. 2017 Nov 10;208(1):349–364. doi: 10.1534/genetics.117.300498

Table 3. Selection on phenotypic traits.

Trait	Model	Structure	Estimate	SE	Vs.	χ²₁	P value
Body weight	1.0	Age*Sex
	1.1	1.0 + PD	−0.0683	0.0225	1.0	8.41	0.004
	1.2	1.1 + Trait	0.0337	0.0018	1.1	356.72	< 0.001
	1.3	1.2 + Trait²	0.0001	0.0001	1.2	0.59	0.443
	1.4	1.2 + Trait*Sex (M)	−0.0059	0.0033	1.2	3.26	0.071
	*1.5*	**1.2 + TraitPD***	*0.0038*	*0.0006*	*1.2*	*34.54*	*< 0.001*
Hind leg length	1.0	Age*Sex
	1.1	1.0 + PD	−0.0631	0.0263	1.0	5.49	0.019
	1.2	1.1 + Trait	0.7476	0.0577	1.1	163.50	< 0.001
	1.3	1.2 + Trait²	−0.5528	0.2179	1.2	6.35	0.012
	1.4	1.3 + Trait*Sex (M)	−0.1024	0.1110	1.2	1.18	0.278
	*1.5*	**1.3 + TraitPD***	*0.1337*	*0.0369*	*1.2*	*12.71*	*< 0.001*
Strongyle FEC	1.0	Age*Sex
	1.1	1.0 + PD	−0.0700	0.0224	1.0	8.82	0.003
	1.2	1.1 + Trait	−0.0112	0.0012	1.1	79.26	< 0.001
	1.3	1.2 + Trait²	0.0000	0.0000	1.2	0.01	0.903
	1.4	1.2 + Trait*Sex (M)	0.0030	0.0024	1.2	1.61	0.204
	*1.5*	**1.2 + TraitPD***	*−0.0026*	*0.0009*	*1.2*	*7.78*	*0.005*
Horn length	1.0	Age
	1.1	1.0 + PD	−0.1179	0.0454	1.0	6.58	0.010
	1.2	1.1 + Trait	0.1697	0.0287	1.1	34.07	< 0.001
	1.3	1.2 + Trait²	0.0288	0.0077	1.2	13.81	< 0.001
	1.4	1.3 + Trait*Sex (M)	NA	NA	NA	NA	NA
	*1.5*	**1.3 + TraitPD***	*0.0217*	*0.0091*	*1.3*	*5.65*	*0.017*
Horn growth	1.0	Age
	1.1	1.0 + PD	−0.1071	0.0488	1.0	4.91	0.027
	*1.2*	*1.1 + Trait*	*0.1300*	*0.0496*	*1.1*	*6.59*	*0.010*
	1.3	1.2 + Trait²	−0.0263	0.0565	1.2	0.22	0.639
	1.4	1.2 + Trait*Sex (M)	NA	NA	NA	NA	NA
	1.5	1.2 + Trait*PD	0.0309	0.0296	1.2	1.06	0.302
Testicular circumference	1.0	Age
	1.1	1.0 + PD	−0.0685	0.0479	1.0	2.17	0.104
	1.2	1.1 + Trait	0.2199	0.0334	1.1	42.62	< 0.001
	1.3	1.2 + Trait²	0.1162	0.0393	1.2	8.75	0.003
	1.4	1.2 + Trait*Sex (M)	NA	NA	NA	NA	NA
	*1.5*	**1.3 + TraitPD***	*0.0518*	*0.0195*	*1.3*	*7.06*	*0.008*

Linear mixed-effects models (LMMs) were used to test for associations between annual fitness and six phenotypic traits, and the interaction between this association and population density (PD). The estimate and SE are given for the model parameter denoted under “Structure”; “Vs.” indicates which model the given model was tested against using a likelihood ratio test; the χ²₁ statistic and P-value were calculated from the likelihood ratio test comparison of the two models. For the size of the data sets and number of individuals measured in each data set, see the Materials and Methods. The models highlighted in bold italics are depicted in Figure 2. M, male; FEC, fecal egg count; NA, not applicable.