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Comparison of Longevity and Fertility Trait Definitions in Theory and Simulation

Explore different methods and models to evaluate non-normally distributed traits related to longevity and fertility. Analyze linear and binomial models, survival analysis, and evaluate sires using simulated data. Compare animal vs sire models and examine the distribution of longevity and days open in Holstein calvings.

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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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