Table 3. Parameter estimates showing the effects of inbreeding, maternal inbreeding, population density and the interaction between inbreeding and population density.

Trait	Sample sizea	Parameter	Main effects only		ID × E interaction fitted
			Estimate	P	Estimate	P
Birth weight	2810	Inbreeding	−0.13 (0.234)	0.579	−1.666 (0.887)	0.597
	697	Maternal inbreeding	−0.865 (0.419)	0.04	1.469 (1.24)	0.037
		Density	−0.001 (0)	<0.001	−0.001 (0)	<0.001
		Density:inbreeding			0.003 (0.002)	0.071
		Density:maternal inbreeding			−0.005 (0.002)	0.045
4-Month hindleg	1665	Inbreeding	−14.616 (6.39)	0.022	−15.922 (24.861)	0.025
	582	Maternal inbreeding	−13.988 (9.411)	0.138	42.509 (31.402)	0.136
		Density	−0.032 (0.003)	<0.001	−0.033 (0.003)	<0.001
		Density:inbreeding			0.003 (0.051)	0.947
		Density:maternal inbreeding			−0.122 (0.064)	0.059
4-Month weight	1661	Inbreeding	−3.881 (1.453)	0.008	−6.794 (5.666)	0.009
	582	Maternal inbreeding	−4.541 (2.339)	0.053	7.994 (7.299)	0.05
		Density	−0.008 (0.001)	<0.001	−0.009 (0.001)	<0.001
		Density:inbreeding			0.006 (0.012)	0.586
		Density:maternal inbreeding			−0.027 (0.015)	0.069
Female first winter survival	1219	Inbreeding	−6.535 (−13.138, 0.717)	0.066	24.112 (−7.898, 60.656)	0.153
	531	Maternal inbreeding	2.385 (−6.207, 11.396)	0.595	−9.781 (−50.485, 30.445)	0.626
		Density	−0.0142 (−0.0208, −0.0075)	<0.001	−0.0144 (−0.0214, −0.008)	<0.001
		Density:inbreeding			−0.064 (−0.136, 0.003)	0.06
		Density:maternal inbreeding			0.024 (−0.053, 0.103)	0.549
Adult female annual survival	640 (3229)	Inbreeding	−11.284 (−17.221, −5.071)	<0.001	27.889 (−6.84, 63.545)	0.115
	371	Maternal inbreeding	−2.363 (−10.13, 4.628)	0.515	−1.904 (−9.046, 5.685)	0.609
		Density	−0.0088 (−0.0142, −0.004)	0.002	−0.0092 (−0.0148, −0.0041)	0.002
		Density:inbreeding			−0.068 (−0.131, −0.009)	0.02
Female annual breeding success	640 (3229)	Inbreeding	−1.915 (−3.573, −0.221)	0.025	−3.191 (−10.274, 4.56)	0.396
	371	Maternal inbreeding	−1.002 (−2.826, 0.689)	0.261	−0.987 (−2.763, 0.779)	0.279
		Density	−5e−04 (−0.001, 1e−04)	0.074	−5e−04 (−0.001, 1e−04)	0.098
		Density:inbreeding			0.003 (−0.012, 0.017)	0.73
Male first winter survival	1035	Inbreeding	−11.37 (−18.878, −2.655)	0.008	−26.53 (−68.359, 18.52)	0.24
	507	Maternal inbreeding	−7.681 (−17.709, 1.954)	0.121	21.771 (−24.959, 67.008)	0.369
		Density	−0.0211 (−0.0325, −0.0113)	<0.001	−0.0217 (−0.0325, −0.0105)	<0.001
		Density:inbreeding			0.03 (−0.054, 0.112)	0.492
		Density:maternal inbreeding			−0.06 (−0.158, 0.028)	0.202
Adult male annual survival	446 (1251)	Inbreeding	−11.088 (−19.592, −2.965)	0.01	−8.427 (−59.569, 41.515)	0.748
	295	Maternal inbreeding	4.223 (−5.628, 13.636)	0.398	4.198 (−5.607, 14.134)	0.389
		Density	−0.0138 (−0.0236, −0.0046))	0.003	−0.0139 (−0.0232, −0.0045)	0.001
		Density:inbreeding			−0.005 (−0.089, 0.084)	0.924
Male annual breeding success	446 (1251)	Inbreeding	−8.753 (−14.812, −2.725)	0.003	−10.635 (−29.217, 5.978)	0.23
	295	Maternal inbreeding	2.752 (−4.501, 9.211)	0.424	2.765 (−4.313, 9.555)	0.427
		Density	−0.0024 (−0.0042, −5e−04)	0.014	−0.0024 (−0.0043, −6e−04)	0.015
		Density:inbreeding			0.004 (−0.031, 0.036)	0.839

Abbreviation: ID × E, inbreeding depression by environment interaction.

Density is for 1 October before birth for the juvenile body size traits and for 1 October before winter and parturition for the fitness components. Parameter estimates show s.e. for juvenile body size traits and 95% credibility intervals for fitness components. Note that slope estimates for density are for each additional sheep in the population which varied between 211 and 672 across the study years. Statistically significant P values are shown in bold.

^aNumbers give the number of unique individuals and the number of observations is shown in parentheses.