Table 1 Top models describing three distinct components of coral reef habitat complexity: surface rugosity (a), terrain ruggedness (b), and absolute curvature (c). Plus signs indicate the presence of variables within each model in the top model set.

Rank	Heat	Dist.	Branching	Plating	Massive	Heat*Dist	df	AICc	ΔAICc	w	R ²
(a) Surface rugosity
1	+	+			+		8	14.89	0.00	0.17	0.54
2	+	+	+		+		9	15.11	0.22	0.16	0.59
3	+	+			+	+	10	16.05	1.16	0.10	0.63
4	+	+					7	16.13	1.24	0.09	0.50
5	+	+	+				8	16.27	1.38	0.09	0.55
6	+	+	+		+	+	11	16.82	1.93	0.07	0.65
7		+	+		+		8	17.16	2.27	0.06	0.57
8	+	+		+	+		9	17.32	2.42	0.05	0.56
9	+	+	+	+	+		10	18.19	3.29	0.03	0.59
10	+	+		+			8	18.66	3.76	0.03	0.51
RVI	0.92	0.94	0.49	0.20	0.72	0.22
(b) Terrain ruggedness
1	+	+	+		+		8	−304.36	0.00	0.32	0.80
2	+	+	+		+	+	10	−303.18	1.18	0.18	0.83
3	+	+	+	+	+		9	−303.11	1.24	0.17	0.80
4	+	+	+	+	+	+	11	−301.32	3.04	0.07	0.83
5	+	+	+				7	−301.08	3.27	0.06	0.76
6		+	+	+	+		8	−300.69	3.67	0.05	0.77
RVI	0.92	0.96	0.95	0.36	0.90	0.28
(c) Absolute curvature
1					+		5	397.40	0.00	0.27	0.23
2			+		+		6	398.94	1.54	0.13	0.27
3				+	+		6	399.34	1.94	0.10	0.25
4	+				+		6	399.73	2.32	0.09	0.22
5		+					6	400.32	2.92	0.06	0.26
6		+			+		7	400.55	3.14	0.06	0.28
7	+		+		+		7	400.66	3.25	0.05	0.25
8	+			+	+		7	401.39	3.99	0.04	0.24
RVI	0.25	0.25	0.30	0.24	0.84	0.00

Heat = heat stress; Dist. = local human disturbance; Branching = branching coral density; Plating = plating coral density; Massive = massive coral density; df = degrees of freedom; AIC_c = AIC corrected for small sample sizes; ΔAIC_c = difference from the lowest AIC_c value, all models within ΔAIC_c of 4 are shown; w = model weight; R² = conditional R² (proportion of variance explained by both fixed and random effects); RVI = relative variable importance.

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