The purposes of this study were 1) to investigate the heritability, reliability, and selection response for survival traits following a Weibull frailty proportional hazard model; and 2) to examine the relationship between genetic parameters from a Weibull model, a discrete proportional hazard model, and a binary data analysis using a linear model. Both analytical methods and Monte Carlo simulations were used to achieve these aims. Data were simulated using the Weibull frailty model with two different shapes of the Weibull distribution. Breeding values of 100 unrelated sires with 50 to 100 progeny (with different levels of censoring) were generated from a normal distribution and two different sire variances. For analysis of longevity data on the discrete scale, simulated data were transformed to a discrete scale using arbitrary ends of discrete intervals of 400, 800, or 1200 d. For binary data analysis, an individual's longevity was either 0 (when longevity was less than the end of interval) or 1 (when longevity was equal or greater than the end of interval). Three different statistical models were investigated in this study: a Weibull model, a discrete-time model (a proportional hazard model assuming that the survival data are measured on a discrete scale with few classes), and a linear model based upon binary data. An alternative derivation using basic expressions of reliabilities in sire models suggests a simple equation for the heritability on the original scale (effective heritability) that is not dependent on the Weibull parameters. The predictions of reliabilities using the proposed formulae in this study are in very good agreement with reliabilities observed from simulations. In general, the estimates of reliability from either the discrete model or the binary data analysis were close to estimates from the Weibull model for a given number of uncensored records in this simplified case of a balanced design. Although selection response from the binary data analysis depends on the end of interval point, there is a relatively good agreement between selection responses in the Weibull model and the binary data analysis. In general, when the underlying survival data is from a Weibull distribution, it appears that the method of analyzing data does not greatly affect the results in terms of sire ranking or response to selection, at least for the simplified context considered in this study.

The Baluchi breed is the most common native breed of Iran adapted to harsh environments in the eastern parts of the country. The data used in the present study, collected from two research flocks at the Abbasabad sheep breeding station in north-east Iran, included 20 534 animals descended from 363 sires, 5992 dams, 282 maternal grandsires, and 2865 maternal granddams during the period 1966 to 1989. The traits recorded were: birth weight (BW), weaning weight (WW), weight at 6 months (W6), weight at 12 months (YW), pre-weaning gain (WG), postweaning gain (PWG), lamb fleece weight (LFW), ewe fleece weight sheared before first joining (FW1) and adult ewe fleece weight (FW). Genetic parameters, estimated with restricted maximum likelihood and a two-trait animal model, were similar in the two flocks. Direct heritabilities for the various body weight traits were moderate and varied between 0-13 and 0-32, while the maternal heritabilities were low and varied between 0-01 and 0-12. Direct and maternal genetic correlations between WW and weights at later ages were moderate to high (0-59 to 0-96). Direct heritabilities of weight gain measures varied between 0-12 and 0-19, while no significant maternal influence on either of these weight gain measures could be detected. The estimates of direct genetic correlation between WG and PWG were positive and varied between 0-54 and 0-74, while negative maternal genetic correlation (-0-17 on average) between WG and PWG was detected. For LFW, direct heritability was low and no maternal heritability could be shown. For FW1, both direct and maternal genetic influences were demonstrated (0-07 to 0-26). Direct genetic correlation between LFW and FW1 was very low and close to zero, while maternal genetic correlation was positive and relatively high (0-72 on average). The relative contributions to phenotypic variance from variance components due to common environmental effects ranged from 0-01 to 0-15 for all traits. The repeatability of FW was low (0-03 to 0-12).

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A genetic study was carried out to: (1) conduct a genetic analysis of longevity of Swedish Yorkshire sows, (2) study the environmental and genetic factors that influence the presence and severity of osteochondrosis, and (3) investigate the relationship between breeding values for osteochondrosis and longevity of sows. The data for the longevity analyses were extracted from the Swedish litter-recording scheme data bank (Quality Genetics, former Scan Avel HB). After editing original data, records of 9814 Yorkshire sows with 7553 (77%) uncensored and 2261 (23%) censored born 1986 through 1997 were used in the analyses. Litter size at first and last farrowing, age at first farrowing, backfat thickness, daily gain and weight at completion of performance test (~170 days) were included as fixed effects in all analyses. The combination of herd-year effect was treated as fixed or random, time-independent or time-dependent in different analyses. Sire effect was considered as the source of genetic variation and thus a sire model was used. The analyses of osteochondrosis were based on information on 14 388 Landrace and 14 458 Yorkshire pigs from the Swedish pig progeny-testing scheme, recorded from 1987 through 1997. The birth herd and the combination of sex, testing station, year and month for start of test were included as fixed effects in the statistical model. Variance and covariance components for osteochondrosis recorded at elbow and knee joints were estimated in a bivariate animal model by the restricted maximum likelihood method within each breed. In the survival analyses (Yorkshire sows), the fixed effects of herd-year (when it was treated as fixed effect), litter size at first and at last farrowing, age at first farrowing, backfat and gain at completion of performance test were highly significant (P < 0·01). Herd-year combination was the major cause of variation for risk of culling, compared with other fixed effects. The risk of being culled at a certain time decreased as the litter size at first and at last farrowing, or backfat of the gilt at completion of performance test increased. With increasing age at first farrowing, the risk of being culled at a certain time increased. Heritability in the original scale for longevity ranged from 0·21 to 0·31. The results for osteochondrosis showed that the combined effect of sex-testing station-year and month of start of test was highly significant (P < 0·01). Estimates of heritabilities for osteochondrosis score were similar for both Landrace and Yorkshire breeds and was, on average, 0·21. The correlations between breeding values for longevity and osteochondrosis were low (on average 0·07, adjusted for genetic trends) but were significant (P < 0·01) and in a favourable direction: higher osteochondrosis load associated with higher risk of being culled.

The estimation of (co)variance components for multiple traits with maternal genetic effects was found to be influenced by population structure. Two traits in a closed breeding herd with random mating were simulated over nine generations. Population structures were simulated on the basis of different proportions of dams not having performance records (0, 0.1, 0.5, 0.8 and 0.9): three genetic correlations (-0.5, 0.0 and +0.5) between direct and maternal effects and three genetic correlations (0, 0.3 and 0.8) between two traits. Three ratios of direct to maternal genetic variances, (1:3, 1:1, 3:1), were also considered. Variance components were estimated by restricted maximum likelihood. The proportion of dams without records had an effect on the SE of direct-maternal covariance estimates when the proportion was 0.8 or 0.9 and the true correlation between direct and maternal effects was negative. The ratio of direct to maternal genetic variances influenced the SE of the (co)variance estimates more than the proportion of dams with missing records. The correlation between two traits did not have an effect on the SE of the estimates. The proportion of dams without records and the correlation between direct and maternal effects had the strongest effects on bias of estimates. The largest biases were obtained when the proportion of dams without records was high, the correlation between direct and maternal effects was positive, and the direct variance was greater than the maternal variance, as would be the situation for most growth traits in livestock. Total bias in all parameter estimates for two traits was large in the same situations. Poor population structure can affect both bias and SE of estimates of the direct-maternal genetic correlation, and can explain some of the large negative estimates often obtained.