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. 2017 Jan 4;118(5):442–452. doi: 10.1038/hdy.2016.116

Table 2. The impact of MHC genotypic combination of mates on fertilization success in Chinook salmon was analyzed using MCMCglmms.

  Estimate Variance (%) Lower 95% CI Upper 95% CI pMCMC
Fixed effects
 Intercept 1.34   0.265 1.993  
 AAI <0.001   −0.001 <0.001 0.728
 SF 0.445   0.977 0.794 <0.001
Random effects
 Female (10) 0.004 0.87 <0.001 0.045  
 Male (27) 0.016 3.46 <0.001 0.045  
 Male–Male Pair (84) 0.439 95.02 0.269 0.689  
 SF (random slope) 1.036   0.642 1.463  
 Additive overdispersion 0.003 0.65 <0.001 0.007  
Summary statistics
 Marginal R2 0.12        
 Conditional R2 0.39        
           
Fixed effects
 Intercept 1.416   0.514 2.435  
 AAII/PBRII −2.063   −3.747 −0.017 0.03
 SF 0.557   0.323 0.806 <0.001
Random effects
 Female (10) 0.008 1.74 <0.001 0.029  
 Male (27) 0.021 4.58 <0.001 0.052  
 Male–Male Pair (84) 0.427 93.03 0.269 0.598  
 SF (random slope) 1.159   0.795 1.591  
 Additive overdispersion 0.003 0.65 <0.001 0.008  
Summary statistics
 Marginal R2 0.13        
 Conditional R2 0.43        
           
Fixed effects
 Intercept 1.218   0.152 2.275  
 PBRI <0.001   −0.001 <0.001 0.736
 SF 0.535   0.290 <0.001 <0.001
Random effects
 Female (10) 0.008 1.66 <0.001 0.032  
 Male (27) 0.015 3.11 <0.001 0.039  
 Male–Male Pair (84) 0.457 94.62 0.290 0.626  
 SF (random slope) 1.223   0.841 1.677  
 Additive overdispersion 0.003 0.62 <0.001 0.009  
Summary statistics
 Marginal R2 0.08        
 Conditional R2 0.42        
           
Fixed effects
 Intercept 1.227   0.243 2.239  
 MxyI 0.052   −0.093 0.186 0.456
 SF 0.538   0.276 0.783 <0.001
Random effects
 Female (10) 0.008 1.68 <0.001 0.029  
 Male (27) 0.015 3.16 <0.001 0.040  
 Male–Male Pair (84) 0.449 94.53 0.286 0.636  
 SF (random slope) 1.211   0.805 1.661  
 Additive overdispersion 0.003 0.63 <0.001 0.008  
Summary statistics
 Marginal R2 0.08        
 Conditional R2 0.39        
           
Fixed effects
 Intercept 1.141   0.199 2.151  
 MxyII 0.134   0.037 0.256 0.008
 SF 0.569   0.297 0.829 <0.001
Random effects
 Female (10) 0.017 3.67 <0.001 0.064  
 Male (27) 0.021 4.54 <0.001 0.052  
 Male–Male Pair (84) 0.422 91.14 0.264 0.599  
 SF (random slope) 1.152   0.770 1.578  
 Additive overdispersion 0.003 0.65 <0.001 0.008  
Summary statistics
 Marginal R2 0.16        
 Conditional R2 0.50        

Abbreviations: CI, confidence interval; MHC, major histocompatibility complex; PBR, peptide-binding region.

Fertilization success was the proportion of a total of 48 genotyped offspring sired by each male in a paired-male fertilization trial. For fixed effects (relative sperm velocity of paired males (SF for slower/faster male in a paired-male trial), MHC divergence), significant pMCMC values (in bold) and the amount of variation explained by fixed effects (marginal R2) and the whole model (conditional R2) are reported. The variance (%) explained by each random effect (female identity (n=10), male identity (n=27), combination of males of which sperm was used in a focal female, denoted Male–Male pair (n=84)) refers to the total variance by all random effects and the additive overdispersion. For different estimates of MHC similarities between mates analyzed see Table 1 legend.