Table 1 Species used for the meta-analysis and relevant statistics comparing \({\hat{R}}_{\theta }\) quantile distribution with the null \({R}_{{\theta }_{0}^{{vm}}}\) and \({R}_{{\theta }_{0}^{r}}\)quantile distributions using chi-square (X²) goodness-of-fit test.

From: Evidence for a consistent use of external cues by marine fish larvae for orientation

Species	Abbreviation	Family	Mean △R_θ	95% CI	X² _CRW-vm	Cohen’s W_CRW-vm	X² _CRW-r	Cohen’s W_CRW-r	Number of individuals	Method	N_obs per individual	Citation	Location
Trachurus spp.	Tra_ spp.	Carangidae	0.59	0.1	–	–	–	–	2	DISC	180	²	MED
Chromis atripectoralis_group	Chr_atri_group	Pomacentridae	0.43	0.1	2.6	0.84	16^**	2.6	23	DISC	90	⁵	GBR
Chromis chromis	Chr_chro	Pomacentridae	0.42	0.05	150^**	1.52	165^**	1.59	65 (67)	DISC	180	²	MED
Chromis atripectoralis_ ind	Chr_atri_ind	Pomacentridae	0.4	0.05	10^**	0.34	65^**	0.9	83 (86)	DISC	90	⁵	GBR
Oblada melanura	Obl_mela	Sparidae	0.35	0.08	66^**	1.73	66^**	1.73	22	DISC	180	²	MED
Premnas biaculeatus	Pre_biac	Pomacentridae	0.32	0.1	19.8^**	1	24.5^**	1	23 (24)	DISC	300	¹	GOA
Diplodus annularis	Dip_annu	Sparidae	0.32	0.07	90^**	1.73	90^**	1.73	30 (35)	DISC	180	²	MED
Spicara smaris	Spi_smar	Sparidae	0.3	0.062	86.9^**	1.6	94.2^**	1.67	34	DISC	180	²	MED
Boops boops	Boo_boop	Sparidae	0.28	0.1	–	–	–	–	7	DISC	180	²	MED
Spondyliosoma cantharus	Spo_cant	Sparidae	0.226	0.176	–	–	–	–	6	DISC	180	²	MED
Pomacentrus lepidogenys	Pom_lepi	Pomacentridae	0.174	0.037	20.3^**	0.6	56.6^**	1	54 (59)	Sc-Fl	21	⁶	GBR
Chaetodon plebeius	Cha_pleb	Chaetodontidae	0.167	0.058	15.6^**	0.7	25.9^**	0.96	28	Sc-Fl	21	⁶	GBR
Epinephelus fuscoguttatus	Epi_fusc	Serranidae	0.136	0.121	–	–	–	–	9 (12)	Sc-Fl	21	⁷	SCS
Eleutheronema tetradactylum	Ele_tetr	Polynemidae	0.132	0.056	6.1^*	0.54	15.3^**	0.85	21 (27)	Sc-Fl	21	⁸	SCS
Chrysiptera rollandi	Chr_roll	Pomacentridae	0.11	0.038	12.3^**	0.49	24.3^**	0.69	51 (56)	Sc-Fl	21	⁶	GBR
Caesio cuning	Cae_cuni	Caesionidae	0.103	0.058	–	–	–	–	10	Sc-Fl	21	⁶	GBR
Chromis atripectoralis_group	Chr_atri_group	Pomacentridae	0.089	0.028	–	–	–	–	15	Sc-Fl	21	⁵	GBR
Neopomacentrus cyanomos	Neo_cyan	Pomacentridae	0.085	0.036	16.7^**	0.44	15.6^**	0.43	85 (98)	Sc-Fl	21	⁶	GBR
Platax teira	Pla_teir	Ephippidae	0.064	0.174	–	–	–	–	7	Sc-Fl	21	⁷	SCS
Caranx ignobilis	Car_igno	Carangidae	0.063	0.082	-–	–	–	–	12 (17)	Sc-Fl	21	⁹	SCS
Epinephelus coioides	Epi_coio	Serranidae	0.061	0.076	–	–	–	–	15 (22)	Sc-Fl	21	⁷	SCS
Chromis atripectoralis_ ind	Chr_atri_ind	Pomacentridae	0.047	0.030	1.8	0.18	8.14^*	0.38	56 (62)	Sc-Fl	21	⁶	GBR
Amblyglyphidodon curacao	Amb_cura	Pomacentridae	0.043	0.045	1.6	0.2	25.6^**	0.7	55 (65)	Sc-Fl	21	¹⁰	GBR
Chaetodon aureofasciatus	Cha_aure	Chaetodontidae	0.030	0.048	0.9	0.1	24.4^**	0.8	42 (48)	Sc-Fl	21	⁶	GBR
Diplodus annularis^s	Dip_annu	Sparidae	0.32	0.07	–	–	–	–	4	DISC	21	⁴⁷	MED
Spicara_smaris ^s	Spi_smar	Sparidae	0.256	0.06	–	–	–	–	10	DISC	21	²	MED
Boops boops ^s	Boo_boop	Sparidae	0.25	0.13	–	–	–	–	3	DISC	21	²	MED
Premnas biaculeatus ^s	Pre_biac	Pomacentridae	0.24	0.072	17.1^**	0.92	17.1^**	0.92	20	DISC	21	⁴	GOA
Chromis atripectoralis_ ind ^s	Chr_atri_ind	Pomacentridae	0.23	0.042	25.3^**	0.59	40.4^**	0.74	74	DISC	21	⁵	GBR
Chromis chromis^s	Chr_chro	Pomacentridae	0.21	0.048	–	–	–	–	11	DISC	21	⁴⁷	MED
Spondyliosoma cantharus^s	Spo_cant	Sparidae	0.15	0.154	–	–	–	–	4	DISC	21	⁴⁷	MED
Chromis atripectoralis_group^s	Chr_atri_group	Pomacentridae	0.13	0.062	0.4	0.14	5.1	0.5	20	DISC	21	⁵	GBR

*The data in⁵ are from trials with individuals and groups of Chromis atripectoralis using the DISC.
^SSubsamples of DISC trials to N_obs = 21 for comparison with Scuba-Following trials.
The following statistics are provided: ΔR: the difference between the observed mean vector (\({\hat{R}}_{\theta }\)) and that expected under CRW (\({R}_{{\theta }_{0}^{{vm}}}\)) (ΔR = \({\hat{R}}_{\theta }\)- \({\bar{R}}_{{\theta }_{0}^{{vm}}}\)), X² test statistics value, Cohen’s W effect size value. One or two asterisks on the X² value represent significant X² tests with P < 0.05 or P < 0.01, respectively. Method abbreviations: Drifting In-Situ Chamber (DISC) and Scuba-Following (Sc-Fl); locations: GBR- Lizard Island, Great Barrier Reef, Australia; MED- Mediterranean Sea, France; SCS- South China Sea, Taiwan Island; GOA – Gulf of Aqaba, Red Sea. The number of directional (Rayleigh’s test, p < 0.05) individuals per species is given as well as the total number of individuals (in brackets). Numbers in brackets are absent in species for which all individuals were directional. Rows are sorted according to descending order of ΔR values. Subsampled DISC trials (N_obs = 21) are given in the bottom part of the table, separated from the rest of the groups with a horizonal line, and notated with (^s).

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Table 1 Species used for the meta-analysis and relevant statistics comparing \({\hat{R}}_{\theta }\) quantile distribution with the null \({R}_{{\theta }_{0}^{{vm}}}\) and \({R}_{{\theta }_{0}^{r}}\)quantile distributions using chi-square (X²) goodness-of-fit test.

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