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... test the statistical significance of LMM-based repeatability estimates (REML); here we describe two. First, likelihood ratio tests can be used to test for significant variance in the random effects (=-=Bolker et al., 2009-=-, but see Faraway, 2006). These can be obtained by comparing twice the difference in loglikelihoods of models with and without the random effect (‘individual identity’), against the χ2 distribution wi...

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...analyses of repeated measures we included individuals nested within clutches as random effect. We did not test for significance of the random effect terms as they were not important for our question (=-=Bolker et al. 2009-=-). All tests are two-tailed with a significance level set to a = 0Æ05. All size, growth and swimming speed data were analysed with LME. For model selection we used the step-down protocols suggested by...

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...l Soil Data Task Group, 2000) and the Global Soil Texture and Derived Water-Holding Capacities dataset (Webb et al., 2000), respectively. For local conditions these metrics may be less accurate, which must be kept in mind when interpreting the outcomes of analyses below. Quantification of environmental drivers of LLS Bivariate and multivariate analyses of LLS versus temperature, water and nutrient variables, or their combinations, were quantified for deciduous and evergreen species separately. For this we used linear mixed models with maximum likelihood (ML) methods, available in spss v.15.0 (Bolker et al., 2009). In contrast to the analyses presented in Wright et al. (2005), an advantage of our mixed model analysis is that it explicitly takes into account that there is more than one data observation (LLS) at each study location. By taking study location as a random factor, it accounts for the fact that errors within each study location are likely to be correlated, i.e. non-independent. Temperature, water, nutrient variables and their interactions were treated as fixed effects. For all bivariate and multivariate analyses of LLS, we used a dataset of a total of 189 observations and 37 study locations f...

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...ere <10 stocks from a given region present in a dataset, two or more levels of region were aggregated in an ‘other’ category to maintain a minimum of 10 observations in each level of a random effect (=-=Bolker et al. 2009-=-). These aggregations involved: for C/Q, USA–Northeast/Mid-Atlantic Coast, USA–South Atlantic Coast/Gulf of Mexico and South America; for F/Freference, Canada–East Coast, USA–South Atlantic Coast/Gulf...

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...ng restricted maximum likelihood, which gives less-biased random-effect variance estimates than maximum likelihood (Pinheiro & Bates 2000, p. 75; Crawley 2007, p. 639; Claeskens & Hjort 2008, p. 271; =-=Bolker et al. 2009-=-, p. 128). supporting analyses We here describe two supporting analyses: one to compare the main set of models with simple models corresponding to the hypothesis that universal relationships between M...

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...ems with maximum likelihood GLMMs, such as difficulties in selecting the number of degrees of freedom when assessing the significance of fixed effects and relying on approximations of the likelihood (=-=Bolker et al., 2009-=-). Credibility intervals can also be calculated directly even for derived parameters such as heritability, as the MCMC routine samples from the posterior distributions of all the model parameters (Nak...

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...unctional group on RCIavg or D RCIavg for monoculture treatment in both experiments. The generalized linear mixed model (REML; F test) was used for this test to take into account random block effect (=-=Bolker et al. 2009-=-). Normality of residuals and homoscedasticity were checked, and response variables were transformed when necessary. When significant functional group effect was found, we compared the mean of functio...