Economic Weighting of Traits

Transcription

1 Economic Weighting of Traits 1 Introduction The breeding objective in any livestock species is to improve the overall economic merit of the animals. Many traits contribute to the Total Economic Value of an animal. Suppose there are t traits of economic importance to a particular species, and let g be a vector of length t of true breeding values of an animal, then the Aggregate Genotype, H, is H = v g, where v is a vector of relative economic values of the t traits in g. The Aggregate Genotype is approximated in practice by a Selection Index, I, as I = w â, where â are the EBVs on m traits for one animal and w are relative economic weights. Note that m could be more, less, or equal to t. The Aggregate Genotype could include more traits than those currently recorded on the species. Another difference between the Aggregate Genotype and Selection Index is that g are the true (unknown) breeding values on t traits and â are the estimated breeding values on m traits, and lastly, w takes into account the reliabilities of the EBVs while v is based on perfect knowledge of the breeding values. One problem with economic indexes is that economics can change over time and sometimes the change can be very rapid. For example, the discovery of BSE (bovine spongiform encephalitis or Mad cow disease) in Canada changed the value of beef cattle overnight from profitable to nothing. Most economic changes are not this drastic, and the relative economic importance of one trait to another stays constant over time. For example, the value of reproductive performance to conformation traits does not fluctuate greatly over time. Genetic improvement is not instantaneous and does take some years to achieve, and hopefully relative economic values stay the same during this time. An assumption of the Selection Index approach is that the value of traits is linear, as the trait EBV gets larger then the economic value also gets larger. However, for some traits, the added value above a particular EBV level actually remains constant or increases at a slower rate. Some traits have intermediate optima, such as birthweights of beef cattle. These are advanced issues that will not be covered in this course. 1

2 2 Aggregate Genotypes The Aggregate Genotype contains all of the traits of economic importance in a species whether or not data are collected for all of these traits. The relative economic values may or may not be known for all of these traits. One must know the genetic variances and covariances among all t traits. These would be difficult to attain if some of the traits are not recorded in the population. The traits included are those that the breeder wishes to change for the better, or to not change while other traits are improved. Here, the breeder must define the longterm goals of the breeding program. The relative economic values may reflect true economic values or may also reflect the breeder s desired importance for one or more traits. The Aggregate Genotype is the plan that will be followed. 3 Selection Index The Selection Index contains EBVs on traits that are readily available from the recording program for that species. The economic weights must be derived. The perfect way to estimate the economic weights would be to calculate the economic value of every animal, from an accountant s point of view. Animals would receive credit for producing offspring, but would lose money based on the amount of feed consumed, health costs, breeding costs, and particular management costs. Most animals that are kept should be net gainers in economic value. The table below contains animals and their EBVs for two traits, one measured in centimeters and one measured in grams, plus a dollar value summarizing their accumulated costs and profits up to a fixed age. To determine the relative economic weights a linear regression model is applied, y = Xb + e, where y is the vector of dollar values of each animal, and X contains the EBVs of the traits, one column per trait, plus an overall mean (column of 1 s). 2

3 Animals, EBVs for two traits, and dollar value of animal. Animal Trait 1 Trait 2 Dollar EBV (cm) EBV (g) Value The least squares equations to solve are ˆµ ŵ 1 ŵ 2 ˆb = (X X) 1 X y, = = , The selection index equation would be I = 2.30(EBV ) (EBV ) 2. Ideally, this equation should be based on many animals. Using this equation, index values would be calculated for each animal as follows: Animal I -$ I values are called the Selection Index Criteria. Animals may be ranked based on the index values and the lower ranking animals may be removed from the breeding population. Thus, both traits 1 and 2 will be improved simultaneously by selecting on the index values. 3

4 The following table contains the top four animals for each trait and for the index value. The last line gives the averages of the four animals. The same four animals were not necessarily selected in each group. Top 4 Ranking Animals by Trait and by Index. By Trait 1 (cm) By Trait 2 (g) By Index ($) EBV I EBV I EBV 1 EBV 2 I If selection was only on the EBV for trait 1 versus the index, the average EBV for trait 1 would be cm compared to cm based on index selection, but the dollar value of the animals selected using only EBV for trait 1 would be $29.53 less than those selected on index value. Selection on EBV of trait 2 only, resulted in a better average EBV for trait 2 than index selection, but a loss of $20.90 in index value. Index selection will maximize the dollar value of animals selected, but will not result in the highest average EBVs for each trait. Therefore, genetic change in traits 1 and 2 will be slower with index selection than selecting on only one trait at a time, and genetic change in index value should be highest. 4 Relative Emphasis In the previous example, by selecting on index values, was more weight put on trait 1 or trait 2? To answer this question the variances and covariances of the True BVs are needed. Variances of true BVs tend to be greater than variances of EBVs. For the example data in Table 14.1, assume that V ar ( BV1 BV 2 ) = ( ). To determine the relative emphasis, the value of a one standard deviation change in traits must be compared. For trait 1, the value of one standard deviation change is w 1 σ a1 = 2.30(40) = 92.00$, and a one standard deviation change in trait 2 is w 2 σ a2 = 1.20(94) = $. 4

5 The relative emphasis of trait 1 to trait 2 in the index is RelativeEmphasis = w 2σ a2 w 1 σ a1 Thus, more emphasis is placed on trait 2 in this index. = If the emphasis is desired to be equal, then the weight on one trait needs to be adjusted so that the value of one standard deviation of each trait is equal. Thus, change w 1 to 2.82 $/cm OR change w 2 to $/g. If the emphasis on trait 2 was to be twice as large than on trait 1, then w 2 = 92.00(2) 94 = 1.96$/g. The index can therefore be manipulated to give the desired results. The regression equation, however, gives an indication of how each trait contributes to total economic value, at the present time and under the current financial situation. One could speculate on future changes in the economics of feed or products and change the dollar values of animals based on those projections. This would give weights on EBVs that are designed for that future financial scenario. 5 Custom Made Indexes Some livestock industries develop selection index weights for producers to help the industry as a whole. However, each producer may have different feed costs and sales markets, so that an index specifically for that herd or flock would be better than a one-size-fits-all index. Some websites allow producers to enter their costs, prices received, and traits to be improved in order to design a custom-made index. That index should maximize the change in dollar value of the animals in that herd based on the producer s goals. This would be a desirable approach, in general. 6 Selection Practices Selection index, if designed appropriately, will maximize the genetic change in dollar value of animals. Even so, other forms of selection are practiced in the industry. Independent Culling Levels. A selection index is used, but added to this are minimum levels for each trait in the index (or for a few of them). For example, the minimum selection index dollar value may be +50, but if the EBV for trait 1 is negative, then that animal is culled regardless of the index dollar value. This changes the relative 5

6 emphasis on the traits and is less efficient at maximizing the genetic change in dollar values. However, trait 1 may be a problem in that herd such that the producer can not afford to use animals with negative EBVs for that trait. Tandem Selection. No selection index is used. The selection criterion changes from one year to the next. This year selection may be on EBVs for trait 1, and next year selection would be on EBVs for trait 2. This could result in no change in dollar value of the animals selected in the long term. Phenotypic Selection. Producers often consider only the phenotypic values of animals and not what is transmitted to offspring. This is much less accurate than the selection index approach or the previous two methods unless the heritability of traits is very high. Residual effects can be very large with phenotypic records. EBVs are the best way to make genetic change. 6