Significant differences and curvilinearity in the self-thinning relationships of 11 temperate tree species assessed from forest inventory data

Table 2 Parameter estimates and goodness of fits for linear models of self-thinning relationships

	Intercept (trees/ha)	lnD _g (cm)	σ ² (trees/ha)	logLik	γ	LRT₁	μ (trees/ha)	LRT₂
Pubescent oak	12.270	−1.809	2.190	−316.683	0.971	***	−2.917	*
Pubescent oak	0.283	0.094	1.285	−316.683	0.017	***	2.470	*
Pedunculate oak	12.138	−1.758	1.731	−820.640	0.965	***	−2.585	***
Pedunculate oak	0.161	0.049	0.401	−820.640	0.009	***	0.865	***
Sessile oak	12.681	−1.911	1.238	−562.624	0.961	***	−2.181	***
Sessile oak	0.181	0.058	0.198	−562.624	0.009	***	0.503	***
Common beech	12.950	−1.941	1.321	−1451.857	0.946	***	−2.236	***
Common beech	0.110	0.034	0.143	−1451.857	0.008	***	0.356	***
Scots pine	11.993	−1.615	1.338	−3,137.467	0.933	***	−1.324	***
Scots pine	0.125	0.039	0.322	−3,137.467	0.013	***	0.689	***
Aleppo pine	12.512	−1.881	0.612	−562.740	0.861	***	0.200	ns
Aleppo pine	0.277	0.081	0.166	−562.740	0.036	***	0.407	ns
Corsican pine	12.104	−1.653	1.166	−204.123	0.936	***	−2.089	ns
Corsican pine	0.211	0.065	0.477	−204.123	0.025	***	1.357	ns
Maritime pine	11.982	−1.711	0.854	−2,669.932	0.903	***	−1.757	***
Maritime pine	0.079	0.024	0.058	−2,669.932	0.010	***	0.193	***
Norway spruce	13.086	−1.878	1.222	−639.428	0.962	***	−2.168	***
Norway spruce	0.108	0.033	0.219	−639.428	0.004	***	0.564	***
Silver fir	12.621	−1.779	0.853	−658.444	0.006	***	−1.797	***
Silver fir	0.108	0.032	0.083	−658.444	0.007	***	0.273	***
Douglas fir	12.133	−1.646	1.128	−511.402	0.941	***	−2.061	***
Douglas fir	0.189	0.057	0.141	−511.402	0.012	***	0.371	***

Standard errors are in italics. LRT₁ corresponds to the likelihood ratio test between the model fitted by OLS and the stochastic frontier model fitted by maximum likelihood (significance of a left-tailed distribution for the residuals). LRT₂ corresponds to the likelihood ratio test of μ (existence of a mode in the left-tailed distribution of residuals)
ns non-significant
***p < 0.001; **p < 0.01; *p < 0.05

ISSN: 1297-966X