Table 4. RRMs were used to test for I*E and G*E for each of our six traits, plus annual fitness.

Trait	Model	Variance components	χ2	d.f.	P value
Body weight	3.1	ID
	3.2	ID + ID*PD	3.16	2	0.206
	3.3	VA + VPE	40.36	1	< 0.001
	3.4	VA + VPE + ID*PD	2.92	2	0.232
	3.5	VA + VPE + VPE*PD + VA*PD	5.00	2	0.082
Hind leg length	3.1	ID
	3.2	ID + ID*PD	0.00	2	0.999
	3.3	VA + VPE	49.22	1	< 0.001
	3.4	VA + VPE + ID*PD	0.00	2	0.999
	3.5	VA + VPE + VPE*PD + VA*PD	0.00	2	0.999
Strongyle FEC	3.1	ID
	3.2	ID + ID*PD	0.66	2	0.719
	3.3	VA + VPE	5.50	1	0.019
	3.4	VA + VPE + ID*PD	0.54	2	0.763
	3.5	VA + VPE + VPE*PD + VA*PD	0.86	2	0.651
Horn length	3.1	ID
	3.2	ID + ID*PD	33.68	2	< 0.001
	3.3	VA + VPE	10.80	1	0.005
	3.4	VA + VPE + ID*PD	31.52	2	< 0.001
	3.5	VA + VPE + VPE*PD + VA*PD	5.82	2	0.054
Horn growth	3.1	ID
	3.2	ID + ID*PD	0.00	2	0.999
	3.3	VA + VPE	1.64	1	0.200
	3.4	VA + VPE + ID*PD	0.00	2	0.999
	3.5	VA + VPE + VPE*PD + VA*PD	0.00	2	0.999
Testicular circumference	3.1	ID
	3.2	ID + ID*PD	22.52	2	< 0.001
	3.3	VA + VPE	9.90	1	0.002
	3.4	VA + VPE + ID*PD	19.66	2	< 0.001
	3.5	VA + VPE + VPE*PD + VA*PD	2.80	2	0.247
Annual fitness	3.1	ID
	3.2	ID + ID*PD	6.34	2	0.042
	3.3	VA + VPE	0.74	1	0.390
	3.4	VA + VPE + ID*PD	6.22	2	0.045
	3.5	VA + VPE + VPE*PD + VA*PD	3.12	2	0.210

For each model, the variance components structure of the individual and/or additive genetic variance component is given, where ID, individual identity; V_A, additive genetic variance; V_PE, permanent environment variance; and PD, population density. Other details of model structure are provided in the Materials and Methods. Also shown are the χ² statistics and P-values associated with the likelihood ratio test used to compare the model in question with a model omitting the term in question. FEC, fecal egg count.