Longevity was defined as the difference in days between the culling date for culled cows (uncensored data) or the last recorded test-day for surviving cows (censored data) and the date of first calving.
Model #
Heritability estimates and breeding values for direct longevity (survival) were obtained using the “survival analysis” method, with the Survival Kit 3.1 package.
A mixed Weibull model with a homogeneous hazard function was applied. The model accounted for fixed environmental effects such as age at first calving, lactation number, lactation stage, relative protein and fat yield within the herd in a given year and calving season, herd size change classes in subsequent years, random herd-year-season effect, and additive paternal genetic effect.
| Genetic parameters of the Weibull distribution | |
| 2,07 | |
| 0,007 | |
| 2,23 | |
| Genetic parameters | |
Sire effect variance  | 0,0451 |
Heritability  | 0,19 |
Estimated breeding values (EBVs) and the relative risk of culling (RR = exp(EBV)) for bulls were transformed by changing the sign so that higher EBVs indicated greater longevity of the bull’s daughters.
Breeding values of bulls were expressed as deviations from a base and then transformed to a variable with a mean of 100 and a standard deviation of 10.
Genetic base #
The genetic base was set as the average breeding value of bulls born between 2009-2011, which had a repeatability of at least 50%.
Repeatability #
The repeatability of the evaluation was approximately determined using the selection index method based on the number of uncensored daughters (Nb) and the number of uncensored paternal half-sisters (Nob) with the formula:
R = (¼ Rob + Rb – 2 ¼ Rob*Rb) / (1 – ¼ *Rob*Rb)
where:
h2 – heritability of survival (0.19)
Rb = Nb/(Nb+(4-h2)/h2) – repeatability of the bull’s breeding value based on the uncensored daughters,
Rob = Nob/(Nob+(4-h2)/h2) – repeatability of the paternal half-sister’s breeding value based on the daughters of the paternal half-sister.
Acceptance criteria for publication of breeding values #
A minimum repeatability of 20% is required for the evaluation of longevity to be recognized and published.