3.3.2.1
Is floristic variation of regrowth forest associated with
DMFE?
To assist in the visualisation of floristic association with DMFE a non-metric multiple dimensional scaling ordination was undertaken using PCOrd 6.08 (McCune and Mefford 2011). For this purpose the data for three distance groups were averaged such that each site was represented by a mature forest plot (-15 and - 35 m DMFE), a close regrowth plot (15 and 35 m DMFE) and a far regrowth plot (120 and 200 m DMFE). The ordination was based on the square root transformed data and a Bray-Curtis resemblance matrix. Results of this analysis are reported in the supplementary results (Appendix 3.2.1).
Three response variables were calculated for testing association of floristic composition with DMFE (Table 3–1).
Table 3-1. Floristic response variables calculated for each plot, together with their method of calculation and the test used to measure their association with distance from the mature forest edge (DMFE).
Response variables
Calculation method Statistical Test
Assemblage Bray-Curtis resemblance matrix of square-root transformed regrowth
plot data PERMANOVA using Primer 6.0
Total species richness
The total number of vascular plant species within the plot excluding ephemerally apparent species such as orchids
Linear Mixed Effect models using gamlss 4.3-0 specifying a normal family distribution
H' Shannon's diversity index calculated in PCOrd 6.08 from species
cover data excluding ephemerally apparent species using the formula
where pi = importance probability in column i and matrix elements are relativized by row totals (Greig-Smith 1983, p. 233)
Mature forest influences some aspects of the regrowth site environment through its capacity to moderate micro-climates by shading and buffering regrowth forest from wind and as a source of the relatively cool moist air in summer. However some aspects of environmental variation will not be caused by mature forest influence and could either obscure or confound floristic responses to mature forest influence. For this reason statistical methods that enabled environmental covariates to be accounted
Chapter 3 – Distance from the mature forest edge for were chosen so that the importance of environmental variation along the gradient in DMFE could be evaluated in more detail.
Distance based linear modelling (DistLM) with the step-wise option and R-squaredas the measure of best fit (Anderson et al. 2008) was used to select environmental predictors most associated with regrowth forest assemblage variation. The nested structure in the sampling design was not accounted for in the DistLM procedure but was accounted for. The co-linearity of selected predictor variables were tested using Spearman's correlation. DistLM was undertaken in Primer 6.0 (Clarke and Gorley 2006). Scatter plots and correlation matrices for the selected environmental variables are provided in the supplementary results (Appendix 3.2.1.2: Table 3–B & Figure 3– B). The final group of selected continuous environmental predictors provided the predictors from which all modelling was developed. In addition four other predictors were used – the relative cover of MFI species within the adjacent mature forest plots (MFIspp cover in MF plot); the environmental dissimilarity between the plot and the average environment of its two nearest mature forest plots (Env.Dis MF plot); the factor coppice (presence in the plot of rainforest trees recovering vegetatively) and the factor fire frequency (two levels: one or more than one disturbance event since 1890). Env.Dis MF plot was generated by importing environmental data for the variables most associated with the full floristic data set and using Principal Component
Analysis to reduce these into three dimensions. The three principal components were then imported and a relative Euclidean distance matrix created to determine the environmental distance between each pair of plots. The dissimilarity of each regrowth plot its nearest two mature forest plots was then averaged to provide the average environmental dissimilarity to adjacent mature forest.
PERMANOVA was used to determine if the a priori groups 'DMFE class' and 'age class' of the silvicultural regrowth explained variation in the Bray-Curtis resemblance matrix. The highest ranking environmental variables were included as covariates in the model together with the fixed effect of the factor age class, the random effects of site (nested in age) and transect (nested in site), after which the fixed effects of distance and the interaction between age and distance were tested. The model is a random block design since only one sample was taken at each distance from the
Chapter 3 – Distance from the mature forest edge significance level of 0.05 were iteratively excluded in order of highest to lowest
P-value. The final model included only parameters with a P-value of < 0.05. Sums of squares were calculated using the TYPE I (sequential) method recommended for unbalanced data sets that result from the incorporation of covariates but the results were compared with those using the TYPE III (partial) method to ensure that the results were stable under both methods. A reduced model using 9999 permutations of residuals was adopted for testing all models. The PERMANOVA assumption of equal dispersion among the fixed factor groups were tested using permutational analysis of multivariate dispersions (Anderson et al. 2008). The reported P-values for
PERMANOVA and all other statistical modelling are rounded to four or fewer
decimal places, hence a reported value of P = 0.0000 actually represents P < 0.00005. Linear mixed effect models were iteratively developed using gamlss 4.3-0 (Rigby and Stasinopoulos 2005; Stasinopoulos and Rigby 2007; Stasinopoulos et al. 2014) within the R software platform (R Core Team 2014) and took into account the nested structure of the data by including sites as a random factor. For a detailed account of the model selection process see Supplementary methods in Appendix 3.1 and for the model development steps for each response variables see Appendix 3.2.2. The gamlss package was chosen because it accommodates a wide range of distribution families including beta. The procedure involves internal transformation of data and provides summary outputs in the transformed scale. The function 're ( )' was used to call on the lme function from the R package nlme to enable the specification of random effects (Pinheiro et al. 2014). The software uses a maximum (penalised) likelihood
estimation method using the RS algorithm. This is a generalization of the algorithm used by Rigby and Stasinopoulos (1996a, 1996b), which does not use the expected values of the cross derivatives. The theoretical justification for the method is described by Breslow and Clayton (1993). The default link functions were used for the distribution families specified. In the case of the beta distribution (variables confined to the interval between 0 and 1) the logit link function was the default for both mu and sigma. For beta distributed response data, sigma, more usually referred to as precision coefficient or phi, is used to model non-uniform variance in the response associated with predictor variables.
Chapter 3 – Distance from the mature forest edge