Table 15 Estimated parameters and goodness of fit of the H–D models for A. araucana fitted to the complete database

Simple H–D model

\({H}_{ij}=1.3+a\times {e}^{-b\times {e}^{-c\times {DBH}_{ij}}}+{\varepsilon }_{ij}\)

 a

26.867225

0.922861

4.57

3.43

0.68

4.57

 b

2.654334

0.119640

 c

0.024083

0.001615

Simple NLME H–D model

\({H}_{ij}=1.3+\left(a+{u}_{i}\right)\times {e}^{-b\times {e}^{-c\times DB{H}_{ij}}}+{\varepsilon }_{ij}\)

\({u}_{i}N\left(0,D\right)\)

\({\varepsilon }_{i}N\left[0,{R}_{i}\right]\)

 a

27.593612

1.1309101

4.24

3.20

0.72

4.37

 b

2.506014

0.1331214

 c

0.022559

0.0016667

\({\sigma }_{u}^{2}\)

4.771740

2.184431

\({\sigma }^{2}\)

1.292337

1.136810

\(\delta\)

0.3023997

Generalized H–D model

\({H}_{ij}=1.3+\left(a0+a1\times {H}_{dom}A{A}_{i}\right)\times {e}^{-\left(b0+b1\times RangeDBHA{A}_{i}\right)\times {e}^{-c0\times {DBH}_{ij}}}+{\varepsilon }_{ij}\)

 a0

16.250751

1.774237

4.26

3.16

0.72

4.29

 a1

0.398350

0.063317

 b0

1.090395

0.353957

 b1

0.008893

0.002231

 c0

0.024126

0.001587

Generalized NLME H–D model

\({H}_{ij}=1.3+\left(a0+{u}_{i}+a1\times {H}_{dom}A{A}_{i}\right)\times {e}^{-\left(b0+b1\times RangeDBHA{A}_{i}\right)\times {e}^{-c0\times {DBH}_{ij}}}+{\varepsilon }_{ij}\)

\({u}_{i}N\left(0,D\right)\)

\({\varepsilon }_{i}N\left[0,{R}_{i}\right]\)

 a0

16.657915

1.7012540

0

4.25

3.16

0.72

4.29

 a1

0.409165

0.0596687

0

 b0

1.093159

0.3614893

0.0026

 b1

0.008203

0.0023067

0.0004

 c0

0.022477

0.0016121

0

\({\sigma }_{u}^{2}\)

2.35871e-06

0.0015358

\({\sigma }^{2}\)

1.23625

1.1118678

\(\delta\)

0.3056402