Construcción del Modelo Relación Cuantitativa Estructura Actividad para la Predicción de

Hill Numbers (Hill, 1973) provide a framework unifying species richness, Shannon’s entropy and Simpson’s index into a diversity measure which is based on effective numbers, and sensitive to

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abundance (Hill 1973). Comparisons of species richness, evenness and dominance are now possible, as diversity is expressed as the number of effective species present, rather than an index (Hill 1973). Hill defines a sensitivity parameter “q” which takes into account the difference between rarer and more common species; as a range of different q values are produced (e.g. q = 0 is equivalent to species richness, q = 1 to Shannon’s entropy and q = 2 to Simpson’s index) it is possible to plot these values as a diversity profile (Leinster and Cobbold, 2012). This allows visual assessment of ecosystem or community diversity across a range of values. In recognition of the fact that species are not always equally different, Leinster and Cobbold 2012 extended these measures to take into account species similarity as distance matrices. Therefore, it is now possible to assess changes in diversity across a range of measures graphically, as effective numbers which are comparable, and constrained by species similarity (Leinster and Cobbold). This approach has been implemented in the “R”

environment, using the package “rDiversity”.

rDiversity requires the construction of a population abundance matrix, a normalised similarity matrix and a range of user determined sensitivity parameters (“q”). I used the “gowdis” function in FD to calculate the functional similarity matrices, which can handle a variety of different data types including categorical traits and missing data. A similarity matrix was constructed for each functional trait separately, then one including all functional traits. Therefore, species which share several functional traits are more similar than species which have only a few functional traits in common (see appendix 4.1, tables 3A - C for examples of unconstrained (naïve), taxonomic and functional similarity matrices).

Since there is insufficient phylogenetic resolution for moths, I constructed taxonomic similarity matrices by determining taxonomic level information to genus for each species, and used the taxa2dist function in the R package “Vegan” to create a taxonomic similarity matrix. Species which are in the same genus or family will be more similar than species in different families (See appendix 4.1, 3B for example of taxonomic similarity matrix). Henceforth, situations where all species are assumed to be equally different will be referred to as “naïve” compared to “taxonomic” (taxonomic similarity incorporated) or “functional” (similarity due to functional trait values included) diversity. All matrices were normalised before further analysis in rDiversity.

4.3.7 Statistical analysis

Study 1: Similar to Chapter 3, I assessed the impact of stand composition, felling and broadleaf cover in the surrounding landscape on moth naïve and constrained diversity, functional redundancy and the extent to which this was driven by the presence of rare species. Many of the local and landscape variables were collinear so I used Principle Components Analysis (PCA) to remove collinearity and reduce the number of predictors, as in chapter 3. Three separate PCAs were conducted for local,

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felling and broadleaf characteristics (See Appendix 4.1, table 4 for an explanation of the variables included in the PC analysis). For each PCA I retained those axes which explained more variation than random using the “broken stick” approach (Jackson, 1993). For all PCAs only the first axis explained more variation than expected by chance (Jackson, 1993) and was used in subsequent modelling. The local PC1, which explained 61% of the variation in stand composition loosely described different stand types, explaining the change from stands with low canopy cover and high understorey vegetation height to stands with low vegetation cover and high canopy cover, (Appendix 4.1, Figure 1A). For felling characteristics (Felling PC), only the first axis explained more variation (63%) than by chance; stands with low values of Felling PC1 were closer to patches of clear fell and surrounded by greater areas of felling in a 1km radius and those loading high on Felling PC1 were further from felling with less overall felling in a 1km radius (Appendix 4.1, Figure 1C). For characteristics relating to broadleaf tree cover in the landscape (Broadleaf PC), only the first axis explained more variation (67%) than by chance; stands loading high on Broadleaf PC1 were further from smaller patches of broadleaf tree cover, with fewer trees in the surrounding landscape whereas sites loading low on Broadleaf PC1 were closer to larger broadleaf patches, with more overall broadleaf forest cover in the surrounding habitat (Appendix 4.1, Figure 1B).

Using an information theoretic approach, I assessed the influence of stand (Local PC1) and landscape (Felling PC1, Broadleaf PC1) variables on measures of macro moth naïve, taxonomically and

functionally constrained richness, diversity and dominance (see appendix 4.1, table 3 for description of all measures), using the value of each metric per stand as the unit of replication. I used linear models with a Gaussian error structure and an interaction between latitude and longitude to account for spatial autocorrelation. Models were validated by visual assessment of the residuals (Crawley, 2007). Continuous variables were standardised and centred around a mean of zero and a standard deviation of 1 to allow comparisons of estimates, and model fit was assessed by comparing the change in AIC, retaining the best model (change in AIC greater than 2). The conditional R2

(variance explained by both the fixed and the random effects (Nakagawa and Schielzeth, 2013) was used to assess the amount of variation explained by each model. For each response measure, since there was no clear “top” model I averaged the coefficients across the top models in the set which accounted for a change in AIC of less than 2, using full averaged models to reduce the bias from explanatory factors which do not appear in every model (Burnham and Anderson 2002). Explanatory variables were considered to have a “significant” effect on the responses if the standard error of the estimate did not cross zero.

I graphically present the results for the single best model for each analysis and standardised parameters and standard errors for all explanatory variables, as well as the number of individual

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models included in model sets. Inferences were made by comparing each parameter’s standardised estimate with other predictor variables to assess its relative importance, the upper and lower 95% quantiles of each parameter obtained from N = 1000 simulated draws from the estimated

distribution (Lintott et al., 2014) and a comparison of selected models using AIC.

Finally, I used a null model approach to test the effects of the occurrence or proximity to clear-felled areas or broadleaf patches on patterns of trait values (Crawley, 2007). Null models allow the

comparison of the observed communities with randomly assembled communities of equal species richness (Swenson, 2014). To generate random communities, I randomly permuted (n=999) moth abundance across stands. For each randomisation I calculated functional diversity measures, using the standardised effect size (SES) to compare the deviation of observed values relative to the null model assemblage (Rolo et al., 2016). The SES is calculated as the ratio of the difference between the observed value and the mean of the null distribution to the standard deviation of the null distribution. The null hypothesis is that the average SES is zero; significantly higher values indicate niche complementarity whereas lower values indicate environmental filtering. I used linear models including an interaction with latitude and longitude to account for spatial autocorrelation and excluded the intercept to determine whether mean SES values significantly deviated from zero. Study 2: Differences in naïve, taxonomic and functional richness, diversity and evenness between plantation and broadleaf woodlands were tested using generalised linear mixed effects models with a gaussian error distribution. Site nested in year was included as a random effect to account for the paired design, and the fact that sampling occurred across two years. Models were validated by visual assessment of the residuals (Crawley, 2007). The conditional R2 _{(variance explained by both the fixed}

and the random effects (Nakagawa and Schielzeth, 2013) were used to assess the amount of variation explained by each model. Explanatory variables were considered to have a “significant” effect on the responses if the standard error of the estimate did not cross zero. The standardised effect size was calculated as above to determine whether communities in broadleaf woodlands and plantation forests showed evidence of environmental filtering in measures of functional richness and diversity.