Estrategias

The association between species traits and population trends was examined using Linear Models implemented in the R software package (R development Core Team, 2008).

In order to reduce the number of factors evaluated in the model selection procedure and to minimize the risk of multi-collinearity among predictors, GVIF (generalized variation inflation factor) and Pearson correlation coefficients were used to determine which variables were highly correlated within each suite of

42 traits. Variables were considered collinear when GVIF > 5 or r2 > 0.7. Furthermore, each predictor trait was tested using univariate linear models to determine their individual effect on population change (see Appendix B) and in case of variable collinearity only the variable with higher explanatory power in univariate analysis was selected for the predictor pool for the multivariate modelling (see further details below) (Appendix A).

Then the relative importance of predictors was evaluated using relaimpo analysis implemented in the R software package with the same name. Relative importance can be defined as “the proportional contribution each predictor makes to R2, considering both its direct effect (i.e. its correlation with the main response variable) and its effect when combined with the other variables in the regression equation” (Johnson & Lebreton, 2004). The metric lmg was used. This partitions R2 by averaging over orders following Lindeman et al. (1980). The lmg has been recommended as the most adequate metric to calculate relative importance of predictors because it not only represents the mean contribution of variables over bootstraps runs in models of different sizes but also uses both direct effects and adjusted effects for other variables in the model (Johnson & Lebreton, 2004; Grömping, 2006;). The lmg also allows for the inclusion of interactions and model weights. Key interaction terms (between pairs of variables including at least one categorical variable) were selected for inclusion in the global model on the basis of exploratory coplots, provided trait groups contained adequate, balanced sample sizes.

The final model was determined using weighted general linear models (GLM) with a stepwise optimal model selection procedure based on corrected AIC (AICc) values. The response variable, the estimate of annual growth rate, was weighted by the inverse of its standard error as a measure of reliability. This process provided a correction of trend estimates by allowing a greater contribution to the model of species with more reliable growth rate estimates (Jiguet et al., 2009). In order to identify the impact that weighting had on the final model, unweighted models were also calculated (see Appendix).

43

Table 2.1. Description of species-specific traits used in the long term population trend analysis. Species-specific values of population growth rates and main trait predictors used for the final model can be found in Appendix A.

Trait group

Variable Description Data source

Phenology Average laying date Median date of the 1st _{egg laying (Julian day) Robinson (2005)}

Average first clutch laying period

Latest recorded date- earliest recorded date (no. days) Robinson (2005) Migration strategy

Mean change in arrival date (only for migrants)

Migrating distance (only for migrants)

Nominal variable: Resident species (1), partial migrant species (2) and migrant species (3)

Mean change in observed date of arrival (no.days)

Mean in ˚ latitude between wintering and breeding grounds Dudley et al.(2006) Sparks et al.(2007) Møller et al.(2008) Resource use

Diet type Nominal variable: small seeds eaters (1), large seed eaters (2), insect eaters (3), invertebrate eaters(4), generalist (5), generalist+carrion (6), highly specialist (7)

Snow and Perrins (1998)

Diet richness Number of items per category in the diet of each species

Snow & Perrins (1998) Nest location Nominal variable: Ground (0), vegetation (1), hole (2) Snow & Perrins

(1998), Siriwardena

et al.(1998)

Habitat preference Nominal variable: Generalist (1), farmland specialist (2), woodland specialist (2), wetland specialist (3), urban specialist (4), Upland specialist (5).

Newson et al. (2004)

Life history Average body weight

Average body weight for the species (♀♂)(g) Snow & Perrins (1998) Productivity (Average clutch size) x( Average brood size/year) Snow & Perrins

(1998) Average clutch size Average number of eggs per clutch Snow & Perrins

(1998) Number of broods

per year

Average number of clutches per year Snow & Perrins (1998) Average nesting

period

Average number of days spend in the nest including incubation and fledging (no. days)

44 To verify the robustness of the final model, a bootstrap procedure was implemented using the R package boot.StepAIC (Austin & Tu, 2004). In this method, 999 random bootstrap samples were drawn repeatedly from the original dataset to investigate the variability of model selection under the AIC stepwise algorithm (Austin & Tu, 2004). Within each bootstrap sample, backward and forward selection was used to determine the most parsimonious predictive model (for further details see Austin & Tu, 2004). This technique determines a variable’s likelihood of being identified as an independent predictor (Austin & Tu, 2004). Models were also constructed for all variables in the predictor pool (global model) and without any variables (null model) to assess the value of the final model. Shapiro tests and diagnostic plots were used to evaluate the normality of model residuals and to identify outliers. If outliers were identified, models were refitted without those species to evaluate the robustness of trait relationships.

Finally, to evaluate the impact of phylogenetic non-independence between species on model selection and performance, phylogenetic generalized least- square (PGLS) regression (Freckleton et al., 2002) was used, implemented in R using the caic package (Paradis et al., 2004). The expected covariance between species was calculated on the basis of the phylogeny developed by Thomas (2008). Lambda, or the weighting of species covariance matrix, was optimised using a maximum likelihood approach (Pagel 1999). Values of lambda vary between 0 and 1, with 0 indicating no phylogenetic autocorrelation or phylogenetic autocorrelation proportional to branch length respectively. Branch lengths were available and were standardised across the species- covariance matrix. We used the same predictor variables selected during the GLM procedure, assuming a Brownian model of trait evolution, (Butler & King, 2004) (see Appendix for further details).

Selection between PGLS regression models and GLMs was made on the basis of AICc and adjusted D2 (Nagelkerke, 1991). This allowed for comparison

45 parameters and therefore selection of the minimum adequate model amongst all possible alternatives.

Mean values of key predictors in final models were compared between trait groups using Student’s t-tests where group variances were equal and Welch t- test (Welch, 1947) otherwise.