et al. 1999; Kimberley et al. 2015; Ahtikoski et al. 2020)—are methods traditionally chosen over developing new models. The authors emphasize that progeny trials for boreal tree species are typically measured at an early age (~10–15 years), which means that the growth patterns of mature improved trees cannot be fully assessed. Mature tested material with known growth patterns may already be surpassed by more productive and recently selected genotypes (Burkhart et al. 2012; Haapanen et al. 2016; Egbäck et al. 2017; Deng et al. 2020). However, our study material derived from progeny trials encompassed current breeding populations (Baumanis et al. 2014; Gailis et al. 2020b), enabling the development of models specifically tailored for young improved stands up to 40 years of age for Scots pine and 20 years for silver birch. We acknowledge that projections for the full rotation time of ca. 80 and 50 years for Scots pine and silver birch, respectively, would still be extrapolation outside fitting data coverage and thus should be used with caution.

Chapman–Richards GADA models are generally recognized to be robust to extrapolation (Manso et al. 2021), and graphical inspection of Scots pine height growth curves tended to confirm this, showing continuous gradual increase in height outside the data coverage tending to reach realistic asymptotes ~30 m for the highest height classes (Fig. 4a). Meanwhile, the King–Prodan GADA model for silver birch showed a tendency for too-fast growth cessation above the upper age limits of tree data used for model fitting (>22 years), therefore quickly reaching an unreasonably low asymptote at older ages (Fig. 4b). Such trend was irrespective of the type of base equation for the GADA derivatives tested. We explain it with characteristics and temporal limits of the underlying data that determine the sigmoid form of the curve (Salas-Eljatib et al. 2021): potentially, the delayed point of the inflection and rapid growth afterwards during the second phase seem to determine a rather fast decrease of the growth rate in the third phase (Fig. 4b). We already noticed a too-long phase of slow growth before the point of inflection during preliminary modelling and analysis of data from solely Latvian trials due to the lack of early height measurements (the first inventory was done at the age of 10 years, Supplementary Table S1). The inclusion of younger height measurement data from Lithuania (age ≥5 years, Supplementary Table S1) appeared to correct the growth trajectories to be more biologically reasonable during the first 10 years, whilst lack of measurements after the age of 22 years still appears to lead to a premature start for the phase of decreased growth rate. Still, the residual analysis did not indicate any trend of underestimating the growth of the highest trees at the upper age limits of the data (Fig. 3), which could be expected when extrapolated to older ages.

The newly calibrated models for improved trees with enhanced growth trajectories can sufficiently improve planning of management in young production stands up to around half of the rotation cycle including first commercial thinnings (Manso et al. 2022). For silver birch, thinning may need to be done as early as around the 12th growing season on high-productivity sites, where the improved trees have reached a height of ca. 15 m (Fig. 4) (Hynynen et al. 2010), whilst the corresponding age for pine could be expected ~25–30 years (Niemistö et al. 2018; Donis et al. 2020). The first commercial thinning at the age of 14 years is reported to be already profitable with an internal rate of return reaching 9.4% for the best improved silver birch genetic entries (Gailis et al. 2020a), which highlights the need for reasonable growth predictions already in young stands.

In addition to being the first attempt to build height growth model for improved FRM in the Baltic region, a major objective of this study was to dynamically incorporate FRM categories into the models to more accurately predict the growth of improved trees categorized as ‘qualified’ and ‘tested’. Consequently, separate sets of parameters were successfully calibrated for each of the two categories (Table 2) and appeared to improve prediction accuracy for both species by determining genetic control of the curves (Gwaze et al. 2002). Such approach with the same functional form, but FRM category-specific parameterization could be easily applicable in practice and communicable across different users, as similarly suggested by Manso et al. (2021) for a common dynamic top height model for various species in Great Britain. For forest owners and managers, who usually have information about the origin of planting stock, such approach may encourage the use of the model in practice.

From the perspective of tree breeders, the developed models allow to compare the differences in height growth dynamics between FRM categories with different genetic improvement levels. Gwaze et al. (2002) emphasize the importance of model parameters in accurately capturing growth patterns in improved stands, as opposed to static height measurements that only reflect the productivity of studied genotypes at a specific age and site (Skovsgaard and Vanclay 2008). We observed varying height growth patterns across different improvement levels (Table 2, Fig. 4). In our study, the height of the category ‘tested’ was on average 7.5% and 10.8% higher for Scots pine and silver birch, respectively, comparing to the ‘qualified’ material at the selected base age of 10 years, but the differences tended to increase with age (Fig. 4). Our results indicate that the superiority of the tested material over the qualified one, observed at a young age, remains at least until the mid-rotation, dismissing concerns of diminishing gains from tree-breeding programmes over time (Hamilton and Rehfeldt 1994). The most distinct differences in growth patterns were observed for silver birch, reflecting the three category-specific coefficients b₁, b₂, and b₃, whilst genetic control was observed for b₁ and b₂ in Scots pine (Table 2). Although the coefficients derived from the base equations do not have straightforward biological meaning, the observed variable genetic gains and drawn height growth curves indicated FRM category-affected asymptote, shape, and rate (Deng et al. 2020). Nevertheless, the strength of the genotype by site interaction determines whether improvement (subsequently, also growth patterns) is consistent across various environments. It is hence of high importance for matching relatively expensive improved planting stock to appropriate sites for the best performance (Bourdon 1977; Kimberley et al. 2015). In our study, we observed that the category-specific differences tended to vary to some extent based on site quality. For Scots pine (Fig. 4a), an increase in differences between categories was observed with site quality. However, for silver birch (Fig. 4b), the dominance of the ‘tested’ category remained relatively consistent across the represented site types. The latter result coincides with earlier extensive research of the silver birch breeding population in Latvia, which found a negligible genotype by environment effect on tree growth over different trials and ages (Gailis et al. 2020b). However, the source of data for model calibration in this study was genetic field trials, which might represent limited growth conditions, as compared to, e.g. datasets from national forest inventories (Sharma et al. 2011). In addition to constraints of use up to the mid-rotation, this limits the application of the model to relatively high-quality sites. We find this to be acceptable, since genetically improved material is typically planted on sites with suitable properties for the particular species. Although earlier studies stress that such factors as higher planting density and different management of genetic field trials may alter tree growth compared to typical productive forest stands (Carson et al. 1999; Deng et al. 2020; Joo et al. 2020), the studied progeny trials were established with initial densities commonly used in practical forestry and maintained to be similar to conventional even-aged productive forest stands. The fitting and prediction statistics confirmed that both models are sufficiently precise (Table 2) to predict height growth for rather high-quality sites represented by the experimental data.

Considering tree height as a reasonable proxy for areal production (Skovsgaard and Vanclay 2008; Liziniewicz et al. 2018; Liziniewicz and Berlin 2019; Manso et al. 2021; Kuehne et al. 2022) and considering the persistent gains of improvement for the studied age range, the developed models of this study can contribute to more accurate growth and yield predictions, when incorporated into forest growth simulators. The intended regional scale use for genetically improved FRM of Scots pine and silver birch may further serve as a tool to evaluate contributions of tree breeding and forest management as such to biomass production and carbon sequestration, hence reducing risks of under- or overestimations resulting from more global functions or empirical models calibrated for other regions (Landsberg 2003; Liepiņš et al. 2018; Socha et al. 2021). This is of high importance, for instance, in developing justified carbon policies and regional reference levels for greenhouse gas emissions (Lazdiņš et al. 2020).

Conclusion

The polymorphic dynamic derivatives of the Chapman–Richards and King–Prodan base equations had the best fit and high accuracy to describe the individual tree height growth of genetically improved Scots pine and silver birch, respectively. We found different growth patterns between the FRM categories ‘qualified’ and ‘tested’, reflected in category-specific sets of estimated model parameters for both species. The observed growth curves showed that superiority in height growth for category ‘tested’ at early age remains at least until mid-rotation, indicating a long-term nature of genetic gains. The differences between both FRM categories appeared to be consistent over the represented site quality range for silver birch, whilst they tended to increase with better site quality for Scots pine, thereby suggesting tree breeding effect to manifest itself more effectively on appropriate sites. We acknowledge the limitations for model application due to the empirical data coverage used for model fitting and hence suggest to use it for young stands up to the age of 40 and 20 years for Scots pine and silver birch, respectively, on sites suitable for the particular species. Still, this modelling approach can provide more precise information for guiding silvicultural activities, such as the timing of first commercial thinnings, and contribute to more precise regional-level biomass estimations, which are essential for evidence-based policy-making in any country or region, where improved planting stock has a substantial share in forest regeneration.

Acknowledgements

We thank Professor Katri Kärkkäinen and Professor Jari Hynynen (Natural Resources Institute Finland) for valuable suggestions and project management that ensured the possibility to prepare the manuscript.

Conflict of interest: None declared.

Funding

The work was supported by European Regional Development Fund project No 1.1.1.1/19/A/111 ‘Decision support tool for increased forest productivity via efficient climate adjusted transfer of genetic gain’ (data and calculations of pine) and project ‘Assess4EST: Seeing trees and forests for the future: assessment of trade-offs and potentials to breed and manage forests to meet sustainability goals’ (data and calculations of birch) supported under the umbrella of ERA-NET Cofund ForestValue by Forest Development Fund. ForestValue has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No 773324.

Data availability

The data underlying this article will be shared on reasonable request to the corresponding author.