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For clarity we excluded ten observations with SD>1000 in this graph. -2 -1 0 data1$es ES (means) 17 1 2 Appendix S3 – Models tested Table SI-1. Model fits (Deviance Information Criteria, DIC) for a set of representative models analyzing effect size as a function of sign of response, type of fragmentation, type of response, biome, vegetation type, functional group and life stage. Model with lowest DIC has the best fit of the data. * Indicate the models we report on in the main text, they were selected on the basis of DIC and of their suitability to answer the proposed questions. Model DIC Effect size~f(sign of response) including study random effects 2129 Effect size~f(sign of response, type of fragmentation) 2038 Effect size~f(sign of response, type of response) 2108 Effect size~ f (sign of response, type of fragmentation, type of response) non- 2012 hierarchical *Effect size~ f (sign of response, type of fragmentation, type of response) hierarchical 1985 *Effect size~ f (sign of response, Biome) 1997 *Effect size~ f (sign of response, Vegetation type) 2063 *Effect size~ f (sign of response, Functional group) 1844 *Effect size~ f (sign of response, Life stage) 2019 18 Appendix S4 – Variance weighted analysis We carried out a variance weighted meta-analysis at the observation level using the difference to mean ratio effect size for the subset of observations that provided standard deviation/standard effort and sample size information. We multiplied each individual ES by the inverse of its variance to give observations with lower variance more weight in the calculation of group mean ES. Each observation within the same publication was treated as an independent sample (Gurevitch & Hedges 2001). The 95% confidence intervals around the mean ES were calculated using critical values from a standard normal distribution (1.96*SE). Fig. SI-3. Results of the variance weighted analysis including those observations that reported variance information. The graph on the left represents the Overall ES, and ES for each of the fragmentation effects is plotted in the right graph. The number of observations included in each calculation is noted at the bottom of the figure. Asterisks indicate that the 95% CI around each ES mean did not include zero (some of 95% CI are very narrow around the mean and cannot be seen in the graphs). 19 Fig. SI-4. Results of the variance weighted analysis including those observations that reported variance information. EF for each type of response associated to each type of fragmentation process. The number of observations included in each calculation is noted at the bottom of the 20 figure. Asterisks indicate that the 95%CI around each EF mean did not include zero (some of 95% CI are very narrow around the mean and cannot be seen in the graphs). Gurevitch, J. & Hedges, L. V. (2001) Meta-analysis - combining the results of independent experiments. Design and Analysis of Ecological Experiments (eds S. M. Scheiner & J. Gurevitch). Oxford University Press, Oxford. 21