# Variation of Cones Production in a Silver Fir (Abies alba Mill.) Clonal Seed Orchard

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Silver Fir Clonal Seed Orchard

#### 2.2. Data Analysis

#### 2.2.1. Genetic Variation

_{ijk}∼ ZIP(λ

_{ikj}, π

_{ijk})

_{0}is the overall fitted mean, O

_{i}is the random effect in the ith observation year (i = 1...6 ∼ NID (0, ${\sigma}_{o}^{2}$), C

_{j}is the random effect in the jth clone (j = 1…44 ∼ NID (0, ${\sigma}_{c}^{2}$)), and OC

_{ij}is the random effect of the interaction between year and clone (NID (0, ${\sigma}_{oc}^{2}$)). The single-year models are similar, with the exception of the presences related to the observation year (i.e., O

_{i}and OC

_{ij}). The models were fitted within a Bayesian framework (package MCMCglmm, version 2.32) [45]. In the Bayesian analysis, the prior influences model results [46] and, for zero-inflated models, there are different reports on the prior influence on the heritability estimates [47,48,49]; our prior analysis is presented in Supplementary Material S3.

#### 2.2.2. Female Fertility Variation

_{i}is the proportional contribution of clone i, and CV

_{f}is the coefficient of variation of the clonal proportion of cones production. Female fertility variation—along with male fertility variation Ψ

_{m}and the component of the clone fertility variation Ψ—is an adimensional measure that relates parents to their progeny and expresses the probability that successful gametes, commonly known as “sibs,” would come from the same parent. Its values cannot be below 1; values Ψ = 1 means that the individuals have the same fertility, while Ψ = 2 means a twice chance that two individuals would share a parent, compared to the above equal parental fertility. For seed orchards, Kang et al. [9] suggested that Ψ = 2.

_{p(f)}) [8]:

## 3. Results

#### 3.1. Genetic Variation

#### 3.2. Female Fertility Variation and Genetic Diversity

_{f}) has a value of 2.28 in pooled data, and inversely depicted the cones production across years, with extremes of 1.37 (2015, ‘top’) and 5.49 (2021, ‘poor’) (Table 5 and Supplementary Material S1, Table S1.2). Similarly, the effective number of female parents (N

_{p(f)}) was smaller in 2021 (8.19) and the largest in 2015 (32.90). The relative effective number (N

_{r}) of female parents was between 19% and 75%, in 2021 and 2015, respectively. The lower genetic diversity in cone crops was associated with the poor year (0.939), which was slightly different than in the good years (0.985) (Table 5).

## 4. Discussion

_{2}= 0.38, 30 years Pinus sylvestris seed orchard) [65]. The overall values are similar to other species, e.g., Pinus nigra [10], with values between 0.61–0.71, higher than in Pinus halepensis [66], and lower than in Pinus radiata [2]-H

_{2}= 0.91 or in Pinus patula (H

_{2}= 0.80) [15] (see the further comments section). The small genetic control found in the zero-component of fertility (data in latent scale) indicates a small, but existing overall probability (4%) that some of the clones will not be fertile, which could increase almost four times in the years of low production.

_{(f)}are slightly higher than expected in seed orchards, but there was marked year-to-year variation, lower than expected in good production years and more than double in poor years. Similar variations of clone fertility over productivity years were reported in young seed orchards [8]. A possible source of variation in female fertility remains the unbalanced number of ramets per clone, as in our case, which will contribute to a larger coefficient; the mentioned reference value Ψ = 2 could be used in order to pass this [7]. The effective number of female parents (N

_{p(f)}), derived from effective population sizes, is used to assess the level of gene diversity in the population and refers to the number of individuals which, in a hypothetical population, would produce the same number of siblings (relatives) as the actual population [5,52]. Our results indicated a value over the years of N

_{p(f)}less than half the number of clones (Table 5) and yearly values which mirror the fertility variation and the cumulative curves. Similarly, the largest deviations from the equal fertility, expected when N

_{p(f)}equals the number of clones in the seed orchard [4], were found in poor years. The relative number of female parents N

_{r%}in pooled data of 44% and annual extremes between 18% and 73% (Table 5) is different than the pattern reported in similar studies, but observed in young seed orchards, where the fertility changes with ageing [52]. The expected gene diversity of seed crops (GD) were in accordance with the other fertility indicators.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Variance explained by random effects in the multi-year model, Poisson (P), and zero-inflated (zi) components. Posterior means (points), 99%, and 95% credible intervals (lines, respective blocks) are in latent scale.

**Figure 2.**Posterior MCMC samples (bars), kernel density estimation (thin solid line), posterior mean (dotted line), and 95% credible intervals (thick solid line) of heritability in zero-inflated (

**a**) and Poisson (

**b**) components of cone crops. Estimates are in data scale.

**Figure 3.**Cone crop parental balance curve over six years, based on the entire orchard clones (n = 44). The straight line represents an ideal orchard with equal contribution among individuals, while the dotted horizontal line is the 20:80 rule.

Provenance (Provenance Region) | Clone IDs | Number of Clones | Latitude N | Longitude E | Altitude (m) | Mean Annual Temperature (°C) | Mean Annual Precipitations (mm) |
---|---|---|---|---|---|---|---|

Avrig (C1) | 3.1–3.18 | 7 | 45°39′ | 24°29′ | 750 | 7.5 | 694 |

Rusca Montană (D2) | 3.55–3.72 | 4 | 45°39′ | 24°29′ | 1000 | 6.6 | 878 |

Sinaia (B2) | 4.17–4.36 | 7 | 45°19′ | 25°32′ | 1150 | 4.8 | 783 |

Văratec (A2) | 158–181 | 26 | 47°08′ | 26°15′ | 600 | 6.9 | 606 |

Parameter/Year | 2013 | 2015 | 2018 | 2020 | 2021 | 2022 | Pooled |
---|---|---|---|---|---|---|---|

Alive ramets (n) | 636 | 636 | 636 | 636 | 636 | 631 | - |

Fertile ramets (%) | 75.3 | 95.12 | 91.5 | 94.3 | 42.6 | 67.5 | 77.7 |

Mean | 28.0 | 67.92 | 79.6 | 47.5 | 7.1 | 16.2 | 41.1 |

Std. deviation | 35.9 | 41.18 | 61.4 | 36.3 | 15.1 | 21.3 | 46.4 |

Median | 14.5 | 67.5 | 70.0 | 42.0 | 0.0 | 7.0 | 25.0 |

Range | 0–206 | 0–200 | 0–350 | 0–215 | 0–115 | 0–110 | 0–350 |

**Table 3.**Proportion of variance explained by random effects and heritability in single-year models. Estimates are reported as posterior mode (95% credible interval, proportion of variance from latent scale, heritability in both latent (H

^{2}

_{l(P)}), and data scale (H

^{2}

_{(zi)}, H

^{2}

_{(P)}), for Poisson (P) and zero-inflated (zi) component of the model.

Parameter/Year | 2013 | 2015 | 2018 | 2020 | 2021 | 2022 |
---|---|---|---|---|---|---|

Clone_{(zi)} | 33.2 (17.9–50.4) | 18.9 (0.1–55.6) | 56.8 (36.9–74.6) | 20.2 (0.1–52.6) | 26.4 (13.1–42.7) | 24.6 (10.1–42.8) |

residual_{(zi)} | 27.3 (20.1–34.2) | 55.4 (30.3–69.9) | 25.9 (15.5–38) | 46 (27.3–58.7) | 31.3 (23.8–38.3) | 37 (27.9–45) |

Clone_{(P)} | 10.2 (5–18.3) | 5.5 (2.2–10.6) | 2.6 (1–5.4) | 6.2 (2.6–11.7) | 5.7 (1.1–13.4) | 6 (2.3–12) |

residual_{(P)} | 29.3 (21.2–37.4) | 20.2 (10.9–26.3) | 14.6 (8.5–21.7) | 27.6 (16.3–36) | 36.7 (27.4–46.2) | 32.4 (24–40.2) |

H^{2}_{(zi)} | 0.127 (0.07, 0.237) | 0 (0, 0.049) | 0.088 (0.033, 0.188) | 0 (0, 0.065) | 0.147 (0.07, 0.229) | 0.106 (0.037, 0.191) |

H^{2}_{l(P)} | 0.83 (0.723, 0.914) | 0.797 (0.663, 0.891) | 0.733 (0.548, 0.846) | 0.783 (0.616, 0.866) | 0.698 (0.323, 0.868) | 0.724 (0.541, 0.877) |

H^{2}_{(P)} | 0.607 (0.543, 0.633) | 0.662 (0.536, 0.751) | 0.616 (0.46, 0.715) | 0.614 (0.486, 0.698) | 0.443 (0.188, 0.594) | 0.549 (0.353, 0.628) |

**Table 4.**Pearson product moment and Spearman’s rank correlation coefficients (above and below the diagonal) among clone mean cone production across years.

Year | 2013 | 2015 | 2018 | 2020 | 2021 | 2022 |
---|---|---|---|---|---|---|

2013 | 1 | 0.473 *** | 0.462 * | 0.297 * | 0.276 | 0.001 |

2015 | 0.535 *** | 1 | 0.797 *** | 0.560 *** | 0.343 * | −0.003 |

2018 | 0.492 ** | 0.811 *** | 1 | 0.588 *** | 0.162 | 0.077 |

2020 | 0.346 * | 0.599 *** | 0.596 *** | 1 | −0.069 | 0.163 |

2021 | 0.280 | 0.329 * | 0.159 | −0.049 | 1 | 0.136 |

2022 | 0.151 | 0.28 | 0.302 | 0.262 | 0.295 | 1.000 |

**Table 5.**Clonal coefficient of variation (CV), female fertility coefficient (Ψ

_{f}), effective number of female parents (N

_{p(f)}), relative effective number of female parents (N

_{r%}), and gene diversity (GD) in the Silver fir clonal seed orchard.

Parameter/Year | 2013 | 2015 | 2018 | 2020 | 2021 | 2022 | Pooled |
---|---|---|---|---|---|---|---|

CV | 128.24 | 60.63 | 77.16 | 76.44 | 211.96 | 131.06 | 113.00 |

Ψ_{(f)} | 2.64 | 1.37 | 1.60 | 1.58 | 5.49 | 2.72 | 2.28 |

N_{p} | 17.02 | 32.90 | 28.21 | 28.40 | 8.19 | 16.56 | 19.76 |

N_{r%} | 37.82 | 73.12 | 62.68 | 63.12 | 18.20 | 36.80 | 43.92 |

GD | 0.971 | 0.985 | 0.982 | 0.982 | 0.939 | 0.970 | 0.975 |

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**MDPI and ACS Style**

Teodosiu, M.; Botezatu, A.; Ciocîrlan, E.; Mihai, G. Variation of Cones Production in a Silver Fir (*Abies alba* Mill.) Clonal Seed Orchard. *Forests* **2023**, *14*, 17.
https://doi.org/10.3390/f14010017

**AMA Style**

Teodosiu M, Botezatu A, Ciocîrlan E, Mihai G. Variation of Cones Production in a Silver Fir (*Abies alba* Mill.) Clonal Seed Orchard. *Forests*. 2023; 14(1):17.
https://doi.org/10.3390/f14010017

**Chicago/Turabian Style**

Teodosiu, Maria, Anca Botezatu, Elena Ciocîrlan, and Georgeta Mihai. 2023. "Variation of Cones Production in a Silver Fir (*Abies alba* Mill.) Clonal Seed Orchard" *Forests* 14, no. 1: 17.
https://doi.org/10.3390/f14010017