Bahadori Khosroshahi et al. • MODELING PRESENCE OF NUTHATCHES 
743 
distance of 300 m from each other to avoid spatial 
autocorrelation (Gibbons et al. 1996). Each 
transect was visited once during the sampling 
period by the same observer. The observer used 
the sit and wail method al each sampling point to 
record observed and/or heard nuthatches, lasting 
on average 20 min. Playback of the male call was 
used to confirm nuthatch absence after each point 
count if the species had not been detected 
(Gonzalez-Varo et al. 2008). We sampled from 
0530 until 1000 hrs and avoided windy and rainy 
weather. There were 78 presence plots and 20 
absence plots during our sampling periods 
(Fig. 1). 
Habitat Structure Sampling. —The habitat of 
nuthatches at each sampling point was described 
in terms of landscape features, forest structure, 
and vegetation profile. These variables were 
chosen because they were the most obvious and 
affected the amount of cover, shelter, nest sites, 
mode of locomotion, and prey availability. We 
postulated a priori these features were most likely 
to influence habitat choice by nuthatches. Thir¬ 
teen structural habitat variables (Table 1) were 
either directly measured within an 11.3-m radius 
(Nuret al. 1999. Dobkin and Rich 2000) centered 
at each sampling point, or calculated for each 
point from field measurements. 
Statistical Analysis. —We first verified the main 
tree species gradient of the study area with 
Correspondence Analyses (CA) for the tree 
species matrix (98 X 12). We extracted the first 
three axes of this analysis which explained 52% 
of tree species variances in the study area, and 
used them as habitat explanatory variables for 
regression analysis. We selected, using an AIC 
criterion, the combination of environmental var¬ 
iables that best explained the presence/absence of 
nuthatches using a binary logistic regression 
procedure. AA1C values of 2 or less were chosen 
tor models which best fit the data (Burnham and 
Anderson 2002, Quinn and Keough 2002 ). 
Presence-absence against significant variables 
was analyzed with binary logistic regression. The 
following linear predictor model for the predicted 
presence of the species was used: 
y= P 0 + P, X\ + P 2 A 2 + P.v *3 (Equation 1) 
where Y is the value of the linear predictor for 
nuthatches, p 0 is the constant coefficient, p, to p 3 
are variable coefficients, and X\ to X 3 are variable 
values. This equation gives the value of the linear 
TABLE 1. 
analysis. 
Habitat variables used in presence/absence 
TN > 25H 
Tree Number > 25 m in height 
TN < 25H 
Tree Number < 25 in in height 
TN > 2QD 
Tree Number 20 cm in diameter 
TN < 20D 
Tree Number < 20 cm in diameter 
SI 
Stand level > 20 m in height 
S2 
Stand level 10-20 m in height 
S3 
Stand level 0-10 m in height 
AS 
Aspect (N, S, E. W. or none) 
AL 
Altitude (m) 
FCC 
Forest Canopy Cover {%) 
CA1 
Axis 1 of the Correspondence Analysis for 
tree species ordination 
CA2 
Axis 2 of the Correspondence Analysis for 
tree species ordinaUon 
CA3 
Axis 3 of the Correspondence Analysis for 
tree species ordination 
predictor for the species and predicted probability 
of presence with known habitat variables, which 
can be calculated by Equation 2 (where Y 
indicates the result of Equation 1): 
t+expF nj’ ( E ^' ion2 > 
The result was a number between 0 and 1. The 
closer to one, the higher the probability of species 
presence. Correlation matrices were first con¬ 
structed for the predictor variable to avoid 
inclusion of highly correlated variables (Pearson’s 
r > 0.5) in the analysis (Gonzdlez-Varo et al. 
2008). We verified high correlation between 
variables TN < 20D and TN < 25H as well as 
TN < 20D and SI, S3 and SI. S3 and CA1, TN < 
20D and S2. TN > 25H and S2, TN < 25H and 
SI. and selected the first in all cases. 
Goodness-of-fit tests were performed to verify 
how well the model described the data (Alizadeh 
Shabani et al. 2009) using Pearson, Deviance, and 
Hosmer-Lemenshow procedures. Thirty new ran¬ 
dom sites were sampled in the study area to 
validate the best model. A Chi-square test was 
used to compare predicted and observed frequen¬ 
cy of nuthatch presence/absence. All analyses 
were performed with STATIST1CA 6.0 (StatSoft 
2001) and MINITAB Version 13.1 (Minitab 
2000 ). 
RESULTS 
Best Predicted Models. — Generalized linear 
models were performed of nuthatch presence- 
