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Table II

Statistics of mixed-effects linear models. Figures in brackets are standard deviations of parameters.

m a b c d σsite(μj) σsite(βj) AIC

M1 –5.24 (5.9) –1.09 (0.12) 23.21** (1.94) 464.5** (28.7) –0.35** (0.06) 17.94 4.36 30.45 228.2 50 248
M2 10.19 (9.68) –0.93** (0.14) 23.18** (1.94) 459.1** (28.8) –0.32** (0.06) 19.98 4.33 29.2 227.8 50 246
M3 14.95 (11.34) –0.55** (0.15) 18.53** (2.02) 415** (29.9) –0.35** (0.06) 19.4 4.4 30.42 240.3 50 042
M4 13.88 (13.02) –0.55** (0.14) 18.66** (1.91) 424** (28.4) –0.28** (0.05) 19.7 4.35 30.21 226.3 49 116

p-value  >  0.05;

**

p-value  <  0.001. M1: model without computation of the date. M2: model with an integration of a linear form of the date. M3: model with an integration of a decadal scale form of the date. M4: model with an integration of a factorial form of the date.