Random regression modelling of genetic covariance when data are available for litters: an application in mice

A recently published model for litter weight in multiparous species defines genetic dam and sire effects as linear random regression slopes on litter size. Building on the interpretation of these effects in terms of maternal and direct breeding values for birth weight, we show how to convert estimates of genetic covariance parameters from that model into direct and maternal genetic (co-)variances for birth weight. Additionally, we introduce a modification of the random regression model that directly provides the same results. As a case study, litter weights from two unselected mouse control lines were first analyzed separately using a univariate approach. Then, bivariate analyses were conducted, adding litter size or one of several body mass traits at later ages as a second trait. The DUKb line contributed weights for 7 241 litters (87 641 pups) from 116 generations, and the DUKssi line 14 496 litter weights (160 334 pups) from 152 generations. The maternal genetic variance of individual birth weight was 2-3 times that of the direct genetic variance. Strong correlations (0.78 and 0.77, respectively) were estimated between direct and maternal genetic effects on birth weight; however, SEs were high at 0.45 and 0.36. Estimates of genetic correlations between the maternal effect on birth weight and LS were negative (-0.63 and -0.59) and of similar magnitude in both lines; their SEs were moderate at 0.05 and 0.06. Genetic correlations between maternal genetic effects on birth weight and body mass traits at later ages (day 21, day 42, and at mating) were strong, ranging from 0.82 to 0.95, depending on line and trait; SEs for these estimates ranged from 0.03 to 0.15. Results obtained by applying the modified random regression model were identical, as expected given its equivalence. In conclusion, litter weight data provide information on the genetic (co-)variability of direct and maternal effects on birth weight and on their (co-)variability with additive-genetic effects on other traits. Previously applied models, in contrast, suffer from confounding with litter size and do not account for sire effects, limiting their ability to extract the full information on birth weight. Thus, litter weight should be regarded as a trait characterising prenatal growth of newborns, and any version of the random regression model should be employed for meaningful analyses.