# Heartwood Relationship with Stem Diameter in Pinus canariensis Plantations of Gran Canaria, Spain

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Field and Laboratory Measurements

_{15}) and tree 30 (D

_{30}), i.e., the furthest of the first 15 and the furthest of the last 15 trees, were measured and used to calculate a stand density index as follows [45]:

#### 2.3. Data Processing and Statistical Model

## 3. Results

#### 3.1. Sampled Trees and Exploratory Data Analysis

#### 3.2. Mixed-Effect Models

_{ij}) = −0.038 + 0.089 diam

_{ij}+ a

_{i}

_{i}∼ N(0, 0.976

^{2}).

_{i}was assumed to be normally distributed with mean 0 and variance 0.976

^{2}, 95% of a

_{i}values would be between −1.96 × 0.976 and 1.96 × 0.976, which resulted in the 95% confidence interval of (−1.913, 1.913). GLMM-predicted probabilities of “tea” presence with respect to (centered) stem diameter for pines at all plots are shown graphically in Figure 6 using the logistic curves for a “typical” plot and for the upper and lower limits of this 95% confidence interval.

#### Further Testing of Fixed Effects

_{ij}) = −0.033 + 0.122 diam

_{ij}− 0.344 R5

_{ij}+ a

_{i}

_{i}∼ N(0, 1.034

^{2}).

## 4. Discussion

^{th}century with Spanish colonization as quality wood was required to build furniture and ships and very large pines were present in the islands, most likely exceeding the height and diameter of any currently remaining pine [35].

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Repeated photographs of the “Monumento natural del Roque Nublo”, Gran Canaria, Spain (the island location is shown by a red asterisk in the map on the right), showing the effective reforestation between 1960 and 2011 obtained by planting the endemic Pinus canariensis (photo credit: Fondo para la Etnografía y el Desarrollo de la Artesanía Canaria—FEDAC).

**Figure 2.**Map of the study area showing plot locations (solid red dots). Universal Transverse Mercator (UTM, zone 28N) coordinates at 6 km intervals are displayed on the left y-axis (“northing”) and on the top x-axis (“easting”). A 30 m digital elevation model (DEM) was used to calculate (

**a**) the topographic wetness index (TWI) and (

**b**) the Sky View factor with elevation contour lines at 200 m intervals.

**Figure 3.**Paired sample linear correlations (Pearson’s) between selected tree variables (see Figure S6 for variable names). Smoothed frequency histograms are plotted on the diagonal, with paired scatterplots (black dots) below the diagonal and correlation values (*** = p-value < 0.001) above it.

**Figure 4.**Estimated stem age when heartwood could first be identified on 222 out of the 450 sampled pines.

**Figure 5.**Relationship between stem size and heartwood radius in Pinus canariensis plantations. The thick black line is the stem diameter–“tea” relationship on a typical plot as linear regression parameters in the GLMM were estimated with respect to an individual plot (thin black lines) due to the random intercept and slope (see text for details).

**Figure 6.**Logistic curves showing the estimated probabilities of “tea” presence for a range of stem diameter anomalies (= centered values). The thick red line in the middle corresponds to a typical plot, i.e., the predicted probability for the “population of locations”, or a

_{i}= 0. The other two red lines are obtained by adding and subtracting 1.913 from the random intercept to the predictor function. Hence, 95% of the plots have logistic curves between these two extremes, and the space between these two curves represents the variation of predicted values per plot.

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**MDPI and ACS Style**

Aguilar, L.F.A.; Rodríguez, P.R.; Biondi, F.
Heartwood Relationship with Stem Diameter in *Pinus canariensis* Plantations of Gran Canaria, Spain. *Forests* **2023**, *14*, 1719.
https://doi.org/10.3390/f14091719

**AMA Style**

Aguilar LFA, Rodríguez PR, Biondi F.
Heartwood Relationship with Stem Diameter in *Pinus canariensis* Plantations of Gran Canaria, Spain. *Forests*. 2023; 14(9):1719.
https://doi.org/10.3390/f14091719

**Chicago/Turabian Style**

Aguilar, Luis Fernando Arencibia, Priscila Rodríguez Rodríguez, and Franco Biondi.
2023. "Heartwood Relationship with Stem Diameter in *Pinus canariensis* Plantations of Gran Canaria, Spain" *Forests* 14, no. 9: 1719.
https://doi.org/10.3390/f14091719