. 2023 Sep 26;13:16078. doi: 10.1038/s41598-023-41298-9

Table 2.

Covariate contributions to generalized additive models describing changes in the proportional mass ( $\bar{M}$ ) of broad prey types with predator mass (a, b, c) and the effects of predator species and mass on estimated foraging depth (d, e).

(a) *Alepisaurus* $\bar{M}$ ~ s(log₁₀(predator mass), by prey type) + prey type, n = 116, *Adj. R² = 0.30*
Parametric coefficients	est	se	z	p
(Intercept)	− 0.90	0.12	− 7.54	4.87 E⁻¹⁴
Fish vs. Mollusk	1.09	0.17	6.24	4.31 E⁻¹⁰
Crustacea vs Mollusk	− 0.36	0.17	− 2.17	0.03
Crustacea vs. Fish	− 1.45	0.17	− 8.48	< 2.00 E⁻¹⁶

Smooth terms	edf	Χ²	p
s(predator mass): Mollusk	1.00	0.70	0.40
s(predator mass): Fish	3.74	13.72	0.01
s(predator mass): Crustacea	3.33	10.94	0.03

(b) *Anoplogaster,* $\bar{M}$ ~ s(log₁₀(predator mass), by prey type) + prey type, n = 81, *Adj. R² = 0.67*
Parametric coefficients	est	se	z	p
(Intercept)	− 1.68	0.13	− 12.99	< 2.00 E⁻¹⁶
Fish vs. Mollusk	0.03	0.18	0.18	0.86
Crustacea vs Mollusk	2.94	0.19	15.71	< 2.00 E⁻¹⁶
Crustacea vs. Fish	2.91	0.19	15.50	< 2.00 E⁻¹⁶

Smooth terms	edf	Χ²	p
s(predator mass): Mollusk	1.00	0.29	0.59
s(predator mass): Fish	1.01	0.52	0.47
s(predator mass): Crustacea	1.00	0.00	0.97

(c) *Omosudis,* $\bar{M}$ ~ s(log₁₀(predator mass), by prey type) + prey type, n = 38, *Adj. R² = 0.34*
Parametric coefficients	est	se	z	p
(Intercept)	− 1.35	0.41	− 3.32	8.98 E⁻⁰⁴
Fish vs. Mollusk	2.58	0.58	4.46	8.34 E⁻⁰⁶

Smooth terms	edf		Χ²	p
s(predator mass): Mollusk	1.66		1.35	0.49
s(predator mass): Fish	2.96		4.47	0.39

(d) Foraging depth ~ s(log₁₀(predator mass), by prey type) + prey type, n = 216, *Adj. R² = 0.22*
Parametric coefficients	est	se	t	p
(Intercept)	346.12	19.21	18.01	< 2.00 E⁻¹⁶
Anoplogaster vs. Alepisaurus	− 143.74	34.19	− 4.20	3.89 E⁻⁰⁵
Omosudis vs Alepisaurus	148.65	37.55	3.96	1.03 E⁻⁰⁴
Omosudis vs. Anoplogaster	292.39	42.90	6.82	9.96 E⁻¹¹

Smooth terms	edf	F	p
s(predator mass):Alepisaurus	3.08	1.33	0.35
s(predator mass):Anoplogaster	1.00	0.84	0.36
s(predator mass):Omosudis	1.00	5.51	0.02

(e) Foraging depth ~ s(log₁₀(predator mass), by species) + species, n = 1220, *Adj. R² = 0.12*
Parametric coefficients	est	se	t	p
(Intercept)	464.52	8.80	52.79	< 2.00 E⁻¹⁶
Anoplogaster vs. Alepisaurus	− 405.458	257.04	− 1.58	0.11
Omosudis vs Alepisaurus	309.30	174.86	1.77	0.08
Omosudis vs. Anoplogaster	714.77	310.62	2.30	0.02

Smooth terms	edf	F	p
s(predator mass):Alepisaurus	3.21	28.73	< 2.00 E⁻¹⁶
s(predator mass):Anoplogaster	1.00	0.39	0.53
s(predator mass):Omosudis	1.00	2.57	0.11

Coefficient estimates (“est.”), standard error (se), z-values, and p-values are given for each parametric term. Estimated degrees of freedom (edf), Chi-squared (Χ²), and p-values are given for each smooth term. Partial effects plots for covariates with p-values < 0.05 from a–c are given in Fig. 2. Partial effects plots for all covariates from each model are given in Fig. S3.