Table 1 Parameter summary for Eqs. (1), (2), and (3)

From: Global warming reduces the carrying capacity of the tallest angiosperm species (Eucalyptus regnans)

   

95% CI

Parameter

Predictor

Mean

Min

Max

Static allometry (Eq. (1))

    

α0

Intercept STL

12.29

12.18

12.39

α1

log(D)

− 1.67

− 1.69

− 1.64

α2

\({{{\rm{MAT}}}}_{{1960-2000}_{{{\rm{j}}}}}\)

− 0.09

− 0.14

− 0.05

\({\sigma }_{{\alpha }_{0}}\)

Plot-level SD

0.12

0.10

0.16

σ

Residual SD

0.06

0.05

0.06

Mortality model (Eq. (2))

    

β0

Intercept

− 29.38

− 32.48

− 26.36

β1

log(D)

2.92

2.51

3.33

β2

log(N)

2.38

2.11

2.66

β3

\({{{\rm{MAT}}}}_{{1960-2000}_{{{\rm{j}}}}}\)

0.15

− 0.05

0.36

β4

\({{{\rm{MAT}}}}_{{{{\rm{anomaly}}}}_{{{\rm{ij}}}}}\)

0.28

0.09

0.47

\({\sigma }_{{\beta }_{0}}\)

Plot-level SD

0.84

0.69

1.03

θ

Shape NB

9.39

6.69

13.04

Intercept

Intercept STL

12.55

12.25

12.88

Slope

Slope STL

− 1.65

− 1.72

− 1.58

\(\frac{{\beta }_{3}}{-{\beta }_{2}}\)

\({{{\rm{MAT}}}}_{{1960-2000}_{{{\rm{j}}}}}\)

− 0.06

− 0.15

0.02

\(\frac{{\beta }_{4}}{-{\beta }_{2}}\)

\({{{\rm{MAT}}}}_{{{{\rm{anomaly}}}}_{{{\rm{ij}}}}}\)

− 0.12

− 0.20

− 0.04

Mortality model (Eq. (3))

    

β0

Intercept

− 29.61

− 32.67

− 26.66

β1

log(D)

2.95

2.56

3.35

β2

log(N)

2.40

2.13

2.68

β5

MATij

0.22

0.09

0.36

\({\sigma }_{{\beta }_{0}}\)

Plot-level SD

0.84

0.69

1.03

θ

Shape NB

9.42

6.71

13.12

Intercept

Intercept STL

12.55

12.26

12.87

Slope

Slope STL

− 1.65

− 1.72

− 1.58

\(\frac{{\beta }_{5}}{-{\beta }_{2}}\)

MATij

− 0.09

− 0.15

− 0.04

  1. The effect size of MAT on the intercept of the self-thinning line (STL) is estimated by α2, \(\frac{{\beta }_{{{\rm{3}}}}}{-{\beta }_{{{\rm{2}}}}}\), \(\frac{{\beta }_{{{\rm{4}}}}}{-{\beta }_{{{\rm{2}}}}}\), and \(\frac{{\beta }_{{{\rm{5}}}}}{-{\beta }_{{{\rm{2}}}}}\).