Genetic relationships of body condition score and locomotion with production, type and fertility traits in Holstein-Friesian cows

•Body condition score and locomotion could help to prevent the worsening health of cows.•Body condition score is moderately heritable and correlated with fertility traits.•Locomotion, lowly heritable, is strongly correlated with feet-and-legs traits.•The positive trend for locomotion and stable trend for second trait are favourable.•Both traits can be added into the selection index to improve fertility and legs health.