3.2 Statistical Analysis
3.2.1 Habitat structure
Kruskal-Wallis test was used to compare habitat variables among four habitats (ZAR
1999). When the among-habitat difference of a variable was found (significance level 0.05), Mann-Whitney U test was further applied for pairwise comparison.
A habitat could be viewed as a complex of all the interlinked variables, which were individually measured (POGUE & SCHNELL 1994, ROTENBERRY & WIENS 1998, MCGARIGAL et al. 2000). Thus the principal component analysis (PCA) was applied to the correlation matrix of 22 habitat variables (Table 3.1), for summarising the variations of these variables. The major trends of variation were represented in the first few principal components. These principal components could be interpreted by their component loadings. Each of the 20 plots was then projected onto the main components according to its component score. Such a graphic could represent the ecological relationship among habitats and indicate the important dimensions of available habitat space (ROTENBERRY & WIENS 1998).
3.2.2 Cavity abundance
To compare the density of different cavity types and the cavity density in different habitats, Kruskal-Wallis test (for number of groups > 2) and Mann-Whitney U test (for number of groups = 2) were applied.
The relationship between cavity abundance and habitat variables was checked with correlation analysis (SANDSTRÖM 1992). Pearson correlation coefficients between the density of each cavity type and habitat variables were calculated. Bonferroni
probability was used to test the null hypothesis of zero correlation.
Cavity density was also correlated with major principal components from the PCA of habitat structure. Cavity density of each plot was projected onto the main
components, for representing the variation of cavity abundance across major environmental gradients.
3.2.3 Cavity occurrence and tree characters
While the previous section was to exam cavity occurrence at habitat level, here the cavity occurrence according to five tree-level variables: tree species, tree DBH, tree condition, the presence of fire scars and the presence of fungi conks was examined.
The distribution of cavities across each tree variable was compared to the distribution of all sampled stems across the same variable with chi-square test (ZAR 1999). If significant difference was found (significance level 0.05) and the variable had more than two classes, further comparisons were conducted with one class versus other classes pooled, for identifying whether the class was disproportionately rich or poor in cavities. Two classes were compared pairwise when the difference of cavity
occurrence between specified classes was interested. Comparisons were also conducted between excavated cavities and non-excavated cavities. In all above comparisons, Yates corrected chi-square test was applied when a 2 × 2 table was encountered.
Cavity holding rate was defined as the percentage of stems with cavities, which was calculated by the number of cavity-holding stems divided by the number of total stems. This was different from the number of cavities divided by the number of stems, since one stem might hold more than one cavity.
Tree DBH was grouped into five classes in the analysis, i.e. < 15 cm, 15 – 30 cm, 30 – 45 cm, 45 – 60 cm and > 60 cm. Tree condition was treated as six classes (Fig. 3.1) in the overall analysis. When examining the interactions between variables, tree
condition was further pooled into three classes: living tree (classes 1 and 2 in Fig.
3.1), dead tree with intact top (class 3 and 4) and dead tree with broken top (class 5 and 6), to avoid too small sample size in each class.
After considering the five tree variables separately, stepwise logistic regression was applied to model the probability of cavity occurrence in a tree (JOBSON 1992).
Whether the tree was deciduous (binary variable), tree DBH (in 5 ranks), tree condition (in 3 ranks), the presence of fire scars (binary variable), the presence of fungi conks (binary variable) and the habitat where the tree stood (as 3 dummy
variables), were used as independent variables. Backward stepwise selection was used to select the variables (significance level 0.05).
3.2.4 Composition of CNB community
Density of CNBs was compared between habitats with Mann-Whitney U test. To compare the species composition in different habitats, Sorensen’s similarity coefficient were applied (KREBS 1989):
b a Ss c
where Ss = Sorensen’s similarity coefficient a = number of species in habitat A b = number of species in habitat B
c = number of species in habitat A and B (joint occurrences)
Correlation analysis was than applied between CNB density and habitat variables, habitat principal components and cavity density. CNB density was then projected onto the main components to investigate the variation of CNB density across major environmental gradients.
The species abundance distribution of the CNB community was compared with lognormal and logseries model with chi-square goodness of fit test (MAGURRAN
1988). Comparisons of species abundance pattern with other studies were also conducted, including the CNB communities in natural forests, in managed woodlands and the CNBs nesting in nest boxes.
3.2.5 Utilisation of trees and cavities by CNBs
In this section, CNBs were considered as a whole instead of individual species. The main purpose was to determine to which extent the trees and cavities were utilised by CNBs, and whether the utilisation was related to tree variables (tree species, tree DBH, tree condition, presence of fire scars and fungi conks) and cavity type.
Data from different habitats were pooled. Only the nests located in plots were
included in the analysis, so that nest data from each habitat had the same contribution
and could be compared with the pooled tree measurements. The difference between years was firstly examined. Since the utilisation pattern of each variable did not differ between years, data for both years were pooled. Utilisation patterns of PCNs and SCNs were also compared, and they were treated separately if there was a significant difference.
For each variable, the distribution of nests was compared with the distribution of all sampled stems. When significant difference arose for a variable of more than two classes, comparison of one class versus other classes pooled was conducted to find out whether the class was utilised overproportionally or underproportionally. The
distribution of SCN nests was further compared with the distribution of cavities across the same variable to test whether cavities were selected according to the variable concerned. Chi-square test was used in all above comparisons, and Yates correction was applied when a 2 × 2 table was encountered.
3.2.6 Nest site selection of individual species
Both nests located inside and outside the plots were used in this part of analysis. Bird species of sample size less than 10 were excluded. Thus only 9 species were studied, including 3 PCNs (D. major, D. minor and P. montanus) and 6 SCNs (the Daurian Redstart Phoenicurus auroreus, the Red-throated Flycatcher Ficedula albicilla, the Coal Tit Parus ater, the Great Tit P. major, the Nuthatch Sitta europaea and the Treecreeper Certhia familiaris).
For each tree and cavity variable, comparison were conducted between bird species to reveal their relative preference. For the variables tree species, tree DBH, tree
condition and cavity type, of which the availability were known, the utilisation pattern of each bird species was also contrasted with the availability to investigate the real selection. However, for variables such as tree species, which differed greatly among habitats, comparison could not be made directly, since this would be largely
influenced by the number of nests found in each habitat.
For continuous variables, Mann-Whitney U test was applied to compare between species, and F test was applied to compare the variance, which indicated the niche
breadth. For categorical variables, chi-square test was used. Niche breadth was measured by Levins’ index (KREBS 1989):
pi = proportion of individuals found in or using resource state i n = total number of resource states
The range of Levins’ B is between 1 and n. Minimum occurs when all individuals use only one resource state, and maximum occurs when the same numbers of individuals are found in each resource state.
Niche overlap was indicated by the Renkonen index of percentage similarity (KREBS
ABRAMS (1980) recommended the Renkonen index of percentage similarity as the best measure of niche overlap. One strength of this index is that it is not sensitive to how one divides up the resource states, since human observers may recognise resource categories different from that animals or plants do.
After checking each variable separately, a cluster analysis was applied to summarise the overall similarity of nest sites among species (JOBSON 1992). Tree species (as 5 dummy variables), tree DBH, tree condition (in 3 ranks), cavity type (as 3 dummy variables), cavity height above ground, substrate diameter, substrate condition (binary variable), cavity opening length and cavity opening width were used to calculate the nest site similarity between species.
A discriminant function analysis was then performed based on these 15 variables (JOBSON 1992). Backward selection was used to select the variables which maximised separation among bird species. The reclassification matrix from discriminant functions could imply the extent of niche overlap between species.
3.2.7 Sequential cavity use
This part of analysis was based on all the nests found in 2002. Beside overall reuse rate, proportion of reuse by the same species (constancy) and reuse by different species (usability) were considered (SEDGWICK 1997). The reuse pattern was compared at both guild level (between PCN, WPCN and SCN) and at species level with chi-square test.
All tree and cavity variables of reused cavities were compared with that of cavities which were not reused. Continuous variables were compared with Mann-Whitney U test, and categorical variables with chi-square test. Logistic regression with backward stepwise selection was than applied to determine which variables could best predict the reuse of cavities.
3.2.8 Nest web analysis
While the previous section was a time sequence observation of interspecific links from cavity suppliers’ side, the nest web analysis was a snap shot approach from cavity demanders’ view. All the nests found in both years were used in the analysis.
Actors in the nest web included all CNB species as well as trees and cavities which were utilised by CNBs (MARTIN & EADIE 1999, MARTIN et al. 2004). Tree species formed the fundamental level in the nest web. PCNs and non-excavated cavities constituted the second level. A PCN species was linked to a tree species if it
excavated in the tree. The strength of the linkage was indicated by the proportion of nests of this PCN species excavated in this tree species. Non-excavated cavities were also linked to tree species depended on the proportion of cavities located in each tree species. SCNs represented the third level in the nest web. A SCN species was linked to a PCN species if it utilised the cavity created by the PCN, or linked to
non-excavated cavities if it nested in them. The strength of linkage was also decided by
the percentage of nest use. However, when a SCN was found nesting in a middle-sized woodpecker hole, in most of the cases the excavator species could not be confirmed. Thus middle-sized woodpeckers were grouped when linked with SCNs.
WPCNs stood at an intermediate level between PCNs and SCNs. They might be linked to a tree species when they excavated in the tree by their own, or be linked to a PCN species or to non-excavated cavities, when they nested in the cavity created by the PCN in non-excavated cavities, respectively.
The nest web was than applied to test the roles of woodpeckers and some tree species in the CNB community.