# Genetic Parameters of Diameter Growth Dynamics in Norway Spruce Clones

^{1}

^{2}

^{*}

## Abstract

**:**

_{g}which ranged between 11.0 and 17.1%, with the highest being for the growth rate. The heritability (H

^{2}) of the diameter at breast height (DBH) reached 0.35 at the age of 40, while CV

_{g}decreased from 12.9% to 7.8% between the ages of 20 and 45. Age–age genotypic correlations were positive and were strong or very strong (>0.76). The realised genetic gain varied from −6.3 to +24.0% around the trial mean. A substantial improvement in DBH was indicated when elite clones were selected for vegetative propagation based not only on early measurements, but also considering the genetic variance in the model parameters.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Site and Material

^{−1}). The rootstock material comprised seedlings of local origin. In total, 421 trees were planted in randomly distributed single-tree plots (11–31 replications (ramets) per clone). Weed control was carried out in the planting year and the first year after planting. No thinning was conducted prior to the sampling. No measurements had been performed before during the trial.

#### 2.2. Modelling Approach

_{iA}is the DBH for the i-th clone at age A, β

_{1}is the asymptotic diameter parameter, β

_{2}is the rate parameter, β

_{3}is the shape parameter and ԑ

_{iA}is a normally distributed zero-expectation random error due to the DBH that was observed at age A [47]. We followed the approach of using models that had been previously fitted successfully by other researchers [48]. The preliminary analyses and previous studies have suggested that the Chapman–Richard function is a biologically reasonable selection for modelling tree growth curves [34,46,49,50].

_{iA}and ԑ

_{iA}are as defined as for Equation (1), β

_{10}, β

_{20}and β

_{30}are fixed effect parameters and b

_{1i}, b

_{2i}and b

_{3i}are random effect parameters for the i-th clone (${b}_{1i}~N\left(0,{\sigma}_{{b}_{1}}^{2}\right)$, ${b}_{2i}~N\left(0,{\sigma}_{{b}_{2}}^{2}\right)$ and ${b}_{3i}~N\left(0,{\sigma}_{{b}_{3}}^{2}\right)$ with no correlation among these parameters). Heteroscedasticity in the error term ԑ

_{iA}was not detected. The autocorrelations of the errors that were due to ring width measurements on the same trees were modelled by mixed first-order autoregressive and moving average structures (ARMA (1,1)). To remove the effects of the various variances in the different clones, we modelled different variances for each factor (clone) using the variance function [51].

#### 2.3. Genetic Parameters

_{ij}is the observation of the ith tree from the jth clone, μ is the overall mean, C

_{i}is the random effect of the cloning and ԑ

_{ij}is the random error. To evaluate the dynamics of the genetic parameters, (i) the broad-sense heritability (H

^{2}) of DBH for each year and (ii) the age–age genotypic correlations of DBH among the years were estimated as follows:

_{g}) [55] in order to describe the extent of genetic variability among the clones for any random effect parameter:

_{g}is the genotypic coefficient of variation, ${\widehat{\sigma}}_{{b}_{x}}^{2}$ is the estimated variance for the random effect parameter x and β

_{x}is the fixed effect parameter x. The CV

_{g}of DBH was calculated for each year. For comparison, the H

^{2}and CV

_{g}of tree height at the age of 50 years was estimated.

## 3. Results

#### 3.1. The Growth Model

_{1i}), random rate (b

_{2i}) and random shape (b

_{3i})) had the lowest value of the AIC statistic (−189.152) (Table 1). Overall, the model fit was significantly improved by addition of the random rate and/or shape into the model that already contained the random effect parameter b

_{1i}compared to the anamorphic random asymptote equation (p < 0.01).

#### 3.2. Dynamics of Genetic Parameters

^{2}) ± standard error (SE) for DBH increased from 0.19 ± 0.087 at the age of 20 years to 0.35 ± 0.131 at the age of 40 years (Figure 3). Afterwards, H

^{2}gradually decreased and was 0.32 ± 0.123 at the age of 50 years. On the contrary, the genotypic coefficient of variation (CV

_{g}) was the highest at the age of 20 years (12.9%) and decreased to 7.8% at the age of 45 years, after which it remained stable for the following 5 years. The H

^{2}and CV

_{g}for tree height at the age of 50 years was 0.41 ± 0.088 and 5.6%, respectively.

_{g}for the DBH growth model parameters β

_{1}, β

_{2}and β

_{3}were 11.0, 17.1 and 11.9%, respectively. Overall, variance in the asymptotic DBH due to the clonal effects was slightly greater (${\sigma}_{{b}_{1}}^{2}$ = 26.69 cm) than the within-group (within-clone) error variance (${\mathsf{\sigma}}_{\epsilon}^{2}$ = 23.05 cm) (Table 1). The realised genetic gains of the clones at the final harvest age varied from −6.3 to +24.0% around the trial mean (Figure 4).

_{G}) were positive and mainly very strong (>0.80), although they were slightly weaker, yet still strong (>0.76), for the older trees (age 20–22 versus age 46–50 years). There was a trend of slightly stronger correlations between similar ages with increasing age. For instance, DBH between age 45 and 50 was 100% genetically correlated, while r

_{G}between ages 20 and 15 was 0.97.

## 4. Discussion

#### 4.1. Dynamics of Clone-Specific Diameter Growth and Its Genetic Parameters over Time

_{g}for DBH in trials involving 19-year-old Norway spruce clones has been reported to vary between 13.6 and 15.9% [71]. Still, our results showed that CV

_{g}and H

^{2}were not constant and changed over time. The estimated H

^{2}increased from 0.19 at the age of 20 years to a peak of 0.35 at the age of 40 years. A similar trend has been observed for the narrow-sense heritability h

^{2}of DBH in open- pollinated progenies of Norway spruce in southern Sweden, for which h

^{2}stabilised at circa 0.22 at the cambial age of 10 years after increasing from close to zero near the pith [72]. For Scots pine full-sib families in Sweden, a trend of increasing h

^{2}has been observed for wood quality traits and cumulative ring width, for which this parameter increased from very low to 0.25 at the age of 20 years [73]. Hannrup et al. [71] reported a H

^{2}of 0.34–0.50 for 19-year-old Norway spruce clones, while a low H

^{2}(< 0.14) was estimated for juvenile white spruce (Picea glauca (Moench) Voss) somatic clones 4 years after outplanting [74].

^{2}, CV

_{g}decreased by almost half from 12.9% at the age of 20 years to 7.8% at the age of 45, after which it remained stable (Figure 3). Similar to descendent trend that was observed for CV

_{g}in our study, spruce clones in series of experiments in northern Germany demonstrated a steady decrease in genetic variance in height from circa 20% at the age of 3 years to a plateau of 7% after the age of 8 years [75]. Joint site data from Sweden showed that the coefficient of additive genotypic variation CV

_{a}for DBH in Norway spruce decreased from 15.45% to 11.91% at the ages of 12 and 21 years, respectively [76]. The estimated CV

_{a}showed a marked decline with age for both H and DBH (from 25–33% to 7–14%) in Silver fir (Abies alba Mill.) up to the ages of 10–15, after which they became stable [77].

^{2}and CV

_{g}stabilised after the age of 40–45 years (Figure 3), which was likely due to reaching the moment of canopy closure and the intensification of inter-tree competition [78] as diameter increment is considered to be the trait that is most (first) affected by competition [79]. Canopy closure depends on the initial planting density and the increment of the trees. The onset of inter-tree competition in loblolly pine has been estimated to be after 5 years in the most densely planted plots (1.2 × 1.2 m) and after 8.6 years in the most sparsely planted plots (3.7 × 3.7 m) [80]. The latter age corresponds to circa 35% of the rotation age for managed P. taeda [81], which indicates a longer period of competition-free early growth for the wider spacing. Although canopy closure in Norway spruce progeny plots in northern Europe with conventional spacing is typically observed at the age of 10–20 years [79], the low planting density (5 × 5 m) in the study site could have delayed it substantially [82,83].

#### 4.2. Age–Age Genotypic Correlations

_{g}> 0.76).

_{G}at older ages have also been reported previously for various conifer tree species, which could be associated with the cumulative nature of the growth traits [93,94]. Our results corresponded well to earlier studies of growth traits in progeny trials, which showed very strong genotypic relations among similar ages, with a slight decline as the age differences increased [72,75,77,78,94].

## 5. Conclusions

^{2}= 0.32) and a significant genotypic coefficient of variation (CV

_{g}= 7.8%), which tended to stabilise at the age of 40–45 years. Although the mainly very strong age–age genotypic correlations would justify selection for DBH at earlier age, we suggest that growth curve parameters are just as important for tree breeding in terms of the selection of elite clones, once the data from long-term clonal tests are available. The substantial genetic variation in growth rate, shape and asymptote suggests the potential for more precise selection using predictions for not only final dimensions, but also desirable patterns of growth trajectories. Based on this information, clone-specific genetic modifiers should be tested using dynamic base–age–invariant functions for future growth predictions in practical forestry in order to improve the prediction accuracy for genetic entries with various genetic gains.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The mean diameter growth trajectories of the 19 Norway spruce clones that were analysed in this study.

**Figure 2.**Statistics of the final fitted Chapman–Richard mixed model that was applied to investigate the clone effect of the diameter–age relationship on the parameters: (

**A**,

**B**) plots of raw (

**A**) and standardised (

**B**) residuals for the final equation. The whiskers denote the 95% confidence intervals of the residuals for the classified fitted values. (

**C**) Quantile–quantile plot of the final fitted model. (

**D**–

**F**) Normal plots of the estimated random effects of the asymptotic diameter parameter β

_{1}(

**D**), the rate parameter β

_{2}(

**E**) and the shape parameter β

_{3}(

**F**) for the final fitted model.

**Figure 3.**Dynamics of the estimated broad-sense heritability (H

^{2}) and genotypic coefficient of variation (CV

_{g}) during the studied period (age 20–50 years) of Norway spruce clones. The whiskers denote the standard error for H

^{2}.

**Figure 4.**Predicted trajectories of DBH growth curves for population mean (fixed), each individual clone (random) and its realised genetic gain (numbers in bold and italic, %) at the final harvest age of 50 years (45 years of breast height age) using the final fitted model. Grey dots represent the sample data for each clone.

**Figure 5.**Growth curves of the selected clones (19, 24, 51, 53) with markedly different DBH growth trajectories.

**Table 1.**Parameter estimates (fixed effect parameters: β

_{10}, β

_{20}and β

_{30}; estimated variance components: ${\sigma}_{{b}_{1}}^{2}$, ${\sigma}_{b2}^{2}$, ${\sigma}_{{b}_{3}}^{2}$, ${\sigma}_{\epsilon}^{2}$) and model statistics (AIC, Akaike’s information criterion; BIC, Bayesian information criterion; logLik, log likelihood test) of the Chapman–Richard base equation when applying different combinations of random asymptotes (β

_{1}), random rates (β

_{2}) and random shapes (β

_{3}), which were fitted to diameter at breast height from the 19 clones that were used in the study.

Random Parameter in Model | Parameter Estimates | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

β_{10} | β_{20} | β_{30} | ${\mathit{\sigma}}_{{\mathit{b}}_{1}}^{2}$ | ${\mathit{\sigma}}_{\mathit{b}2}^{2}$ | ${\mathit{\sigma}}_{{\mathit{b}}_{3}}^{2}$ | ${\mathit{\sigma}}_{\mathbf{\epsilon}}^{2}$ | AIC | BIC | logLik | |

β_{1} | 46.403 | 0.0466 | 1.610 | 16.417 | n/a | n/a | 24.253 | −73.140 | 96.806 | 61.57 |

β_{1}, β_{2} | 46.630 | 0.0472 | 1.640 | 25.116 | 3.53 × 10^{−5} | n/a | 23.509 | −184.040 | −0.498 | 119.02 |

β_{1}, β_{3} | 46.262 | 0.0471 | 1.650 | 15.141 | n/a | 0.0436 | 23.0467 | −153.329 | 30.213 | 103.66 |

β_{1}, β_{2}, β_{3} | 46.991 | 0.0467 | 1.624 | 26.686 | 6.37 × 10^{−5} | 0.0371 | 21.678 | −189.152 | 14.783 | 124.58 |

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**MDPI and ACS Style**

Zeltiņš, P.; Kangur, A.; Katrevičs, J.; Jansons, Ā.
Genetic Parameters of Diameter Growth Dynamics in Norway Spruce Clones. *Forests* **2022**, *13*, 679.
https://doi.org/10.3390/f13050679

**AMA Style**

Zeltiņš P, Kangur A, Katrevičs J, Jansons Ā.
Genetic Parameters of Diameter Growth Dynamics in Norway Spruce Clones. *Forests*. 2022; 13(5):679.
https://doi.org/10.3390/f13050679

**Chicago/Turabian Style**

Zeltiņš, Pauls, Ahto Kangur, Juris Katrevičs, and Āris Jansons.
2022. "Genetic Parameters of Diameter Growth Dynamics in Norway Spruce Clones" *Forests* 13, no. 5: 679.
https://doi.org/10.3390/f13050679