Statistical Analysis

2.3.4.1 Environmental variables  

To check for confounding differences in the underlying environmental factors at

lyrebird and control sites and microhabitats, a Principal Components Analysis (PCA) of normalised environmental variables recorded from transects in each microhabitat was performed using PRIMER-E 6 software (Clarke and Gorley 2006). Leaf litter cover and exposed mineral soil cover were excluded from analysis, as they were likely to be directly influenced by lyrebird activity. The remaining variables were: canopy cover, understorey cover, ground vegetation cover, nonvascular plants & bryophytes cover, rock cover, leaf litter depth and stand density. To establish whether lyrebird disturbance varied across microhabitat types at the time of the survey the mean level of lyrebird disturbance (extent, age and intensity) in the sample plots within the three microhabitat types at lyrebird sites was also calculated. Mean cover of leaf litter and exposed mineral soil in sample plots within each microhabitat type at lyrebird sites were also calculated to compare the relative availability of each substrate type.

2.3.4.2 Macroinvertebrate analysis  

Subsamples collected by the two researchers within each sample plot were averaged to estimate the mean abundance of individuals, taxonomic richness, Pielou’s evenness (J’) in each plot. The latter metric provides a measure of the relative distribution of

individuals among the taxa present in a community (Pielou 1966, Magurran 1988). Pielou’s evenness uses the ratio of observed Shannon diversity (H’) to maximum

diversity (Hmax) that could occur if all species were equally abundant. An evenness

value of 1 indicates that all species are equally abundant.

2.3.4.3 Univariate analyses: macroinvertebrate assemblage structure  

The influence of lyrebird presence/absence and of microhabitat on macroinvertebrate community structure was investigated using generalised linear mixed models (GLMMs) to account for the presence of random factors and non-normal data, without the need to

transform the data prior to analysis (Faraway 2005, Zuur et al. 2009). The response variables for the models were mean macroinvertebrate richness, taxonomic abundance and evenness. Models with a Poisson error distribution and log-link function were fitted for abundance and richness counts data, while a Gaussian error distribution and identity- link function were most appropriate for evenness. Lyrebird status (two levels: presence and absence of lyrebirds) and microhabitat (three levels: riparian, slope and ridge) were crossed fixed factors, with sites and researcher identity treated as random effects. Poisson models were checked for over dispersion following Zuur et al. (2009) and Wetherill and Brown (1991), and the standard diagnostic plots of residuals were inspected to assess conformation to assumptions. Fixed effects were tested using

likelihood ratio tests (2_{) on models fitted via maximum likelihood; once fixed effects}

were simplified, final models were fitted using restricted estimate maximum likelihood (REML) following Zuur et al. (2009). GLMMs were also used to test whether there were differences in the mean abundance of leaf litter dwellers and generalist/soil dwellers. Poisson distributions and log-link functions were fitted to mean abundance data for these two substrate habitat affinity types and the models used the same design as the assemblage structure GLMMs described above. All univariate analyses were conducted using the function ‘glmer’ in the ‘lme4’ library (Bates et al. 2011) for the R software package version R 2.15.2 (R Development Core Team 2012).

2.3.4.4 Multivariate analyses: macroinvertebrate assemblage composition   Singletons were excluded from analysis because they do not contribute to general patterns across sites (McCune and Grace 2002). Abundance data was square-root transformed to reduce the influence of numerically dominant taxa (Clarke 1993). All multivariate statistical analyses were conducted using PRIMER-E 6 (Clarke and Gorley 2006) with the PERMANOVA + add-on package (Anderson et al. 2008). Permutational multivariate analysis of variance (PERMANOVA) was used based on the same mixed model design as the univariate analyses to test for significant differences in overall macroinvertebrate assemblage composition between lyrebird and control sites.

However, high taxonomic richness and the large number of rare taxa recorded at single sites could potentially obscure any signal of superb lyrebird influence on assemblage composition. Therefore, taxa were also pooled together as leaf litter dwellers or generalist/soil dwellers and a second PERMANOVA test was conducted.

Each PERMANOVA was based on a Bray-Curtis similarity matrix of square-root transformed abundance data (total abundance for the first PERMANOVA and abundance of leaf litter and generalist/soil dwellers in the second) and used 9999 unrestricted permutations under a reduced model (Anderson et al. 2008). As the number of unique permutations in this design was relatively small, I used the Monte Carlo asymptotic P-value for the test statistic (Anderson and Robinson 2003). PERMDISP (Anderson 2004), a distance based test, was then used to test the homogeneity of multivariate dispersion, or scatter, between samples from each lyrebird status group and their group centroids (Anderson et al. 2006). PERMDISP makes it possible to

distinguish the relative influence of the centroids versus dispersion of samples around their centroid in driving any differences between lyrebird and control site assemblages. A nonmetric multidimensional scaling (nMDS) ordination based on the Bray-Curtis similarity matrix was used to visually inspect the pattern of macroinvertebrate

composition. The individual taxa that contributed the most to the overall dissimilarity between assemblages at lyrebird and control sites were identified using the similarity percentage procedure (SIMPER) (Clarke and Gorley 2006).

The Distance-based Linear Modelling (DISTLM) routine was used to determine which environmental variables best explained the variation in the macroinvertebrate data (Legendre and Anderson 1999, McArdle and Anderson 2001). DISTLM allows for significance testing of explanatory environmental variables for a multivariate response variable in the form of a resemblance matrix, in this case the same Bray-Curtis

similarity matrix of macroinvertebrate abundance data, generated as above (Anderson et al. 2004, Anderson et al. 2008). Prior to conducting the DISTLM, a draftsman plot of environmental variables was examined to check whether any environmental variables required transformation. The presence of highly correlated variables (r>0.8, Clark and Gorley 2006) was also checked, and depending on their ecological meaning, all but one of the correlated variables was removed in order to avoid biases associated with multi- collinearity (Clarke and Gorley 2006). As expected, several variables related to lyrebird disturbance were highly correlated: plot leaf litter, plot exposed mineral soil, transect leaf litter cover, transect leaf litter depth, lyrebird disturbance extent, lyrebird

disturbance age and lyrebird disturbance intensity. Therefore, all except for plot leaf litter cover were omitted, which serves as a proxy for the other variables in the analysis. The DISTLM was then fitted using the BEST selection procedure, and the Akaike

Information Criterion (AIC) was used as a measure of goodness-of-fit to identify the most parsimonious explanatory model (the smaller the AIC value, the better the fit). DISTLM analysis was then repeated using only the subset of variables included in the most parsimonious model (Anderson et al. 2008).

To examine the relationship between macroinvertebrate assemblages and environmental factors, both constrained and unconstrained ordinations of macroinvertebrate

assemblages were conducted. A distance-based redundancy analysis (dbRDA) was used to specify the relationship between macroinvertebrate communities and the optimal model predictors, based on the multivariate regression model generated by the DISTLM (Legendre and Anderson 1999, McArdle and Anderson 2001). In addition, the

unconstrained ordination technique, nMDS, was used to validate the pattern displayed in the dbRDA analysis because the nMDS technique is based on the assumption that the relationship between the dependent (macroinvertebrate) and independent

(environmental) variables is linear. The spatial arrangement of samples in the nMDS would therefore be similar to that shown in the dbRDA if the relationship is indeed linear.