# Effects of Hardwood Content on Balsam Fir Defoliation during the Building Phase of a Spruce Budworm Outbreak

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

_{0}× (1 − x) (which we term the simplified linear model), where fir defoliation in a mixedwood stand (y) is a function of percent hardwood (x) and fir defoliation level in a pure fir stand (D

_{0}). The relationship was quantified using defoliation data collected in the declining years (1989–1993) of the last outbreak and were subsequently used in Needham et al. [26] and Sainte-Marie et al. [27]. In this study, we examine whether this relationship holds true in the building phase of an outbreak.

## 2. Materials and Methods

#### 2.1. Study Area and Stand Sampling

#### 2.2. Defoliation Measurements

#### 2.3. The Simplified Linear Model

_{0}) were used to predict fir defoliation in fir-hardwood mixed stands (y). We used the average plot defoliation in our softwood plots (i.e., with 0%–25% hardwoods) calculated each year as D

_{0}. In Su et al. [15], intercept from simple linear regression for defoliation as a function of percent hardwood content each year were used as D

_{0}. In our data, preliminary analysis suggested that average plot defoliation in softwood plots was highly correlated (r = 0.995) with the intercepts from simple linear regressions. We chose to use the empirical average plot defoliation in softwood plots instead of the theoretical extrapolated “defoliation-with-zero-hardwood” from the statistical models, because it is based on measured data.

#### 2.4. Analyzing the Relationship between Annual Balsam Fir Defoliation and Hardwood Content Using Generalized Linear Mixed-Effects Model

_{0}= average plot defoliation in softwood plots (as in Equation (1)); β

_{i}’s are the fixed effects parameter estimates; and b

_{0}is the random effects. Year as a categorical variable was not included in the model since the annual differences were already incorporated in D

_{0}. Plot was included as random effect and a serial correlation structure CorAr1 was included in the model error term to control for temporal autocorrelation. Averaged annual defoliation for each stand type was calculated and differences among the three stand types were tested using Kruskal-Wallis analysis by ranks.

#### 2.5. The Random Forests Model

_{0}, mean DBH, mean height, basal area (BA), mean DBH of bF, mean height of bF, standard deviation of bF height, mean bF crown base height, standard deviation of bF crown base height, tree density, elevation, and slope. Random Forests does not hold formal distributional assumptions of data and is relatively insensitive to multicollinearity [40], but removing multicollinearity and redundancy to improve predictive power is recommended [49,50]. Correlation analysis indicated that, HW% and bF%, mean DBH of bF and mean height of bF, and mean DBH and density were highly correlated with coefficients (r) of −0.97, 0.87, and −0.84, respectively. HW%, mean DBH of bF, and mean DBH were selected over their counterpart variables because HW% should be included as a predictor in attempts to estimate defoliation reduction caused by hardwood; and mean DBH is readily available in most forest inventories and can be quickly assessed with an efficient sampling design. Therefore, 11 variables were retained and tested using Random Forests: HW%, D

_{0}, mean DBH, mean height, mean DBH of bF, BA, standard deviation of bF height, mean bF crown base height, standard deviation of bF crown base height, elevation, and slope.

#### 2.6. Statistical Analyses

## 3. Results

#### 3.1. Relationship between Defoliation and Hardwood Content

_{0}had significant effects on balsam fir defoliation (Table 2), with a significant interaction between percent hardwood and D

_{0}, indicating that the relationship between defoliation and percent hardwood varied significantly with overall defoliation severity each year. Examining the fitted relationships from GLMM, balsam fir defoliation was negatively related to percent hardwood content each year from 2012 to 2016 (Figure 2). The fitted lines indicated that the relationship between defoliation and hardwood amount was weak in 2012 and became stronger in 2013 and 2014, the second and third years of defoliation, then declined 2015 and 2016. Defoliation was highest in softwood plots in 2014 and 2015 (means of 79% and 87%, respectively), and in those years mean defoliation in hardwood plots was 12% and 55%, respectively (Figure 3). In 2012, the first year of defoliation, mean defoliation of balsam fir in softwood, mixedwood, and hardwood plots was 27%, 14%, and 12%, respectively. Average plot defoliation was significantly different among stand types (softwood > mixedwood > hardwood) in 2013 and 2014, when defoliation rapidly increased in softwood and mixedwood plots (Figure 3). Defoliation in softwood was significantly higher than in hardwood plots in all 5 years, but was significantly higher than in mixedwood plots only in 2013 and 2014. Defoliation peaked in 2015 in all three stand types, with means of 87%, 70%, and 55% defoliation in softwood, mixedwood, and hardwood plots, respectively (Figure 3). Defoliation declined in 2016, to 47% and 42% defoliation in softwood and mixedwood and 15% defoliation in hardwood plots, comparable to years prior to 2015. Over the 5 years, defoliation in softwood plots averaged 14% higher than in mixedwood plots, and defoliation in mixedwood plots averaged 20% higher than in hardwood plots. Average fir defoliation in hardwood plots remained below 20% in all years except 2015, the year with the highest defoliation in all stand types (Figure 3).

#### 3.2. Defoliation Estimated Using Three Model Formulations

_{0}on balsam fir defoliation well (R

^{2}= 0.85 considering fixed effects only and 0.94 considering both fixed and random effects [53]).

_{0}) and percent hardwood content were the most important predictor variables, at increases in mean square error of 43% and 18%, respectively (Figure 5). D

_{0}was important as an indicator of the overall spruce budworm outbreak severity in a given year, while inclusion of percent hardwood content confirmed its significance in predicting budworm defoliation. Mean DBH, mean height, elevation, and standard deviation of bF height ranked as the third to the sixth most important predictors, at 8%–9% increases in mean square error (Figure 5). Other predictor variables included in the model (BA, slope, mean DBH of bF, standard deviation of bF crown base height, and mean bF crown base height) each had <5% increase in mean square error (Figure 5). We tried running the Random Forests model eliminating some of the variables with little contribution to accuracy (e.g., using only the top several variables in Figure 5), and the resulting correlation between measured defoliation and the model estimate dropped by 2%–3%. Variables in the Random Forests model and the GLMM essentially converged, along with the addition of DBH or Height and Elevation in the Random Forests model.

## 4. Discussion

#### 4.1. Relationships between Defoliation and Hardwood Content during Building Phase of a Spruce Budworm Outbreak

#### 4.2. Which Model Provides the “Best” Defoliation Estimates?

_{0}), reflecting average regional severity of defoliation in a particular year. Hardwood content was a significant factor in predicting budworm defoliation, similar to findings of MacKinnon and MacLean [30] and Colford-Gilks et al. [31]. Mean DBH and mean height ranked as the third and fourth important variables, suggesting that average tree size had some importance in predicting budworm defoliation. It has repeatedly been observed that mature and over-mature stands have the highest susceptibility and vulnerability to budworm outbreaks (e.g., [17]). Standard deviation of bF height was the only variable with >5% increase in mean square error among variables related with canopy structure, indicating that canopy structure had little importance in predicting defoliation in these plots, which were mature with a single canopy layer. We conclude that incorporating more independent variables improved the accuracy of defoliation predictions, but at the cost of constructing a larger and more complex model. Such models could be difficult to construct using traditional parametric approaches due to complex interactions among variables and violation of distributional assumptions. Nevertheless, hardwood content and D

_{0}as the two most important independent variables were not correlated and we suggest that they should be included in any budworm defoliation modeling attempts.

_{0}as an indicator of average annual defoliation severity can be estimated relative easily from either regional defoliation surveys carried out by government agencies in softwood stands, or regional spruce budworm population sampling such as second instar larval or moth sampling. With these data and Equation (1), defoliation in fir-hardwood stands could be quickly estimated. However, either traditional parametric (GLMM) model or non-parametric Random Forests model provided more accurate defoliation estimates than the simplified linear model. In similar analyses, we suggest that data about the average defoliation level, or another indicator of annual outbreak severity, should be included in addition to percent hardwood content.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Measured balsam fir defoliation and fitted relationships from generalized linear mixed-effects model to test the effects of percent hardwood content on annual plot defoliation from 2012 to 2016, for 27 plots near Amqui, Quebec.

**Figure 3.**Average annual balsam fir defoliation (± one standard error) from 2012 to 2016, for nine plots in each of three stand types with varied hardwood contents, near Amqui, Quebec. Different letters indicate significant differences among stand types in each year.

**Figure 4.**Annual plot defoliation, estimated with: (

**A**) the simplified linear model (Equation (1)); (

**B**) a generalized linear mixed-effects model; and (

**C**) the Random Forests model, plotted against measured defoliation for 27 plots each year from 2012 to 2016.

**Figure 5.**Variable importance (percent increase in mean square error of the Random Forests model when the data for that variable were randomly permuted) of the 11 predictors used to predict spruce budworm defoliation in fir-hardwood mixed stands. High values of percent increase in mean square error indicate more important variables in the Random Forests model. The 11 predictor variables were: average annual defoliation in softwood plots (D

_{0}), percent hardwood basal area (HW%), mean DBH (DBH), mean height (Height), elevation, standard deviation of balsam fir (bF) height (StdHTbF), basal area (BA), slope, mean DBH of bF (DBHbF), standard deviation of bF crown base height (StdCbHTbF), and mean bF crown base height (CbHTbF).

Plot No. ^{b} | Density (stems/ha) | DBH ^{c} (cm) | Ht ^{c} (m) | DBHbF ^{c} (cm) | BA ^{c} (m^{2}/ha) | Species Composition % Basal Area ^{d} | Total HW ^{d} (%BA) | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

bF | wS | OS | sM | yB | IH | |||||||

Softwood ^{a} | ||||||||||||

1 | 1020 | 20.0 ± 1.1 | 16.3 ± 0.6 | 20.7 ± 1.1 | 37 | 78 | 4 | 9 | ‒ | 2 | 8 | 9 |

2 | 2800 | 13.6 ± 0.5 | 12.8 ± 0.4 | 14.1 ± 0.6 | 49 | 78 | 3 | ‒ | ‒ | 4 | 15 | 19 |

3 | 920 | 21.5 ± 1.4 | 15.7 ± 0.8 | 23.4 ± 1.3 | 39 | 64 | 17 | 16 | ‒ | ‒ | 3 | 3 |

4 | 2975 | 13.1 ± 0.5 | 12.9 ± 0.3 | 13.1 ± 0.5 | 47 | 84 | 3 | 12 | ‒ | ‒ | 1 | 1 |

5 | 1650 | 16.1 ± 0.9 | 14.6 ± 0.7 | 15.8 ± 1.0 | 40 | 81 | ‒ | 5 | ‒ | ‒ | 14 | 14 |

6 | 2125 | 15.6 ± 0.5 | 15.8 ± 0.3 | 15.8 ± 0.6 | 44 | 95 | ‒ | 2 | ‒ | ‒ | 3 | 3 |

7 | 2100 | 15.6 ± 0.8 | 13.9 ± 0.4 | 16.0 ± 0.8 | 50 | 69 | 7 | 8 | ‒ | 1 | 16 | 16 |

8 | 1100 | 16.5 ± 1.7 | 12.7 ± 0.8 | 21.5 ± 2.2 | 38 | 81 | ‒ | ‒ | ‒ | ‒ | 19 | 19 |

9 | 1380 | 16.4 ± 1.1 | 14.1 ± 0.7 | 22.5 ± 1.4 | 39 | 79 | ‒ | ‒ | ‒ | 8 | 13 | 21 |

Mixedwood | ||||||||||||

10 | 2540 | 11.2 ± 0.7 | 9.7 ± 0.5 | 7.3 ± 0.7 | 36 | 20 | 10 | 7 | ‒ | 34 | 30 | 64 |

11 | 760 | 19.2 ± 2.1 | 12.5 ± 1.0 | 20.8 ± 2.6 | 32 | 36 | 2 | ‒ | 29 | 19 | 13 | 62 |

12 | 1620 | 14.1 ± 1.1 | 10.7 ± 0.6 | 14.1 ± 1.3 | 37 | 45 | ‒ | ‒ | 1 | 23 | 31 | 55 |

13 | 960 | 20.1 ± 1.5 | 18.7 ± 1.0 | 20.9 ± 1.7 | 39 | 33 | 11 | 7 | ‒ | 1 | 49 | 49 |

14 | 980 | 21.5 ± 1.9 | 17.5 ± 1.2 | 19.0 ± 1.8 | 49 | 27 | 1 | 17 | ‒ | 7 | 55 | 55 |

15 | 1280 | 17.8 ± 1.0 | 17.5 ± 0.9 | 18.1 ± 1.5 | 39 | 42 | 5 | 2 | ‒ | 2 | 53 | 53 |

13a | 1980 | 11.0 ± 0.7 | 9.7 ± 0.5 | 10.0 ± 1.3 | 26 | 40 | ‒ | ‒ | ‒ | ‒ | 59 | 60 |

14a | 1620 | 13.7 ± 0.9 | 11.0 ± 0.6 | 13.3 ± 1.3 | 32 | 44 | ‒ | ‒ | ‒ | ‒ | 56 | 56 |

15a | 1780 | 15.1 ± 0.8 | 12.0 ± 0.5 | 14.4 ± 0.9 | 40 | 57 | 4 | ‒ | ‒ | 5 | 35 | 40 |

16 | 1260 | 17.7 ± 1.1 | 15.0 ± 0.5 | 19.0 ± 1.2 | 38 | 48 | ‒ | ‒ | 9 | 16 | 28 | 52 |

17 | 1200 | 16.9 ± 1.1 | 14.5 ± 0.6 | 18.9 ± 2.3 | 33 | 43 | ‒ | ‒ | 8 | 22 | 28 | 57 |

18 | 1200 | 17.3 ± 1.4 | 14.0 ± 0.6 | 16.7 ± 1.9 | 40 | 33 | 4 | ‒ | 6 | 17 | 40 | 63 |

Hardwood | ||||||||||||

19 | 800 | 18.2 ± 1.8 | 16.7 ± 0.8 | 26.9 ± 7.3 | 28 | 10 | ‒ | ‒ | 90 | ‒ | ‒ | 90 |

20 | 1080 | 16.8 ± 1.4 | 14.5 ± 0.8 | 21.3 ± 3.7 | 33 | 24 | ‒ | ‒ | 35 | 9 | 31 | 76 |

21 | 520 | 22.8 ± 2.3 | 16.5 ± 1.0 | 20.0 ± 2.3 | 27 | 12 | ‒ | ‒ | 51 | 8 | 29 | 88 |

22 | 1000 | 18.5 ± 1.7 | 12.0 ± 0.7 | 11.4 ± 2.0 | 38 | 12 | 3 | ‒ | 34 | 24 | 26 | 84 |

23 | 620 | 22.6 ± 2.7 | 17.2 ± 1.4 | 26.8 ± 4.1 | 35 | 14 | ‒ | ‒ | 86 | ‒ | ‒ | 86 |

24 | 640 | 18.7 ± 2.4 | 12.6 ± 1.0 | 25.7 ± 1.2 | 27 | 8 | ‒ | ‒ | 16 | 28 | 49 | 92 |

25 | 1120 | 13.7 ± 1.0 | 15.2 ± 0.7 | 22.9 ± 3.9 | 22 | 8 | ‒ | ‒ | 81 | 2 | 10 | 92 |

26 | 800 | 17.2 ± 1.7 | 16.5 ± 0.8 | 19.7 ± 4.4 | 25 | 5 | ‒ | ‒ | 79 | 14 | 2 | 95 |

27 | 560 | 24.8 ± 2.3 | 17.2 ± 0.6 | 19.6 ± 2.8 | 33 | 10 | ‒ | ‒ | 44 | 28 | 18 | 90 |

^{a}Softwood, mixedwood, and hardwood stand types were classified by hardwood basal area percentage: softwood (0%–25%), mixedwood (40%–65%), and hardwood (75%–95%).

^{b}The ‘a’ suffix denotes three sample plots established 1 year after initial sampling to replace original plots which were harvested.

^{c}Abbreviations: DBH = mean diameter at breast height; Ht = mean total height; DBHbF = mean DBH of balsam fir; BA = basal area. DBH, Ht, and DBHbF are shown as plot average ± one standard error of the mean.

^{d}Species abbreviations: bF balsam fir; wS white spruce; OS other softwood = black spruce (Picea mariana (Mill.) BSP), eastern white-cedar (Thuja occidentalis L.), and eastern larch (Larix laricina (Du Roi) K. Koch); sM sugar maple; yB yellow birch; IH intolerant hardwood = red maple, white birch, trembling aspen (Populus tremuloides Michx.), and balsam poplar (Populus balsamifera L.), HW hardwood = sM + yB + IH.

**Table 2.**Results of generalized linear mixed-effects model to test the effects of percent hardwood content (HW%) and average annual defoliation in softwood plots (D

_{0}) on defoliation for 27 plots from 2012 to 2016 in Quebec.

Fixed Effects | Parameter Estimates | Analysis of Deviance | |||
---|---|---|---|---|---|

Par. | Est. | SE | X^{2} | p | |

Intercept | β_{0} | −2.1225 | 0.3434 | ||

HW% | β_{1} | −0.0089 | 0.0061 | 46.68 | <0.001 |

D_{0} | β_{2} | 0.0490 | 0.0055 | 175.70 | <0.001 |

HW% × D_{0} | β_{4} | −0.0002 | 0.0001 | 6.51 | 0.011 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Zhang, B.; MacLean, D.A.; Johns, R.C.; Eveleigh, E.S.
Effects of Hardwood Content on Balsam Fir Defoliation during the Building Phase of a Spruce Budworm Outbreak. *Forests* **2018**, *9*, 530.
https://doi.org/10.3390/f9090530

**AMA Style**

Zhang B, MacLean DA, Johns RC, Eveleigh ES.
Effects of Hardwood Content on Balsam Fir Defoliation during the Building Phase of a Spruce Budworm Outbreak. *Forests*. 2018; 9(9):530.
https://doi.org/10.3390/f9090530

**Chicago/Turabian Style**

Zhang, Bo, David A. MacLean, Rob C. Johns, and Eldon S. Eveleigh.
2018. "Effects of Hardwood Content on Balsam Fir Defoliation during the Building Phase of a Spruce Budworm Outbreak" *Forests* 9, no. 9: 530.
https://doi.org/10.3390/f9090530