J. Dairy Sci. 100:10234–10250
`https://doi.org/10.3168/jds.2017-12954
`© American Dairy Science Association®, 2017.
`A 100-Year Review: Methods and impact of genetic selection in dairy
`cattle—From daughter–dam comparisons to deep learning algorithms1
`K. A. Weigel,*2 P. M. VanRaden,† H. D. Norman,‡ and H. Grosu§
`*Department of Dairy Science, University of Wisconsin, Madison 53706
`†Animal Genomics and Improvement Laboratory, USDA-ARS, Beltsville, MD 20705
`‡Council on Dairy Cattle Breeding, Bowie, MD 20716
`§National Research and Development Institute for Biology and Animal Nutrition, 077015 Balotesti, Romania
`
`
`
`ABSTRACT
`
`In the early 1900s, breed society herdbooks had been
`established and milk-recording programs were in their
`infancy. Farmers wanted to improve the productivity of
`their cattle, but the foundations of population genet-
`ics, quantitative genetics, and animal breeding had not
`been laid. Early animal breeders struggled to identify
`genetically superior families using performance records
`that were influenced by local environmental conditions
`and herd-specific management practices. Daughter–
`dam comparisons were used for more than 30 yr and,
`although genetic progress was minimal, the attention
`given to performance recording, genetic theory, and
`statistical methods paid off in future years. Contem-
`porary (herdmate) comparison methods allowed more
`accurate accounting for environmental factors and ge-
`netic progress began to accelerate when these methods
`were coupled with artificial insemination and progeny
`testing. Advances in computing facilitated the imple-
`mentation of mixed linear models that used pedigree
`and performance data optimally and enabled accurate
`selection decisions. Sequencing of the bovine genome
`led to a revolution in dairy cattle breeding, and the
`pace of scientific discovery and genetic progress accel-
`erated rapidly. Pedigree-based models have given way
`to whole-genome prediction, and Bayesian regression
`models and machine learning algorithms have joined
`mixed linear models in the toolbox of modern animal
`breeders. Future developments will likely include elu-
`cidation of the mechanisms of genetic inheritance and
`epigenetic modification in key biological pathways,
`and genomic data will be used with data from on-farm
`sensors to facilitate precision management on modern
`dairy farms.
`
`Received March 29, 2017.
`Accepted June 11, 2017.
`1 This review is part of a special issue of the Journal of Dairy Science
`commissioned to celebrate 100 years of publishing (1917–2017).
`2 Corresponding author: kweigel@wisc.edu
`
`Key words: genetic selection, dairy cattle, genomic
`selection, statistical models
`
`THE BUILDING BLOCKS
`
`Performance Recording
`
`Pedigree records and performance data were the key
`building blocks in developing effective genetic selection
`programs in the pre-genomic era, as noted in Appendix
`Table A1. Pedigree records traced back to the origin of
`breed societies in the late 1800s, and widespread collec-
`tion of performance data began shortly thereafter, with
`the encouragement of early dairy industry pioneers
`such as W. D. Hoard. The first statewide association
`for recording milk weights and analyzing butterfat
`samples was formed in Michigan in 1905, and by 1908,
`the United States Department of Agriculture (USDA)
`Bureau of Animal Industry began organizing local and
`state cow testing associations into the national Dairy
`Herd Improvement Association (DHIA). Responsibil-
`ity for this effort was transferred to federal extension
`workers in 1914, and participation in milk testing grew
`rapidly (VanRaden and Miller, 2008), as shown in Fig-
`ure 1.
`Monthly DHIA testing was the norm for many de-
`cades, but now about two-thirds of dairy farms use
`labor-efficient a.m./p.m. testing plans, in which milk
`samples are taken at alternate times each month. Future
`strategies that focus on more frequent DHIA sampling
`of recently fresh cows or cows in the highest-producing
`pens may provide more useful data for cows that are
`at peak efficiency and at the greatest risk for common
`health disorders. Electronic measurement of data, via
`radiofrequency identification (RFID) sensors and inline
`sampling systems, has replaced manual entry of pedi-
`gree and performance data, as shown in Figure 2.
`Local bull associations were common during the 1920s
`and 1930s, until the widespread adoption of AI in the
`1940s, when dozens of regional AI cooperatives were
`formed. Because virtually all traits of interest in dairy
`cattle are sex-limited, genetic evaluation of a bull’s own
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`100-YEAR REVIEW: METHODS AND IMPACT OF GENETIC SELECTION
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`10235
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`Figure 1. Participation in milk recording programs in the United States, from 1908 to 2017.
`
`Figure 2. Recording of performance data for dairy cows then (1936, left panels) and now (2017, right panel).
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`WEIGEL ET AL.
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`phenotypes is not useful, and strategies for estimating
`a bull’s genetic superiority or inferiority based on the
`performance of his offspring were needed.
`
`Pedigree Data
`
`Despite the fact that dairy cattle breed societies as-
`signed unique identification numbers to individual cows
`and bulls as early as the late 1800s, a large proportion
`of nonregistered animals (“grades”) were not included
`in breed society herdbooks. An alternative identifica-
`tion method was needed, and USDA introduced metal
`ear tags with unique numbers in 1936. These evolved
`into the 9-digit tag series (e.g., 35ABC1234) introduced
`by the Animal and Plant Health Inspection Service
`(APHIS) and National Association of Animal Breed-
`ers (NAAB) in 1955, which are still used for many
`cows today. The American ID series, introduced in
`1998, features a 2-character breed code, 3-character
`country code, and 12-digit identification number (e.g.,
`HOUSA00035ABC1234 or HO840012345678910). This
`system was designed to be unique worldwide and to in-
`clude both registered and grade animals, and it allows
`multiple identification codes for individual animals to
`be cross-referenced to a single unique number.
`
`EARLY METHODS TO PREDICT BREEDING VALUES
`
`Daughter–Dam Comparison
`
`The lactation performance of a cow was long thought
`to be influenced by heredity, and early selection deci-
`sions were based simply on an individual cow’s pheno-
`type for milk or butter yield. The idea of comparing a
`cow’s milk production with that of her dam emerged
`near the turn of the 20th century. Several indices were
`proposed for this purpose (Davidson, 1925; Graves,
`1925; Yapp, 1925; Goodale, 1927; Gowen, 1930; Bon-
`nier, 1936; Allen, 1944) and their relative accuracy was
`compared by Edwards (1932). In practice, the earliest
`known daughter–dam differences in the United States
`were computed by individual bull associations around
`1915, based on a handful of sires with a few offspring
`apiece—this was the first serious attempt to improve
`dairy cattle by selection. By 1927, approximately 250
`cooperative dairy bull associations, representing more
`than 6,000 farmers, provided data to the USDA and,
`for the next 4 decades, the USDA computed daugh-
`ter–dam comparisons for dairy bulls and mailed the
`results to their owners. Artificial insemination became
`available in the late 1930s, and with it, the opportunity
`for superior bulls to produce hundreds or thousands
`of offspring in many herds. Large groups of daughters
`performing under a variety of management and envi-
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`
`ronmental conditions greatly enhanced the accuracy
`of genetic predictions. During this period, the work of
`giants such as R. A. Fisher (1918, 1930) and J. B. S.
`Haldane (1932) laid the foundations of population and
`quantitative genetics, which allowed pioneers such as
`Sewall Wright (1932) and Jay Lush (1931, 1933) to
`develop the science of animal breeding and the sta-
`tistical methodologies needed for accurate evaluation
`of dairy sires. Various indices based on daughter–dam
`comparisons were developed, including those of Wright
`(1932) and Lush et al. (1941).
`Daughter–dam comparisons facilitated genetic evalu-
`ation of bulls that were used in multiple herds, as long
`as performance data were available for the dam and
`her daughters. This method accounted for herd-specific
`management practices and local environmental condi-
`tions if the dam and daughter were housed in the same
`herd. Changes in management or environmental con-
`ditions that occurred in the time between dam’s and
`daughter’s performance were ignored. Relationships
`between sires and their mates were not considered, and
`this assumption was sometimes violated if the bull was
`used in his herd of origin. Variation in the phenotypic
`performance of the dam, relative to her actual genetic
`merit, was a huge source of error in the resulting pre-
`dictions. Genetic trends over time were ignored, but ge-
`netic progress was negligible in most herds at the time.
`An important limitation was that sire evaluations were
`not regressed to the mean, so bulls evaluated based on
`only a few daughter–dam pairs were more likely to have
`extremely high or low genetic predictions. During this
`period, methods were developed to standardize records
`for lactation length (305 d), milking frequency (2×),
`and age at calving (mature equivalent). Adjustments
`for season of calving were also developed, but differ-
`ences in environmental conditions between years were
`generally ignored.
`
`Selection Index
`
`Hazel and Lush (1942) introduced the selection
`index for EBV for individual traits, and this method
`was used by Lush (1944) to derive weights for various
`sources of information in daughter–dam comparisons.
`The EBV of a selection candidate was predicted using
`multiple linear regression, where each independent vari-
`able represented individual or mean performance for a
`specific type of relative, such as dam, sire, maternal
`half-siblings, paternal half-siblings, or progeny. The
`regression coefficients represented index weights, which
`were a function of genetic relationships and the amount
`of information contributed by the phenotypic record or
`average (e.g., number of lactations or number of off-
`spring). The amount of information from various types
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`100-YEAR REVIEW: METHODS AND IMPACT OF GENETIC SELECTION
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`10237
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`of relatives often differed between selection candidates,
`so index weights were adjusted for the number of rela-
`tives or lactations contributing to mean performance,
`based on heritability and repeatability parameters.
`
`Contemporary (Herdmate) Comparisons
`
`Contemporary comparisons represented a huge leap
`in the accuracy of genetic evaluations because of their
`ability to account for the specific management and en-
`vironmental conditions under which phenotypes were
`expressed (Robertson et al., 1956). Robertson and
`Rendel (1954) are credited with introducing contempo-
`rary comparisons, and Henderson et al. (1954) formally
`published the herdmate comparison model in the same
`year. However, Searle (1964) noted that this method
`had been used in New Zealand before either publication.
`The concept of contemporaries or herdmates exposed
`to similar management and environmental conditions is
`much like that of an epidemiological “cohort,” in which
`patients are grouped based on commonalities in demo-
`graphic features (e.g., age, sex, or geographical region)
`and lifestyle characteristics (e.g., exercise regimen or
`tobacco usage). A critical consideration in designing
`contemporary groups is the balance between a precise
`definition of the cow’s environmental conditions and
`the need for enough herdmates to provide an accurate
`estimate of the contemporary group effect.
`Progeny testing became widespread during the era of
`daughter–dam comparisons. However, the introduction
`of contemporary comparisons allowed AI centers to
`fully capture the benefits of distributing the semen of
`young bulls to dozens or hundreds of herds with differ-
`ent geographical locations, environmental conditions,
`and management practices. Contemporary comparisons
`were enhanced by regressing average daughter contem-
`porary deviations (now known as daughter yield devia-
`tions) toward zero, based on heritability and number
`of progeny, because mean deviations for bulls with few
`offspring have larger variance than mean deviations for
`bulls with many offspring. Some contemporary com-
`parison models also included a herd by sire interaction
`adjustment to limit the effect of a single herd on a sire’s
`EBV.
`Cornell University implemented a regional sire evalu-
`ation system based on contemporary comparisons in
`the mid-1950s (Henderson, 1956), in which records
`were weighted based on the number of lactations per
`cow and a repeatability parameter. However, informa-
`tion about the number of daughters or contemporaries
`was not used when combining daughter contemporary
`deviations to compute the sire’s EBV. The contempo-
`rary comparison method was applied by the USDA in
`1961, replacing the daughter–dam comparison system.
`
`This model allowed the inclusion of cows for which
`performance records of the dam were unknown. Herd-
`year-season contemporary groups were based on a 5-mo
`moving average, and herdmate averages were adjusted
`for seasonal effects. As in the Cornell model, sire effects
`were regressed to the mean, so a bull could not rank
`highly unless he had a significant number of daughters.
`Records of cows that were culled or sold for dairy pur-
`poses were extended to 305 d, whereas longer records
`were truncated at 305 d.
`Other adjustments were implemented at this time,
`including factors for extending short lactations to 305
`d that were specific to breed, region, season, and parity,
`and records were weighted by length of lactation. A
`time lag between the cow’s calving date and initiation
`of the sire summary ensured that records from culled
`cows with short lactations did not bias the genetic
`evaluations of their sires. This was an obvious limita-
`tion as regards timeliness of data entering the genetic
`evaluation system, at least until 1975, when records
`in progress became available for all cows in the herd.
`Estimates of sires’ genetic merit were published as
`the predicted difference (PD) in performance of their
`daughters relative to contemporaries in a typical herd.
`The term “repeatability” (later “reliability”) was used
`to denote the accuracy of a bull’s PD, and it indicated
`the level of confidence a farmer should have when pur-
`chasing the bull’s semen. This method, which was used
`until 1973, allowed the inclusion of more data, tended
`to be less biased, and provided a cow index for ranking
`elite females.
`Several competing methods for sire evaluation were
`introduced during this period. Most were closely re-
`lated to each other and to the weighted least-squares
`approaches of C. R. Henderson (1952, 1963) and Cun-
`ningham (1965), as well as simplified versions of the
`best linear unbiased prediction (BLUP) models de-
`scribed in subsequent sections (Thompson, 1976). The
`cumulative difference method of Bar-Anan and Sacks
`(1974) is essentially equivalent to the contemporary
`comparison method but with an adjustment for the
`genetic level of sires of the cow’s contemporaries. The
`term “cumulative” recognized that performance data of
`a bull’s daughters accumulate over time, resulting in
`increased accuracy of predictions, and this method was
`the basis of the modified cumulative difference method
`proposed by Dempfle (1976).
`Genetic evaluations of dairy sires were unified at
`USDA in 1968 (Plowman and McDaniel, 1968), when
`dairy cattle breed associations discontinued their own
`sire rankings for production traits. In 1972, the USDA
`Division of Dairy Herd Improvement Investigations
`was renamed as the USDA-ARS Animal Improvement
`Programs Laboratory (AIPL)—this laboratory set the
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`WEIGEL ET AL.
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`global standard for translational research on genetic
`evaluation of dairy cattle for the next 45 years.
`
`and her sire’s PD (and later her dam’s cow index),
`with weights depending on the amount of information
`contributing to each component.
`
`Modified Contemporary Comparison
`
`In 1974, the modified contemporary comparison
`(MCC) method was introduced (Dickinson et al., 1976;
`Norman et al., 1976). In this model, a bull’s PD repre-
`sented a weighted average of his pedigree value and the
`deviation in performance of his daughters from their
`contemporaries. In previous methods, a bull’s pedigree
`information was generally discarded when data from
`milking daughters became available. The MCC method
`also allowed the inclusion of sire and maternal grandsire
`pedigrees. The genetic merit of competing sires within a
`given herd (i.e., sires of contemporaries) was taken into
`account, and this approach could better accommodate
`genetic trends over time (Norman et al., 1972). These
`features of the MCC method were increasingly impor-
`tant, because modern selection tools and advanced
`reproductive technologies now allowed some farmers
`to make more rapid genetic progress than their peers
`(McDaniel et al., 1974). In addition, positive assorta-
`tive mating had become popular, as farmers “mated
`the best to the best” to improve their herds (Norman
`et al., 1987). The first 5 lactation records from a given
`cow were included in the MCC model, which provided
`a more accurate picture of an animal’s genetic superior-
`ity or inferiority in lifetime productivity. Contemporary
`groups differed for primiparous and multiparous cows
`within a herd. As previously, a bull’s evaluation was
`regressed based on heritability, number of daughters,
`and lactations per daughter, but regression was toward
`his pedigree value, rather than the population mean.
`The MCC method produced results that were nearly
`identical to those of BLUP in a sire model, but with
`substantially lower computing requirements. The prac-
`tice of resetting the genetic base was initiated during
`this time, so farmers would be reminded to raise their
`sire selection standards as the breed made genetic prog-
`ress. However, periodic resetting of the genetic base
`“forgives” undesirable genetic trends that may occur as
`correlated responses to selection (e.g., female fertility)
`or biases in the perceived value of certain traits (e.g.,
`stature). The MCC method was widely accepted by
`pedigree breeders and AI studs, and it led to impressive
`annual genetic gains of about 45 kg of milk per cow per
`lactation. Another innovation during this period was the
`incorporation of pricing data for milk, fat, and protein,
`so that estimates of genetic merit could be expressed
`as the financial gain or loss relative to an average sire
`of the same breed (PD$). Cow indices became widely
`used during the MCC era; these represented a weighted
`average of the cow’s modified contemporary deviation
`
`Journal of Dairy Science Vol. 100 No. 12, 2017
`
`LINEAR MODELS
`
`Mixed Linear Models
`
`Henderson (1953) advocated the use of statistical
`models to partition genetic and environmental variance
`components and predict the genetic merit of dairy sires,
`and this led to the development of BLUP methodology.
`Despite its theoretical appeal, computing limitations
`prevented implementation of BLUP until 1972, when
`Cornell University implemented BLUP in a sire model;
`this model was later modified to include genetic rela-
`tionships among sires.
`A mixed linear model is expressed most succinctly in
`matrix notation as
`
`
`
`y = Xb + Zu + e,
`
`where y is a vector of phenotypic measurements on a
`group of animals; b is a vector of continuous or categor-
`ical fixed effects that are known to influence the pheno-
`type, such as age at calving or herd-year-season con-
`temporary group, as one would encounter in a tradi-
`tional least-squares analysis; u is a vector of random
`effects, such as sire breeding values; X and Z are inci-
`dence matrices that map the phenotypic observations
`in y to the fixed and random effects in b and u, respec-
`tively, and e is a vector of random residual effects, such
`as temporary environmental conditions or measurement
`2, correspond-error. The variance components σu2 and σe
`
`
`ing to the random effects u and e, can be estimated
`using a variety of methods, such as maximum likeli-
`hood (Harville, 1977).
`
`Sire and Maternal Grandsire Models
`
`If the vector u in the mixed model equations com-
`prises the breeding values of dairy sires and y contains
`the lactation records of their daughters, the aforemen-
`tioned mixed linear model would be considered as a
`= (
`)
`2
`N
` this
`“sire model.” If we specify that G
`
`0,
`,σ
`I
`u
`model assumes that sires are unrelated to each other,
`and the resulting sire EBV are regressed toward the
`2
`population mean in proportion to the magnitude of σu
`2. The assumption that sires are unrelated
`relative to σe
`to each other is highly unrealistic, given the widespread
`use of AI and embryo transfer, which lead to large
`families of paternal half-siblings and small families of
`
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`10239
`
`full-siblings, respectively. The concept of modeling cor-
`relations between the elements of u when specifying G
`is straightforward, and in this application pedigree in-
`formation was used to derive a matrix of expected ad-
`= (
`)
`2
`N
` The
`ditive genetic relationships, where G
`
`0,
`.σ
`A
`u
`resulting A matrix is very large, of the order of the
`number of elements of u, and it could not be inverted
`with computational resources available at the time.
`Henderson (1976) developed a set of rules for construct-
`ing A−1 directly, without building A. This allowed
`more precise modeling of relationships among sires
`than the MCC model, as well as relationships between
`sires and cows or relationships between sires and mater-
`nal grandsires (Henderson, 1975). Later, this method
`was extended to allow efficient construction of A−1 in
`the presence of inbreeding (Tier, 1990).
`In the sire model implemented for the Northeast AI
`Sire Comparison at Cornell University in 1972, the vec-
`tor b included the fixed effects of herd-year-season of
`calving and genetic group of the sire, where the latter
`was based on birth year of the bull and the AI orga-
`nization from which he came. The idea was that all
`young bulls purchased by a given AI center in a given
`year were of similar genetic merit, which facilitated the
`assumption that the sires in u represented indepen-
`dent (unrelated) samples from the same distribution.
`Only first-lactation records of AI daughters were used,
`although this restriction was later relaxed if the ad-
`ditional records were from the same herd (Ufford et al.,
`1979). Random mating between sires and dams was as-
`sumed, and maternal relationships between cows were
`ignored.
`To address the naïve assumption that sires were ran-
`domly mated to dams, Quaas et al. (1979) proposed
`a maternal grandsire model. This model included an
`additional random effect, which represented the addi-
`tive genetic merit of the maternal grandsire, as well as
`an additional fixed effect, which represented the genetic
`group of the maternal grandsire. Although this was a
`positive step in addressing assortative mating, it still
`assumed that each mate of a given bull represented
`a random sample of all daughters of that maternal
`grandsire. Maternal relationships between dams were
`ignored and the model did not add value in cases where
`the maternal grandsire was unknown. A comprehensive
`examination of assortative mating for milk yield by
`Norman et al. (1987) showed that herds with higher
`average genetic level consistently used genetically su-
`perior bulls. However, the primary concern was bias
`due to within-herd assortative mating, which was not
`common at the time (Norman et al., 1987), and few
`AI bulls were affected negatively in the national sire
`evaluation system.
`
`100-YEAR REVIEW: METHODS AND IMPACT OF GENETIC SELECTION
`Animal Model
`The inability of sire or maternal grandsire models
`to fully account for nonrandom mating of sires with
`expensive semen to cows and heifers with highest per-
`ceived value within a given herd was well known. In
`addition, farmers who wished to market superior breed-
`ing stock were no longer content with a genetic evalu-
`ation system that focused on sires and treated cows as
`a by-product. In 1989, AIPL scientists introduced the
`“animal model” (Wiggans and VanRaden, 1989), which
`used all known relationships between cows and their
`maternal and paternal ancestors. In this model, the
`additive genetic effects of animals represent an infinite
`number of alleles with very small effects—the so-called
`infinitesimal model of inheritance.
`Once implemented, by using an iteration on data al-
`gorithm and the supercomputer at Cornell University,
`the animal model became the global standard for ge-
`netic evaluation of dairy cattle. The statistical method-
`ology, which had been derived almost 3 decades earlier,
`allowed precise accounting of the genetic merit of mates
`and provided a consistent framework for simultaneous
`evaluation of male and females. The breeding value of
`an individual animal is represented as the sum of one-
`half of the additive genetic merit of its sire, one-half of
`the additive genetic merit of its dam, and a Mendelian
`sampling term that represents its deviation from the
`average additive genetic merit of its full-siblings due to
`random sampling of alleles represented in the gametes.
`All known relationships are considered in the A matrix,
`so the performance of one animal contributes to the
`EBV of all known paternal and maternal relatives, with
`degree of the contribution depending on proximity of
`the relationship. Users typically provide at least 4 or 5
`generations of pedigree data, and pedigrees are rarely
`traced beyond the 1970s, when herdbook records were
`computerized. When pedigree data are missing, un-
`known (phantom) parent groups (Westell et al., 1988)
`can be used to account for differences in the genetic
`merit of missing ancestors.
`In the USDA animal model, management groups
`were defined according to parity (first vs. later), regis-
`try status (registered vs. grade), and 2-mo time blocks
`within herd-year. As in previous systems, adjustments
`were used to account for age, milking frequency, and
`length of lactation, and these factors were specific to
`breed and geographical region. Records in progress
`have been used in the United States since 1975; this
`increased genetic progress by up to 10% by reducing
`the time lag between data collection and breeding value
`prediction (Powell et al., 1975). Incomplete lactation
`records were projected to a 305-d basis once the cow
`had completed 2 or 3 monthly DHI tests, to produce
`
`Journal of Dairy Science Vol. 100 No. 12, 2017
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`Exhibit 1011
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`10240
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`WEIGEL ET AL.
`Random Regression Models
`and Covariance Functions
`
`timely genetic predictions and enable rapid selection
`decisions for cows and their sires. Data collection rat-
`ings (DCR) were introduced by USDA in 1998; these
`are based on the number and spacing of test-day milk
`records relative to standard monthly supervised record-
`ing of all milkings per day, which receives a score of
`100. The DCR system allows weighting of records ac-
`cording to their expected value in genetic evaluations,
`and they can be used as a guide to reimburse farmers
`who provide high quality data.
`The accuracy of EBV produced by an animal model
`can be calculated from the elements of the inverse of
`the mixed model coefficient matrix, but this is compu-
`tationally infeasible, so approximations are used (Har-
`ris and Johnson, 1998). A practical approach is to sum
`the number of daughter equivalents that contribute to
`the genetic prediction of a given animal (VanRaden
`and Wiggans, 1991), where the quantities of informa-
`tion from the animal’s descendants, own phenotypic
`records, and ancestors (noting that siblings and cousins
`contribute through the animal’s parents) are counted
`when computing reliability values.
`
`Test-Day Model
`
`In 1993, Cornell University was granted a US patent
`for the “test-day model,” in which the performance of
`an animal relative to its herdmates was evaluated us-
`ing daily milk weights from the herd’s monthly test,
`rather than standardized 305-d lactation yields. This
`model was introduced for routine genetic evaluations
`in several countries (e.g., Canada, Germany) in which
`the genetic evaluation center obtained a license or suc-
`cessfully challenged the patent. However, because of
`this patent, a test-day model was not implemented for
`routine genetic evaluations in the United States. The
`Cornell patent was controversial because many organi-
`zations (including USDA) had been providing informa-
`tion for decades about the performance of an individual
`cow relative to her herdmates on a given test date, and
`Australia had formally implemented a test-day genetic
`evaluation model in 1984. However, no one had previ-
`ously considered patenting this relatively well known
`statistical process (Rothschild and Newman, 2002). An
`interesting feature of test-day models is their ability to
`produce genetic evaluations for lactation persistency;
`for example, the ratio of expected milk yield at 280 d
`versus 60 d postpartum. Animals with greater lacta-
`tion persistency may be more likely to remain healthy
`throughout the lactation and might be able to meet
`their nutritional needs with a less expensive ration
`because they do not experience the extremes of DMI
`or negative energy balance of their less-persistent con-
`temporaries.
`
`Journal of Dairy Science Vol. 100 No. 12, 2017
`
`Data that are collected over time, such as test-day
`milk weights of lactating cows or periodic body weights
`of growing heifers, are often analyzed using a random
`regression model (Henderson, 1982; Ali and Schaeffer,
`1987; Jamrozik et al., 1997). Functions such as Leg-
`endre polynomials or splines can be used to describe
`the trajectory of genetic, permanent environment, and
`temporary environment effects during the lactation.
`Numerous linear and nonlinear functions have been
`proposed for modeling these effects. For example, the
`Ali and Schaeffer (1987) model included a random herd-
`test date contemporary group effect, as well as fixed
`(overall mean) and random (additive and permanent
`environmental) regression coefficients corresponding to
`4 functions of the time during lactation when the cow’s
`milk weight was recorded. In that study, the residual
`variance was assumed fixed throughout the lactation
`but, in general, random regression models can provide
`estimates of the genetic, permanent environmental,
`and residual variances (as well as heritability and
`repeatability) at any time point during the lactation.
`The EBV of selection candidates can be computed at
`various time points during the lactation, and random
`regression models offer greater flexibility in accom-
`modating variation in the frequency of milk recording
`between farms.
`A similar approach, known as covariance functions
`(Kirkpatrick et al., 1990), can be used to analyze
`longitudinal data and explain the interrelationships
`between genetic and environmental factors over time.
`These models can be computationally demanding, and
`one must ensure that trajectories of additive genetic,
`permanent environment, and temporary environment
`effects are modeled appropriately. The goal of model-
`ing the trajectory of genetic, permanent environment,
`and temporary environment effects precisely using a
`complicated function with 4 or 5 parameters must be
`balanced with the reality that parameter estimates will
`have large standard errors when applied to monthly
`DHIA records with only 8 to 10 data points per cow
`per lactation.
`Random regression models and covariance functions
`can provide insight about the trajectory of biological
`processes during the lactation (e.g., milk fat synthesis,
`body tissue deposition). In addition, these models can
`provide information about correlated responses to se-
`lection for traits expressed over time, such as the effect
`of selection for peak milk yield in early lactation on
`milk composition in late lactation. The results of ran-
`dom regression models or covariance functions can also
`be used to facilitate the development of efficient data
`
`Exhibit 1011
`Select Sires, et al. v. ABS Glo