Optimum bias in selection index parameters estimated with uncertainty

Economic values under inappropriate normal distribution assumptions

The objectives of this study were to quantify the errors in economic values (EVs) for traits affected by cost or price thresholds when skewed or kurtotic distributions of varying degree are assumed to be normal and when data with a normal distribution is subject to censoring. EVs were estimated for a continuous trait with dichotomous economic implications because of a price premium or penalty arising from a threshold ranging between -4 and 4 standard deviations from the mean. In order to evaluate the impacts of skewness, positive and negative excess kurtosis, standard skew normal, Pearson and the raised cosine distributions were used, respectively. For the various evaluable levels of skewness and kurtosis, the results showed that EVs can be underestimated or overestimated by more than 100% when price determining thresholds fall within a range from the mean that might be expected in practice. Estimates of EVs were very sensitive to censoring or missing data. In contrast to practical genetic evaluation, economic evaluation is very sensitive to lack of normality and missing data. Although in some special situations, the presence of multiple thresholds may attenuate the combined effect of errors at each threshold point, in practical situations there is a tendency for a few key thresholds to dominate the EV, and there are many situations where errors could be compounded across multiple thresholds. In the development of breeding objectives for non-normal continuous traits influenced by value thresholds, it is necessary to select a transformation that will resolve problems of non-normality or consider alternative methods that are less sensitive to non-normality.

Increasing accuracy in estimation of economic values for resistance to gastrointestinal helminths in meat sheep

The impact of utilising different indices and numbers of index traits in estimation of economic values (EVs) for resistance to gastrointestinal (GI) helminths were investigated. Seven indices based on yearling weight (YW), litter size (LS) and ewe live weight (ELW) were evaluated under a scheme that considered individual records (Scheme 1) and one that utilised extra information from individual's relatives (Scheme 2). Under an objective where index response in YW was maximum (R(IYW) = max) economic values were US$ 0.00, 0.41, 0.35 and 1.58 in scheme 1 and -0.07, 0.25, -1.10 and -0.02 in scheme 2 for indexes 1, 2, 3 and 4 respectively. In the determining the effect of the number of index traits on the estimates of EVs, calculations were done for five breeding objectives. Eight scenarios (indices) under each objective that differed in the number of traits considered were evaluated. In all scenarios, EVs under R(IYW) = max were positive and were US$ 0.00, 0.79, 2.68, 2.66, 2.66, 2.62, 2.44 and 2.62 for scenarios 1-8 respectively. Generally, economic value estimates varied across breeding schemes and objectives.

Impact of milk pricing system on the economic response to selection on milk components

The impact of various milk pricing systems on the economic weights and the resulting selection responses for milk yield and fat and protein contents in Holstein and Czech Fleckvieh were investigated. The calculations were done for the situations with and without quotas on milk yield and fat content. There was a substantial influence of the milk pricing system on the selection response. The use of index weights based on a 'wrong' pricing system reduced the total economic selection response by up to 51% of the selection response expected for an index based on the 'correct' pricing system. Financial losses in the selection response were greater with quotas than without quotas. Higher losses were also calculated for Holstein compared with Czech Fleckvieh. Incorrect assumptions on the output limitation (absence or presence of milk quotas) led only to minor reductions in the total selection response (mostly <2%) if the other parameters were correct. The results indicate that customized subindices for milk production traits would increase farmers' profit from sire selection when selling milk on the basis of different pricing systems.

Risk-adjusted expected return for selection decisions1

The results of genetic evaluation are predictions of breeding values for the selection candidates, and these involve uncertainty with regard to future returns from the use of those selected individuals. This uncertainty is due to differential variability in BLUP of breeding values and can be translated into risk: High fluctuations mean greater risk, which is not taken into account by just looking at expected return. In this research, the methodology of value at risk (VaR) and expected shortfall is introduced for animal breeding decisions as a means to adjust the expected return for the cost of uncertainty in prediction of breeding values. This methodology has recently received a great deal of attention from financial institutions. Given a specified probability alpha, VaR is the alpha-quantile of the distribution of economic returns. The conditional value at risk (CVaR), or expected shortfall, is the expectation of the economic returns, which are less or equal to the VaR. By subtracting the CVaR from the predicted aggregate genotype (muR), a risk-adjusted expected return (RAER) measure was obtained. The measures muR, VaR, and RAER were calculated for a data set with progeny of 161 Polled Hereford bulls belonging to a beef cattle company. The Pearson and Spearman correlations between muR and RAER were 0.89 (P < 0.001) and 0.90 (P < 0.001), respectively. Even though the latter correlation was high, some bulls ranked differently for muR compared with RAER. The Pearson correlation between muR and VaR was low (0.124) and nonsignificant (P > 0.05), whereas the correlation between VaR and RAER was -0.31 (P < 0.0001). The results indicate the need to take into account the adjustment for risk in expected return in order to alleviate the effects of possible losses when overrated animals are selected.