Table 1 SE models with different climate variables and time lags.

Initial models were formulated according to the causal diagram in Fig. 3. For each model, nonsignificant (P ≥ 0.05) terms were removed successively using the AIC. Asterisks (*) indicate removed terms. Bold numbers indicate parameter estimates significantly (P < 0.05) different from zero. RMSEA, root mean square of approximation; CFI, confirmatory fit index; NS, not significant.

Model specificationModel fitStandardized parameter estimates
Climate variable included in the modelTime lag (years)χ2 (df, P value)CFIRMSEAR2 endogenous variablesMay NDVIJunAugNDVIPopulation growth
May NDVIJunAug NDVIPopulation growthClimate variablePopulation sizeClimate variablePopulation sizeClimate variablePopulation sizeMay NDVIJunAug NDVI
Annual sea ice concentration00.43 (1, 0.51)100.1430.5880.2860.230.32−0.77*0.25−0.14*−0.29
10.63 (3, 0.89)100.1480.5300.2300.250.30−0.73****−0.48
20.53 (3, 0.91)100.1170.4770.2100.210.26−0.69****−0.46
30.39 (2, 0.82)10*0.5720.149**−0.73−0.15***−0.39
Date of snowmelt 00.28 (1, 0.59)100.1540.1400.2850.240.34−0.37*−0.18−0.15*−0.55
11.02 (3, 0.80)100.0790.1390.264*0.28−0.37*−0.21**−0.55
21.28 (4, 0.87)100.0650.0400.210*0.26−0.20****−0.46
30.42 (2, 0.81)10*0.0830.149**−0.20−0.22***−0.39
Annual snow cover00.57 (1, 0.45)100.1460.0680.2880.220.33−0.26*−0.19−0.14*−0.53
12.84 (3, 0.42)100.0710.0830.308*0.27−0.29*−0.26*0.16−0.57
22.34 (4, 0.67)100.0680.0130.211*0.26*****−0.46
30.37 (1, 0.54)10*0.0430.149***−0.21***−0.39
May temperature03.07 (3, 0.38)0.9980.0170.1910.0250.2460.290.310.19****−0.50
12.85 (3, 0.42)100.156*0.2590.290.24****0.13−0.49
23.39 (3, 0.34)0.9880.0420.232*0.2240.420.19*****−0.47
33.99 (4, 0.41)100.1440.0830.1490.35**−0.23***−0.39
June-to-August temperature03.28 (4, 0.51)100.1070.0450.246*0.330.21****−0.50
11.43 (3, 0.70)100.0700.1000.287*0.270.32*−0.21NS0.13−0.43
21.16 (3, 0.76)100.0660.0310.248*0.260.18*−0.20**−0.42
31.51 (2, 0.47)10*0.0750.149**0.18−0.23***−0.39