Environmental differences make it difficult to compare pigs tested at different locations, at different times, or under different management. The use of standard selection indexes based on contemporary group comparisons, however, removes much of the influence of these environmental factors. Thus, more valid comparisons of genetic merit are possible. This appendix contains details about the indexes recommended in these Guidelines.

Parameter Estimates

^A Economic values are in dollars per 1 unit of change (i.e. 1 pig/litter, 1 in. of backfat, etc.)
^B A-mode ultrasound.
^C B-mode ultrasound or metal probe.

Table 9. Phenotypic and genetic correlations used in construction of recommended selection indexes.

		Genetic Correlations
		L	LB	W	NW	D	B	F	G	M
	L	-	0.63	0.12	0.88	­0.2	0.0	­0.2	-	-
	LB	0.8	-	0.69	0.67	0.43	­0.4	-	0.0	-
	W	0.0	0.66	-	0.93	0.0	0.0	­0.3	-	-
Phenotypic	NW	0.6	0.7	0.86	-	-	-	-	-	-
Correlations	D	0.1	0.0	0.0	-	-	­0.2	0.65	-	0.1
	B	0.0	­0.1	0.0	-	­0.18	-	0.33	0.22	­0.9
	F	-	-	-	-	0.6	0.25	-	­0.7	­0.4
	G	-	0.2	-	-	-	0.2	­0.4	-	­0.2
	M	-	-	-	-	0.1	­0.7	­0.3	­0.1	-

Table 10. Heritability estimates (diagonal), phenotypic (below diagonal) and genetic correlations (above diagonal) for muscle quality traits.¹

Trait	F	G	D	B	pH	W	I	T	C
F	-	-.70	.65	.34	0	0	0	0	0
G	-.65	-	-.90	.14	-.11	.07	.06	-.07	.11
D	.60	-.87	-	-.05	.10	-.06	-.09	.07	-.11
B	.25	.20	-.18	-	.03	-.05	.30	-.17	.09
Ultimate ph (pH)	0	-.08	.09	.08	.38	-.50	0	-.42	-.66
Water holding capacity (W)	0	.06	-.06	-.06	-.50	.16	.05	.22	.49
Intramuscular fat % (I)	0	.07	-.07	.30	.01	-.28	.47	-.17	.15
Instron tenderness (T)	0	-.06	.06	-.16	-.37	.19	-.11	.20	.23
Minolta L* color (C)	0	.09	-.07	.08	-.54	.50	.12	.19	.29

¹ Source: National Pork Producers Council. 1995. Genetic Evaluation: Terminal line program results.

Economic Values

No single set of economic values is appropriate for all herds or even regions of the U.S., and those appropriate for a particular region should be developed as data become available. A short explanation and details of the calculations used to obtain the values given in Table 8 follow.

L	The concept used in Iowa State University's Farrow to Finish Enterprise Analysis and Budget computer program was used for this calculation. It considers the cost of keeping replacement gilts from market to breeding, and on through gestation; the cost associated with the sire; the prorated loss from less than perfect conception rates and of death loss of breeding stock (based on the salvage value of first parity sows). Once the appreciation in value of the first litter sow is subtracted, a total cost of $15.32 is associated with producing an extra pig per litter. Calculations approximate for older sows kept for succeeding parities follow the same procedures and result in a cost of $12.93 per extra pig. If a herd consists of 80% sows and 20% gilts an overall herd value of $13.41 ($13.50 when rounded) is obtained.
LB	Assume total litter birth weight averages 30 lb. $13.50/30=$.45.
W	This value is rounded to $.50. It includes the cost of raising a pig to 21 days of age, prorating to a per lb basis.
NW	Assume 21-day-old pigs weigh 12 lb. $.50 * 12 = $6.10.
D	This value (-$.12) is based on a range of 6-19 cents per day for housing, labor and utilities.
B	The -$15.00 is rounded from the value calculated below, and assumes carcass merit systems will be the rule, not the exception.
F	The -$12.58 below was rounded to -$13.00.
G	Based on the cost of keeping pigs in a test situation, the calculated value of $5.60 was rounded to $6.00.

Calculation of Economic Values

One major advantage of selection indexes is that genetic values of the traits can be weighted by their relative economic value. Although it is impossible to establish economic values that are suitable for all situations, an explanation of the values chosen for use in the recommended indexes is given.

Number Born Alive
Gilt
	Feed for 2 months @ $.07/lb*6 lb/d (selection to breeding)	$ 25.20
	Feed for gestation: 114d @ $.07/lb*6 lb/d	$ 47.88
	Maintenance for 174d @ $.15/d (60d + 114d)	$ 26.10
	Boar ($500 @ 40 litters/boar)	$ 12.50
		$111.68
	8 L * 85% conception	÷ 6.8
	Cost per pig	$ 16.42
	Death loss 3%/yr = 1.5%/litter (300lb gilt @ $.38/lb * 1.5%,8 pigs)	$ .21
		$ 16.63
	Appreciation ([(300lb*$.38)-(230lb*$.45)], 8 pigs)	$ -1.31
		$ 15.32
Sow
	Maintenance: 141d @ $.25/d (114d + 6d post weaning)/.85 conception rate	$ 35.35
	Feed for 141d * 5lb/d * $.07/lb	$ 49.35
	Breeding fee	$ 30.00
	Cost per litter	$114.60
	9 L	÷ 9
	Cost per pig	$ 12.73
	Death loss: 450lb*$.35*.03*141/(365*.9)	$ .20
		$ 12.93
	20% gilts @ $15.32 + 80% sows @ $12.93 = $13.41
21-Day Litter Weight
	Value of pig at weaning	$ 22.45
	Value of pig to transfer	$ 15.50
	Cost of extra pig: $.74 + $.33	$ 1.07
	(feed/pig/d = $.035*21 d+labor etc.)	$ 5.88/pig
	Pig gain (15 lb - 3 lb)	÷ 12 lb
		$ .49
Days to 250 Pounds
	range of $.06 - $.19/d = $.125/day
Backfat at 250 Pounds
	From the average of three carcass value pricing systems. The values for a 1 inch reduction in backfat for a 185 lb. carcass was:
	Packer	Value
	A	$17.75
	B	$ 9.66
	C	$ 16.40
	Average	$14.60
Feed Efficiency
	Purdue University recommendations F/G has its largest impact from 60 to 250 lbs. 170 lb/unit decrease @ $.074/lb = $12.58 / unit
Average Daily Gain
	In most test station situations, there is a 170-lb gain, and nonfeed costs are higher than those for on-farm program. Therefore:
	190 lb gain (250 - 60)
	$.20/d maintenance
	Range 2-3 lb gain/day
	190/2 = 95d * $.20/d =	$19.00
	190/3 = 63d * $.20/d =	$12.60
		$ 6.40

Analysis Procedures for Calculating Indexes

E.P. Cunningham's SELIND computer program (1970) was used originally to generate the indexes, and much of the following terminology comes from the documentation of that program. Many graphing calculators now have the capability of solving the matrix equations needed to generate selection indexes.

where	X = n x 1 vector of traits measured phenotypically,
	Y = m x 1 vector of traits evaluated genetically,
	b = n x 1 vector of index weights, and
	a = mx 1 vector of economic values.

To solve for b:	Pb =Ga
	[P][b] = [G][a]
and	b = P-1Ga,

where	P = n x n matrix of phenotypic variances and covariances for X
	b = n x 1 vector of index weights
	G = n x m matrix of covariances of X with Y, and
	a = m x 1 vector of economic values.

C is a m x m matrix of genetic variances and covariances for Y, and is used to generate statistics useful in evaluating indexes.

When information from relatives of the animal being evaluated is included, the degree of relationship is accounted for in the correlations, which are part of the covariances:

where X = trait being measured on the animal and Y = trait being measured on the relative.

Since variances (s²) are special cases of covariances, G is a true covariance matrix. It is based on C and is modified to account for different sources of information expressed in P.

Statistics which are useful include:

Correlation (I,H) = r_IH = s_I / s_H

Another useful statistic calculated by SELIND is the percentage of economic value of total genetic gain accounted for by gain in each trait:

This is based on the regression of the index on each trait in the aggregate genotype. A similar statistic which weights the emphasis given to each trait in the index is the standard partial regression:

Example Calculations for Indexing Pigs

1. Maternal Index. The gilt to be indexed was born in a first parity litter of 11 and reared in a litter of 10 which weighed 178 lb at 23 days of age. Her weight at 160 days of age was 240 lb, and her B-mode ultrasound backfat reading at that weight was .9 inches.

   To calculate the index value for this gilt, her records must be adjusted to standard conditions. This gilt was born in a first-parity litter, so her dam=s record for number born alive must be increased by 1.2 pigs (Table 1): 11 + 1.2 = 12.2 pigs. Since the litter was weighed at 23 days of age, the weight should be multiplied by .94 (Table 2). Litter weight should also be adjusted for parity by adding 6.2 lb (Table 4). No adjustment for litter size is necessary because the litter had 10 or more pigs. The final adjusted litter weight is (178*.94)+6.2=173.5 lb.

   The gilt=s record for days to 250 lb is calculated using the equation on page 13. The desired weight is 250 lb, actual weight was 240 lb, actual age was 160 days, and the correction factor for gender is 40 days, giving an adjusted days to 250 lb of 165 days. Adjusted backfat is calculated in a similar manner using the equation on page 11. The adjusted backfat for this gilt is .94 inches.

   The adjusted values for the traits must also be calculated for all gilts in the contemporary group and averaged to yield L, W, D, and B. If the average adjusted values for this gilt=s contemporary group were L = 9.4 pigs, W = 158 lb, D = 163 days, and B = 1.04 inches, her maternal index (page 14) is

   I = 100 + 6*(12.2-9.4) + .4(173.5-158) - 1.6(165-163) - 81(.94-1.04) = 128 index points

2. Terminal Index. Assume you wish to determine the index of a boar that required 150 days to reach 250 lb in a contemporary group that averaged 165 days. His adjusted backfat (B-mode) was .6 inches and the group average was .75 inches. He was born and reared in a second parity litter of 9 which weighed 200 lb at 22 days. The contemporary group adjusted values for litter size and weight are 9.1 and 185, respectively.

   To calculate the terminal index, we simply use the adjusted values already determined in the index for B-mode backfat scans (page 14):

   I = 100 - 1.4(150-165) - 106(.6-.75) = 137 index points

   Note that we can ignore the litter information because this boar will be used to sire only market pigs. If we were interested in using him to sire replacement gilts we would need to use the maternal index.

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