Table 1.

Summary of model outputs from LMM's incorporating all predictors of nest initiation and lay date. (Significance asterisks show p-values (*0.05). Temperature shows the slope for the best temperature predictor found for each response in the electronic supplementary material, table A2 (mean night-time temperature for both responses), tree phenology shows the slope for the best tree phenology predictor for each response in the electronic supplementary material, table A3 (birch budburst for both responses), invertebrate availability shows the slope for the best invertebrate availability predictor for each response in the electronic supplementary material, table A4 (mean availability between days 82–95 for nest initiation, days 93–123 for lay date), and photoperiod shows the slope for latitude as a proxy for photoperiod. Random effect variances for each model are also shown (site, year and residual). In spaMM models, nu was fixed at 0.5 to constrain the spatial autocorrelation to follow an exponential decay.)

response	model	intercept	temperature	tree phenology	invertebrate availability	photoperiod proxy	site variance	year variance	residual variance	R2 marginal	R2 conditional
nest initiation	null	104.5 ± 1.5					28.2	4.1	97.9	0.00	0.25
	lmer	139.8 ± 102.7	−2.00 ± 1.27	0.07 ± 0.14	−1.18 ± 1.63	−0.59 ± 1.74	22.9	3.1	98.3	0.06	0.25
	spaMM	127.6 ± 99.6	−1.86 ± 1.16	0.07 ± 0.14	−1.25 ± 1.57	−0.39 ± 1.69	28.7	1.7	89.8		rho = 283.5
lay date	null	123.2 ± 2.4					17.2	16.2	34.2	0.00	0.49
	lmer	139.7 ± 67.2	−1.65 ± 0.69*	0.22 ± 0.09*	−1.50 ± 1.07	−0.50 ± 1.15	10.5	1.2	33.6	0.20	0.44
	spaMM	129.0 ± 67.9	−1.48 ± 0.69*	0.23 ± 0.08*	−1.29 ± 1.04	−0.37 ± 1.16	14.3	1.4	29.7		rho = 267.3