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ASSESSING TRAIT ECONOMIC IMPACTS AT THE LEVEL OF THE INDIVIDUAL ANIMALS CONSIDERED IN SELECTION
S.A. Barwick and A.L. Henzell
Animal Genetics and Breeding Unit, University of New England, Armidale, NSW 2351
SUMMARY
This paper outlines a method for assessing trait economic impacts, at the level of the individual animals considered in selection, for traits where the economic value changes across the range of the trait. Results are compared with those from linear methods for price patterns that are common for traits, such as beef carcase fat depth, weight and marbling score, which affect market acceptability and preference. Some important deviations from linearity were seen in the change in index that occurs with change in estimated breeding value (EBV) for these traits. The deviations were most evident at the extremes of the EBV range, which could affect the animals selected. Simple extensions of the method are also suited for use in mate selection and other important areas where non-linearity is encountered.
Keywords: non-linear, economic values, selection index, market specifications, carcass quality
INTRODUCTION
Selection problems quite commonly involve non-linear elements even though most formulations of breeding objectives and selection indexes are linear (Goddard 1983; Weller et al. 1996). Sources of non- linearity include non-additive and interaction effects underlying phenotypes, properties of the involved trait distributions, and differences in the economic value of traits that can occur for differing levels of traits. When non-linear effects are involved, it can be that there is no uniformly best solution for the aggregate selection criterion (Weller et al. 1996). Here we consider effects on the aggregate selection criterion, referred to throughout as the selection index, that are introduced when the economic value of trait change is not constant across the range of the trait. We outline a method for valuing these impacts at the level of individual animals, contrast results for this and linear methods, and briefly describe how other knowledge can be exploited to better customise the index to the selection context.
BACKGROUND
Selection indexes in multiple trait genetic evaluation. Schneeberger et al. (1992) showed the weightings to apply to estimated breeding values (EBVs) û from multiple-trait genetic evaluations in selection indexes are given by b = G11-1 G12 v . Here, G11 and G12 are matrices of genetic variances and covariances applying respectively among the EBV selection criteria and between the criteria and the breeding objective traits, and v is a vector of breeding objective trait economic values.
Analogously to the situation in conventional selection index theory, the index when linear can also be obtained as g'v, where g are EBVs for the breeding objective traits and g' = û' G11 -1
G12. When there are both traits with linear impacts and traits with non-linear impacts, the selection index as well has linear and non-linear components that can be summed. If, for animal i, the economic impact of a trait assessed in progeny is TEIi, the contribution to the index (?I) for animal i is TEIi x 2k, where k is a discounting factor. The 2 is used to approximate the scale of other parts of the index where the units of these are breeding value (Barwick and Henzell 1999).
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Example of non-linear trait economic impacts: breeding for market acceptability and preference. Non-linear trait economic impacts can occur when different prices apply to different levels of a trait. This is common for traits that affect market acceptability and preference. The value of a unit of trait change then is not constant across the range of the trait and is potentially different for each animal. Patterns of price premiums and discounts can be identified. They include where price is constant across an acceptable range of the trait but is discounted outside of this range; and where price increases at a constant, increasing or decreasing rate with increase in the trait. The first pattern is common for carcase weight and fatness, and the latter patterns for marbling and muscling, for example, in markets for beef. The patterns may have relevance more widely. Here we compare results obtained with the proposed and linear methods for these described price patterns.
VALUING TRAIT ECONOMIC IMPACTS AT THE LEVEL OF INDIVIDUAL ANIMALS The method is illustrated here for beef carcase marbling score in the context of selection of bulls for joining in a particular herd. Estimates of s2P and s2G for the trait are assumed available. Steps involve prediction and calibration of EBVs for the breeding objective trait under consideration, a step for assessing economic impact, a processing step where index contributions are determined and tabulated for all likely levels of EBV, and a look-up step where the index contribution is read for each animal.
The prediction step involves derivation of EBVs for, in this case, carcase marbling score (MSEBV) for all animals. MSEBVs are then ‘calibrated’ to marbling score phenotype by estimating, and relating through a mapping function, distributions (µ,s) of MSEBV and of marbling score for the breed of animals considered and the production system assumed in the breeding objective. The marbling score information that is used to relate phenotype to the breed MSEBV distribution may be herd-specific or for the whole breed. Knowledge at herd level increases the ability to customise the index to the selection context. Where herd level knowledge is not available, breed level knowledge can be used.
For the economic impact assessment step, the details needed include estimates of price differences for all levels of the trait, MSEBVs for the animals to be considered, and the mapping relation described above between MSEBV and marbling score. The economic impact of trait change is assessed for animal i by valuing the shift in the progeny marbling score distribution for animal i relative to that for an animal that would produce no herd change in the trait. The value is then expressed on the same basis as other index components (Barwick and Henzell 1999). Discounting is achieved using a variation of the procedure of McArthur and del Bosque Gonzalez (1990). Where the herd mean marbling score is µH and that associated with the MSEBV of animal i is µi, the expected mean marbling score of animal i progeny is (µH + µi)/2. The standard deviation of the distribution of animal i progeny, comprising of half-sibs, is (s2P – ¼s2G)½. The progeny distribution for an animal that produces no trait change in the herd has mean µH and standard deviation (s2P – ¼s2G)½. In the processing step, the index contribution (?I) from trait change is assessed across all likely levels of MSEBV and for suitably small MSEBV intervals. These details are retained for look-up then for each animal evaluated, using interpolation as required.
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Figure 1. The relationship between trait EBV and the associated index contribution (?I), assessed with the outlined (non-lin.) and linear methods, for price patterns that are common for traits that affect market acceptability and preference. Illustrations in each case are for a change in carcase marbling score EBV.
COMPARISON OF RESULTS
Figure 1 shows the relationship between trait EBV and the associated index contribution (?I) over a range of MSEBVs and for the price patterns described. Also included is the case where price increases at a constant rate over the range of the trait (Figure 1a). This is the situation where a linear index applies. For this case the outlined method reproduces the appropriately linear relationship (Figure 1a). Figure 1b and 1c show that significant deviations from linearity occur for other price patterns, suggesting that a linear index sometimes over- or under-values index contributions. The results in Figure 1b and 1c are for a herd that has some proportion of steers which are too lean and which have a marbling score less than 2. This occurs quite commonly. The deviations from linearity seen were most evident for animals of highest EBV, which means the animals selected could be affected.
DISCUSSION
The deviations from linearity seen in ?I are sensitive to the existing trait distributions and price patterns. The size and importance of the deviations will change between traits in accordance with their impact on the total index. In Figure 1, the index was for a breeding objective addressing 220- day feedlot-fed steer production for the Japanese B3 market. Marbling score is an important trait in this objective. Figure 1c shows that a linear index would substantially over-value MSEBV
(a)
(b)
(c)
Constant rate of price increase
0 50 100 150 200 250 300
0 1 2 3 4 5 6 7 8 9 10 11 12 Trait level
Price per kg carcase
Example fat depth price pattern
0 10 20 30 40 50 60
0 1 2 3 4 5 6 7 8 9 10 11 12
Trait level Price per kg carcase
Example marbling price pattern
0 50 100 150 200 250
0 1 2 3 4 5 6 7 8 9 10 11 12
Trait level Price per kg carcase
E B V c o n t r i b u t i o n t o t h e i n d e x
- 4 0 - 3 0 - 2 0 - 1 0102030405060700
- 0 . 8 -0.4 0 0 . 4 0 . 8 1 . 2 1 . 6 T r a i t E B V
∆ I ($)
linear non-lin.
E B V c o n t r i b u t i o n t o t h e i n d e x
- 4 0 - 3 0 - 2 0 - 1 01 02 03 04 05 06 07 00
- 0 . 8 -0.4 0 0.4 0 . 8 1 . 2 1 . 6 T r a i t E B V
∆ I ($)
linear
non-lin.
E B V c o n t r i b u t i o n t o t h e i n d e x
- 4 0 - 3 0 - 2 0 - 1 01 02 03 04 05 06 07 00
- 0 . 8 -0.4 0 0.4 0 . 8 1 . 2 1 . 6 T r a i t E B V
∆ I ($)
linear, non-lin.
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contribution to the index in animals of highest EBV. Perhaps as importantly is the ability of the method to be used more generally for non-linearity from a number of sources. With only minor variation the method can be used in mate selection. For mate selection the progeny distribution shift to be valued is that for mating pair i relative to a mating pair that produces no change in the trait. The progeny distribution for mating pair i has mean (µ1i + µ2i)/2, where µ1i and µ2i are marbling scores associated with the MSEBVs for mates 1 and 2 of pair i; and standard deviation (s2P – ½s2G)½. The progeny distribution for a mating pair producing no change in the trait has mean µH and standard deviation (s2P – ½s2G)½. The mean EBV of the mating pair, or alternatively the progeny mean phenotype, is a convenient basis for the ?I look-up.
The method can also be used in other important applications. These include when animals to be evaluated are of mixed breed, and progeny express differing amounts of heterosis, and when animals have information available on individual gene or marker effects. Details for these applications are given elsewhere. The method is being considered for use in the customised breeding objective and selection index system ‘BreedObject’ (Barwick et al. 1992; Barwick and Henzell 1998).
CONCLUSIONS
Important deviations from linearity can occur in the change in index that is associated with change in EBV for traits where price varies across the range of the trait. Examples are beef carcase fat depth, weight and marbling score, traits which affect market acceptability and preference. A method is outlined for use in these situations. Use of a linear index may over- or under-value index contributions, and this could affect the animals selected. The method outlined can also be used in mate selection and to address non-linearity in other important applications.
ACKNOWLEDGEMENTS
We are grateful to NSW Agriculture and to Meat and Livestock Australia for salary and funding support of the work, which was conducted under MLA Project BFGEN.100.
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