Table 1 Summary of Bayesian hierarchical model

From: Reward regulation in plant–frugivore networks requires only weak cues

Response ~ predictor variable

Estimate (95% CI)

P

BF

Lipid content ~

   

(rm2 = 0.23, rc2 = 0.51)

   x

0.02 (−0.2, 0.3)

0.31

−1.6

   y

0.01 (−0.1, 0.2)

0.29

−1.8

   z

0.004 (−0.2, 0.2)

0.27

−2.0

   a

0.4 (0, 0.7)

0.95

6.0*

Sugar content ~

   

(rm2 = 0.11, rc2 = 0.23)

   x

−0.009 (−0.3, 0.2)

0.33

−1.4

   y

0 (−0.2, 0.2)

0.29

−1.8

   z

0 (−0.3, 0.3)

0.31

−1.6

   a

−0.3 (−0.7, 0)

0.77

2.5*

Protein content ~

   

(rm2 = 0.029, rc2 = 0.16)

   x

0 (−0.3, 0.3)

0.34

−1.4

   y

0.04 (−0.1, 0.4)

0.37

−1.1

   z

0.03 (−0.2, 0.4)

0.36

−1.2

   a

0 (−0.3, 0.3)

0.32

−1.5

Anthocyanin content ~

   

(rm2 = 0.35, rc2 = 0.42)

   x

−0.05 (−0.5, 0.3)

0.44

−0.44

   y

0.2 (−0.01, 0.6)

0.68

1.5

   z

0.2 (−0.07, 0.6)

0.57

0.60

   a

−0.5 (−0.9, 0)

0.97

6.8*

  1. The model tested the relationships between the chromatic colour components (x, y, z) and the brightness of fruits (a) in the avian colour space (see Methods for details) and the lipid, sugar, protein and anthocyanin concentrations in the fruit pulp. Plant phylogeny was included as a random factor. The sample size was nspecies = 44 plant species. Given are posterior means of effect estimates (with shrinkage), 95% credible intervals (CI), selection probabilities (P) and 2loge(Bayes factor) (BF) as a measure of support for a given effect. BF-values < 2 indicate no support; values between 2 and 6 indicate positive support; values between 6 and 10 indicate strong support; and values > 10 indicate decisive support. Effects that were supported by the variable selection with BF > 2 are shown with an asterisk. The r2 values depict the marginal (rm2) variance explained by fixed factors only as well as the conditional (rc2) variance explained by fixed and random factors combined39
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