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Comparison of Longevity and Fertility Trait Definitions in Theory and Simulation

Comparison of Longevity and Fertility Trait Definitions in Theory and Simulation. Goals. Compare methods to evaluate non-normally distributed traits Linear analysis of length of time Binomial analysis of culling rate Survival analysis for log(culling rate) Try to understand parameters

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Comparison of Longevity and Fertility Trait Definitions in Theory and Simulation

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  1. Comparison of Longevity and Fertility Trait Definitions in Theory and Simulation

  2. Goals • Compare methods to evaluate non-normally distributed traits • Linear analysis of length of time • Binomial analysis of culling rate • Survival analysis for log(culling rate) • Try to understand parameters • Evaluate sires from simulated data

  3. Current Longevity Evaluations • Linear animal or sire models • Binomial culling rate • Single EBV = c (SWE, Cornell) • Multiple EBV = ct (CAN, AUS, IRL) • Productive life • Single EBV = 1/c (USA, GBR, ISR) • Multiple EBV = 1/ct (NZL) • Non-linear sire-MGS models • Survival analysis • Single EBV = log(c * envt) (DEU, FRA, NLD, ITA, BEL, CHE)

  4. Animal vs Sire-MGS Models • Value of maternal relatives • Average of 5 maternal brothers for bulls proven in USA • Extra info is worth 10-20 daughters when heritability is low (.10 to .03) • Animal vs sire models differ more than linear vs non-linear (Boettcher et al 1999 JDS 82:1034) • All relatives or non-linear math?

  5. Distribution of Longevity

  6. Distribution of Days OpenHolstein Calvings 1990 - 2001 Cows culled for reproductive reasons ≤ 50 ≥ 250

  7. Toss Coin Until Head Observed

  8. Maximum Likelihood • Define fraction of cows culled in each lactation = c and number of lactations survived by cow i = yi • Prob(yi | c) = c (1 – c)(Yi – 1) • ML estimate of c = n / Σ yi • Linear estimate of (1/c) = Σ yi / n • Culling rate is just reciprocal of number of lactations (no info lost)

  9. Prior Distributions • Sire effects normal for: • Number of lactations (linear model) • Culling rate (binomial model) • Log of culling rate (survival model) • Differences are small if heritability is low • Prob (y | c) can be the same, but Prob (c) differs

  10. Comparison of Priors

  11. Simulated Data • 500 sires with 10-1000 daughters, 10 replicates • Sire effects normal for log (c / .33) • BV for log(relative risk) transformed to culling rate and longevity by non-linear formulas • True BV had product-moment (linear) correlations of .98 to .995. • What scale should MACE work on?

  12. Simulation Results • Heritability estimates • .106 for number of lactations • .038 for culling rate (per lactation) • .091 for log(number of lactations) • True accuracy, or corr (EBV, BV) • .72 for number of lactations • .72 for culling rate • .70 for log(number of lactations)

  13. Conclusions • Including all relatives is more important when heritability is low • EBV from repeated binomial models are reciprocals of PL • True reliabilities are similar, but reported reliabilities differ slightly • Linear functions of data seem OK

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