Table 1 Relationship between performance, brain neuroanatomical traits and population density.

From: Brain morphology predicts social intelligence in wild cleaner fish

Fitted model	N	Chi²	p-value	rank (i)	FDR-derived significance threshold	Pseudo-R²	95% CI		Effect size (Cohen’s d)
Fitted model	N	Chi²	p-value	rank (i)	FDR-derived significance threshold	Pseudo-R²	Upper	Lower	Effect size (Cohen’s d)
Performance ~ Forebrain size proportion * density
Forebrain size proportion	18	0.563	0.453	20	0.0909	0.42	−5.29	2.39	0.05
Density		0.030	0.862	27	0.1227		−1.43	6.99	0.12
Forebrain size proportion × density		8.291	0.004	1	0.0045		−23.69	−1.36	0.86
Performance ~ Midbrain size proportion * density
Midbrain size proportion	18	1.037	0.309	14	0.0636	–	−2.09	0.62	0.07
Density		0.007	0.933	30	0.1364		−1.64	1.35	0
Midbrain size proportion × density		0.646	0.422	19	0.0864		−0.84	2.53	0.06
Performance ~ Cerebellum size proportion * density
Cerebellum size proportion	18	1.257	0.262	12	0.0545	0.41	0.07	12.62	0.43
Density		0.002	0.968	31	0.1409		−0.42	10.69	0.28
Cerebellum size proportion × density		7.194	0.007	2	0.0091		1.45	31.7	0.68
Performance ~ Brain stem proportion * density
Brain stem size proportion	18	0.870	0.351	17	0.0773	–	−2.04	0.68	0.09
Density		0.032	0.858	26	0.1182		−1.59	1.24	0
Brain stem size proportion × density		0.001	0.976	32	0.1455		−1.26	1.29	0
Performance ~ Forebrain cell proportion * density
Forebrain cell proportion	20	0.158	0.691	25	0.1136	–	−1.02	1.66	0.01
Density		0.448	0.503	21	0.0955		−2.29	0.95	0.04
Forebrain cell proportion × density		0.000	0.990	33	0.1500		−1.36	1.36	0
Performance ~ Forebrain cell density * density
Forebrain cell density	18	0.008	0.930	29	0.1318	–	−1.83	0.86	0.02
Density		0.008	0.927	28	0.1273		−1.38	1.59	0
Forebrain cell density × density		1.173	0.279	13	0.0591		−0.54	2.21	0.11
Performance ~ Cerebellum cell proportion * density
Cerebellum cell proportion	20	0.216	0.642	23	0.1045	–	−1.15	2.28	0.04
Density		0.203	0.652	24	0.1091		−1.65	1.58	0.01
Cerebellum cell proportion × density		2.179	0.140	6	0.0273		−2.85	0.32	0.19
Performance ~ Cerebellum cell density * density
Cerebellum cell density	20	2.200	0.138	5	0.0227	0.43	−11.57	−0.63	0.43
Density		0.414	0.520	22	0.1000		−0.61	5.39	0.23
Cerebellum cell density × density		6.885	0.009	3	0.0136		−35.47	−1.8	0.62
Social competence ~ Forebrain size proportion * density
Forebrain size proportion	18	6.118	0.013	4	0.0182	0.34	0.71	8.73	0.77
Density		2.096	0.148	7	0.0318		−6.67	0.08	0.39
Forebrain size proportion × density		1.517	0.218	10	0.0455		−1.26	7.04	0.2
Social competence ~ Cerebellum size proportion * density
Cerebellum size proportion	18	0.976	0.323	15	0.0682	–	−2.11	0.69	0.06
Density		0.790	0.374	18	0.0818		−2.59	0.58	0.13
Cerebellum size proportion × density		1.874	0.171	8	0.0364		−4.63	0.4	0.16
Social competence ~ Cerebellum cell density * density
Cerebellum cell density	20	1.512	0.219	11	0.0500	–	−0.97	1.86	0.03
Density		1.569	0.210	9	0.0409		−2.55	0.31	0.22
Cerebellum cell density × density		0.876	0.349	16	0.0727		−0.63	3.09	0.06

All statistical tests were two-sided binomial tests.
Values in bold indicate statistically significant outcomes. Significance threshold alpha was set at p ≤ 0.05. Due to multiple comparisons with a total of eleven models, values were then confirmed with a False Discovery Rate significance threshold adapted to each p-value.
False Discovery Rate (FDR)-derived significance threshold was estimated with the following function: (i/m)Q, (with i: p-value rank; m: number of comparisons (here are 11 models); Q: maximum acceptable FDR set at 0.05⁶⁷).
Pseudo-R² is a goodness-of-fit measure estimated as 1 − (residual deviance/null deviance).
Cohen’s d interpretation: 0.2, small; 0.5, medium; ≥0.8 large effect.
95% CI 95% confidence interval.

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Table 1 Relationship between performance, brain neuroanatomical traits and population density.

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