Table 1. Summary of model structures and the predictive performances in WAIC.

Response variable	model	Hierarchical structure	Conditioning variables	Link function	Distribution	WAIC (nat)	dWAIC (nat)	Plot
Choice	1_1	intercept_L	CW_L Leg_L CW_NO Leg_NO	softmax	categorical	−2.13	0.00	Fig. 3A
Choice	1_2	intercept_L	CW_L CW_NO	softmax	categorical	−1.87	0.26	–
Choice	1_3	intercept_L	–	softmax	categorical	−0.88	1.25	–
Choice	1_4	intercept_L	Leg_L Leg_NO	softmax	categorical	−0.78	1.35	–
Choice	1_5	–	CW_L CW_NO	softmax	categorical	0.85	2.99	Fig. 3C
Choice	1_6	–	CW_L Leg_L CW_NO Leg_NO	softmax	categorical	0.87	3.01	–
Trimmed size	2_1	intercept_1 intercept_2	CW Choice	logit log	ZIP	−2.08	0.00	Fig. 4A
Trimmed size	2_2	intercept_2	Choice	logit log	ZIP	0.81	2.89	–
Trimmed size	2_3	intercept_2	CW Choice	logit log	ZIP	0.86	2.95	–
Trimmed size	2_4	intercept_2	–	logit log	ZIP	1.23	3.32	–
Trimmed size	2_5	intercept_2	CW	logit log	ZIP	1.37	3.46	–
Trimmed size	2_6	–	CW Choice	logit log	ZIP	7.40	9.48	Fig. 4B
Trimmed size	2_7	–	CW	logit log	ZIP	10.05	12.13	–
Trimmed size	2_8	–	–	logit log	ZIP	12.55	14.63	–
Cap cavity size	3_1	intercept	CW	log	gamma	4.45	0.00	Figs. 5A
Cap cavity size	3_2	–	CW	log	gamma	4.54	0.08	Figs. 5B
Cap cavity size	3_3	–	CW Gender	log	gamma	4.69	0.24	–
Cap cavity size	3_4	intercept	–	log	gamma	4.71	0.26	–
Cap cavity size	3_5	–	CW	identity	normal	4.75	0.30	–
Cap cavity size	3_6	intercept cw	CW	log	gamma	6.18	1.73	–
Latency for making	4_1	intercept_2	CW	logit log	ZIP	1.10	0.00	Fig. 6A
Latency for making	4_2	intercept_2	–	logit log	ZIP	1.28	0.18	–
Latency for making	4_3	–	–	logit log	ZIP	1.28	0.19	Fig. 6B
Latency for making	4_4	–	Choice	logit log	ZIP	1.30	0.20	–
Latency for making	4_5	–	CW	logit log	ZIP	1.38	0.28	–
Latency for making	4_6	–	CW Choice	logit log	ZIP	1.72	0.62	–

Notes.

Abbreviations

intercept_L

intercept in the linear predictor (LP) for the choice of L

intercept_1

intercept in the LP for the decision of trimming

intercept_2

intercept in the LP for the mean of the trimmed size of the sponge

CW

carapace width

Leg

degree of the leg lack

_L and _NO

parameters for L sponge and skipping, respectively

Choice

choice of whether to cut the sponge or not

Gender

gender of the animal

intercept_2

intercept in the LP for the mean of the days to carrying

Choice

choice of sponge size

ZIP

Zero-inflated Poisson distribution

WAIC

value of Widely-Applicable Information Criterion per sample

dWAIC

the difference of the WAIC of the model against the best-performed model