# Modeling Post-Fire Mortality in Pure and Mixed Forest Stands in Portugal—A Forest Planning-Oriented Model

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## Abstract

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## 1. Introduction

^{3}ha, 16% of the total forest area). In fact, limited effort has been devoted to promote mixed-species stands in Portugal as compared with the effort devoted to quantifying productivity on single-species stands [11]. This information could be an important tool for forest managers’ options.

## 2. Materials and Methods

#### 2.1. Data Collection

#### 2.1.1. Wildfire Perimeters and Inventory Plots Status

^{3}ha), 23.7% (7.37 × 10

^{3}ha) and 23.4% (7.14 × 10

^{3}ha), respectively. The remaining area is occupied by holm oak (10.5%), stone pine (Pinus pinea, 6%) and other broad-leaved tree species and conifer species (17%) [1]. These forests encompass a wide variety of ecosystems ranging from intensive silviculture plantations for wood production to plantations for coastal dune protection and agroforestry systems.

^{5}ha [42]. Therefore, the development of preventive forest management including fire hazard reduction strategies should be of primary importance.

^{®}9.3 software, Esri, Redlands, CA, USA) were used to identify the plots from the 5th National Forest Inventory (NFI, carried out in 2005–2006 period) where a wildfire occurred between 2006 and 2008. The wildfire perimeters and the 12,258 plots of the NFI (with 5267 plots of forest stands) were overlaid for that purpose (Figure 1b). In total, 38 NFI plots with 795 trees had been measured prior to wildfire occurrence (pre-fire inventory). In the same period, 203 additional burned plots distributed all over the country from the framework of ForFireS Project [43], and encompassing 1725 trees were further measured (post-fire inventory in 2007 and 2008) (Figure 1d). All these plots were sampled in areas where the fire perimeter was known and trees had not been harvested.

#### 2.1.2. Reverse Engineering to Rebuild the Tree Characteristics

#### 2.2. Post-Fire Model Description

#### 2.2.1. Statistical Approach

#### Fixed-Effects Logistic Regression

_{1}to x

_{p}are independent variables, β

_{0}is the intercept, and β

_{1}to β

_{p}are parameters to be estimated or regression coefficients.

#### Mixed-Effects Logistic Regression

**β**(β

_{0}, and β

_{1}to β

_{p}) is now expanded with a vector of random effects

**u**: not all the parameters need to include a random effect but at least one of them should include a fixed and a random part to be considered a mixed-effects model. The vector

**u**is assumed to follow a multivariate normal distribution with mean zero and a variance-covariance matrix to be estimated in the fitting procedure, in addition to the fixed-effects parameters and the error variance. The fitting procedure is based on a log-likelihood maximization and was performed with the glmer function of the lme4 package [54] of the R statistical software [51]. Within the mixed-effects modeling context, we have evaluated the predictions made only with fixed-effects parameters, i.e., the mean prediction. Therefore, note that mixed-effects modeling was only considered in the fitting procedure in order to account for the existing hierarchical data structure rather than for estimating random effects whose aim would be the improvement in the model prediction. Due to the nested structure of the data (trees inside plots), parameters associated with plot variables (e.g., slope, G, and N) are considered only fixed parameters because these variables are already accounting for the variability between plots. However, the parameters associated to tree-level variables (e.g., group of species, BAL, dbh or h) might have a random effect that accounts for the variability between plots.

#### 2.2.2. Stand-Level Modeling

^{−1}). In our analysis, the mortality of the Mediterranean evergreen broadleaves (cork and holm) stands did not differ from other broadleaved stands. Thus, as in the previous sub-model PsDead, for modeling purposes the stands were classified according to the proportions (0 ≤ Pcovertype ≤ 1) of three cover types (“eucalyptus”, “conifers” and “other broadleaves”). A number of stand-level variables related to topography (slope, altitude, aspect), biometric variables (e.g., mean tree diameter at breast height of the stand, Avgdbh) and structure (e.g., standard deviation of tree heights, sh) were tested.

#### 2.2.3. Tree-Level Modeling

_{Ec}= 939), “other broadleaves” (n

_{Broad}= 174), “conifers” (n

_{Con}= 1271) and “oak trees” (n

_{Oak}= 136). In this model we distinguish the oak trees (cork and holm oak) from the other broadleaves. This was done because previous studies focusing on the factors influencing post-fire tree survival and regeneration capacity showed that fire injury and individual tree characteristics are the main factors [21,56], which depends on fire-resistance or avoidance mechanisms, and in flammability of species [22]. The model PdTree includes dummy variables for the different cover types. In the case the tree is from one of the cover types the value of the dummy variable is “1”. Here a logistic regression mixed-effects model that assigns a probability of mortality to an individual tree given its size (e.g., stand height (h), basal area of the tree (g), and quadratic mean diameter of trees (dg)) (Table 1), species identity (represented by classes of cover types), competitive environment (distance-independent competition index that incorporates tree size such as BAL, dbh/dg, dbh

^{2}/dg

^{2}, and ht

_{i}/ht) and physical environment which are biologically related to the mortality process were used (Summary statistics of the data sets used are presented in Table 1, Table 2 and Table 3). The explanatory variables were selected by testing whether they improved the model.

#### 2.2.4. Assessment of Model Selection

## 3. Results

#### 3.1. General Response Patterns

#### 3.2. Stand-Level Mortality

#### 3.2.1. Predicting Whether Stand Level Mortality Will Occur

^{2}/ha), and dg is the quadratic mean diameter of trees (cm). The predictor G/dg is a density measure non-linearly related to the number of trees per hectare. Sd is the standard deviation of trees’ diameters at breast height (cm). The predictor Sd/dg expresses the relative variability of tree diameters. The variable is close to “1” in rather uneven stands and approaches “0” in homogeneous stands (0 < Sd/dg < 1). PBr is the proportion of other broadleaved trees in the stand (0 ≤ Pcovertype ≤ 1) where “0” indicates no presence and “1” indicates the stand is purely occupied by broadleaves; PEc is the proportion of pine trees in the stand. The sum of PC, PEc and PBr gives “1”. The variable PC is the specie composition omitted for inclusion in the model.

^{2}/ha of Basal area (G) and 1.22 of stand density (G/dg). The model was successful in predicting whether mortality occurred after wildfire in 82% of the stands (i.e., percentage of concordant pairs). The area under the ROC curve (0.821) indicated excellent discrimination [50].

#### 3.2.2. Estimating Stand-Level Post-Fire Mortality

#### 3.3. Estimating Post-Fire Tree Mortality

#### 3.4. Cut-Off Point Value Selection

## 4. Discussion

#### 4.1. Forest Composition, Heterogeneity and Structure

#### 4.2. Pre and Post-Fire Smart Management: Applicability

## 5. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Inventory plots location for data acquisition: (

**a**) the map displays the distribution of fire perimeters occurred in Portugal between 2006–2008 larger than 5 ha; (

**b**) the 5th National Forest Inventory (NFI) plots covering the forest area of Portugal in a systematic 2 × 2 km grid (12,258 plots); (

**c**) the overlaid from fire perimeters and plots of the 5th NFI; and (

**d**) the sample plot 38 NFI (795 trees) from the post-fire inventory of plots in 2007 and 2008 and additional 203 plots from ForFireS Project (1725 trees).

**Figure 3.**Effect of the relative variability of tree diameters (predictor Sd/dg) on the probability of mortality on a stand considering pure stands of eucalyptus (PEc = 1, PBr = 0), conifers (PEc = 0, PBr = 0), other broadleaves (PBr = 1, PEc = 0) and mixed stands of other broadleaves and Conifers (PBr = 0.5 + PEc = 0). The values were calculated according model PsDead for a stand with 7.55 m

^{2}/ha Basal area (G) and 1.22 stand density (G/dg).

**Figure 4.**Effect of stand average diameter at breast height (Avgdbh in cm) on the proportion of dead trees in the stand for different cover types considering: (

**a**) pure stands of Eucalyptus (PEc = 1, PBr = 0), conifers (PEc = 0, PBr = 0) and other broadleaves (PBr = 1, PEc = 0); and (

**b**) mixed stands of other Broadleaves and Conifers (PBr = 0.5 + PEc = 0), other broadleaves and Eucalyptus (PBr = 0.5 + PEc = 0.5), and Conifers and Eucalyptus (PEc = 0.5 + PBr = 0). The values were calculated according to model PdMort for a stand located at 300 m above sea level with a slope of 15°.

**Figure 5.**Effect of basal area (G, m

^{2}/ha) and two extreme values of dbh: (

**a**) 7 cm; and (

**b**) 30 cm on the probability of each tree species mortality. The values were calculated according to PdTree1 for a stand with a slope of 15°.

**Table 1.**Descriptive statistics for tree level data and individual tree mortality by species (Tree status: D, dead; S, Survival,) tested as model predictors in the range of study (n = 2520, 16 species), concerning the period of analyses (2006–2008).

Tree Species | Tree Status | n | dbh (cm) | h (m) | g (m^{2}) | |||
---|---|---|---|---|---|---|---|---|

Mean | Range | Mean | Range | Mean | Range | |||

Ec | S | 177 | 15.24 | 5.20–59.30 | 15.13 | 5.40–30.40 | 0.022 | 0.002–0.276 |

D | 762 | 10.06 | 5.00–46.30 | 12.24 | 1.40–28.20 | 0.008 | 0.002–0.168 | |

OB | S | 37 | 10.88 | 7.00–21.00 | 6.92 | 4.90–11.60 | 0.010 | 0.004–0.035 |

D | 43 | 10.19 | 7.00–23.00 | 5.97 | 3.12–9.90 | 0.009 | 0.004–0.042 | |

OC | S | 11 | 25.09 | 7.00–59.00 | 15.09 | 7.98–26.90 | 0.073 | 0.004–0.273 |

D | 5 | 13.40 | 9.00–21.00 | 9.79 | 8.22–11.44 | 0.015 | 0.006–0.035 | |

Pp | S | 263 | 19.17 | 6.00–51.00 | 13.89 | 5.50–28.50 | 0.035 | 0.003–0.204 |

D | 981 | 14.63 | 7.00–51.00 | 11.09 | 3.80–28.50 | 0.021 | 0.004–0.149 | |

Ppi | S | 7 | 31.23 | 18.00–43.00 | 17.45 | 7.35–24.40 | 0.086 | 0.025–0.145 |

D | 4 | 13.70 | 8.50–22.60 | 7.22 | 3.97–8.90 | 0.017 | 0.006–0.040 | |

Qr | S | 20 | 16.82 | 8.00–39.00 | 5.09 | 3.83–7.60 | 0.028 | 0.005–0.119 |

D | 10 | 19.08 | 7.00–64.00 | 4.99 | 3.40–7.50 | 0.051 | 0.004–0.321 | |

Qs | S | 58 | 20.01 | 4.30–62.00 | 6.72 | 2.70–13.90 | 0.044 | 0.001–0.302 |

D | 48 | 17.53 | 4.50–59.80 | 6.34 | 2.95–10.70 | 0.042 | 0.002–0.281 | |

Qsp | S | 42 | 12.21 | 7.00–24.00 | 8.61 | 5.00–13.80 | 0.013 | 0.004–0.045 |

D | 52 | 10.09 | 7.00–21.30 | 7.25 | 4.20–12.50 | 0.009 | 0.004–0.035 |

^{2}). Ec: Eucalyptus globulus; OB: Others Broadleaves; OC: Others conifers; Pp: Pinus pinaster; Ppi: Pinus pinea; Qr: Quercus rotundifolia; Qs: Quercus suber; Qsp: Other oak trees. Range: minimum–maximum.

**Table 2.**Descriptive statistics for variables tested as model predictors at stand level for pure stands.

Stands with Dead Trees (n = 96) | Stands without Dead Trees (n = 68) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Eucalyptus | Conifers | Other Broadleaves | Eucalyptus | Conifers | Other Broadleaves | |||||||

Variable (Code) | Range | Mean (S.d.) | Range | Mean (S.d.) | Range | Mean (S.d.) | Range | Mean (S.d.) | Range | Mean (S.d.) | Range | Mean (S.d.) |

Avgdbh | 2.92–14.50 | 9.03 (3) | 7–26.25 | 13.75 (5.81) | 7.5–38.03 | 18.85 (9.05) | 7–27.45 | 11.49 (3.63) | 13–32.8 | 20.18 (6.76) | 8–73.36 | 30.11 (17) |

Avgh | 3.49–15.24 | 10.18 (3.35) | 3.8–19.37 | 9.78 (4.08) | 3.93–9.4 | 6.45 (1.53) | 6.5–21.9 | 13.84 (3.68) | 3.47–19.73 | 12.01 (4.42) | 4.7–18.23 | 8.12 (4.23) |

dg | 5.59–26.03 | 8.98 (4.17) | 5.14–45.09 | 18.64 (11.9) | 13.6–45.09 | 28.77 (10.14) | 6.03–45.09 | 13.54 (8.13) | 10.08–45.09 | 27.16 (15.78) | 17.04–45.09 | 34.14 (9.96) |

G | 0.31–11.04 | 4.91 (2.57) | 0.077–38.16 | 7.15 (9.46) | 0.08–26.51 | 3.9 (6.54) | 0.08–29.73 | 7.62 (7.2) | 0.27–33.13 | 8.2 (11.01) | 0.1–13.81 | 4.09 (3.75) |

G/dg | 0.012–1.80 | 0.66 (0.42) | 0.0017–3.78 | 0.78 (1.1) | 0.002–1.95 | 0.23 (0.48) | 0.002–3.4 | 0.8 (0.84) | 0.006–3.2 | 0.71 (1.1) | 0.002–0.81 | 0.15 (0.19) |

N | 60–1299 | 691.48 (347.55) | 20–1539 | 318.7 (353.86) | 20–220 | 72 (57.09) | 20–1811 | 617.4 (429.62) | 20–623 | 181.62 (213.82) | 20–140 | 46.96 (33.91) |

Sd | 0.78–5.37 | 3.28 (1.3) | 0–12.41 | 3.63 (3.13) | 0–26.02 | 7.31 (8.67) | 0–7.91 | 2.88 (1.89) | 0–11.72 | 4.3 (4.27) | 0–19.8 | 4.58 (6.01) |

Sh | 0.4–6.96 | 3.43 (1.98) | 0–5.46 | 1.57 (1.38) | 0–3.81 | 0.96 (1.08) | 0–5.07 | 2.2 (1.23) | 0–4.09 | 1.34 (1.46) | 0–5.91 | 0.75 (1.28) |

Sd/dg | 0.03–0.88 | 0.45 (0.25) | 0–1.34 | 0.33 (0.35) | 0–1.26 | 0.34 (0.43) | 0–1.07 | 0.27 (0.21) | 0–1.13 | 0.33 (0.37) | 0–0.93 | 0.18 (0.25) |

Altitude | 0–272 | 179 (81) | 0–893 | 330.42 (171.77) | 76–800 | 296.55 (152.55) | 0–491 | 192 (150.53) | 106–931 | 441 (331.3) | 0–861 | 313.39 (224.44) |

Slope | 0–26.6 | 10.27 (6.2) | 0–29 | 13.3 (7.92) | 0–22.8 | 8.27 (6.53) | 0.6–32 | 13.09 (8.68) | 1.8–27 | 11.48 (6.8) | 0–25.2 | 9.38 (6.27) |

^{2}/ha); G/dg, non-linearly a density measure related to the number of trees per hectare, N, tree density number of trees per ha; G, stand basal area (m

^{2}/ha); sd, standard deviation of tree diameters; sh, standard deviation of tree heights of the trees in the stand. The predictor Sd/dg expresses the relative variability of tree diameters. The variable is close to “1” in rather uneven stands and approaches “0” in homogeneous stands (0 < Sd/dg < 1); Slope, in degrees (°), Range: minimum–maximum. (S.d.): Standard deviation.

**Table 3.**Descriptive statistics for variables tested as model predictors at stand level for mixed stands.

Stands with Dead Trees | Stands without Dead Trees | |||
---|---|---|---|---|

(n = 56) | (n = 20) | |||

Variable (Code) | Range | Mean | Range | Mean |

(S.d.) | (S.d.) | |||

Altitude | 0–940 | 337.78 | 0–919 | 268.15 |

(232.79) | (285.51) | |||

Avgdbh | 7.64–25.67 | 15.41 | 7.99–26.88 | 14.7 |

(4.84) | (5.54) | |||

Avgh | 3.72–22.7 | 10.99 | 4.92–17.06 | 11.15 |

(4.19) | (3.48) | |||

dg | 5.64–31.88 | 13.04 | 10.08–26.03 | 13.66 |

(5.31) | (4.93) | |||

G | 0.55–30.52 | 9.29 | 0.93–33.18 | 8.81 |

(7.89) | (8.76) | |||

G/dg | 0.02–3.33 | 0.95 | 0.051–3.29 | 0.79 |

(0.94) | (0.88) | |||

N | 40–1279 | 398.02 | 60–1769 | 486.3 |

(297.73) | (433.8) | |||

PBr | 0–0.98 | 0.27 | 0–0.82 | 0.25 |

(0.33) | (0.29) | |||

PCon | 0–0.99 | 0.56 | 0–0.95 | 0.4 |

(0.35) | (0.29) | |||

PEc | 0–0.97 | 0.16 | 0–0.95 | 0.35 |

(0.3) | (0.41) | |||

Sd | 0.7–15.4 | 6.57 | 1.42–16.96 | 6.54 |

(3.31) | (4.53) | |||

Sh | 0.55–6.49 | 3.13 | 0.69–6.53 | 3.37 |

(1.58) | (1.82) | |||

Sd/dg | 0.06–1.54 | 0.58 | 0.09–1.02 | 0.49 |

(0.37) | (0.3) | |||

Altitude | 0–940 | 337.78 | 0–919 | 268.15 |

(232.79) | (285.51) | |||

Slope | 0–32 | 13.53 | 0.6–22.6 | 13.7 |

(7.77) | (6.06) |

Proportion of Dead Trees (%) | 0 | 1–20 | 21–40 | 41–60 | 61–80 | 81–99 | 100 |
---|---|---|---|---|---|---|---|

No. of plots | 88 | 19 | 16 | 18 | 11 | 15 | 74 |

**Table 5.**Estimated parameters, standard errors (SE), z values statistics and p-values for the model PsDead predicting whether mortality will occur in a stand.

Effect | Variables | Estimate | SE | Z Value | p-Value |
---|---|---|---|---|---|

β_{0} | Intercept | 1.3816 | 0.3380 | 4.0876 | <0.0001 |

β_{1} | PEc | −2.1698 | 0.4192 | −5.1757 | <0.0001 |

β_{2} | PBr | −1.0619 | 0.4438 | −2.3929 | 0.0167 |

β_{3} | G | −0.5553 | 0.1264 | −4.3934 | <0.0001 |

β_{4} | G/dg | 4.3280 | 1.1765 | 3.6790 | 0.0002 |

β_{5} | Sd/dg | 3.2549 | 0.8187 | 3.9760 | <0.0001 |

**Table 6.**Estimated parameters, standard errors (SE), z values statistics and p-values statistics and p-values for the model PdMort predicting degree of mortality caused by a wildfire.

Effect | Variables | Estimate | SE | Z Value | p-Value |
---|---|---|---|---|---|

β_{0} | Intercept | 0.3573 | 0.0392 | 9.118 | <0.0001 |

β_{1} | PEc | −0.1364 | 0.0258 | −5.293 | <0.0001 |

β_{2} | PBr | −1.3878 | 0.0361 | −38.495 | <0.0001 |

β_{3} | Slope | 0.0525 | 0.0013 | 39.118 | <0.0001 |

β_{4} | Altitude | 0.0017 | 0.0001 | 28.711 | <0.0001 |

β_{5} | Avgdbh | −0.0393 | 0.0018 | −20.832 | <0.0001 |

**Table 7.**Estimates of mixed-effects parameter, random effects variances (${\mathit{\sigma}}_{\mathit{i}}^{\mathbf{2}}$) and covariances (${\mathit{\sigma}}_{\mathit{i}\mathbf{,}\mathit{j}}$) for the model PdTree 1 predicting the probability of an individual tree die due a forest fire (n = 2520).

Effect | Variables | Estimate | SE | Z Value | p Value |
---|---|---|---|---|---|

β_{0} | Intercept | 4.493 | 0.9044 | 4.968 | <0.0001 |

β_{1} | Ec | 2.296 | 0.6599 | 3.480 | <0.0001 |

β_{2} | Con | 3.143 | 0.4721 | 6.657 | <0.0001 |

β_{3} | G | −0.1778 | 0.04572 | −3.890 | <0.0001 |

β_{4} | dbh | −0.1299 | 0.04559 | −2.849 | 0.00438 |

${\mathit{\sigma}}_{{\mathit{\beta}}_{\mathbf{0}}}^{\mathbf{2}}$ | - | 12.54 | - | - | - |

${\mathit{\sigma}}_{{\mathit{\beta}}_{\mathbf{4}}}^{\mathbf{2}}$ | - | 0.06780 | - | - | - |

${\mathit{\sigma}}_{{\mathit{\beta}}_{\mathbf{0}},{\mathit{\beta}}_{\mathbf{4}}}$ | - | −0.3681 | - | - | - |

© 2017 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**

Botequim, B.; Arias-Rodil, M.; Garcia-Gonzalo, J.; Silva, A.; Marques, S.; Borges, J.G.; Oliveira, M.M.; Tomé, M.
Modeling Post-Fire Mortality in Pure and Mixed Forest Stands in Portugal—A Forest Planning-Oriented Model. *Sustainability* **2017**, *9*, 390.
https://doi.org/10.3390/su9030390

**AMA Style**

Botequim B, Arias-Rodil M, Garcia-Gonzalo J, Silva A, Marques S, Borges JG, Oliveira MM, Tomé M.
Modeling Post-Fire Mortality in Pure and Mixed Forest Stands in Portugal—A Forest Planning-Oriented Model. *Sustainability*. 2017; 9(3):390.
https://doi.org/10.3390/su9030390

**Chicago/Turabian Style**

Botequim, Brigite, Manuel Arias-Rodil, Jordi Garcia-Gonzalo, Andreia Silva, Susete Marques, José G. Borges, Maria Manuela Oliveira, and Margarida Tomé.
2017. "Modeling Post-Fire Mortality in Pure and Mixed Forest Stands in Portugal—A Forest Planning-Oriented Model" *Sustainability* 9, no. 3: 390.
https://doi.org/10.3390/su9030390