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Abstract Background Control of the environmental variability by genetic selection offers possibilities for new selection objectives for productive traits. This methodology aims at reducing heterogeneity in productive traits and has been applied to several traits and species for which animal homogeneity is profitable. In horse breeding programmes, rank in competitions is a common selection objective but has been challenging to model. In this study, the parameters of environmental variability for the rank of a horse were computed to analyse the capability of a horse to maintain the best ranking across competitions that consist of long-distance races in which the adapted physical condition of the horse is essential. The genetic component of the environmental variance for the rank in endurance competitions was evaluated, which resulted in proposing a new transformation of horse scores in competitions. Results Homogeneous and heterogeneous variance models were compared by assaying three random effects that affect both the rank and its variability, using endurance ride data consisting of 2863 records. The pedigree relationship matrix contained 5931 animals. The rank trait was transformed into a normalized variable to prevent false estimates of the genetic correlation by inappropriate artificial skewness. The models included the number of participants in the race, sex, and age as systematic effects. The rider, the rider-horse interaction, or an environmental permanent effect were tested as random effects, in addition to additive genetic and residual effects. The models were analysed using the GSEVM program. Estimates of heritability for rank ranged from 0.12 to 0.15. The heterogeneous variance model that fitted the rider was assessed as the best model based on the deviance information criterion. Estimates of genetic variance for rank variability ranged from 0.12 to 0.13. The genetic correlation between the rank and its environmental variability was low and did not differ from 0. Conclusions These results offer an opportunity to select animals for canalization by reducing the variability of race results and achieving the best positions, which could be a new selection objective by weighting estimated breeding values for rank and its variability in a selection index.

Abstract Background Selection of mice for decreased environmental variability of birth weight has achieved higher survivability and larger litter size as a correlated response to canalized selection, which suggests higher welfare and robustness, and animals that are more homogeneous. However, in these studies, animals were not exposed to an environmental challenge. To demonstrate the advantages of this mouse line with a low environmental variability of birth weight, animals from two divergent lines (high and low variability of birth weight) were subjected to feed restriction. The objective of this study was to use these divergent lines to compare their response in terms of robustness against an environmental challenge. At weaning, 120 females, i.e. four full-sib females from 10 random litters of three consecutive generations of selection, were chosen from these divergent lines. The total number of females was divided into four groups, which were subjected to a feeding regimen by imposing different levels of feed restriction (i.e. 75, 90 and 85% of full ad libitum feed across three generations, respectively) in different combinations during the growth and reproduction periods. Results Animals from the “low” line were less sensitive to a change in feed level than those from the “high” line. Regarding reproduction, the “low” line performed better in terms of number of females having parturitions, number of parturitions, and litter size. Imposing a feed restriction on female mice during their growth period did not affect the birth weight of their pups. The “low” line was preferred because of its higher reproductive efficiency and survival under an environmental challenge. Conclusions Selection for decreased environmental variability of birth weight produces animals that are less sensitive to environmental conditions, which can be interpreted as having greater robustness.