Table S1
Model-selection results for the presence of long-term trends in Song Sparrow survival rates.
Survival ()
a) Adult survival
RefA + T + T2 + Winter Tempd + Rain
RefA + T + T2
Reft
RefA + T
RefA
b) Juvenile survival
Reft
RefJ + T
RefJ + T + T2
RefJ
k
AICc
69
67
95
66
65
8370.01
8379.18
8383.72
8391.67
8392.09
95
65
66
64
8383.72
8386.70
8386.91
8392.25
ΔAICc
w
Dev
R2Dev
0.00
9.17
13.71
21.66
23.08
0.989
0.010
0.001
0.000
0.000
1470.13
1483.42
1430.02
1497.97
1501.45
0.44
0.25
1.00
0.05
–
0.00
2.98
3.19
8.53
0.694
0.156
0.141
0.010
1430.02
1495.06
1493.21
1502.66
1.00
0.10
0.13
–
Notes: Linear (T) and quadratic (T2) trends in survival were added to the baseline reference
model for each age class (RefA and RefJ, respectively) and compared to Reft, the primary
reference model with full year-dependent survival (Table 2a). There was strong support for a
quadratic trend in adult survival, so we fit another model to determine whether the strong support
for an effect of winter weather on adult survival (Table 2b) was due solely to similar quadratic
trends in adult survival and winter average temperature (Fig. 1a). The final model included both
the quadratic trend in survival and the de-trended winter average temperature (subscript d).
Table S2
Model-selection results for the difference in effects of weather on adult and juvenile survival.
Survival ()
k
AICc
Age * (Winter Temp + Rain + Wintert-1 Temp + Rain2)
Age + (Winter Temp + Rain + Wintert-1 Temp + Rain2)
Reft
44
39
95
8362.59
8379.42
8383.72
ΔAICc
0.00
16.83
21.13
w
Dev
1.000
0.000
0.000
1513.92
1540.92
1430.02
Notes: Our model-selection process identified support for a direct effect winter weather
on adult survival and an indirect effect of prior winter weather on juvenile survival (Table 2).
These results suggest either that these variables had different effects on each age class, or that the
effects were similar but that there was more uncertainty in the effect on one of the age classes.
To help distinguish between these possibilities, we compared the fit of two models that
combined these effects. The first allowed effects of each variable to vary by age class, while the
second constrained the effect of each variable to be the same for each age class.
Table S3
Model-selection results for the effects of age, year, weather, and density on survival.
Survival ()
Recapture (p)
k
AICc
a) Effects of age and year
Reft = At + Jt
t
95 8383.72
At + Jt
1
64 8391.71
RefJ = At + J
t
64 8392.25
RefA = A + Jt
t
65 8393.09
At + J
mt
96 8409.66
At + J
1
33 8416.78
At + Jt
mt
127 8417.65
A + Jt
mt
97 8418.05
A + Jt
1
34 8433.04
b) Effects of weather and density on adult survival
RefA + Winter Temp + Rain
67 8365.87
2
RefA + Winter Temp + Rain
68 8367.61
RefA + Winter Temp + Rain2
68 8367.92
2
2
RefA + Winter Temp + Rain
69 8369.63
Reft
95 8383.72
2
RefA + Density
67 8384.67
RefA + Summer Temp
66 8387.77
2
RefA + Summer Temp
67 8389.66
RefA + Wintert-1 Temp + Rain
67 8390.79
2
RefA + Wintert-1 Temp + Rain
68 8392.36
RefA + Wintert-1 Temp2 + Rain
68 8392.48
RefA
65 8393.09
2
2
RefA + Wintert-1 Temp + Rain
69 8393.98
RefA + Density
66 8394.54
c) Effects of weather and density on juvenile survival
RefJ + Wintert-1 Temp + Rain2
67 8378.12
2
2
RefJ + Wintert-1 Temp + Rain
68 8380.11
Reft
95 8383.72
2
RefJ + Wintert-1 Temp + Rain
67 8386.79
RefJ + Wintert-1 Temp + Rain
66 8387.74
2
RefJ + Summer Temp
66 8389.76
2
RefJ + Density
66 8390.08
RefJ + Density
65 8391.23
RefJ
64 8392.25
2
RefJ + Winter Temp + Rain
67 8392.85
ΔAICc
R2Dev
H#
1470.11
1469.79
1470.10
1469.76
1430.02
1488.91
1494.07
1493.90
1493.90
1495.03
1494.55
1501.45
1494.12
1500.83
0.44
0.44
0.44
0.44
1.00
0.18
0.10
0.11
0.09
0.10
0.10
–
0.10
0.01
H2
H2
H2
H2
–
H4
H1
H1
H3
H3
H3
–
H3
H4
1482.36
1482.29
1430.02
1491.03
1494.04
1496.06
1496.38
1499.58
1502.66
1497.09
0.28
0.28
1.00
0.16
0.12
0.09
0.09
0.04
–
0.08
H3
H3
–
H3
H3
H1
H4
H4
–
H2
w
Dev
0.00
7.98
8.53
9.37
25.94
33.06
33.93
34.33
49.32
0.960
0.018
0.013
0.009
0.000
0.000
0.000
0.000
0.000
1430.02
1502.11
1502.65
1501.45
1453.88
1590.47
1396.89
1460.18
1604.70
0.00
1.73
2.05
3.76
17.85
18.79
21.90
23.79
24.91
26.49
26.61
27.22
28.11
28.66
0.518
0.218
0.186
0.079
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.00
1.99
5.60
8.67
9.62
11.64
11.96
13.11
14.13
14.73
0.684
0.253
0.042
0.009
0.006
0.002
0.002
0.001
0.001
0.000
RefJ + Winter Temp + Rain
RefJ + Summer Temp
RefJ + Winter Temp2 + Rain2
RefJ + Winter Temp2 + Rain
66
65
68
67
8392.92
8394.29
8394.36
8394.90
14.80
16.17
16.24
16.78
0.000
0.000
0.000
0.000
1499.22
1502.64
1496.54
1499.14
0.05
0.00
0.08
0.05
Notes: Survival model notation includes effects of juvenile (J) and adult (A) age classes,
with the subscript denoting year-dependent (t) or constant (no subscript) survival. Recapture
models include year-dependent (t), constant (1), or an effect of time-since-marking (mt). For (bc), we added linear and quadratic effects of each variable to RefA and RefJ, the baseline reference
model for each age class from (a). We present models including quadratic effects with a
shortened notation, but these models do include both the linear and quadratic terms. See Table 1
for the definition of each variable and the hypothesis (H#) it represents.
H2
H1
H2
H2
Figure S1
Sensitivity to missing values of the estimated effects of weather variables on (a) adult survival
and (b) juvenile survival. For both age classes, we initially replaced missing weather values with
zero (equivalent to the standardized mean), but we also repeated the analyses after replacing
missing weather values with -2, -1, +1, and +2 (equivalent to 1 or 2 standard deviations below or
above the mean). In each analysis, support was strongest for the effects of winter average
temperature and precipitation on adults, and the effects of prior winter average temperature and
precipitation on juveniles. Shown are the estimated effect sizes of these variables from each
analysis.