# Relationships between Tree Vigor Indices and a Tree Classification System Based upon Apparent Stem Defects in Northern Hardwood Stands

^{1}

^{2}

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## Abstract

**:**

_{-1-5}) was significantly different between the lowest and highest tree vigor classes. Yet, temporal changes in BAI

_{-1-5}helped classify correctly only 16% of high-vigor trees that became poorly vigorous 8–10 years later. Overall, these results suggest that the tree classification system is weakly related to actual tree vigor and its application likely generates few significant gains in future stand vigor. Modifying and simplifying the tree vigor system must be considered to facilitate the tree marking process that is required to improve the vigor of degraded stands.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Sites

#### 2.2. Tree Sampling

^{2}) that were first measured in 2006 and a second time in 2016. In total, we sampled 154 trees (91 sugar maple (sM) and 63 yellow birch (yB) trees) from Duchesnay, 31 (31 sM) from Mont-Laurier, 30 (30 sM) from Biencourt, 19 (11 sM, 8 yB) from Domtar 1, 33 (20 sM, 13 yB) from Domtar 2, and 31 (31 sM) from Domtar 3. The number of sampled trees decreased with increasing diameter class, consistent with the negative exponential distribution that is typical of uneven-aged stands (Table 1).

#### 2.3. Tree Vigor Classification

#### 2.4. Vigor Indices

#### 2.4.1. Growth Efficiency Index

^{2}), $CSA$ is crown surface area (m

^{2}), which corresponds to the area of the geometric shape of sugar maple and yellow birch crowns (calculated with crown height and mean quadratic radius—Moreau et al. [30]), ${\beta}_{1}$ is 1.121 for sugar maple and 1.021 for yellow birch, and ${\beta}_{2}$ is 0.981 for sugar maple and 1.035 for yellow birch. The average stemwood mass produced annually ($\Delta {W}_{s}$) and tree leaf area ($LA$) were then used to calculate the growth efficiency index (GE) of each tree as

#### 2.4.2. Indices Solely Based upon Tree Diameter Measurements

#### 2.5. Statistical Analysis

^{2}). In a second step, we used a linear mixed ANOVA model to determine which growth-based index was best related to tree vigor classes (i.e., a categorical variable). The growth-based index that was best related to both growth efficiency index and tree vigor classes was then used to quantify its temporal changes between two qualitative determinations of tree vigor class.

^{2}.

## 3. Results

#### 3.1. Relationship between the Growth Efficiency Index and Tree Vigor Classes

#### 3.2. Growth-Based Indices and Changes in Tree Vigor Class

_{-1-5}) was the growth-based index that was most closely related to the growth efficiency index (Table 2), and was among the best indices that were related to tree vigor classes (Table 3). This index value was significantly different between the lowest and highest tree vigor classes (i.e., M and R classes) at both vigor evaluations (p = 0.0192 and p = 0.0009, respectively), and between the M and the C classes at the second vigor evaluation (p = 0.0007). Therefore, we included the temporal changes of BAI

_{-1-5}between the two vigor evaluations as an explanatory variable in the logistic regression model to predict the binary tree vigor classes. Validation of this model indicates that 66% of the trees (i.e., 107 of 161) were correctly classified as vigorous or non-vigorous trees (Table 4). Yet, the validation procedure also indicates that only 16% of trees (i.e., 5 of 32) that became non-vigorous at the second vigor evaluation were correctly classified. The weak capacity of the model to classify correctly vigorous trees that later became non-vigorous is illustrated by the substantial overlapping of BAI

_{-1-5}between observed vigorous and non-vigorous trees (Figure 3). This considerable overlap may explain the small range of predicted values of probability that trees remain vigorous, which are all close to the probability threshold (0.78) separating vigorous and non-vigorous trees (Figure 3).

#### 3.3. Predicting the Growth Efficiency Index

^{2}of only 0.05. When the same state variables were related to the three most relevant growth-based indices, the most parsimonious models included tree crown surface area and relative height. Although, the predictive abilities of these models were higher than that of the preceding one, with R

^{2}varying from 0.37 to 0.39, both parameters were never significantly (α = 0.05) different from zero (results not shown), suggesting weak relationships.

## 4. Discussion

#### 4.1. Relationships between Quantitative and Qualitative Tree Vigor Indices

_{-1-5}, which is a growth-based index that is closely related to tree vigor classes (Table 3), to determine whether its temporal changes were related to changes in tree vigor classes. In focusing only upon tree vigor changes that were observed over time for the same trees, this analysis allowed us to remove a portion of the between-tree variation from the vigor class determinations, which can notably be influenced by tree hierarchical position [35,36] and age [37]. Even when this inter-tree variation was removed, only 16% of vigorous trees that became non-vigorous 8–10 years later could be correctly classified. Nevertheless, significant differences in BAI

_{-1-5}were detected between the two extreme classes (i.e., M and R classes), while the intermediate classes were not distinguished from the extreme classes. These results agree with those of Hartmann et al. [10] and Guillemette et al. [9], who significantly differentiated only classes M and R using a growth-based index to predict the mortality probability of sugar maple trees.

#### 4.2. Possible Drawbacks of the Growth Efficiency Index

#### 4.3. Estimating the Growth Efficiency Index from State Variables

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Box-and-whisker plots of the growth efficiency index as a function of tree vigor classes for the combined responses of sugar maple and yellow birch. The bold horizontal line within the boxes corresponds to the median (50th percentile), while the lower and upper limits of the boxes (interquartile range, IQR) represent the 25th and 75th percentiles, respectively. The whiskers are upper and lower values of 1.5 × IQR, and the individual points are outliers.

**Figure 3.**Probability that a vigorous tree at the first evaluation period either becomes non-vigorous (0) or remains vigorous (1) at the second evaluation period as a function of the growth-based index BAI

_{-1-5}. The horizontal line represents the probability threshold (0.78) below which a tree was considered as non-vigorous.

**Table 1.**Number of trees that were sampled at the six sites by diameter class at breast height (DBH, 1.3 m) and tree vigor class

DBH (cm) | M | S | C | R | Total |
---|---|---|---|---|---|

20–29.9 | 29 | 13 | 39 | 29 | 110 |

30–39.9 | 16 | 20 | 28 | 28 | 92 |

40–49.9 | 15 | 16 | 21 | 20 | 72 |

50–59.9 | 6 | 9 | 7 | 2 | 24 |

Total | 66 | 58 | 95 | 79 | 298 |

**Table 2.**Statistics for the best linear mixed models that related the growth efficiency index to different growth-based indices. All models also include an intercept, tree species (the fixed effect), and a random site effect.

Growth-Based Index | AIC | Δ_{i} | $\text{}{\mathit{W}}_{{\mathit{t}}_{\mathit{i}}}\text{}$ | R² |
---|---|---|---|---|

BAI_{-1-5} | 2232.1 | 0 | 9.0 × 10^{−1} | 0.35 |

BAI_{-1-7} | 2236.5 | 4.5 | 9.6 × 10^{−2} | 0.34 |

BAI_{-1-3} | 2249.3 | 17.3 | 1.6 × 10^{−4} | 0.31 |

BAI_{-1-10} | 2251.0 | 19.9 | 4.2 × 10^{−5} | 0.31 |

BAI_{-1-3}/BA_{-4} | 2268.2 | 36.2 | 1.3 × 10^{−8} | 0.27 |

BAI_{-1-5}/BA_{-6} | 2275.6 | 43.5 | 3.6 × 10^{−10} | 0.26 |

_{i}is the difference in AIC between each model and the model with the lowest AIC, ${W}_{{t}_{i}}$ is the probability that a model is the best among those being compared, and R

^{2}is the coefficient of determination. The subscripts that are associated with growth-based indices correspond to the years during which the variables were computed, with year 0 corresponding to the time of tree vigor evaluation.

**Table 3.**Results of the analyses of variance (one-way ANOVAs) relating the most relevant growth-based indices to tree vigor classes. All models also included an intercept, the tree species (fixed effect), and a random site effect.

First Vigor Evaluation (n = 225) | Second Vigor Evaluation (n = 298) | |||
---|---|---|---|---|

Growth-Based Index | F | p-Value | F | p-Value |

BAI_{-1-7} | 10.68 | <0.0001 | 5.83 | 0.0007 |

BAI_{-1-5} | 9.56 | <0.0001 | 5.83 | 0.0007 |

BAI_{-1-10} | 11.63 | <0.0001 | 5.73 | 0.0008 |

BAI_{-1-3} | 7.86 | <0.0001 | 4.65 | 0.0034 |

BAI_{-1-7}/BA_{-8} | 3.18 | 0.0249 | 5.90 | 0.0006 |

BAI_{-1-5}/BA_{-6} | 2.76 | 0.0430 | 5.70 | 0.0008 |

**Table 4.**Validation of the model predicting non-vigorous (0) and vigorous (1) trees based upon differences in BAI

_{-1-5}between the two tree vigor evaluations.

Predicted = 0 | Predicted = 1 | |
---|---|---|

Observed = 0 | 5 | 27 |

Observed = 1 | 27 | 102 |

**Table 5.**Statistics of linear mixed models relating the growth efficiency index (GE) and three growth-based indices to state variables at tree and stand levels. All models also included an intercept, tree species (fixed effect), and a random site effect.

Dependent Variables | Independent Variables | AIC | Δ_{i} | $\text{}{\mathit{W}}_{{\mathit{t}}_{\mathit{i}}}\text{}$ | R² |
---|---|---|---|---|---|

GE | RH | 2327.5 | 0.0 | 9.5 × 10^{−1} | 0.05 |

CSA + RH | 2333.2 | 5.7 | 5.4 × 10^{−2} | 0.11 | |

BAI_{-1-5} | CSA + RH | 2943.9 | 0.0 | 1.0 × 10^{−1} | 0.39 |

CSA | 2958.4 | 14.5 | 6.9 × 10^{−4} | 0.38 | |

BAI_{-1-7} | CSA + RH | 3139.9 | 0.0 | 1.0 × 10^{−1} | 0.39 |

CSA | 3157.8 | 17.9 | 1.3 × 10^{−4} | 0.37 | |

BAI_{-1-10} | CSA + RH | 3320.1 | 0.0 | 1.0 × 10^{−1} | 0.37 |

CSA | 3339.8 | 19.7 | 5.5 × 10^{−5} | 0.36 |

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**MDPI and ACS Style**

Moreau, E.; Bédard, S.; Moreau, G.; Pothier, D.
Relationships between Tree Vigor Indices and a Tree Classification System Based upon Apparent Stem Defects in Northern Hardwood Stands. *Forests* **2018**, *9*, 588.
https://doi.org/10.3390/f9100588

**AMA Style**

Moreau E, Bédard S, Moreau G, Pothier D.
Relationships between Tree Vigor Indices and a Tree Classification System Based upon Apparent Stem Defects in Northern Hardwood Stands. *Forests*. 2018; 9(10):588.
https://doi.org/10.3390/f9100588

**Chicago/Turabian Style**

Moreau, Edouard, Steve Bédard, Guillaume Moreau, and David Pothier.
2018. "Relationships between Tree Vigor Indices and a Tree Classification System Based upon Apparent Stem Defects in Northern Hardwood Stands" *Forests* 9, no. 10: 588.
https://doi.org/10.3390/f9100588