# Spatial-Temporal Patterns of Spruce Budworm Defoliation within Plots in Québec

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data Collection

^{2}) study plots were established in 2014, with 19 plots about 15 km northwest of Amqui and 38 plots about 40 km southwest of Causapscal. These are a subset of plots studied by Donovan et al. [35] and Zhang et al. [25], and additional description of the sites is available there. Plot locations are shown in Figure 1 of [35]. However, we have omitted 15 plots that were harvested from 2016 to 2018, and three plots missing some defoliation data in 2015. A portion of our studied plots were protected by aerial spraying of Bacillus thuringiensis biological insecticide to control defoliation each year: 28% of plots in 2014, 42% in 2015, 30% in 2016, 26% in 2017, and 38% in 2018. The plots included a total of 3693 trees, of which 3200 were balsam fir or spruce.

#### 2.2. Point Pattern Analyses

^{2}, in this study). Generally, if the average distance is less than the average for a hypothetical random distribution (R < 1), the distribution is considered to be clustered; if R > 1, the distribution tends to be dispersed, and if R = 1 the distribution follows a random arrangement. The standard deviation, z-score was calculated as [40]:

#### 2.3. Spatial Autocorrelation Analyses

#### 2.4. Tree Defoliation Regression Model

^{2}, and mean bias (predicted-observed).

## 3. Results

#### 3.1. Stand and Plot Characteristics

^{−1}density, and 34.9 to 47.7 m

^{2}ha

^{−1}basal area (Table 1). Basal area of each host species in the stands was 6% to 98% balsam fir, 0% to 70% black spruce, and 0% to 65% white spruce (Table 1). Plot species composition averaged 64% balsam fir, 19% black spruce, 10% white spruce, 2% other softwood species, and 5% hardwood species (Table 1). Annual defoliation in the 5 years from 2014 to 2018 averaged 34%, 51%, 28%, 38%, and 32% by ocular estimation, and 45%, 52%, 34%, 54%, and 38% by shoot defoliation estimation on sampled branches. Plot locations were specifically selected in 2014 to represent the full range of defoliation from <10% to 90%–100%, and insecticide sprayed plots were the only way to obtain low defoliation levels.

#### 3.2. Spatial Patterns of Tree Stems within Plots

#### 3.3. Spatial Patterns of Current Year Defoliation for Plots

^{2}ha

^{−1}; Figure 1a). Overall, annual plot defoliation levels increased with the proportion of balsam fir in plots (Figure 1b). Plots with clustered defoliation had higher defoliation in all balsam fir % basal area classes than plots with non-clustered defoliation, significantly different for 50% to 75% basal area fir plots (43% versus 33% defoliation in clustered and non-clustered plots; Figure 1b). Plots with clustered defoliation consistently had higher standard deviations of tree defoliation than plots with non-clustered defoliation, with significant differences of 9.1% and 6.4% defoliation for plots with 0% to 25% and 50% to 75% balsam fir (Figure 1c).

#### 3.4. Hot Spot and Cold Spot Trees within Plots

#### 3.5. Prediction of Subject Tree Balsam Fir Defoliation Using Regression Models

^{2}, RMSE, and bias, compared to Model 1. This suggested that including neighboring host tree basal area can slightly improve performance compared to a model that including only plot average balsam fir defoliation.

## 4. Discussion

#### 4.1. Is Defoliation of Individual Trees Clustered

#### 4.2. Interpretation of Local Hot and Cold Spot Trees

^{2}plots, may have resulted from higher defoliation in some trees. Over the longer term, mortality creating such ‘holes’ in stands is also probably exacerbated by windthrow disturbance [58,59].

#### 4.3. Prediction of Subject Balsam Fir Defoliation

## 5. Conclusions

- Including all host species, 47%, 28%, 35%, 30%, and 33% of plots showed significantly clustered defoliation patterns from 2014 to 2018. Plots with clustered defoliation tended to have higher and less uniform defoliation among trees. Results suggested that spatial defoliation patterns resulted from uneven SBW pressure on trees, perhaps from oviposition site selection.
- Plots with severe defoliation generally tended to exhibit cold spot trees, and plots with light defoliation tended to have hot spot trees, because whether defoliation was high or low enough to be a hot or cold spot depended on the defoliation level of the entire plot.
- Plot-level average defoliation combined with subject tree basal area explained 80% of the variability of subject balsam fir defoliation, which was 2% to 5% higher than variability explained by the neighboring tree defoliation.
- Spatial variability of defoliation decreased with larger radius neighborhoods from 3 to 5 m, suggesting that a neighborhood search radius larger than 5 m (and thus plot sizes larger than 400 m
^{2}(11.3 m radius) to deal with edge effects) may provide better predictions of subject balsam fir defoliation. - For these primarily balsam fir plots, species composition at both plot and tree levels were not significant predictors of individual balsam fir defoliation.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Comparison of plots with and without significant clustering of defoliation (based on results of global Moran’s I analyses (α = 0.05) for all host trees) by 25% balsam fir plot basal area classes for (

**a**) total basal area in the plot, (

**b**) average current year defoliation, and (

**c**) standard deviation of individual tree defoliation within plots.

**Figure 2.**Average current year defoliation of plots, ordered from highest to lowest defoliation each year from 2014 to 2018 (

**a**–

**e**), showing plots with significantly clustered (α = 0.05) defoliation (*), with hot spot trees (

**red**), cold spot trees (

**blue**), both hot and cold spot trees (

**yellow**), and only non-significant trees (

**grey**), based on results of Getis-Ord Gi* analyses (α = 0.05).

**Figure 3.**Proportion of plots with hot spot trees, cold spot trees, both hot and cold spot trees, and only non-significant trees (based on results of Getis-Ord Gi* analyses (α = 0.05)) by 25% annual defoliation classes from 2014 to 2018 (

**a**–

**e**).

**Figure 4.**Stem maps of tree locations (diameter at breast height (DBH) ≥ 10 cm) of three example plots for five years, showing spatial distribution of defoliation. The three example plots were selected to represent generally low (1_01), moderate (12_02), and high (3_01) defoliation levels that contained hot spot and cold spot trees (shown in Figure 5).

**Figure 5.**Stem maps of tree locations shown for the inner 6 m center of three example plots (same as in Figure 4) for five years, showing spatial distribution of hot spot trees, cold spot trees, and non-significant trees (based on results of Getis-Ord Gi* analyses; α = 0.05).

**Figure 6.**Relative influence (%) of the six most important predictor variables based on Gradient Boosting Machine analysis to predict current year defoliation of individual balsam fir trees (%) with neighborhood tree search radius (R) of (

**a**) 3 m, (

**b**) 4 m, or (

**c**) 5 m. Predictor variable abbreviations are described in Table 4, and predictors marked with * were highly correlated with each other (correlation coefficient r ≥ 0.7).

**Table 1.**Summary of mean ($\overline{\mathrm{X}}$) and standard deviation (σ) characteristics per stand of 57 plots located in 19 stands near Amqui and Causapscal, Québec, Canada.

Stand No. | No. Plots ^{1} | Density (stem ha^{−1}) | DBH ^{2}(cm) | Height (m) | Basal Area (m^{2} ha^{−1}) | Species Composition ^{3}(% Basal Area) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

$\overline{X}$ | σ | $\overline{X}$ | σ | $\overline{X}$ | σ | $\overline{X}$ | σ | BF | BS | WS | HW | OSW | ||

1 | 4 | 1919 | 289 | 15.0 | 1.1 | 13.7 | 0.9 | 38.8 | 3.8 | 54 | 30 | 4 | 6 | 7 |

2 | 5 | 1775 | 417 | 17.0 | 1.4 | 16.5 | 1.0 | 42.8 | 4.3 | 51 | 42 | 3 | 3 | |

3 | 2 | 1913 | 636 | 16.0 | 1.4 | 16.0 | 0.9 | 41.8 | 6.7 | 83 | 1 | 11 | 5 | |

4 | 1 | 1200 | 20.1 | 18.0 | 39.8 | 6 | 27 | 65 | 2 | |||||

5 | 2 | 1825 | 159 | 15.8 | 0.1 | 16.1 | 0.2 | 38.1 | 1.7 | 98 | 1 | 1 | ||

6 | 5 | 1600 | 329 | 16.5 | 2.2 | 14.8 | 2.0 | 38.7 | 4.0 | 77 | 7 | 4 | 7 | 7 |

7 | 1 | 1950 | 14.9 | 14.8 | 38.3 | 78 | 20 | 2 | ||||||

8 | 2 | 1800 | 159 | 15.8 | 0.4 | 15.5 | 0.6 | 38.1 | 1.7 | 70 | 20 | 5 | 6 | |

9 | 3 | 1808 | 426 | 16.7 | 2.6 | 16.2 | 1.3 | 44.2 | 4.2 | 86 | 2 | 11 | 1 | |

10 | 3 | 1475 | 275 | 17.2 | 0.9 | 15.9 | 0.5 | 36.3 | 2.7 | 22 | 70 | 7 | 1 | |

11 | 2 | 1238 | 106 | 18.1 | 1.0 | 16.5 | 0.7 | 34.9 | 1.8 | 54 | 41 | 2 | 2 | |

12 | 5 | 1775 | 191 | 17.0 | 0.8 | 17.3 | 1.0 | 43.5 | 5.7 | 50 | 38 | 9 | 2 | |

13 | 5 | 1250 | 317 | 20.0 | 1.7 | 18.4 | 1.1 | 42.2 | 5.5 | 57 | 41 | 2 | ||

14 | 4 | 1844 | 236 | 16.5 | 0.8 | 16.2 | 0.6 | 42.4 | 4.5 | 90 | 10 | |||

15 | 5 | 1730 | 224 | 16.7 | 0.4 | 15.2 | 0.7 | 40.3 | 5.3 | 69 | 28 | 2 | 1 | |

16 | 2 | 1113 | 177 | 22.2 | 1.1 | 19.2 | 0.2 | 47.7 | 2.7 | 55 | 43 | 2 | ||

17 | 2 | 1075 | 159 | 20.3 | 0.9 | 16.1 | 0.2 | 40.0 | 2.0 | 71 | 11 | 6 | 15 | |

18 | 2 | 1325 | 265 | 17.5 | 0.3 | 13.5 | 0.6 | 44.0 | 4.5 | 80 | 20 | |||

19 | 2 | 1763 | 636 | 17.3 | 2.9 | 14.2 | 3.0 | 51.3 | 8.5 | 59 | 11 | 14 | 18 |

^{1}We originally (in 2014) established at least three plots per stand [35], but 15 of the original 75 plots were harvested from 2016 to 2018, and three plots had missing defoliation data. Analyses in this paper are all within plots, and stands were used here only to summarize general characteristics.

^{2}DBH = diameter at breast height.

^{3}Species abbreviations: BF = balsam fir; BS = black spruce; WS = white spruce; HW = hardwood species, including balsam poplar (Populus balsamifera), American mountain ash (Sorbus americana), trembling aspen (Populus tremuloides), willow (Salix spp.), white birch, yellow birch (Betula alleghaniensis), red maple (Acer rubrum), mountain maple (Acer spicatum), and striped maple (Acer pensylvanicum); OSW = non-host softwood species, including eastern white cedar (Thuja occidentalis), eastern white pine (Pinus strobus), and eastern larch (Larix laricina).

**Table 2.**Number and percentage of plots with clustered, dispersed, or random tree stem locations based on average nearest neighbor analyses (α = 0.05), for balsam fir, black spruce, white spruce, hardwoods, and all host species per plot.

Balsam Fir | Black Spruce | White Spruce | Hardwoods | All Host Species | |
---|---|---|---|---|---|

Clustered | 0 | 1 (2%) | 0 | 3 (5%) | 0 |

Dispersed | 21 (37%) | 3 (5%) | 1 (2%) | 2 (4%) | 22 (39%) |

Random | 35 (61%) | 20 (35%) | 12 (21%) | 25 (44%) | 35 (61%) |

**Table 3.**Number and percentage of plots with significantly clustered patterns of defoliation of trees, based on global Moran’s I analyses among years, for balsam fir, black spruce, white spruce, and all host species in each plot (α = 0.05, search radius = 5 m).

Year | Balsam Fir | Black Spruce | White Spruce | All Host Species |
---|---|---|---|---|

2014 | 19 (33%) | 1 (2%) | 2 (4%) | 27 (47%) |

2015 | 11 (19%) | 3 (5%) | 0 | 16 (28%) |

2016 | 13 (23%) | 1 (2%) | 0 | 20 (35%) |

2017 | 6 (11%) | 2 (4%) | 0 | 17 (30%) |

2018 | 15 (26%) | 2 (4%) | 0 | 19 (33%) |

**Table 4.**Abbreviations and description of predictor variables at both plot and tree levels included in Gradient Boosting Machine analysis to determine their relative importance in predicting annual defoliation of a subject balsam fir tree.

Predictor Variables | Description |
---|---|

Plot level | |

PlotAvgDefol | Average annual defoliation of all host species per plot (%) |

PlotAvgBFDefol | Average annual defoliation of balsam fir per plot (%) |

PlotBFBA | % basal area of balsam fir |

PlotBSBA | % basal area of black spruce |

PlotWSBA | % basal area of white spruce |

PlotHWBA | % basal area of hardwoods |

Spray | Dummy variable: whether the plot was sprayed by insecticide (1) in corresponding given year or not (0) |

Tree level ^{1} | |

BA | Basal area of the subject balsam fir (m^{2} ha^{−1}) |

PreYearDefol | Annual defoliation of subject balsam fir in previous year (%) |

NeiAvgDefol | Average annual defoliation of neighboring^{1} host trees (%) |

NeiAvgBFDefol | Average annual defoliation of neighboring balsam fir (%) |

NeiAvgBSDefol | Average annual defoliation of neighboring black spruce (%) |

NeiAvgWSDefol | Average annual defoliation of neighboring white spruce (%) |

NeiHostBA | Total basal area of neighboring host trees (m^{2} ha^{−1}) |

NeiBFBA | Total basal area of neighboring balsam fir (m^{2} ha^{−1}) |

NeiSPBA | Total basal area of neighboring spruce trees (m^{2} ha^{−1}) |

NeiHWBA | Total basal area of neighboring hardwoods (m^{2} ha^{−1}) |

NeiHBA | Total basal area of all trees with basal area greater than the subject balsam fir in the neighborhood (m^{2} ha^{−1}) |

NeiHostHBA | Total basal area of host trees with basal area greater than the subject balsam fir in the neighborhood (m^{2} ha^{−1}) |

NeiSPHBA | Total basal area of spruce trees with basal area greater than the subject balsam fir in the neighborhood (m^{2} ha^{−1}) |

NeiBFHBA | Total basal area of balsam fir with basal area greater than the subject balsam fir in the neighborhood (m^{2} ha^{−1}) |

^{1}Search radii of 3, 4, and 5 m were used for balsam fir trees in a circular subplot of 6 m inside each plot.

**Table 5.**Adjusted r

^{2}, root mean squared error (RMSE), and mean bias of predictions of individual balsam fir defoliation (%) by candidate models with neighborhood tree search radius equal to 3, 4, and 5 m. Predictor variable abbreviations are described in Table 4.

Candidate Models | Predictors | Fit Statistics ^{1} | ||
---|---|---|---|---|

Adjusted r^{2} | RMSE | Bias | ||

Model 1 | PlotAvgBFDefol + BA | 0.8001 | 0.1411 | 0.0028 |

Search radius = 3 m | ||||

Model 2 | NeiAvgBFDefol + BA | 0.7539 | 0.1566 | 0.0017 |

Model 3 | PlotAvgBFDefol + BA + NeiHostHBA | 0.8015 | 0.1406 | 0.0025 |

Search radius = 4 m | ||||

Model 4 | NeiAvgBFDefol + BA | 0.7823 | 0.1473 | 0.0019 |

Model 5 | PlotAvgBFDefol + BA + NeiHostBA | 0.8007 | 0.1409 | 0.0027 |

Search radius = 5 m | ||||

Model 6 | NeiAvgBFDefol + BA | 0.7889 | 0.1450 | 0.0025 |

^{1}The fit statistics were tested for fixed effect models without random effect terms, which in previous model runs had little contribution to models by likelihood ratio tests (p = 0.9).

© 2019 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/).

## Share and Cite

**MDPI and ACS Style**

Li, M.; MacLean, D.A.; Hennigar, C.R.; Ogilvie, J.
Spatial-Temporal Patterns of Spruce Budworm Defoliation within Plots in Québec. *Forests* **2019**, *10*, 232.
https://doi.org/10.3390/f10030232

**AMA Style**

Li M, MacLean DA, Hennigar CR, Ogilvie J.
Spatial-Temporal Patterns of Spruce Budworm Defoliation within Plots in Québec. *Forests*. 2019; 10(3):232.
https://doi.org/10.3390/f10030232

**Chicago/Turabian Style**

Li, Mingke, David A. MacLean, Chris R. Hennigar, and Jae Ogilvie.
2019. "Spatial-Temporal Patterns of Spruce Budworm Defoliation within Plots in Québec" *Forests* 10, no. 3: 232.
https://doi.org/10.3390/f10030232