. 2020 Jan 8;10(3):1233–1251. doi: 10.1002/ece3.5978

Table 3.

Detailed results on criteria (3) and (4) on type II invariance of life history traits

	Trait	DF	R ²	Adj. R ²	p	Slope	CI_s	Intercept	CI_i	λ
Amphibians
OLS	Age at maturity	209	.07	.06	<.01	0.08	0.04, 0.12	0.28	0.22, 0.33	–
PGLS	Age at maturity	188	–	–	<.01	0.09	0.05, 0.09	0.20	−0.11, 0.20	0.90
OLS	Birthweight	16	<.01	−.06	.83	0.13	−1.07, 1.33	0.20	−1.31, 1.71	–
PGLS	Birthweight	16	–	–	.81	−0.17	−1.69, 1.34	0.59	−1.74, 2.91	0.58
OLS	Offspring size	402	.02	.02	<.01	0.05	0.02, 0.08	0.22	0.19, 0.26
PGLS	Offspring size	327			<.01	0.05	0.02, 0.09	0.40	0.09, 0.72	0.92
OLS	Clutch size	445	.18	.18	<.01	0.48	0.39, 0.57	1.97	1.85, 2.09	–
PGLS	Clutch size	365	–	–	<0.01	0.30	0.21, 0.40	1.29	0.34, 2.25	0.91
OLS	Reproductive output	553	<.01	<.01	.95	−0.01	−0.01, 0.01	0.02	0.01, 0.03
PGLS	Reproductive output	445	–	–	.92	<0.01	−0.01, 0.01	0.92	0.77, 1.07	0.81
OLS	Egg mass	14	<.01	−.07	.94	−0.03	−0.89, 0.82	−1.62	−2.80, −0.45	–
PGLS	Egg mass	14	–	–	.74	−0.23	−1.68, 1.21	−1.39	−1.35, −1.30	1.00
OLS	Incubation time	60	<.01	<.01	.97	<0.01	−0.20, 0.21	1.30	1.01, 1.59	–
PGLS	Incubation time	57	–	–	.06	0.19	−0.01, 0.38	0.97	0.16, 1.77	0.95
OLS	Larval period	39	<.01	−.02	.80	0.02	−0.19, 0.24	1.96	1.71, 2.20	–
PGLS	Larval period	39	–	–	.53	0.08	−0.17, 0.33	2.06	1.52, 2.60	0.76
OLS	Max. longevity	209	.13	.12	<.01	0.15	0.10, 0.20	0.77	0.69, 0.85	–
PGLS	Max. longevity	189	–	–	<.01	0.19	0.14, 0.19	0.38	0.69, 0.99	0.70
OLS	Metamorphosis size	46	.04	.02	.18	−0.08	−0.19, 0.03	1.49	1.35, 1.63	–
PGLS	Metamorphosis size	41	–	–	.72	−0.03	−0.20, 0.14	1.39	1.05, 1.74	0.63
OLS	Size at maturity	211	.08	.08	<.01	0.13	0.07, 0.19	0.83	0.74, 0.92	–
PGLS	Size at maturity	191	–	–	<.01	0.18	0.11, 0.17	0.45	0.45, 0.76	0.59
Anura
OLS	Age at maturity	139	.14	.13	<.01	0.12	0.07, 0.16	0.16	0.09, 0.23	–
PGLS	Age at maturity	124	–	–	<.01	0.11	0.05, 0.17	0.16	−0.14, 0.46	0.91
OLS	Birthweight	10	.19	.10	.18	−1.01	−2.95, 0.34	1.99	0.05, 0.34	–
PGLS	Birthweight	10	–	–	.05	−1.31	−2.65, 0.02	2.23	0.03, 4.44	0.91
OLS	Offspring size	344	.02	.01	.02	0.04	0.01, 0.07	0.20	0.16, 0.24
PGLS	Offspring size	274	–	–	<.01	0.05	0.02, 0.09	0.35	0.10, 0.60	0.89
OLS	Clutch size	378	.28	.27	<.01	0.58	0.46, 0.67	2.00	1.88, 2.11	–
PGLS	Clutch size	304	–	–	<.01	0.35	0.24, 0.46	1.78	1.00, 2.56	0.88
OLS	Reproductive output	476	<.01	<.01	.74	<0.01	−0.01, 0.02	0.02	0.01, 0.04
PGLS	Reproductive output	373	–	–	.86	<0.01	0.00, 0.01	0.03	−0.25, 0.30	1.00
OLS	Egg mass	9	<.01	−.12	.92	−0.05	−1.07, 0.96	−1.53	−3.20, 0.14	–
PGLS	Egg mass	9	–	–	.73	0.11	−0.63, 0.84	−1.49	−2.61, −0.36	0.88
OLS	Incubation time	31	.01	−.02	.58	−0.07	−0.31, 0.17	0.98	0.67, 1.30	–
PGLS	Incubation time	31	–	–	.13	0.25	−0.08, 0.57	0.51	−0.12, 1.14	0.87
OLS	Larval period	22	.01	−.03	.61	−0.04	−0.17, 0.10	1.90	1.73, 2.07	–
PGLS	Larval period	22	–	–	.72	−0.03	−0.18, 0.12	1.89	1.62, 2.17	0.94
OLS	Max. longevity	142	.23	.23	<.01	0.21	0.14, 0.24	0.60	0.50, 0.69	–
PGLS	Max. longevity	125	–	–	<0.01	0.22	0.15, 0.22	0.75	0.46, 1.05	0.79
OLS	Metamorphosis size	30	<.01	−.04	.76	−0.03	−0.22, 0.16	1.39	1.11, 1.69	–
PGLS	Metamorphosis size	22	–	–	.55	−0.07	−0.32, 0.17	1.41	1.06, 1.77	0.14
OLS	Size at maturity	144	.17	.16	<.01	0.20	0.13, 0.27	0.63	0.53, 0.75	–
PGLS	Size at maturity	127	–	–	<.01	0.21	0.13, 0.29	0.82	0.53, 1,11	0.59
Caudata
OLS	Age at maturity	68	.06	.05	.03	0.05	0.01, 0.10	0.44	0.37, 0.51	–
PGLS	Age at maturity	64	–	–	.13	0.04	−0.01, 0.10	0.42	0.16, 0.68	0.78
OLS	Birthweight	6	–	–	–	–	–	–	–	–
PGLS	Birthweight	6	–	–	–	–	–	–	–	–
OLS	Offspring size	56	.08	.06	.04	0.07	0.01, 0.14	0.40	0.30, 0.48	–
PGLS	Offspring size	53	–	–	.04	0.07	0.01, 0.13	0.44	0.01, 0.87	1.00
OLS	Clutch size	65	.04	.03	.08	0.18	−0.02, 0.38	1.57	1.28, 1.00	–
PGLS	Clutch size	61	–	–	.30	0.11	−0.11, 0.33	1.51	−0.04, 3.05	1.00
OLS	Reproductive output	75	<.01	−.01	.79	−0.01	−0.04, 0.03	−0.01	−0.06, 0.04	–
PGLS	Reproductive output	72	–	–	.05	0.07	0.00, 0.13	0.44	0.01, 0.88	1.00
OLS	Egg mass	5	–	–	–	–	–	–	–	–
PGLS	Egg mass	5	–	–	–	–	–	–	–	–
OLS	Incubation time	27	.01	−.03	.58	0.06	−0.15, 0.27	1.69	1.38, 2.01	–
PGLS	Incubation time	26	–	–	.35	0.10	−0.12, 0.32	1.53	0.85, 2.21	1.00
OLS	Larval period	18	.17	.11	.09	0.38	−0.04, 0.80	1.85	1.47, 2.23	–
PGLS	Larval period	17	–	–	.37	0.23	−0.30, 0.75	2.26	1.49, 3.04	0.57
OLS	Max. longevity	65	.10	.09	<.01	0.09	−0.01, 0.16	1.07	0.97, 1.16	–
PGLS	Max. longevity	64	–	–	<.01	0.13	0.05, 0.21	0.86	0.60, 1.12	0.44
OLS	Metamorphosis size	22	<.01	−.04	.84	−0.02	−0.24, 0.19	1.49	1.31, 1.66	–
PGLS	Metamorphosis size	19	–	–	.88	0.02	−0.20, 0.24	1.37	1.08, 1.65	0.95
OLS	Size at maturity	65	.02	<.01	.22	0.05	−0.03, 0.13	1.16	1.04, 1.28	–
PGLS	Size at maturity	64	–	–	.04	0.10	0.01, 0.19	0.96	0.68, 1.25	0.33
Reptiles—HG2018
OLS	Age at maturity	118	.65	.64	<.01	0.20	0.17, 0.22	2.60	2.52, 2.68	–
PGLS	Age at maturity	119	–	–	<.01	0.19	0.08, 0.16	2.82	2.66, 2.98	0.55
OLS	Birthweight	75	.69	.68	<.01	0.44	0.37, 0.51	−0.40	−0.60, −0.19	–
PGLS	Birthweight	77	–	–	<.01	0.41	0.32, 0.51	−0.36	−0.68, −0.04	0.26
OLS	Clutch size	209	.47	.47	<.01	0.24	0.20, 0.27	0.31	0.21, 0.41	–
PGLS	Clutch size	208	–	–	<.01	0.23	0.19, 0.28	0.37	0.11, 0.63	0.77
OLS	Clutches p.a.	134	<.01	−.01	.86	0.01	−0.03, 0.04	0.23	0.14, 0.31	–
PGLS	Clutches p.a.	134	–	–	.97	−0.01	−0.05, 0.05	0.29	0.07, 0.51	0.67
OLS	Egg mass	59	.90	.90	<.01	0.52	0.47, 0.57	−0.52	−0.68, −0.37	–
PGLS	Egg mass	61	–	–	<.01	0.45	0.37, 0.53	−0.34	−0.65, 0.04	0.85
OLS	Incubation time	173	.10	.09	<.01	0.04	0.02, 0.06	1.79	1.74, 1.85	–
PGLS	Incubation time	174	–	–	.06	0.03	−0.01, 0.06	1.82	1.67, 1.96	0.72
OLS	Max. longevity	277	.39	.38	<.01	0.15	0.13, 0.17	0.85	0.79, 0.91	–
PGLS	Max. longevity	274	–	–	<.01	0.13	0.10, 0.16	0.92	0.75, 1.09	0.73
OLS	Size at maturity	51	.60	.59	<.01	0.29	0.23, 0.36	0.70	0.47, 0.94	–
PGLS	Size at maturity	53	–	–	<.01	0.27	0.20, 0.34	0.75	0.46, 1.04	0.93

Criteria were applied to all amphibians, the amphibian orders Anura and Caudata, and the reptiles. For reptiles, the results from Hallmann and Griebeler (2018) are shown (HG2018). Criteria were explored under ordinary least squares regression analysis (OLS, Price et al., 2014) and phylogeny‐informed regression analysis (PGLS) on log₁₀‐log₁₀‐transformed data. DF = degrees of freedom; R ² = coefficient of determination (<.05 indicates invariance, Price et al., 2014); Adj R ² = adjusted R ²; p = p‐value (≥.05 indicates invariance); CI_s = 95% confidence interval of slopes; CI_i = 95% confidence interval of intercepts. Lambda (λ) values rate the impact of the phylogeny on studied relationships between life history traits and body mass (residuals). Please note that adjusted R ² can drop below zero. This happens if R ² is zero or close to zero and usually indicates that the model fits poorly the data. Bold highlights values consistent with type II invariance. – = not applicable under PGLS or sample size too small.