# Size–Density Trajectory in Regenerated Maritime Pine Stands after Fire

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}and 960 plants per 500 m

^{2}(17,000–19,190 plants per ha, respectively), while Calvo et al. [10] refer to average values of 6.53–11.53 seedlings per m

^{2}(65,300–115,300 plants per hectare). Secondly, there is a gap of knowledge about the attainable maximum densities at a given size for young stands. Lastly, there are no scientific-based guidelines supporting the definition of silvicultural prescriptions and thinning decisions of these self-regenerated forests. The management of the self-regenerated pine stands in post-fire conditions is, therefore, a silvicultural challenge.

^{−1}, quadratic mean diameter ($dg$) of 19.7 ± 9.6 cm, and stand age of 38 ± 17 years. The model [28] is incorporated in the stand density management diagram developed for the species, for stands with a minimum average diameter of 10 cm [28]. It is also a basis for the simulation of management scenarios for maritime pine stands 12 years old and older in the ModisPinaster model [29]. Research about the self-thinning line for the species was later presented to pinewoods in France [26] and Spain [21,30].

_{0}) the allometric model developed by reference [28] for the species adequately describes the size–density trajectory for maritime pine at early development stages (mean diameters < 10 cm) versus hypothesis (H

_{a}) a deviance from the straight line occurs at the lower end of the curve. In case of prevailing H

_{a}, the existing self-thinning line needs reevaluation, to account for that deviance.

## 2. Materials and Methods

#### 2.1. Study Area Characteristics

#### 2.2. Supporting Material

^{2}. The plots of S2 were of square shape and have 4 m

^{2}of unit area. For sets 1, 2, and 3, the maximum age of the observed stands does not exceed 20 years.

#### 2.3. Selection of Maximum Values of Size–Density

#### 2.4. Size–Density Relationship Modeling and Statistical Analysis

^{2}adj) and root mean square error (RMSE). The statistical analyses were conducted with JMP

^{®}(v. 10.0) software (Cary, NC, USA) of SAS

^{®}Institute Inc.

## 3. Results

#### 3.1. Representativeness of the Data Set and Pattern of the Density–Size Trajectory

#### 3.2. Maximum Size–Density Sample Data

#### 3.3. Representation of the Size–Density Pattern for the Border Points and Fitted Lines

^{2}adj) for the proposed models was higher than 88%, as shown in Table 3. The VIF value for Equation (2) was equal to or less than 5 (VIF = 3.1), implying that no severe implications of multicollinearity are expected.

#### 3.4. Maximum Size–Density Trajectory over All the Stages of Development

^{−1}), and $dg$ is the quadratic mean diameter over bark (cm) measured at the height level of 1.30 m.

## 4. Discussion

#### 4.1. Representativeness of the Database

^{−1}. This is a wider interval than the ones reported in the literature in concurrent studies [21,26,30].

#### 4.2. Size–Density Trajectory and Self-Thinning Line

^{2}> 0.95), instead of using the straight linear model. The description of the curvature with the three parameters of Equation (2) avoids the use of segment models or piecewise regression models, which require more parameters to estimate.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Diagram of dispersion and relationship between the logarithm of N (trees.ha

^{−1}) and the logarithm of quadratic mean diameter (dg (cm)), for the observations of the four data subsets. Two lines are imposed: the estimated maximum size–density values according to the allometric model by Luis and Fonseca [28] (L & F), and a hypothesized line (hand-drawn, dashed) placed close to the extreme pairs of (dg, N) values registered for the young stands. The shaded area represents the domain region of the L & F model, for the diameter variable.

**Figure 3.**Diagram of dispersion and relationship between the logarithm of N (trees.ha

^{−1}) and the logarithm of dg (cm) for the dataset of 30 border points. The straight line corresponds to the fitted linear model (Equation (1)) and the curve to the quadratic model (Equation (2)).

**Figure 4.**Plots of the residuals for the fitted linear model (Equation (1)) and the quadratic model (Equation (2)).

**Table 1.**Summary characteristics of the number of trees per hectare (N) and quadratic mean diameter (dg) for the sampled plots of maritime pine.

Source | n | N (trees.ha^{−1}) | dg (cm) | ||||||
---|---|---|---|---|---|---|---|---|---|

Min | Mean | Max | sd | Min | Mean | Max | sd | ||

S1 | 4 | 1560 | 3985 | 7500 | 2708 | 7.5 | 9.8 | 11.2 | 1.6 |

S2 | 59 | 1500 | 9536 | 32,500 | 8549 | 0.2 | 4.0 | 9.9 | 2.6 |

S3 | 153 | 50 | 3091 | 90,000 | 8460 | 0.1 | 8.0 | 27.5 | 8.0 |

S4 | 25 | 110 | 1724 | 7680 | 1705 | 6.8 | 27.2 | 53.3 | 12.0 |

^{−1}); dg—quadratic mean diameter measured at the height level of 1.30 m; Min—data minimum; Mean—data average; Max—data maximum; and sd—data standard deviation.

Source | n | N (trees.ha^{−1}) | dg (cm) | ||||||
---|---|---|---|---|---|---|---|---|---|

Min | Mean | Max | sd | Min | Mean | Max | sd | ||

Border points | 30 | 110 | 7121 | 90,000 | 17,366 | 0.5 | 23.3 | 53.3 | 14.1 |

^{−1}); dg—quadratic mean diameter measured at the height level of 1.30 m; Min—data minimum; Mean—data average; Max—data maximum; and sd—data standard deviation.

**Table 3.**Coefficients (standard errors) and fit statistics of the estimated models to support the definition of the maximum size–density trajectory for maritime pine (n = 30 observations). RMSE: root mean square error.

Model (Equation) | Estimates (Stand Error) | Fit Statistics | ||||
---|---|---|---|---|---|---|

Intercept | r | s | $\overline{\mathbf{l}\mathbf{n}\mathit{d}\mathit{g}}$ | R^{2}_{adj} | RMSE | |

Equation (1) | 11.115 (0.270) | −1.290 (0.090) | - | - | 0.876 | 0.541 |

Equation (2) | 12.969 (0.328) | −1.832 (0.100) | −0.280 (0.042) | 2.796 | 0.954 | 0.341 |

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**MDPI and ACS Style**

Enes, T.; Lousada, J.; Aranha, J.; Cerveira, A.; Alegria, C.; Fonseca, T. Size–Density Trajectory in Regenerated Maritime Pine Stands after Fire. *Forests* **2019**, *10*, 1057.
https://doi.org/10.3390/f10121057

**AMA Style**

Enes T, Lousada J, Aranha J, Cerveira A, Alegria C, Fonseca T. Size–Density Trajectory in Regenerated Maritime Pine Stands after Fire. *Forests*. 2019; 10(12):1057.
https://doi.org/10.3390/f10121057

**Chicago/Turabian Style**

Enes, Teresa, José Lousada, José Aranha, Adelaide Cerveira, Cristina Alegria, and Teresa Fonseca. 2019. "Size–Density Trajectory in Regenerated Maritime Pine Stands after Fire" *Forests* 10, no. 12: 1057.
https://doi.org/10.3390/f10121057