AIPL RESEARCH REPORT
Net merit as a measure of lifetime profit - 2000 versionP.M. VanRaden
Animal Improvement Programs Laboratory, ARS-USDA, Beltsville, MD 20705-2350
301-504-8334 (voice) ~ 301-504-8092 (fax) ~ email@example.com ~ http://aipl.arsusda.gov
Superceded by 2003 update
Beginning in August 2000, the net merit (NM$) index became a lifetime profit function that uses actual incomes and expenses as proposed and developed through Project S-284, Genetic Enhancement of Health and Survival for Dairy Cattle, a collaborative research effort of the Southern Association of Agricultural Experiment Station Directors.
Selection of animals to be parents of the next generation should be more accurate if all traits of economic value are included in NM$. Previously, type traits affected NM$ of Holstein bulls only through correlations with productive life (PL). For bulls and cows of other breeds and for Holstein cows, type traits were not included in NM$.
The genetic merit for each trait of economic value can be predicted from both direct and indirect measurements (multitrait methods). Many traits affect the cow's PL and also the incomes and expenses within lactations. New programs were developed to enhance PL evaluations with correlated information from type, yield, and somatic cell score (SCS) evaluations similar to those of Weigel et al. (1998, Journal of Dairy Science 81:2040). Further information on calculation of multitrait PL can be found in "Multitrait Productive Life" [VanRaden and Wiggans, 2000, AIPL Research Report PL1(11-00)]. To create an index of net merit, all traits should be combined according to economic value.
An economic value is the profit change when a given trait changes by one unit and all other traits in the index remain constant. For example, an economic value for protein is determined by holding pounds of milk and fat constant and examining the increase in price when milk contains an extra pound of protein. A trait's value may change if other traits are included in the index. For example, if no yield traits were included, the trait dairy form might have value as an indicator of yield. However, when a bull's true merit for yield is known, dairy form would lose its value as an indicator because true yield is used instead. Dairy form could still have value in multitrait predictions when yield is not measured precisely or for predictions of other correlated expenses such as health traits that are not included directly in the index.
Large cows and bulls were favored by dairy cattle breeders for many years. Research studies (VanRaden, 1988, Journal of Dairy Science 71:Suppl. 1:238; Metzger et al., 1991, Journal of Dairy Science 74:Suppl. 1:262) that were funded by Holstein Association USA at the Universities of Wisconsin and Minnesota concluded that cow size should have negative value in an index because milk income already was accounted for but feed costs were not. Within each breed, the larger cows tend to eat more feed and are less efficient (Dickinson et al., 1969, Journal of Dairy Science 52:489). Holstein Association USA acted on this research and ranked bulls on an alternative index called the Commercial Herd Selection Criteria from 1990 through 1995. In that index, selection for smaller stature, strength, and body depth received 10% as much emphasis as higher yield.
With the many traits available, the use of a profit function can help to
account for all the incomes and expenses. Unfortunately, some costs are
difficult to measure. In the 1980's as part of Project NC-2 of the North
Central Regional Association of Agricultural Research Experiment Station
Directors, researchers developed a profit function to compare genetic lines in
their experimental herds:
|lifetime profit||=||milk value + salvage value + value of calves|
|- rearing cost - feed energy - feed protein - health cost - breeding cost.|
The main difference between the updated NM$ index and the 1980's profit function is that a predicted transmitting ability (PTA) is calculated for each trait and then combined instead of combining each cow's phenotypic data directly. The PTA approach is more accurate because heritabilities of traits differ, genetic correlations are not the same as phenotypic correlations, and all phenotypes are not available at the same time. The new NM$ index includes more of the traits that affect profit because type traits now receive direct selection.
In 1999, scientists in the S-284 Health Traits Research Group proposed that yield traits, health traits, and type traits all be combined using a lifetime profit function. Previously, economic values of yield, PL, and SCS in NM$ were obtained as averages of independent literature estimates. Profit functions provide a more direct method of assigning economic values. To measure profit, estimates of actual incomes and expenses are needed.
Beginning with August 2000 evaluations, NM$ is defined as the expected lifetime profit as compared with a breed base and is calculated by summing yield (Yield$), udder (Udder$), and other (Other$) subindexes.
NM$ = Yield$ + Udder$ + Other$.
Incomes and expenses that repeat for each lactation are multiplied by the cow's expected number of lactations. This multiplication makes the economic function a nonlinear function of the original traits. For official NM$, a linear approximation of this nonlinear function is used as recommended by Goddard (1983, Theoretical and Applied Genetics 64:339). The linear function is much simpler to use and was correlated with the nonlinear function by .999. The three subindexes are each on a net lifetime basis and have the same units as NM$. The fluid merit (FM$) and cheese merit (CM$) indexes are computed by using fluid and cheese pricing, respectively, instead of standard milk-fat-protein pricing (MFP$) to obtain Yield$.
The Yield$ subindex is the value of the cow's milk, fat, and protein
converted from a lactation value to a net lifetime value. The premiums paid for
low SCS are in the Udder$ instead of Yield$ subindex. Economic values of yield
are calculated for three different pricing methods: MFP$, milk-fat dollars
(MF$), and cheese yield dollars (CY$). From any of those pricing
formulas, Yield$ is obtained by subtracting feed costs per lactation
(Feed$) and multiplying by the number of lactations (#Lact) and
the ratio of actual yield to mature-equivalent yield
(Yield/YieldME). As with previous net merit indexes, Feed$ is
calculated as 30% of the component prices used in MFP$ and includes other costs
such as electricity to cool the extra milk and a bulk tank to hold it. Then,
Yield$ for the three different pricing methods is calculated by:
|NM$:||(MFP$ - Feed$)(#Lact)(Yield/YieldME)|
|FM$:||(MF$ - Feed$)(#Lact)(Yield/YieldME)|
|CY$:||(CY$ - Feed$)(#Lact)(Yield/YieldME)|
|MFP$||=||.010(PTA milk) + 1.15(PTA fat) + 2.55(PTA protein)|
|MF$||=||.087(PTA milk) + 1.15(PTA fat),|
|CY$||=||-.008(PTA milk) + 1.15(PTA fat) + 3.17(PTA protein), and|
|Feed$||=||.003(PTA milk) + .35(PTA fat) + .77(PTA protein).|
The expected prices for milk, fat, and protein were obtained from average U.S. prices over recent years. A base milk price of $12.70 was assumed.
The profit function requires that PL be expressed in lactations instead of months. The variable #Lact is defined as the average number of lactations (3.0) plus a regression on PL (.12):
#Lact = 3.0 + .12(PTA PL).
The regression is larger than .1 (1 lactation = 10 months) to allow for PL beyond 84 months and lactations longer than 10 months.
If cows stay in the herd for an average of three lactations, then Yield/YieldME = .89 using the age adjustment factors of Schutz (1995, unpublished data). Cows with longer PL have slightly higher Yield/YieldME, which is calculated as
Yield/YieldME = .89 + .0037(PTA PL).
Selection for lower SCS (PTA SCS) and improved udder traits both lead to reduced labor and health costs. Lower PTA SCS also leads to higher milk prices in markets where quality premiums are paid. Fetrow et. al (2000, Proceedings of the 39th Annual Meeting of the National Mastitis Council, p. 3-47) surveyed price premiums and penalties across the nation and found an average price decrease of $.20 for each unit of PTA SCS (a doubling of somatic cell count).
The Udder$ subindex is calculated as
Udder$ = [10(PTA udder) - 51(PTA SCS - breed SCS)](#Lact),
where PTA udder is an udder composite. For Holsteins, PTA udder is the
Udder Composite Index that is calculated by Holstein Association USA (2000,
Holstein Type-Production Sire Summaries, August, p. 12). For other
breeds, the PTA's for udder traits are converted to standardized transmitting
abilities (STA's) by dividing by the standard deviation (SD) of
the true transmitting ability and then are combined into an udder composite.
Relative values of each trait in PTA udder are:
|Udder trait||Relative value (%)||SD|
|Rear udder height||16||1.00||1.45|
|Rear udder width||12||1.00||1.51|
A value of $10 per lactation was set for PTA udder. The emphasis placed on udder traits in NM$ is similar to that proposed by Rogers (1993, Journal of Dairy Science 76:664; 1998, Proceedings of the 1998 U.S. National Dairy Genetics Workshop, Orlando, FL, p. 5-11). Selection for higher udders is important when also selecting against large body size.
The value of PTA SCS per lactation was set at -$51, which includes a premium of $41 plus $10 for labor, drugs, and discarded milk. As in the past, PTA SCS includes breed SCS, which is 3.10 for Holsteins. The breed average is removed when including PTA SCS in Udder$. The emphasis placed on SCS is much greater than in the August 2000 Type-Production Index (TPI) formula of Holstein Association USA.
Linear type traits provide additional information about incomes and expenses that were not included in the previous NM$ formula (VanRaden and Wiggans, 1995, Journal of Dairy Science 78:631). Instead of directly using PTA's for all 17 type traits, composites for feet and legs (PTA F&L) and for body size (PTA size) are used.
The lifetime net income or loss from PL and the remaining linear type
traits are included in Other$ as
|Other$||=||Profit$(#Lact) - Loss$ + 5(PTA F&L)(#LACT)|
|- 24(PTA size)[Maint$(#Lact)(Weight/WeightME) + Replace$var - Beef$],|
where Profit$ = lactation profit, Loss$ = culling loss, Maint$ = maintenance costs, Weight = cow's actual weight, WeightME = cow's mature-equivalent weight, Replace$var = variable cost of replacement per pound of WeightME, and Beef$ = beef income.
For Holsteins, PTA F&L and PTA size are the Feet and Legs Composite
and Body Size Composite Indexes, respectively, that are calculated by Holstein
Association USA (2000, Holstein Type-Production Sire Summaries, August,
p. 12-13). For other breeds, the PTA's are converted to STA's by dividing by
the SD of the true transmitting ability before combining the traits into
composites. Because the traits rear legs (rear view) and feet and legs score in
the Holstein Feet and Legs Composite are not available for the other breeds,
the STA for foot angle is used for PTA F&L for those breeds. Relative
values of each trait in PTA F&L are:
|Foot or leg trait||Relative value (%)||SD|
|Holstein||Other breeds||Holstein||Other breeds|
|Rear legs (side view)||-8||. . .||1.00||. . .|
|Rear legs (rear view)||18||. . .||1.00||. . .|
|Feet and legs score||50||. . .||1.00||. . .|
|Feet and legs composite||100||100||.88||1.00|
Relative values of each trait in PTA size are:
Because multiple lactations are needed to cover the cost of raising the cow, PL has a large economic value. Positive selection for PTA F&L and negative selection for PTA size also are included. Compared with a value of $10 per lactation for PTA udder, the value of PTA F&L is set at $5 per lactation based on research by Rogers (1993, Journal of Dairy Science 76:664).
Maintenance costs include the increased cost of feed per lactation that is eaten by heavier cows for body maintenance [$.18 per pound based on findings by the National Research Council (1978, Nutrient Requirements of Dairy Cattle, 5th rev. ed.), Yerex et al. (1983, Journal of Dairy Science 66:Suppl. 1:115), and Metzger et al. (1991, Journal of Dairy Science 74:Suppl. 1:262) plus increased housing costs [$.03/lb based on Bath et al. (1985, Dairy Cattle: Principles, Practices, Problems, Profits, 3rd ed.) and Etgen et al. (1987, Dairy Cattle Feeding and Management, 7th ed.)] minus net income from heavier calf weights ($.06/lb of cow's weight):
Maint$ = $.18 + $.03 - $.06 = $.15.
Replacement costs include a fixed charge of $400 plus $.60/lb of body weight at first calving. Additional growth from first calving to mature weight costs only $.30/lb because maintenance after calving is included in Maint$. If Holstein replacements average 1,275 lb and mature cows average 1,500 lb:
Replace$var = [1,275($.60) + (1,500 - 1,275)$.30]/1,500 = $.56/lb.
Total cost of growing a replacement to mature weight (Replace$) is
Replace$ = $400 + 1,500 ($.56) = $1,240.
Beef income is the price received for mature cull cows, which is estimated to be
Beef$ = $.35/lb.
Culling loss is the loss from culling cows at a beef price lower than cost of growing replacements. Average Loss$ is
Loss$ = Replace$ - 1,500(Beef$) = $708.
Lactation profit is the increased profit when a cow stays for an additional lactation. The profit from producing milk for 3 lactations equals Loss$ so that total profit equals 0 for an average cow after all costs including interest, labor, and management are deducted:
Profit$ = Loss$/3.0 = $236.
Mature weight in pounds is obtained by multiplying PTA size by 24 based on Holstein data from the University of Minnesota size-selection herd. The Weight/WeightME ratio is 91% for an average herd. Cows with longer PL spend more of their lives as mature cows:
Weight/WeightME = .91 + .0027 PTA PL.
Averages and SD's of the various traits differ by breed, but official NM$ is calculated by using Holstein values instead of having a slightly different NM$ formula for each breed.
Recent research (Rogers, 1998, Proceedings of the 1998 U.S. National Dairy Genetics Workshop, Orlando, FL, p. 5-11) indicates that other traits such as dairy form and teat length also affect profit and may deserve selection.
The total of all incomes and expenses provides a nonlinear profit
function. Economic values were obtained by taking partial derivatives of that
profit function with respect to each trait evaluated with all other traits at
the population average. Official NM$, FM$, and CM$ are calculated from this
simpler, linear version of the profit function:
|Index||PTA trait||SD||Value ($/PTA unit)||Relative value (%)|
|Lifetime merit||Milk (lb)||832||.018||.224||-.029||5||43||-6|
The PTA for each trait is multiplied by the corresponding economic value and then summed. An exception is that the breed average first must be subtracted from PTA SCS. Relative values for each trait were obtained by multiplying the economic value by the SD for true transmitting ability. Those individual values are divided by the sum of their absolute values to express each as a percentage of relative value.
The three subindexes add up to the released NM$, FM$, and CM$ if calculated using linear algebra instead of the nonlinear formulas. For each subindex, the traits are multiplied by their economic values and summed. Less emphasis is placed on PTA PL than in the previous NM$ index because some of the economic value of PTA PL has shifted to the linear type traits and also because some of the extra costs such as health and fertility expenses within lactation that are correlated to PL are not included in the profit function.
Relative values also can be expressed for the three subindexes instead
of the individual traits within each of the merit formulas:
|Index||SD||Value ($)||Relative value (%)|
Reliability (REL) of NM$ is computed from REL of the eight PTA
traits and genetic correlations among those traits:
|PTA trait||PTA trait|
|*Holstein heritabilities in blue on diagonal; heritabilities for other breeds are the same except for yield traits (.35), size (.35), and udder (.20).|
For all breeds, genetic correlations of the linear type composites with yield, PL, and SCS were computed from literature values for Holstein linear type traits (Short and Lawlor, 1992, Journal of Dairy Science 75:1987; Schutz, 1993, Journal of Dairy Science 76:658; Weigel, 1993, Ph.D. thesis). Genetic correlations among the type composites were calculated from official Holstein genetic correlations for linear type traits (Misztal et al., 1994, Journal of Dairy Science 75:544).
The REL of NM$ is the variance of predicted NM$ divided by the variance of true NM$ and can be expressed best with matrix algebra:
REL NM$ = r'Gr/v'Gv.
where r contains the relative economic values multiplied by the square root of each PTA trait's REL, G contains the genetic correlations between the eight PTA traits, and v contains the relative economic values for the traits.
The calculation of NM$ also can be expressed in matrix form:
NM$ = a'u,
where a contains the economic values for the eight PTA traits and u contains the traits. The breed average for SCS must be subtracted from PTA SCS in the element of u that contains information for SCS.
An example Holstein can be used to demonstrate calculation of NM$ and
|PTA trait||PTA||REL (%)|
After subtracting the Holstein breed average for SCS of 3.10 from PTA SCS, the NM$ for this animal would be +$311, and REL of NM$ would be 77%.
Expected genetic progress
An expected annual genetic gain for each trait can be calculated from
genetic correlations of each trait with NM$, FM$, or CM$. A standardized gain
was also calculated by dividing the actual gain by the potential gain from
single-trait selection for that trait:
|PTA trait||Actual annual PTA gain||Standardized annual PTA gain|
To compute trend, a simple formula for mass selection (Van Vleck, 1993, Selection Index and Introduction to Mixed Model Methods) was used that did not account for differing REL or generation intervals in the four paths of selection (sire of sires, dams of sires, sires of dams, and dams of dams).
Although NM$ measures the additional lifetime profit that is expected to
be transmitted to an average daughter, it does not include the additional
profit that will be expressed in granddaughters and more remote descendants.
Gene flow methods and discounting of future profits could provide a more
complete summary of an animal's total profit. The profit function approach lets
breeders select for many traits by combining the incomes and expenses for each
trait into an accurate measure of overall profit. Producers should use the
lifetime merit index that corresponds to the market pricing that they expect a
few years in the future when buying breeding stock and 5 years in the future
when buying semen.
Acknowledgments: The author thanks George Wiggans for designing the database that was needed to calculate NM$ and Lori Smith and Suzanne Hubbard for review and revision of this research report.