18. Breed Utilisation and Crossbreeding

Brian Kinghorn

Learning objectives

On completion of this topic you should:

• Understand the issues that affect which is the best crossing system to adopt • Have a good feel for what makes dominance good and epistasis bad in crossing systems

Key terms and concepts

Dominance gain is good, Epistatic loss is bad, These two things can be difficult to estimate together as they are largely confounded, Crossbreeding decisions can be integrated with other issues.

Introduction to the topic

Selection and crossbreeding are two key tools for animal breeders. This topic gives sufficient theoretical background on crossbreeding to show how we can exploit it. It also introduces us to integrating crossbreeding with other issues in animal breeding.

18.1 Review of the mechanisms driving heterosis

Figure 18.1 illustrates how crossbreeding can lead to dominance gain and epistatic loss.

Figure 18.1 Mixing genes from different breeds leads to dominance gain and epistatic loss. Mix genes from different breeds (A and B) in one individual.

DOMINANCE Where the individual's parents come from two different breeds, the individual will carry a wider range of genes, sampled from two breeds rather than just one. It is thought that this better equips the individual to perform well, especially under a varying or stressful environment. We would thus expect dominance to be a positive effect, and there is much evidence to support this.

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©2009 The Australian Wool Education Trust licensee for educational activities University of New England EPISTASIS When we cross breeds, genes find themselves having to interact or 'cooperate' with other genes which they are not used to. The crossbred animal may thus be ‘out of harmony’ with itself, and we predict that epistasis, if important, is a negative effect.

A note on the dominance model The example on this page illustrates that "Breed-of-Origin heterozygosity" is proportional to Allelic heterozygosity.

Genotype: A1A1 A1A2 A2A2 Frequency: p² 2pq q² Value: +a d -a

Breed X px=0.3 qx=0.7

px=0.3 .09 .21 a d +a d -a d Breed X = -0.4a + 0.42d qx=0.7 .21 .49

Breed Y py=0.9 qy= 0.1

Breed Y = 0.8a + 0.18d py=0.9 .81 .0

Parental Mean: P = 0.2a + 0.3d qy=0.1 .09 .0 1 F1 Cross px=0.3 qx=07

F1 Cross = 0.2a + 0.66d Heterosis = .36d = d(p - p )² x y py=0.9 .27 .63

Breed-of-origin Heterozygosity =1

qy=0.1 .03 .07

F2 Cross 0.6 0.4

F2 Cross = 0.2a + 0.48d px+py = 0.6 Heterosis =.18d = ½d (px -py)² 2 .36 .24

Breed-of-origin Heterozygosity =½ qx+qy .24 .16 = 0.4 2

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18.2 Models of epistasis

You can treat the detail in section 18.2 as background reading. But please note key concepts: Epistasis and dominance are difficult to estimate together; Epistatic loss can be damaging (e.g. Figure 18.2)

A knowledge of the genetic basis of heterosis is fundamental to the planning of complex crossbreeding programs. As described above, the non-additive components of merit involved are based on interaction within loci (dominance) and interaction between loci (epistasis). When considering dominance as a component of heterosis, heterozygosity with respect to breed of origin of genes is taken into account. However, epistasis can be classified in two general categories:

i. interaction between single genes and the total genotype at all other loci. This is seen as a scale effect (as described by Kinghorn 1982).

ii. interaction within small groups of loci whose products are interdependent in function (eg. Dickerson 1969; Kinghorn 1980).

Scale effects in the expression of heterosis can be tested for in a relatively simple manner (Mather and Jinks 1977; Kinghorn 1982), but interaction within small groups of loci is the subject of a number of models, as described by Kinghorn (1980; 1982; 1987)

We will concentrate on the one specific model of epistasis which has been widely used - the additive x additive model. It is also the only model which has received some experimental support over its competitors (Kinghorn 1983; 1987).

The additive x additive model of epistasis

The proportion of maximum (F1) dominance gain [p(D)] that is expressed is equal to the degree (0 to 1) of heterozygosity with respect to breed of origin. This is quite simple because there are only two states (homozygous and heterozygous), the relative incidence of which can be described by one parameter. However the proportion of maximum epistatic loss which is expressed [p(E)] cannot be described so simply, as there are many possible states. For 2-locus epistasis, there can be (homo-homo), (homo-hetero), (hetero-homo), (hetero-hetero), and other combinations when more than two breeds are involved.

For epistatic loss we should have a biologically sensible model of how genes interact. Figure 18.2 illustrates the most used model, additive x additive epistatic interaction.

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Figure 18.2 A biological interpretation of additive x additive epistatic interaction between 2 loci. K and L represent alleles derived from different breeds. In this illustration both loci shown are heterozygous for breed of origin. Products from the two loci combine to form dimers. Where coadaptation has taken place within breeds, products derived from the same breed are more compatible than products derived from different breeds. For the genotype configuration shown, half the dimers are expected to involve a difference in breed of origin of component gene products, such that only half of the favourable epistatic effect is expressed. Source: Kinghorn (1987).

Figure 18.2 shows two loci randomly sampled from, in this case, an F1 cross between breeds K and L. We assume that merit is related directly to the proportion of dimer enzymes which are 'harmonised'. If this biological model were an accurate reflection of all 2-locus interactions, then p(Eaa) = ½ for an F1 cross, as half the dimers are 'harmonised'.

In general, the coefficient for a given configuration is the probability that two alleles chosen randomly, one from each locus, are of different breed-of-origin.

Table 18.1 lists some coefficients of D and Eaa, and Figure 18.3 illustrates the relationships between them.

Table 18.1 Coefficients of D and Eaa under various mating systems.

GENOTYPE p(D) p(Eaa)

Purebred 0 0 F1 Cross 1 ½ Ax(BxC) 1 5/8 Ax(AxB) ½ 3/8 (AxB)x(CxD) 1 3/4 n breed synthetic (n-1)/n (n-1)/n n breed rotation (2n-2)/(2n-1) 2(2n-2)/3(2n-1)

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Figure 18.3 The relationship between the coefficients of dominance (p(D)) and epistatic loss (p(Eaa)) under various mating systems.

p(Eaa)

The solid line relates to coefficients for repeated backcrossing involving two breeds, one parent always being purebred. Here p(Eaa) = p(D) - p(D)²/2. For these mating systems alone, the coefficient of dominance describes about 92% of the variation in the coefficient of epistatic loss, and vice versa. Rotational crosses are at equilibrium for the number of breeds indicated. The slope for synthetic or “composite” breeds covers both balanced and unbalanced breed mixtures, but numbers given indicate the number of breeds involved for balanced synthetics.

It can be seen that there is a strong co-linearity between p(D) and p(Eaa). This means that fitting p(Eaa) in an analysis of crossbred data tends to explain little more variation if p(D) has already been fitted. This observation has been taken to mean that epistasis is of little importance, and yet such a judgment cannot be made in this way, as the argument works just as well the other way around!

Evidence for epistatic interaction Evidence for epistatic loss has been found has been found in chickens, sheep and notably dairy cattle under tropical conditions. Sheridan (1981) gave a comprehensive review of this area.

Recombination loss [This section is for clarification alone, not to be examined.] Dickerson (1969) used the term 'Recombination loss', r, to describe loss due to epistatic effects. This is related to Eaa and d as follows (Kinghorn, 1983): p(Eaa) = (p(r) + p(d))/2

Analyses that fit recombination loss are equivalent to those that additive x additive epistasis. This is because these analyses also fit the parameter h (heterosis, see Dickerson, 1969), which in fact involves both full dominance and some epistatic effects. Coefficients of h and D are always identical.

Koch et al. (1985) accommodate a range of models in their analysis, including a modified version of recombination loss (Dickerson, 1973), all of these being equivalent to additive x additive epistasis.

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18.3 Evaluating breed resources

Genetic evaluation of breed resources is relatively simple wherever good estimates of mean performance are available for the environment and production systems of interest. This is because the effects involved can be measured with high accuracy from much data, and can be treated as fixed effects. These effects constitute an inventory of genetic resources, and the economic value of each breed genotype can be estimated by simply multiplying predicted performance for each trait by its corresponding economic weight, and summing across traits. In contrast, when we come to evaluating the genetic merit of individual animals, there is much less data available per estimate, and the random nature of breeding values makes the process much more difficult, especially for traits which are difficult to measure, such as feed conversion efficiency and disease resistance.

Breed evaluations can be extended to the evaluation of different crossbreeding systems, with breeding objectives being calculated according to the specific role of each component breed or cross. For example, the breeding objective for a terminal sire breed would involve little or no pressure on female fertility traits, as these will only be important within that breed, which will constitute only a small part of the total system.

Refresher: Predicting merit od untested crossbred genotypes:

Example

Yearling weight in cattle, three parental breeds: 1, 2 and 3. Hypothetical values of the following parameters:

Direct additive effects Ad1, Ad2 and Ad3 The expression of these is equal to the proportion of genes from each breed.

Maternal additive effects Am1, Am2 and Am3 These relate to dam genotype, and are probably caused by milk production and rearing ability. Note that these effects add to zero - they describe the relative maternal performance of each pure breed.

Direct dominance effect Dd This is the effect of heterosis in crossbred individuals, when fully expressed, as in an F1 cross.

Maternal dominance effect Dm This is the effect of heterosis due to crossbreeding in the dam, when fully expressed, as in an F1 dam.

Table 18.2. Multiply the coefficients shown in the body of the table by the VALUES of the corresponding EFFECTS. Adding the products gives the prediction of yearling weight, MERIT in the last column. If MERIT is observed as data, this can be used in a least squares analysis to estimate the crossbreeding EFFECTS. EFFECTS: A A A A A A D D d1 d2 d3 m1 m2 m3 d m VALUES(KG): 300 280 260 -6 -1 +7 20 10 MERIT Breed 1 1 0 0 1 0 0 0 0 294.0 Breed 2 0 1 0 0 1 0 0 0 279.0 Breed 3 0 0 1 0 0 1 0 0 267.0 Best F1 (1x2) ½ ½ 0 0 1 0 1 0 309.0 Best 3 Brd-X (1x23) ½ ¼ ¼ 0 ½ ½ 1 1 318.0 Best Backcrs (1x12) .75 ¼ 0 ½ ½ 0 ½ 1 311.5 Balanced (1,2) ½ ½ 0 ½ ½ 0 ½ ½ 301.5 Synthetics (1,2,3) .33 .33 .33 .33 .33 .33 .67 .67 300.0 Optimum (1,2) .63 .37 0 .63 .37 0 .47 .47 302.4 Synthetics (1,2,3) .57 .31 .12 .57 .31 .12 .56 .56 303.0 Rotations (1,2) ½ ½ 0 ½ ½ 0 .67 .67 306.5 (1,2,3) .33 .33 .33 .33 .33 .33 .86 .86 305.7 Notes: Synthetics at equilibrium, rotations at equilibrium and averaged over years.

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18.4 Choice of crossing system

Gregory and Cundiff (1980) reported maternal and direct (or individual) dominance effects between Bos taurus breeds at 14.8% and 8.5% respectively, for weight of calf weaned per cow exposed. This indicates the importance of crossbred cows in the production system, even though maternal dominance is generally reduced at older ages, for example at slaughter age. Gregory and Cundiff used these figures to estimate the genetic merit of a wide range of crossing systems in beef cattle.

In New Zealand, Wei et.al. (2003) developed software to evaluate sheep crossbreeding systems based on a meta analysis of direct and maternal additive and heterotic effects and minimising differences between observed and predicted crossbreed performances.

The best crossing system to use depends to a large extent on the value of the breeds available, as well as the amount of heterosis expressed in crossbred animals. This is illustrated in Table 18.3 by describing the conditions under which each crossbred genotype is worthy of choice.

Table 18.3 Conditions appropriate for different crossing systems.

Purebreed When no cross is better. The Merino is a good example. F1 Cross When direct heterosis is important. 3-Breed Cross When both direct and maternal heterosis are important. 4-Breed Cross When paternal heterosis is important as well. When only 2 good parental breeds are available and/or when Backcross direct heterosis is not important. When F cross females are too expensive to either buy in or to Rotational Cross 1 produce in the same enterprise. When both males and females are too expensive to import. A Open or Closed few initial well judged importations establish the synthetic, and Synthetic it can then either be closed (which helps to establish a breed 'type'), or left open to occasional well judged importations.

Of course, care should be taken to consider factors other than the predicted genetic merit of candidate crosses for the traits of importance. The key factor here is the cost of maintaining structured crossing systems, where separate breeding units are required to give ongoing supply of purebred and/or crossbred parents. These costs often outweigh the genetic benefits of more structured crosses, especially in low fecundity species such as cattle, where the parental breeding units must be relatively large to supply the final cross.

18.5 Integration of selection and crossbreeding

When setting up a breeding program, the breeder must consider not only crossing parameters, but also within-breed genetic merit (i.e. selection opportunities) and cost factors, such as the cost of buying in breeding animals. This can be done by simply finding the strategy that is predicted to give the maximum genetic merit in progeny, taking account of costs. This involves use of an algorithm that allocates mating pairs or groups. Figure 18.5 shows an example of this.

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Figure 18.5 An example of mate allocation that maximises genetic merit whilst accounting for costs.

Bulls

Cows

Notes on Figure 18.5

• “Crossing” is the predicted merit of the offspring from the matings indicated, given information on breed of parents alone. This takes account of direct and maternal additive and heterotic effects.

• “EBV” is the estimate of breeding value having fitted all between-breed effects.

• “Cost” is the cost of purchasing or otherwise using each candidate as a parent. The red breed (see CD coloured figures) is taken as the homebred breed, and costs are deviated from this. Costs must be in index units in order to be able to combine all the components in the total score. Notice that cost values are generally higher for females. This is because each female leaves a smaller number of progeny, and therefore each of these progeny must be better by a larger amount in order to cover the actual cost of buying or rearing this female.

Having calculated the predicted value of progeny from each possible mating, the task is now to make selections and mate allocations. When the value of a mating does not depend on what other matings will be made, as in the current case, simple Linear Programming (LP) can be used to find the best solution. In more complex cases, an Evolutionary Algorithm can be used, as described in Chapter 19.

The LP method used is the same as that to solve the classical 'transport problem'. Bulls are analogous to warehouses and cows are analogous to retail stores, and the product to be transported is semen. The objective is to minimise transport cost, or, in our case, to maximise the total merit of offspring from the matings made.

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Constraints are put on rows and columns to ensure that, for example, each female is only mated one time, and each bull is mated no more than the maximum permissible number of times.

To effect selection, a dummy bull is used to absorb all culled females, and likewise a dummy cow is used to absorb all culled males. Merit for matings involving these dummy animals is set artificially high such that the mating algorithm will seek to make such matings for individuals that cannot contribute well to normal matings. The example shown in Figure 18.6 is for two single pair matings to be made from our set of three candidates of each sex.

Typical outcomes from this strategy are shown in Table 18.4.

Table 18.4 Typical outcomes from mate selection involving breed crosses.

Conditions Outcome

Direct and maternal heterosis high 3- and 4-breed crosses

Female import costs high Rotation crossing

Import sires for some generations then Male import costs also high closed composite

Within breed genetic variance high Opportunistic crossing

GENUP module MATE can be used to investigate the key aspects of selection with crossbreeding. The file Mate.doc in your GENUP directory contains a guide and some questions.

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©2009 The Australian Wool Education Trust licensee for educational activities University of New England A note on selection with crossbreeding The ranking of sires on true breeding value can be dependent on the breed genotype of mates. For example, the best Angus bull to use over Angus cows may not be the best Angus bull to use over Hereford cows. The underlying concept here is that the average effect of an allele substitution (α) depends on the genetic background involved.

α = a + d(q – p) … Chapter 7, Falconer and Mackay (1996)

This can be a within-locus effect, as allele frequency can differ between breeds, and there will be more dominance expressed for alleles that are more rare in the opposite sex (in this case a and d are unchanged, but p and q change).

However epistasis may play en even bigger role – an allele conferring higher appetite will be less effective in a breed that already has a sufficiently high appetite as dictated by other genes (in this case a and/or d are changed, but p and q could be unchanged).

The underlying parameter of interest here is r for groups i and j. This is “the breeding value Aij correlation between groups” or “The genetic correlation between purebred performance and crossbred performance”

'Normal' r example: The relevance of weight genes to expression of fertility A Example for this r : The relevance of Angus genes to expression in Hereford background A

See Swan and Kinghorn (1992) for more detail.

[PS. GENUP module MATE can be used to investigate some aspects of selection with crossbreeding. However, one thing it doesn't cover fully is estimating breeding values when candidates could be used in a crossing program. MATE assumes that the ranking of animals' EBV's remains constant across mate genotypes, and of course this may not always be valid.]

Readings

1. Kinghorn, B.P. 1987, 'Crossbreeding in domestic animals', Proceedings of the Association for the Advancement of Animal Breeding and Genetics, vol. 6, pp. 112-123. 2. Kinghorn, B.P. 2000, 'The genetic basis of crossbreeding', Chapter 4 in Animal Breeding – Use of New Technologies, Kinghorn, B.P., van der Werf, J.H.J. and Ryan, M. (eds.), The Post Graduate Foundation in Veterinarian Science of the University of Sydney, pp. 35. ISBN 0 646 38713 8.

Summary

Two key tools that animal breeders can use to increase genetic gains are selection and crossbreeding. Heterosis is a key consequence of crossbreeding and this can consist of dominance gain and epistatic losses. These are therefore two important issues to consider when designing a crossbreeding program.

References

Dickerson, G.E. 1969, 'Experimental approaches in utilising breed resources', Animal Breeding Abstracts, vol. 37, pp. 191-202. Dickerson, G.E. 1973, 'Inbreeding and heterosis in animals', in Proceedings of the Animal Breeding and Genetics Symposium in Honour of Dr. J.L. Lush, American Society of Animal Science, Champaign, IL, pp. 54-77. Dillard, E.U., Rodriguez, O., and Robison, O.W. 1980, 'Estimation of additive and non-additive

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©2009 The Australian Wool Education Trust licensee for educational activities University of New England direct and maternal genetic effects from crossbreeding beef cattle', Journal of Animal Science, vol. 50, pp. 653-63. Falconer, D. S., and T. F. C. Mackay. 1996. Introduction to Quantitative Genetics, Ed 4. Longmans Green, Harlow, Essex, UK. Gregory, K.E. and Cundiff, L.V. 1980, 'Crossbreeding in beef cattle: evaluation of systems', Journal of Animal Science, vol. 51, pp. 1224-1242. Hayman, B.I. and Mather, K. 1955, 'The description of genic interactions in continuous variation', Biometrics, vol. 11, pp. 69-82. Kinghorn, B.P. 1980, 'The expression of recombination loss in quantitative traits', Journal of Animal Breeding and Genetics, vol. 97, pp. 138-143. Kinghorn, B.P. 1982, 'Genetic effects in crossbreeding. I Models of merit', Journal of Animal Breeding and Genetics, vol. 99, pp. 59-68. Kinghorn, B.P. 1983, 'Genetic effects in crossbreeding. III Epistatic loss in crossbred mice', Journal of Animal Breeding and Genetics, vol. 100, pp. 209-222. Kinghorn, B.P. 1987, 'The nature of 2-locus epistatic interactions in animals: evidence from Sewall Wright's guinea pig data', Theoretical and Applied Genetics, vol. 73, pp. 595-604. Kinghorn, B.P. and Vercoe, P.E. 1989, 'The effects of using the wrong genetic model to predict the merit of crossbred genotypes', Animal Production, vol. 49, pp. 209-216. Koch. R.M., Dickerson, G.E., Cundiff, L.V. and Gregory, K.E. 1985, 'Heterosis retained in advanced generations of crosses among Angus and Hereford cattle', Journal of Animal Science, vol. 60, pp. 1117-1132. Mather, K. and Jinks, J.L. 1977, Introduction to biometrical genetics, Chapman and Hall, London. McGloughlin, P. 1980, 'The relationship between heterozygosity and heterosis in reproductive traits in mice', Animal Production, vol. 30, pp. 69-77. Robison, O.W., McDaniel, B.T., and Rincon, E.J. 1981, 'Estimation of direct and maternal additive and heterotic effects from crossbreeding experiments in animals', Journal of Animal Science, vol. 52, pp. 44-50. Sheridan, A.K. 1981, 'Crossbreeding and Heterosis', Animal Breeding Abstracts, vol. 49, pp. 131- 144. Swan, A.A. and Kinghorn, B.P. 1992, 'Evaluation and Exploitation of crossbreeding effects in dairy cattle', Journal of Dairy Science, vol. 75, pp. 624-639. Wei, W., Cottle, D.J., Sedcole, J.R. and Bywater, A. 2003, 'Simulation of sheep crossbreeding systems: a risk analysis', Proceedings of Australian Association for the Advancement of Animal Breeding and Genetics, vol. 15, pp. 290-294.

Glossary of terms

Allelic Heterozygous genotype where both alleles although different have heterozygosity originated from the one breed Breed of origin Heterozygous genotype where one allele has come from one breed heterozygosity and the other from another breed Interactions between linked alleles derived from the same gamete (on the same chromosome). These often involve gene Cis-acting effects expression/regulation factors that operate along the DNA molecule. Opposite of trans-acting effects Crossbreeding The mating of animals from different breeds The wider variety of genes in crossbred animals (ie genes from two Dominance gain breeds) better equips the animal to perform well The wider variety of genes in crossbred animals (ie from two Epistatic loss breeds) results in changes in the way that the genes interact with each other, generally resulting in adverse effects on the animal The advantage in performance of a cross bred animal over the Heterosis mean of its two parents Recombination loss Loss due to epistatic effects

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