Appendix F. Analyses of the effect of mayfly density and their emergence on Gray-crowned Rosy-Finch abundance.
TABLE F1. Results of the best fitting multiple linear regression model (determined by AICc) testing the relationship between Gray-crowned Rosy-Finch abundance (average observed per 10 min count at a lake during the mayfly emergence period) and the number of mayfly nymphs sampled at the 24 lakes sampled in 2006 (adjusted R2 = 0.5004).
Source |
Sum of Squares |
df |
F |
P |
Number of mayfly larvae |
0.584 |
1 |
12.58 |
0.0046 |
Lake pair |
1.787 |
11 |
3.5 |
0.0244 |
TABLE F2. AICc rankings of multiple linear regression models testing the relationship between Gray-crowned Rosy-Finch abundance (average per 10 min count during mayfly emergence) and the number of mayflies, lake pair, and all combinations of up to three of the six habitat parameters (i.e., covariates) at the 24 lakes sampled in 2006.
Covariate |
k |
AICc |
∆AICc |
w |
no covariates |
13 |
-29.99 |
0.00 |
0.958 |
elevation |
14 |
-22.92 |
7.07 |
0.028 |
perimeter |
14 |
-18.82 |
11.17 |
0.004 |
depth |
14 |
-18.37 |
11.62 |
0.003 |
tree density |
14 |
-18.27 |
11.72 |
0.003 |
surface area |
14 |
-17.97 |
12.03 |
0.002 |
perimeter:surface area |
14 |
-17.75 |
12.24 |
0.002 |
elevation, depth |
15 |
-11.10 |
18.89 |
0.000 |
elevation, perimeter |
15 |
-7.77 |
22.22 |
0.000 |
elevation, perimeter:surface area |
15 |
-7.73 |
22.26 |
0.000 |
tree density, elevation |
15 |
-7.59 |
22.40 |
0.000 |
elevation, surface area |
15 |
-7.59 |
22.41 |
0.000 |
perimeter, depth |
15 |
-6.81 |
23.19 |
0.000 |
surface area, perimeter:surface area |
15 |
-5.99 |
24.00 |
0.000 |
perimeter, perimeter:surface area |
15 |
-5.90 |
24.09 |
0.000 |
tree density, perimeter |
15 |
-5.88 |
24.11 |
0.000 |
surface area, perimeter |
15 |
-5.34 |
24.66 |
0.000 |
surface area, depth |
15 |
-4.46 |
25.53 |
0.000 |
tree density, surface area |
15 |
-4.22 |
25.78 |
0.000 |
tree density, depth |
15 |
-3.26 |
26.73 |
0.000 |
perimeter:surface area, depth |
15 |
-3.11 |
26.88 |
0.000 |
tree density, perimeter:surface area |
15 |
-3.05 |
26.94 |
0.000 |
elevation, perimeter, depth |
16 |
5.24 |
35.23 |
0.000 |
elevation, surface area, depth |
16 |
6.77 |
36.76 |
0.000 |
tree density, elevation, depth |
16 |
7.11 |
37.10 |
0.000 |
elevation, perimeter:surface area, depth |
16 |
8.22 |
38.21 |
0.000 |
surface area, perimeter:surface area, depth |
16 |
10.36 |
40.35 |
0.000 |
elevation, surface area, perimeter:surface area |
16 |
10.42 |
40.41 |
0.000 |
elevation, perimeter, perimeter:surface area |
16 |
10.55 |
40.54 |
0.000 |
perimeter, perimeter:surface area, depth |
16 |
10.65 |
40.64 |
0.000 |
tree density, perimeter, depth |
16 |
10.89 |
40.88 |
0.000 |
elevation, surface area, perimeter |
16 |
10.93 |
40.92 |
0.000 |
surface area, perimeter, depth |
16 |
11.37 |
41.36 |
0.000 |
tree density, elevation, perimeter |
16 |
11.71 |
41.70 |
0.000 |
tree density, elevation, perimeter:surface area |
16 |
11.92 |
41.91 |
0.000 |
tree density, elevation, surface area |
16 |
12.11 |
42.10 |
0.000 |
tree density, perimeter, perimeter:surface area |
16 |
12.55 |
42.54 |
0.000 |
tree density, surface area, perimeter:surface area |
16 |
12.66 |
42.66 |
0.000 |
tree density, surface area, perimeter |
16 |
12.84 |
42.83 |
0.000 |
surface area, perimeter, perimeter:surface area |
16 |
13.66 |
43.65 |
0.000 |
tree density, surface area, depth |
16 |
13.85 |
43.84 |
0.000 |
tree density, perimeter:surface area, depth |
16 |
16.11 |
46.11 |
0.000 |
Note: Models ranked in order of minimum AICc value; w = Akaike weight |
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TABLE F3. AICc rankings of general linear mixed effects models used to analyze repeated measures data (n = 92) from all years of the study across 26 lakes. Gray-crowned Rosy-Finch abundance (average per 10 min count) predicted as a function of mayfly emergence period, fish presence, year, their interactions, and all combinations of up to three of the six habitat parameters (i.e., covariates).
Covariate |
k |
AICc |
Δ AICc |
w |
tree density, perimeter:surface area |
20 |
403.59 |
0.00 |
0.899 |
tree density |
19 |
409.16 |
5.56 |
0.056 |
tree density, perimeter:surface area, depth |
21 |
411.00 |
7.41 |
0.022 |
perimeter:surface area |
19 |
412.26 |
8.66 |
0.012 |
tree density, elevation, perimeter:surface area |
21 |
413.40 |
9.81 |
0.007 |
tree density, depth |
20 |
416.53 |
12.94 |
0.001 |
tree density, perimeter, perimeter:surface area |
21 |
416.90 |
13.31 |
0.001 |
no covariates |
18 |
417.97 |
14.38 |
0.001 |
tree density, elevation |
20 |
418.53 |
14.94 |
0.001 |
perimeter:surface area, depth |
20 |
419.43 |
15.84 |
0.000 |
elevation, perimeter:surface area |
20 |
419.53 |
15.94 |
0.000 |
tree density, perimeter |
20 |
424.73 |
21.14 |
0.000 |
elevation |
19 |
424.76 |
21.16 |
0.000 |
depth |
19 |
425.06 |
21.46 |
0.000 |
perimeter, perimeter:surface area |
20 |
425.63 |
22.04 |
0.000 |
tree density, elevation, depth |
21 |
425.90 |
22.31 |
0.000 |
tree density, surface area, perimeter:surface area |
21 |
426.70 |
23.11 |
0.000 |
elevation, perimeter:surface area, depth |
21 |
426.70 |
23.11 |
0.000 |
elevation, depth |
20 |
431.83 |
28.24 |
0.000 |
tree density, perimeter, depth |
21 |
432.10 |
28.51 |
0.000 |
perimeter, perimeter:surface area, depth |
21 |
432.90 |
29.31 |
0.000 |
tree density, surface area |
20 |
433.33 |
29.74 |
0.000 |
perimeter |
19 |
433.36 |
29.76 |
0.000 |
elevation, perimeter, perimeter:surface area |
21 |
434.20 |
30.61 |
0.000 |
tree density, elevation, perimeter |
21 |
434.40 |
30.81 |
0.000 |
surface area, perimeter:surface area |
20 |
435.33 |
31.74 |
0.000 |
elevation, perimeter |
20 |
440.53 |
36.94 |
0.000 |
perimeter, depth |
20 |
440.53 |
36.94 |
0.000 |
tree density, surface area, depth |
21 |
440.80 |
37.21 |
0.000 |
surface area |
19 |
441.96 |
38.36 |
0.000 |
elevation, surface area, perimeter:surface area |
21 |
442.10 |
38.51 |
0.000 |
tree density, elevation, surface area |
21 |
442.60 |
39.01 |
0.000 |
surface area, perimeter:surface area, depth |
21 |
442.60 |
39.01 |
0.000 |
tree density, surface area, perimeter |
21 |
445.60 |
42.01 |
0.000 |
surface area, perimeter, perimeter:surface area |
21 |
447.10 |
43.51 |
0.000 |
elevation, perimeter, depth |
21 |
447.70 |
44.11 |
0.000 |
elevation, surface area |
20 |
448.53 |
44.94 |
0.000 |
surface area, depth |
20 |
449.23 |
45.64 |
0.000 |
surface area, perimeter |
20 |
454.03 |
50.44 |
0.000 |
elevation, surface area, depth |
21 |
455.80 |
52.21 |
0.000 |
surface area, perimeter, depth |
21 |
461.40 |
57.81 |
0.000 |
elevation, surface area, perimeter |
21 |
461.50 |
57.91 |
0.000 |
Note: Models ranked in order of minimum AICc value; w = Akaike weight |
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