A large database supports the use of simple models of post-fire tree mortality for thick-barked conifers, with less support for other species

Cansler, C. Alina; Hood, Sharon M.; van Mantgem, Phillip J.; Varner, J. Morgan

doi:10.1186/s42408-020-00082-0

Fire Ecology

Table 5 Models predicting pre-fire tree mortality designed for use before the fire occurs, from this study of post-fire tree mortality models from the USA, from fires occurring from 1981 to 2016. The Ryan and Amman model (R-A) model can be applied to any species for which bark thickness can be estimated. The other models are species-specific; hereafter, “pre-fire models.” These models are used in the First Order Fire Effects Modeling system (FOFEM), which predicts post-fire mortality for species in the USA. We evaluated dead and live tree status at three years post fire, unless otherwise noted

From: A large database supports the use of simple models of post-fire tree mortality for thick-barked conifers, with less support for other species

Species	Reference	Model form ^a	β₀	β₁	β₂	β₃	β₄
R-A model (many species)^b	Ryan and Reinhardt 1988; Ryan and Amman 1994	\( {P}_{\mathrm{m}}=\frac{1}{1+{e}^{\left({\upbeta}_0+{\upbeta}_1\left(1-{e}^{\upbeta_2 BT}\right)+{\upbeta}_3{CVS}^2\right)}} \)	−1.941	6.316	−0.3937	−0.000535
Abies concolor	Hood and Lutes 2017	\( {P}_{\mathrm{m}}=\frac{1}{1+{e}^{\left(-\left({\upbeta}_0+{\upbeta}_1 CLS-{\upbeta}_2{CLS}^2+{\upbeta}_3{CLS}^3\right)\right)}} \)	−3.5083	0.0956	0.00184	0.000017
Abies lasiocarpa	Hood and Lutes 2017	\( {P}_{\mathrm{m}}=\frac{1}{1+{e}^{\left(-\left({\upbeta}_0+{\upbeta}_1 CVS-{\upbeta}_2{CVS}^2+{\upbeta}_3{CVS}^3\right)\right)}} \)	−1.6950	0.2071	0.0047	0.000035
Abies magnifica	Hood and Lutes 2017	\( {P}_{\mathrm{m}}=\frac{1}{1+{e}^{\left(-\left({\upbeta}_0+{\upbeta}_1{CLS}^3\right)\right)}} \)	−2.3085	0.000004059
Calocedrus decurrens	Hood and Lutes 2017	\( {P}_{\mathrm{m}}=\frac{1}{1+{e}^{\left(-\left({\upbeta}_0+{\upbeta}_1{CLS}^3\right)\right)}} \)	−4.2466	0.000007172
Larix occidentalis	Hood and Lutes 2017	\( {P}_{\mathrm{m}}=\frac{1}{1+{e}^{\left(-\left({\upbeta}_0+{\upbeta}_1 CVS-{\upbeta}_2 DBH\right)\right)}} \)	−1.6594	0.0327	0.0489
Picea engelmannii	Hood and Lutes 2017	\( {P}_{\mathrm{m}}=\frac{1}{1+{e}^{\left(-\left({\upbeta}_0+{\upbeta}_1 CVS\right)\right)}} \)	0.0845	0.0445
Pinus albicaulis ^b	Hood and Lutes 2017	\( {P}_{\mathrm{m}}=\frac{1}{1+{e}^{\left(-\left({\upbeta}_0+{\upbeta}_1 CVS-{\upbeta}_2{CVS}^2+{\upbeta}_3{CVS}^3- eDBH\right)\right)}} \)	−0.3268	0.1387	0.0033	0.000025	0.0266
Pinus contorta	Hood and Lutes 2017	\( {P}_{\mathrm{m}}=\frac{1}{1+{e}^{\left(-\left({\upbeta}_0+{\upbeta}_1 CVS-{\upbeta}_2{CVS}^2+{\upbeta}_3{CVS}^3-{\upbeta}_4 DBH\right)\right)}} \)	−0.3269	0.1387	0.0033	0.000025	0.0266
Pinus lambertiana	Hood and Lutes 2017	\( {P}_{\mathrm{m}}=\frac{1}{1+{e}^{\left(-\left({\upbeta}_0+{\upbeta}_1{CLS}^2\right)\right)}} \)	−2.0588	0.000814
Pinus palustris	Wang et al. 2007	\( {P}_{\mathrm{m}}=\frac{1}{1+{e}^{\left({\upbeta}_0+\left({\upbeta}_1 BT\right)+\left({\upbeta}_2{BT}^2\right)-{\upbeta}_3{\left(\frac{CVS}{10}\right)}^2\right)}} \)	0.169	5.136	14.492	0.348
Pinus ponderosa ^c	Hood and Lutes 2017	\( {P}_{\mathrm{m}}=\frac{1}{1+{e}^{\left(-\left({\upbeta}_0+{\upbeta}_1{CVS}^3\right)\right)}} \)	−2.7103	0.000004093
Pinus ponderosa ^d	Keyser et al. 2006	\( {P}_{\mathrm{m}}=\frac{1}{1+{e}^{\left(-\left({\upbeta}_0+{\upbeta}_1 DBH+{\upbeta}_2 CLS+{\upbeta}_3(DBH)(CLS)\right)\right)}} \)	1.104	−0.156	0.0013	0.001
Populus tremuloides ^e	Brown and DeByle 1987	\( {P}_{\mathrm{m}}=\frac{1}{1+{e}^{\left({\upbeta}_0+{\upbeta}_1 DBH-{\upbeta}_2 CH\right)}} \)	−2.157	0.0858	0.118
Populus tremuloides ^f	Brown and DeByle 1987	\( {P}_{\mathrm{m}}=\frac{1}{1+{e}^{\left({\upbeta}_0+{\upbeta}_1 DBH-{\upbeta}_2 CH\right)}} \)	−4.407	0.251	0.07
Pseudotsuga menziesii	Hood and Lutes 2017	\( {P}_{\mathrm{m}}=\frac{1}{1+{e}^{\left(-\left({\upbeta}_0+{\upbeta}_1 CVS-{\upbeta}_2{CVS}^2-{\upbeta}_3{CVS}^3\right)\right)}} \)	−2.0346	0.0906	0.0022	0.000019

^aVariables used in the model are defined in Table 1
^bPost-fire status data came from three years after fire, with the exception of the following: Notholithocarpus densiflorus R-A (1 year), Pinus albicaulis pre-fire (1 year), Pinus coulteri R-A (2 years), Populus deltoides ssp. wislizeni R-A (2 years), Tsuga mertensiana R-A (1 year)
^cPre-fire Pinus ponderosa model
^dPre-fire Black Hills Pinus ponderosa model
^ePre-fire moderate Populus tremuloides model
^fPre-fire low Populus tremuloides model

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