744 
THE WILSON JOURNAL OF ORNITHOLOGY • VoL 123. No. 4. December 2011 
TABLE 2. Generalized linear models of the presence/absence of Eurasian Nuthatch against five environmental 
variables related to altitude, climate, geomorphology, and vegetation. Models were ranked in each case by AIC from best to 
worst fitting model, and only models with A AIC < 2 are listed. We included the standardized coefficients, allowing 
assessment of relative importance for each variable included in each model. 
Model TN a 25H TN < 20D 
1 0.858** -0.602* * 
2 0.72** -0.69* 
3 0.731** -0.616** 
4 0.661** -0.601* 
** P < 0.005. 
* P < 0.05. 
ns. P > 0.05. 
Predictors In model 
S3 
AL 
CA3 
AAIC 
IP 
P kvd o( iiwfcl 
0 
0.61 
0.000 
-0.051* 
1.25 
0.54 
0.000 
0.001 ns 
1.54 
0.43 
0.001 
0.21 ns 
1.91 
0.50 
0.001 
absence against five significant (P < 0.05) 
variables (TN > 25H, TN < 20D, S3, AL, 
CA3). The other variables (TN < 20D, AS. FCC, 
CA2) did not have a significant relationship with 
presence-absence of nuthatches (P > 0.05). The 
best predicted model (AIC 29.3, P < 0.001) 
included two variables (Table 2), including abun¬ 
dance of tall trees (TN > 25H = positive effects) 
and abundance of voung trees (TN < 7()D = 
negative effects). TN > 25H was a “highly 
significant predictor and had a positive influence 
on the dependent variable in all four equivalent 
models. In contrast. TN < 20D influenced the 
dependent variable. The four best selected models 
were identified among all models using AIC (i.c 
A ^ C < 2) (Tab,e 2) - We tested the effect of 
adding the variable, understory of forest (stand 
evel 0-10 m in height TS3] = negative effects) to 
the second model, forest altitude (AL = positive 
effects) to the third model, and third axis of CA 
or tree species (CA3 = positive effects) to the 
fourth model. These changes did not have any 
significant effect (Z = -0.78, P = 0.055; Z = 
0.9, P = 0.08; Z = 0.3, P = 0.08, respectively). 
The third axes was allocated to Fagus orientate 
(51%). Carpinus betulus (16%), and Acer insign 
(15%) in the CA analysis. 
The log-likelihood of the models was calculat¬ 
ed using G'-statistie. This tests whether ail 
coefficients associated with the model variable 
are equal to zero versus not being equal to zero 
This value is especially useful when the /’-valueis 
>0.05. The log-likelihood of the four modd' 
(range - -9.043 to -9.379), G (range = 80-81). 
and P-valuc (all P < 0.01) were similar. Bus 
there is sufficient evidence that at least one of the 
coefficients is different from zero, given the 
accepted y. level is <0.05. 
Goodness-of-fit Tests. —We performed Pearson. 
Deviance, and Hosmer-Lemenshow tests to verify 
how well the models describe the data. Our result 1 ' 
did not have significant P-values from the 
Hosmer-Lemenshow test for all four selected 
models (Table 3), indicating our models describe 
TABLE 3. 
Goodness-of-fli tests of the 
presence/absence records to 
verify how well the nu 
jdels describe the data. 
Method 
X 1 
df 
Model 1 
Model 2 
Model 3 
Model 4 
Pearson 
Deviance 
Hostner-Lemeshow 
Pearson 
Deviance 
Hosmer-Lemeshow 
Pearson 
Deviance 
Hosmer-Lemeshow 
Pearson 
Deviance 
Hosmer-Lemeshow 
26.36 
18.76 
1.21 
24.69 
18.08 
0.94 
24.22 
188.4 
1.4 
28.8 
18.7 
85 
85 
8 
85 
85 
8 
93 
93 
8 
92 
92 
1 
1 
0.997 
I 
1 
0.999 
1 
1 
0.994 
1 
1 
8 n.996 
