Appendix B. A description of the univariate and multivariate methods of analysis.
For univariate analyses, variance components were estimated using one-way ANOVAs with time as a factor, fitted separately to each response variable in each patch. This method produced estimates of temporal variance that were independent of sampling error (Searle et al. 1992). Negative values were considered as underestimates of null variances and were set to zero.
Although replicate quadrats were placed haphazardly in a patch at each time of sampling and the total area sampled in each occasion was only 11.5% that of an entire patch, repeated sampling might have given rise to non-independent data. This was assessed by fitting a full model with time as a factor to the original data and examining the patterns of correlation through time of the residuals (Neter et al. 1996). Correlation was low (mostly in the range of 0.05 – 0.18) for most of the response variables, but larger values were occasionally present. Data were not analyzed statistically when temporal correlation was large and significant.
ANOVA was also used to compare multivariate responses to manipulated factors. Multivariate pseudo-variance components (hereafter referred to as multivariate variance) for factor Time were calculated on the basis of the Bray-Curtis dissimilarity (Bray and Curtis 1957) for each patch separately using the program PERMANOVA (courtesy of M. J. Anderson) (Anderson and Millar 2004). Pseudo-variance components were then analyzed with a three-way ANOVA as in the univariate case. The whole analysis was repeated on presenceabsence data to examine effects of treatments on compositional changes of assemblages.
Anderson, M. J., and R. B. Millar. 2004. Spatial variation and effects of habitat on temperate reef fish assemblages in northeastern New Zealand. Journal of Experimental Marine Biology and Ecology 305:191221.
Bray, J. R., and J. T. Curtis. 1957. An ordination of the upland forest communities of Southern Wisconsin. Ecological Monographs 27:325349.
Searle, S. R., G. Casella, and C. E. McCulloch. 1992. Variance components. John Wiley and Sons, New York, New York, USA.
Neter, J., M. H. Kutner, C. J. Nachtsheim, and W. Wasserman. 1996. Applied linear statistical models. McGraw-Hill, Boston, Massachusetts, USA.