Table 1.

Results of: (a) the generalized mixed model on offspring crawling‐out behavior; (b) the linear mixed model on offspring snail size (PC1); and (c) the linear mixed model on offspring shell thickness (PC2) (PC1 and PC2 are the principal components of the principal component analysis on offspring snail mass, shell thickness, and four shell size traits)

	Fixed effects	Estimate (SE)	df	Χ2	p
a. Crawling‐out	Grand‐parental env. (E1)	0.848 (0.6812)	1	8.29	.0040
	Parental env. (E2)	−0.090 (0.3864)	1	0.4	.5274
	Offspring env. (E3)	1.738 (0.3544)	1	114.46	<.0001
	E1 × E2	−0.389 (0.7696)	1	0.01	.9315
	E1 × E3	−0.168 (0.7882)	1	1.89	.1687
	E2 × E3	−0.146 (0.4242)	1	0.01	.9072
	E1 × E2 × E3	0.855 (0.8915)	1	0.91	.3395

	Random effects	Variance	df	Χ2	p
	Family	0.489	1	14.98	.0001
	Individual	0.391	1	8.26	.0040

	Fixed effects	Estimate (SE)	Numdf, Dendf	F	p
b. Snail size (PC1)	Grand‐parental env. (E1)	0.037 (0.8837)	1, 41.93	0.47	.4986
	Parental env. (E2)	−0.212 (0.4689)	1, 48.96	0.45	.4528
	Offspring env. (E3)	−0.915 (0.4717)	1, 355.06	17.40	<.0001
	E1 × E2	−0.183 (0.9912)	1, 56.62	0.10	.7589
	E1 × E3	−0.150 (1.0779)	1, 349.40	0.18	.6695
	E2 × E3	0.052 (0.5811)	1, 363.02	0.005	.9463
	E1 × E2 × E3	−0.075 (0.2114)	1, 358.88	0.003	.9505

	Random effect	Variance	df	Χ2	p
	Family	0.3572	1	4.60	.0320

	Fixed effects	Estimate (SE)	Numdf, Dendf	F	p
c. Shell thickness (PC2)	Grand‐parental env. (E1)	0.055 (0.2821)	1, 41.14	0.11	.7409
	Parental env. (E2)	−0.227 (0.1484)	1, 49.44	0.06	.8066
	Offspring env. (E3)	0.313 (0.1543)	1, 356.26	45.04	<.0001
	E1 × E2	0.103 (0.3155)	1, 58.24	0.48	.4923
	E1 × E3	−0.406 (0.3535)	1, 350.40	4.11	.0433
	E2 × E3	0.410 (0.1904)	1, 363.97	6.67	.0102
	E1 × E2 × E3	0.099 (0.3975)	1, 359.66	0.06	.8036

	Random effect	Variance	df	Χ2	p
	Family	0.026	1	1.72	.1892

Bold values indicate significant p‐values (p < .05).