Table 1.
Summary of AIC analysis for all-sites (PA), Geraniaceae sites (PG) and Helianthemum sites (PH) phenomenological models, with null models (null) for comparison, showing slopes of productivity (ρ) and phenology (mean flight date, μ) on site northing, between-brood temperature (BBT), July–August rain (JAR), late summer temperature (LST), overwinter (October–March) temperature leading into the focal year k (OWT−) and overwinter temperature leading into year k+1 (OWT+). Also showing the mean (±s.d.) of the intercept for these slopes across years (based on year-to-year variation in productivity and phenology), all on the log scale, and the mean productivity and phenology (across sites and years) for each brood (ρk,1, ρk,2, μk,1 and μk,2). Standard errors of slope estimates are presented in parentheses, based on the model Hessian matrix. LL, log-likelihood; k, number of parameters; ΔAIC, change in AIC relative to lowest-AIC model (denoted ‘best’). The final selected model in each case is denoted ‘final’.
| model | ρ1 estimates | ρ2 estimates | μ1 estimates | μ2 estimates | LL | k | ΔAIC | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| mean ρk,1 | int. (mean ± SD) | slope: north | slope: BBT | slope: OWT− | mean ρk,2 | int. (mean ± s.d.) | slope: north | slope: JAR | slope: LST | slope: OWT+ | mean μk,1 | int. (mean ± s.d.) | slope: north | slope: OWT− | mean μk,2 | int. (mean ± s.d.) | slope: north | slope: BBT | ||||
| PAfinal | 2.749 | 0.908 (0.463) | 0.134 (0.008) | – | – | 0.435 | −0.920 (0.406) | −0.127 (0.008) | – | – | – | 9.239 | – | – | – | 20.520 | – | – | – | −121748.3 | 151 | 0.00 |
| PAnull | 2.476 | – | – | – | – | 0.400 | – | – | – | – | – | 8.957 | – | – | – | 20.437 | – | – | – | −142250.7 | 6 | 24372.74 |
| PGbest | 6.250 | 1.588 (0.707) | 0.019 (0.002) | −0.034 (0.006) | – | 0.249 | −1.538 (0.552) | – | 0.049 (0.005) | 0.083 (0.006) | – | 9.272 | 2.221 (0.108) | 0.017 (0.004) | 0.005 (0.001) | 19.807 | 2.352 (0.077) | −0.019 (0.004) | −0.019 (0.004) | −22876.25 | 161 | 0.00 |
| PGfinal | 6.262 | 1.590 (0.707) | 0.019 (0.002) | −0.034 (0.006) | – | 0.249 | −1.540 (0.550) | – | 0.049 (0.005) | 0.083 (0.006) | – | 9.273 | 2.222 (0.108) | 0.013 (0.004) | – | 19.808 | 2.352 (0.076) | −0.018 (0.004) | −0.017 (0.003) | −22877.36 | 160 | 0.23 |
| PGnull | 4.979 | – | – | – | – | 0.206 | – | – | – | – | – | 8.888 | – | – | – | 19.600 | – | – | – | −26752.47 | 6 | 7442.44 |
| PHfinal | 2.471 | 0.801 (0.521) | – | – | −0.241 (0.012) | 0.476 | −0.828 (0.517) | – | – | – | 0.225 (0.010) | 9.346 | 2.228 (0.117) | 0.044 (0.001) | – | 20.631 | 2.419 (0.075) | −0.055 (0.002) | – | −94444.9 | 155 | 0.00 |
| PHnull | 2.260 | – | – | – | – | 0.435 | – | – | – | – | – | 8.965 | – | – | – | 20.593 | – | – | – | −113349.2 | 6 | 37510.6 |