Table 1 Commonality analysis for the best regression models describing TL for the 32 islands

Variable	Coefficient	Total %
*Pocillopora* hTL: log(TL_Mean) ~ island + Symbiodinicaeae + bacteria (R² adj = 0.43)
Unique to island	0.2453	48.11
Unique to Symbiodiniaceae	0.0684	13.41
Unique to bacteria	0.0242	4.74
Common to island, and Symbiodiniaceae	0.1324	25.96
Common to island, and bacteria	0.0312	6.11
Common to Symbiodinicaeae, and bacteria	−0.0106	−2.07
Common to island, Symbiodiniaceae, and bacteria	0.0191	3.74
Total	0.5099	100
*Pocillopora* sTL: log(TL_Mean) ~ island + Symbiodiniaceae (R² adj = 0.55)
Unique to island	0.2897	47.33
Unique to Symbiodiniaceae	0.0387	6.32
Common to island, and Symbiodiniaceae	0.2837	46.34
Total	0.6121	100
*Porites* hTL: log(TL_Mean) ~ island (R² adj = 0.29)
*Porites* sTL: log(TL_Mean) ~ island + Symbiodiniaceae (R² adj = 0.33)
Unique to island	0.2732	62.46
Unique to Symbiodinicaeae	0.065	14.85
Unique to bacteria	0.0992	22.69
Total	0.4373	100

Unique contributions measure the variance uniquely accounted for by a single variable; whereas common contributions indicate the variance that is common between two or more variables. The sum of all coefficients of each model corresponds to the total variance of TL explained by the model, which is the multiple R² (non-adjusted). Negative coefficients occur in presence of suppression or when some of the correlations among variables have opposite signs (see details in ref. ¹⁰⁰).

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