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

Table 5 Parameter estimates and goodness of fits for curvilinear models of self-thinning relationships

	Intercept (trees/ha)	lnD _g (cm)	lnD ²_g (cm)	σ ² (trees/ha)	logLik	γ	LRT₁	μ (trees/ha)	LRT₂	LRT₃ or ∆AIC
Common beech	9.790		−0.296	1.359	−1,446.128	0.948	***	−2.270	***	−11.450
Common beech	0.058		0.005	0.116	−1,446.128	0.007	***	0.271	***	−11.450
Scots pine	2.279	4.701	−1.023	1.368	−3,121.937	0.934	***	−1.410	***	***
Scots pine	1.624	1.047	0.169	0.286	−3,121.937	0.012	***	0.592	***	***
Aleppo pine	9.575		−0.299	0.602	−560.725	0.859	***	0.212	ns	−4.030
Aleppo pine	0.166		0.013	0.160	−560.725	0.034	***	0.394	ns	−4.030
Maritime pine	9.307		−0.272	0.843	−2,665.869	0.900	***	−1.742	***	−8.120
Maritime pine	0.034		0.003	0.089	−2,665.869	0.012	***	0.292	***	−8.120
Silver fir	4.700	3.000	−0.718	0.773	−638.180	0.941	***	−1.705	***	***
Silver fir	0.923	0.557	0.084	0.104	−638.180	0.009	***	0.360	***	***
Norway Spruce	10.043		−0.287	1.259	−636.381	0.964	***	−2.203	***	−6.100
Norway Spruce	0.063		0.005	0.123	−636.381	0.005	***	0.295	***	−6.100
Douglas fir	0.607	5.192	−1.009	1.146	−503.321	0.944	***	−2.080	***	***
Douglas fir	1.095	0.638	0.094	0.154	−503.321	0.009	***	0.417	***	***

Standard errors are in italics. LRT₁ and LRT₂ are as in Table 3. LRT₃ corresponds to the likelihood ratio test of the quadratic term when relevant (see Section 3). ∆AIC is provided when considering models with the same number of parameters
ns non-significant
***p < 0.001; **p < 0.01; *p < 0.05

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