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Figure S1 Mean degree of complementarity and convergence for three sets of initial conditions of trait values: traits sampled from normal distribution (green), from uniform distributions (red) and from distributions based on actual data on species-specific phenotypic values (yellow). Error bars represent the associated 95% confidence intervals.

Figure S2 Mean degree of complementarity (a), convergence among animals (b) and plants (c) for different ratios between rates of directional (q) and random (p) phenotypic changes. Error bars represent 95% confidence interval. The red circles represent the benchmark value for the parameter.

Figure S3 Mean degree of complementarity (a), convergence among animals (b) and plants (c) for different values of m (relationship between ecological and evolutionary dependence). Error bars represent 95% confidence interval. The red circles represent the benchmark value for the parameter.

Figure S4 Mean degree of complementarity (a), convergence among animals (b) and plants (c) for different values of heritability. Error bars represent 95% confidence interval. The red circles represent the benchmark value for the parameter.

Figure S5 Mean complementarity (a), convergence (animals, b; plants, c) for simulations with different number of time steps. Time steps were measured using the number of independent events of change (IEC, the sum of events by p and q). Error bars, 95% confidence interval. The red circles, benchmark value for the parameter.

Table S1 Mutualistic networks used in the coevolutionary simulations. The matrices describing the networks analyzed are available under request. Network labels follow (Bascompte et al. 2006; Rezende et al. 2007b).

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