L. Klei, R. L. Quaas, E. J. Pollak, and B. E. Cunningham

American Simmental Association, Bozeman, MT and

Cornell University, Ithaca, NY.

Perhaps the major reason for a multiple breed evaluation would be to compare animals of different breeds utilizing information from pooled data sets. This pooling of data is not likely to happen soon. There is still reason, however, to consider procedures that allow for data sets that include measurements on animals of various breeds and breed compositions. This is because some of the current data sets used for national cattle evaluations include such animals. One such database belongs to the American Simmental Association (ASA). This database includes many crossbred animals produced during the process of grading up to Simmental (backcrosses to Simmental sires). Also, it has the various Simmental-Brahman crosses needed to produce a purebred Simbrah (). Finally, to a much lesser extent, progeny of sires from breeds other than Simmental (or Brahman) are included. Our objective is to describe a multiple breed evaluation (MBE) procedure designed for this data set but which may serve as a prototype for other multiple breed applications.

In the current evaluation for Simmental cattle, only progeny of purebred Simmental sires are evaluated and contemporary groups (CG) are defined on a within-percentage Simmental basis. These features result in breed and heterosis effects being confounded with (and removed by) the CG effects. It means that F₁s resulting from mating a Simmental cow to a bull of another breed are not evaluated. By incorporating the ideas of an MBE, these animals (~20,000) can be included if they meet other criteria for evaluation. Another major assumption of the current Simmental genetic evaluation is that the dams of F₁s have the same genetic ability as a purebred Simmental born in 1986 (the base year), i.e., 0. Because of this assumption, no direct comparisons of EPDs can be made between 50%, 75%, and purebred Simmental animals even though they are evaluated in the same within-breed genetic evaluation. This assumption, which affects ~750,000 animals, can be relaxed with an MBE.

Another benefit of an MBE is that Simmental and Simbrah animals can be evaluated simultaneously. By combining the data, all progeny of an animal influence its EPD. This should lead to higher accuracies for the Simbrah animals (~35,000). Also, every Simmental or Simbrah animal will have one set of EPDs that can be used in either population. Currently some Simmental animals have two sets of EPDs.

In summary, the Simmental MBE aims to evaluate more animals, to evaluate the current animals better, and to include Simmental and Simbrah cattle in the same evaluation.

A multiple-trait animal model is currently used for the Simmental and Simbrah genetic evaluations. The model includes contemporary group, direct and maternal additive genetic, and permanent environmental effects. Contemporary groups are defined by sex, percent Simmental and management codes within breeder herds. Records are pre adjusted for age of dam effects, which are divided into 12 discrete classes. In the evaluation, heterogeneous variances are used for different sex-by-percent Simmental subclasses. Evaluations are obtained simultaneously for birth weight, direct and maternal weaning weight, postweaning gain and permanent environment for weaning weight.

Switching to an MBE requires various model modifications to account properly for the various breed and breed combinations represented in the data. In the Simmental data (~3 million records), an animal’s breed composition is identified by four out of a possible 63 breeds.

Differences in genetic origin of the animals are incorporated by adding direct and maternal additive breed and heterosis effects to the model. In the Simmental MBE, maternal components are only used for weaning weight. In addition to these new effects in the model, the age of dam (AOD) effect becomes breed dependent and is included in the model; records are no longer pre adjusted for AOD. In the current MBE, the heterogeneous variances depend on the sex and percent Simmental of the calf, similar to the current system. Whether these should depend more specifically on breed composition of the calf will be addressed in future research.

Finally, because of the multiple breed component of the MBE, contemporary groups are redefined. Each of the modifications is described in more detail in the following sections.

For the MBE, a CG is formed with all animals of the same sex managed the same way. Animals of different percent Simmental are no longer separated into different contemporary groups as they are in the current evaluation. This can lead to larger contemporary groups, which is beneficial for estimation purposes. Combining animals of different percentage into one CG is also required for estimating breed and heterosis effects.

Before describing the other effects in the model, it is useful to think about the problem of estimating the various effects. For example, a calf’s weaning weight observation impacts the estimates or predictions of nine different effects: 1) contemporary group, 2) age of dam, 3) direct and 4) maternal heterosis, 5) direct and 6) maternal additive breed, 7) direct and 8) maternal animal additive genetic, and 9) permanent environmental effects.

Instead of estimating all these effects from the data, one could pre adjust the records for some effects, e.g., 2) through 6), and estimate others. The question that arises is how to obtain good values to be used as adjustments for the effects. An obvious choice for the heterosis and breed effects would be to use the many crossbreeding studies that have been conducted over the last decades. This approach assumes the animals in the experiments were a representative sample of the same founder populations that contributed to the animals in the MBE data set.

Another approach is to incorporate in the model all necessary effects. When this model is used, the data determine the estimates. Because most crossbreds in the Simmental data set resulted from upgrading, confounding of effects can make this impossible. For instance, the best estimate of direct heterosis for a cross requires both purebreds as well as the reciprocal F₁s, all in the same contemporary groups. This will hardly ever be the case in field data. Another problem with this approach is that some of the breeds in the data are represented by a small number of animals. Estimating effects based on these few animals can be inaccurate. For some of these breeds, not only is information lacking in the data but good estimates from the literature may be wanting. Grouping breeds by biological type and estimating effects for biological types instead of breeds can solve this problem.

A combination of the two alternatives is provided with a Bayesian approach, i.e., the literature values are combined with the information contained in the data. Bayesian methodology requires specification of a "prior." The prior has a mean (m _p), the literature values, and a prior variance (V_p). The m _p is our "best guess" prior for looking at the data while V_p quantifies our certainty about that guess: large values indicate uncertainty; small values indicate certainty. A typical system of equations,, becomes m _p when prior information is incorporated. This method is similar to BLUP for the additive genetic animal effects, where m _p is zero while V_p is the genetic (co)variance matrix.

There are two extreme cases. With little or no confidence in prior information, the prior is known as non informative or flat. The value for V_p is chosen to be very large , +¥ , resulting in and m _p being close to zero and the estimate for is as when no prior information was used. With complete confidence in the prior information, the value of V_p is close to zero, is very large, overwhelms C, and m _p, the prior mean. This is effectively equivalent to pre-adjusting the records. With intermediate values for V_p, the information coming from priors and data is combined. With enough information from data, however, the prior is overwhelmed (ignored).

Priors can be incorporated in the Simmental MBE for all effects except CG (i.e., flat priors for CG). Non informative priors were subsequently chosen for the AOD curves because in preliminary analyses it was observed that the information in the data overwhelmed any reasonable choices for uncertainty about AOD curve priors. The prior means (m _p) for the other effects were obtained from various crossbreeding and germplasm evaluation experiments reported in the literature (Cunningham and Kirschten, 1996). The values chosen for the prior variances V_p are described in more detail in the sections for heterosis and breed.

The AOD effect is divided into twelve discrete subclasses in the current Simmental and Simbrah. Also, separate AOD adjustment factors are being used for different percent Simmental-by-sex subclasses. It is clear from these percent Simmental subclasses that different AOD adjustments should be used for dams from different genetic origin in the Simmental MBE.

Work at the University of Georgia has shown that, instead of using discrete AOD classes, better adjustments for age can be made by fitting a continuous AOD curve, e.g., a 4^th order polynomial (Nelson et al., 1992; Bertrand et al., 1994). For an MBE, separate curves for sex within the different breeds are fit. In contrast with the current Simmental evaluation where records are pre adjusted for the AOD effect, AOD curves in the Simmental MBE are estimated simultaneously with all the other effects in the model. The general form of the fourth order AOD polynomial is:

(2)

where y_ij is the observation for trait i (birth weight, weaning weight, post weaning gain) for animal of sex j (male or female), is the n^th order regression coefficient for trait i and sex j, with indicating the intercept, and ageⁿ: is AOD to the n^th power. A maternal additive genetic breed effect for weaning weight is fitted in the Simmental MBE; as a result, the intercept for the weaning weight polynomial is not necessary (n=1,..,4 instead of n=0,..,4). For birth weight and post weaning gain, differences in intercepts, within sex and trait, can be interpreted as average maternal breed differences.

McConnel (1996) showed that the AOD curves for crossbred dams can be computed as the weighted average of the breeds represented, as illustrated in Example I. To avoid having to estimate age of dam curves for the 63 different breeds represented in the data, dam breeds were grouped by breeds and biological types. The biological types used were Simmental, Angus, Hereford, Brahman, British, Continental, and others.

In Figure 1 a comparison is given of the current step-wise AOD adjustment for weaning weight (WWT) of calves out of purebred Simmental cows and the corresponding continuous curve. The largest impact of this change is for the younger dams and the oldest; e.g., for the 2.5-to 3-year-old dams the WWT AOD adjustment was ~-42 lb for all dams falling in this age group. When using the WWT AOD curve, a calf of a 2.5-year-old dam has ~65 lb added to its weight while the calf from the 3-year-old has ~42 lb added to its weight.

It is well documented that F₁s (Bos Taurus ´ Bos Indicus) weigh less at birth than reciprocal crosses resulting from mating Bos Indicus sires to Bos Taurus dams (e.g., Reynolds et al., 1980; Thallman et al., 1992; Rohrer et al., 1994). This can be viewed as a maternal breed of founder effect for birth weight (BWT). The Simmental MBE does not incorporate this effect in the model. Figure 2 shows that this effect is reflected in the intercept b_o of the AOD curve; e.g., the BWT of a bull calf out of a mature Brahman dam (6 years old) is adjusted by ~ 13 lb to be comparable to the record of a calf of a mature Simmental cow.

Also, Figure 2 illustrates the use of breed specific AOD curves to create the curve for a crossbred dam. In this case the Simbrah AOD curve is 5/8 the AOD curve for Simmental plus 3/8 the AOD curve for Brahman. A male calf of a 6-year-old Simbrah cow has its BWT adjusted by 5/8 ´ 0 + 3/8 ´ (13) = ~ 4.8 lb.

One of the benefits of cross breeding animals is the influence of heterosis on their performance (e.g., Cundiff et al., 1992; Gregory and Cundiff, 1991). Heterosis will influence the direct performance of a crossbred animal and the maternal performance of crossbred dams. Direct heterosis effects are included in the MBE model for all traits; a maternal heterosis effect is also included for weaning weight.

Heterosis occurs due to the interaction of genes inherited from different breeds. It is observed as the deviation of the performance of a crossbred animals from the weighted average of the parental breeds. Heterosis can be caused by either dominance, the interaction of individual genes, or epistasis, the interaction of gene complexes. Results from the Meat Animal Research Center support the hypothesis that heterosis is primarily due to dominance (Gregory and Cundiff, 1991). This allows heterosis to be modeled as being proportional to the probability of getting genes from different breeds at a locus. It is further assumed that no difference exists between reciprocal crosses in the amount of heterosis expressed.

The 63 different breeds represented in the data could lead to some 2000 different F₁s. Heterosis effects (three direct and a maternal) cannot be estimated for each of these. Most of these breed combinations are represented by a only few animals, if any at all. Also, many of the breed combinations are not represented in the literature (e.g., Longhorn ´ Africander maternal) Therefore the breeds were grouped by four biological types: British (B), Continental (C), Zebu (Z), and others (O). This leads to 10 combinations:, B´ B, B´ C, B´ Z, B´ O, etc. For example, Angus´ Hereford crosses would be included in the B´ B combination.

Example II illustrates the procedure to determine the fraction of F₁ heterosis that can be expected in an animal. The cross between a Simmental ´ (Angus´ Hereford) sire and a Simmental ´ (Angus´ Brahman) dam yields an expected heterosis of 1/16 h_BB+ 3/8 h_BC + 1/8 h_BZ + 1/8 h_CZ, where h_BB, h_BC, h_BZ and h_CZ denote the heterosis (lb) in an F₁ of breeds of the various types.

Prior means for heterosis effects were obtained from the literature (Cunningham and Kirschten, 1996). The associated prior variance for the i^th trait is, where is the residual variance for trait i. Direct heterosis results for BWT are in Figure 3. The MBE estimates are in general close to the prior values except for the B*C combination. Estimates can be close to the priors because the priors were close to what the data predict and/or the information in the data is insufficient to modify the prior belief. The latter is the case for the Z*Z class where the data provide no information.

The combination with the most data (B*C) shows a slightly negative heterosis estimate. As mentioned earlier estimating direct heterosis -- well -- requires purebreds and crosses, which are rare in a population such as the Simmental (upgraded from primarily Hereford and Angus). From these results and similar results for the other direct heterosis effects, it appears that most emphasis must be placed on the priors to account for direct heterosis.

Maternal heterosis priors and MBE solutions are in Figure 4. In general, the values of the MBE are smaller than those indicated by the prior values. In contrast to direct heterosis, maternal heterosis is relatively easy to estimate from field data. To obtain a clean estimate for maternal heterosis, one needs purebreds of one breed, F₁s, and the backcross to the original purebred in one contemporary group. This can be the case in field data where upgrading is happening.

To account for breed composition differences, animals’ pedigrees are traced as far as possible and breed of the founders, the most distant animals in each line of the pedigree, checked. All the genes in an animal come from these "founders." Knowing the breeds of all the founders and how many generations each is removed determines the genetic (breed) composition of the animal. The expected genetic merit of an animal is the weighted average of breed of founder (BOF) effects as illustrated in Example III. The term ‘breed of founder’ is used to indicate that this effect accounts for the genes from animals of various breeds (founders) that contributed to the Simmental population. The ‘founder’ is to emphasize that these animals need not be representative of any registered population.

To allow for any genetic trend, yearly BOF effects are defined. This means that not only do we account for the ¼ Hereford genes in an animal but whether the Hereford genes were sampled in 1970 or 1990 or a mixture of several years. Some breeds are grouped because small numbers of observations; 12 BOF effects (rather than 63) were included in the model for each year. These are Simmental, Angus, Hereford, Brahman, Charolais, Gelbvieh, Limousin, American, British, Continental, dairy, and mixed.

Large fluctuations among the yearly estimates can occur if only a few founders of a given breed (group) come into the population each year. To compensate for this an auto-regressive structure (Wade and Quaas, 1993) was used in the prior (co)variance matrix, V_p, for the year within breed effects. Specifying a high correlation between successive years indicates a prior belief that these BOF should not change drastically from year to year. It ‘smoothes’ the estimates quite effectively. When the prior variance is assumed to have an auto-regressive structure, two parameters have to be defined, the correlation r _i and the variance for trait i. For the Simmental MBE, default values are r _i =Ö .95 for all traits and the variance = . Prior means for a breed were constant across years; the constants were obtained from the literature (Cunningham and Kirschten, 1996).

The BOF effects were fit by the procedure of Westell et al. (1988): unknown parents were matched to appropriate BOF effects, 3 direct and one maternal. The procedure was modified slightly (Quaas, 1988) to handle crossbred founders, e.g., numerous "black baldies."

In Figure 5 the BOF priors and MBE solutions for WWT are given for Simmental and Angus. These values are represented on a breeding value scale. This figure shows that the prior mean for Simmental was assumed to be zero while the prior mean for Angus was constant at ~-60 lb. The MBE solutions show that a slight increase occurred in the Simmental BOF effect. The figure also shows that the prior means were lower than the BOF effect for the Angus in the Simmental population. Over time the difference between founders from the Angus and the Simmental breeds has reduced by approximately 10 lb over time. This might largely be due to the influx of Angus bulls in the later years compared to the early years when most of the Angus founders were dams. It is also due to the genetic trend that has occurred in the Angus population.

To show genetic changes over time, genetic trends are traditionally computed as the average expected progeny difference (EPD) for a well-defined group of animals by birth year. For the current Simmental evaluation, the average EPD for purebred Simmentals is computed to show the genetic trend in the population. With an MBE, it becomes difficult to define some groups of animals; e.g., purebred Simmentals are defined but there are no comparable groups for other breeds. To overcome this problem a trend, referred here as the gametic trend, is computed as the within-year least squares regression of EPD on breed composition. The resulting value attempts to quantify the genetic merit of genes of a particular origin (breed) present in animals born in a particular year. This differs from the BOF trends, which quantify genes entering the population in a given year. The gametic trend quantifies all the founder genes that contribute to a calf crop. In the traditional genetic trend, only a pre defined subset of animals are considered, e.g., purebreds; the gametic trend is computed using all animals in the population. All animals that have a fraction of Simmental genes contribute to the estimation of the Simmental gametic trend.

The relationship between the gametic and genetic trends for WWT is shown in Figure 6. The genetic base is set so that the EPDs for purebred Simmentals born in 1986 average zero. Purebred Simmental was defined under the ASA rules and bylaws, and the designation was supplied with the animal’s record. The two trends are essentially parallel. The difference can be accounted for by the maximum of 1/8^th of genetic material from another breed that is allowed in purebred Simmental females (for males this is 1/16^th).

Gametic trends can be used to show differences in selection practices on genes for each of the different breeds. Figure 7 shows the gametic trends for Simmental and Hereford. Note from this figure that between 1980 and 1988, the gametic trend for Hereford was essential zero. This can be contributed to the large number of founder dams in those years. Since 1988, not many Hereford founders have been added to the population, and the increasing gametic trend observed can be attributed to selection on the Hereford genes in the population. In contrast, the Simmental gametic trend has increased steadily over these years. This is most likely due to selection on Simmental genes and the relative small number of Simmental founder animals coming into the population.

The gametic trend can be used to show trends in any type of crossbred animal in the population. In Figure 8 the relationship between the Simmental, Brahman and Simbrah milk gametic trends as well as the purebred Simbrah milk genetic trend is shown. The Simbrah gametic trend is derived as 5/8 ´ Simmental gametic trend + 3/8 ´ Brahman gametic trend. The purebred Simbrah genetic could not be computed before 1982 because of the small number of animals in this group before that time. This problem does not occur with the gametic trend. Moreover, Figure 8 also shows that the gametic and purebred genetic trends for Simbrah are similar; the difference being that a purebred Simbrah is not always a 5/8^th:3/8^th animal and is allowed to have 1/16^th of another breed in its genetic makeup.

1. The multiple-breed evaluation allows for the forming of true contemporary groups, and no subdivision has to be made to account for differences in genetic composition of calves.
2. Average age of dam curves can be used to account for dams of mixed genetic origin.
3. Priors can be used effectively for combining field and research information in a genetic evaluation.
4. Upgrading data does not yield good estimates for direct heterosis and more emphasis needs to be placed on research information when incorporating this effect in the model.
5. Time trends are observed for the breed of founder effects.
6. Gametic trends can be used to describe genetic trends in animals of different breed composition.