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Data S1. Estimation of the magnitude of the variance of individual random effects with a restrictive and penalizing prior.

Figure S1. Histograms representing the probability density of the variance () for the two different priors used for model H2: (a) & (c) uniform U(0,10) distribution on the corresponding standard deviation σα; (b) & (d) inversegamma (4,0.05) distribution on . For better readability, we show the densities on two different x-axis scales: histograms (a) and (b) are scaled on [0;0.15], where the density of values under the inversegamma prior (b) can more easily be interpreted; histograms (c) and (d) are scaled on [0;100], where the full extent of the density of values under the uniform prior (c) can be better seen. We see that the density of values is heavily shifted toward very small values in the case of the inversegamma (4,0.05) prior distribution compared with the case of the uniform U(0,10) prior distribution. On the [0;100] scale, the density of the inversegamma (4,0.05) distribution looks as a single peak at zero.

Table S1. Summary of the parameter posterior distributions from model H2 (“fixed heterogeneity” hypothesis; see main text) using two contrasted priors on the variance () of random individual effects: (i) the inversegamma (4,0.05) distribution on which puts a lot of weight on very small values (close to zero), and thus strongly penalizes high values; (ii) the uniform U(0,10) distribution on the corresponding standard deviation σα, which is a very vague prior and has more weight on high values of variance. The mean, the standard deviation (SD), 2.5% and 97.5% percentiles (perc.) of the posterior distribution are shown. Symbols with a star (e.g., ) correspond to parameters back-transformed to the more interpretable scale of a probability of reproduction (i.e., in the interval [0,1]). See main text for more details.

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