Composites

Composite development may be indicated when heterosis is essential, if initial unfavorable recombination effects are negligible, when there are new objectives or altered management conditions, and in areas where the simplicity of the breeding program is essential. Zebu, some exotic breeds, and native breeds have been used in some instances for developing Composites in the tropics (Canchin and Montana in Brazil, Bonsmara in South Africa, Droughtmaster in Australia, Santa Gertrudis, Bradford, Brangus, and Charbray in the Southern United States).

(1) Management: Synthetic breeds will contribute to more straightforward management requirements. ^{Kowalsky (2020}) described the Venezuelan cattle herd structure: 94,6 % are smallholdings, 87% own less than 30 crossbred cows. They are well-served with just one bull. As in any pure stock, sires of similar genetic composition are used. Thus, the number of pastures required will be minimal, particularly favorable to small ranchers.

(2) Selection for additive traits: Lopez-Fanjul (n.d.) has shown that when heritabilities have been estimated in composites, their value was not found to differ from those in their parental breeds. But, selection intensity will be limited in the first generations, if inbreeding is to be kept at minimal levels as well as a need for increased numbers as the breed develops.

(3) The exploitation of heterosis and heterosis retention: Heterosis, the difference between the average performance of a cross and the average performance of the parents, has two main components. The first and most important is the result of differences in gene frequencies between the two parental populations and the degree of dominance present. ^{Willham (1970}) has shown how heterosis at a single locus in the F1 is equal to ∆ p 2 d, where ∆ 𝑝 is the difference in the gene frequency between the two parental populations, and 𝑑 is the degree of dominance. After the first filial generation F1, the gene frequencies remain constant according to the Hardy-Weinberg equilibrium, then the amount of heterosis remains constant in the successive generations. As the gene frequencies in the F1 becomes intermediate between the parental gene frequencies, the degree of heterosis is equal to ½ ∆ 𝑝 2 𝑑; meaning that half the original heterosis is retained in successive generations. In general, if n breeds are utilized in the Composite development, 1/n of the original heterosis is lost, or (n-1)/n is retained. The second component of heterosis is due to favorable epistatic combinations of linked genes in the repulsion phase (inherited separately), which had been fixed by selection or isolation in the parental breeds. Under interse mating, successive crossing over and recombination will tend to destroy those linked groups. After two or three generations, all these epistatic effects will probably be lost. When the epistatic effects are significant, loss of heterosis will be larger than what is theoretically expected. ^{Koch et al. (1985}) result supports the hypothesis that heterosis effects of crosses among Bos taurus breeds, for traits related to growth and size as well as for reproductive and maternal traits, can be accounted for by the dominance effects of genes. Nevertheless, strengthen that large-scale comprehensive experiment is needed to estimate retention of heterosis in advanced generations of interse mated composite populations with contributions by both Bos taurus and Bos indicus breeds. Indeed, ^{Sanders et al. (2005}) present additional questions regarding the validity of the dominance model for the prediction of heterosis and heterosis retention for reproductive and maternal traits in Bos indicus x Bos taurus females. Heterosis retention estimates for the traits of interest were found to be lower than expectations of the dominance model for some groups and higher than expectations of the dominance model for other groups. ^{Plasse et al. (2005}a) suggested that line formation was difficult since crosses among tropical breeds under conventional management did not exceed the best parental breed. ^{Madalena, (2001}) concluded that in Bos taurus and Bos indicus crosses for milk, the performance of the F1s has been much higher than the other crosses, followed by the rotational crosses, while the "bimestizos" (in Brazil, daughters of mestizo parents) have had very poor performance. The relative economic performance of F1, rotational cross, new breed (Composite), and Holstein were, respectively, 100, 59, 30, and 21, in privates farms.

(4) Minimum population numbers: ^{Lopez-Fanjul (1974}) states that the primary advantage of increased heterozygosity can be "squandered" by renewed inbreeding unless large population numbers are kept. How large should the experimental herd be to keep inbreeding at a low level can be estimated with some approximation.

The rate of inbreeding Δ𝐹 is a function of effective population size. ^{Lush (1948}) showed how Δ𝐹= 1 2𝑁𝑒 where 𝑁𝑒 is the effective population size and Δ𝐹 is the variation in inbreeding per generation. When there is a different number of males and females, 𝑁𝑒 becomes 1 𝑁𝑒 = 1 4𝑁𝑚 + 1 4𝑁𝑓 , where (ec1) number of males and number of females (ec2). The rate of inbreeding Δ𝑓 per generation can be rewritten as Δ𝑓= 1 8𝑁𝑚 + 1 8𝑁𝑓 . As population size becomes larger, Δ𝑓 becomes smaller, and the generation with the smallest number has the most significant effect. However, as the population size increases, the previous inbreeding is not eliminated but remains where it was before the increase in number because new inbreeding is reduced. Thus, the first three or four generations, while the Composite is being tested, are the most important ones in terms of inbreeding. More than ten to twelve unrelated bulls and two hundred and fifty to three hundred cows are required per generation if less than one percent increase in inbreeding per generation is desired, assuming random mating, which is not the case. Even if selection and further assortative mating are used, the above holds because Lush, (1948) has shown them to be almost powerless in changing heterozygosis. Selection will be limited to the extent that more sires per generation will have to be used, which will reduce intensity. 𝑁𝑚=𝑝 ×𝑁, where 𝑁 is the number of males reaching reproductive age and 𝑝 the proportion saved. If selection intensity 𝑖= 𝑍 𝑝 , for i to be large, 𝑝 must be small, but if 𝑝 is small, Nm will also be small in the Composite, making Δ𝑓 large. Then the advantage of more considerable additive variance can be neutralized by the requirement of keeping inbreeding at a low level.

In conclusion, a large population is a condition for full utilization of heterosis resulting after crossing different breeds for the development of Composites. The cost of keeping such a large population can limit the effectiveness of this proposal.

(5) Flexibility against risk: The success or failure of the Composite is determined at the precise moment of the population closure. Sampling errors, loss of heterosis due to renewed inbreeding, or recombination, the variation in prevailing conditions (environment or market), or unexpected performance of the Composite may result in the loss of resources, time, and efforts. If, after three or four generations, the results are unsatisfactory, everything will have to start all over. The literature contains just the successful trails, while many failures stay undisclosed to the public. This risk factor must be considered before any breed development is begun. ^{Plasse (2000}) concludes, "The author is not aware of any information in the current Latin American scientific literature that would allow him to responsibly recommend this system (composite) to livestock practice." While ^{Leachman (2000}) proposed "composed populations of several original breeds, permanently open to new genetic contributions."

3.2 Modified Absorption

A second alternative to rotation system could be one that combines the simplicity of the purebred mating, exploits heterosis in successive generations with the versatility of totally open herds. Such a mating system was empirically purposed in previous papers (^{Ordóñez, 1975}, cited by Ordóñez, 1990) based on earlier work by ^{Cartwright & Fitzhugh (1972}) and ^{Koger (1973}). A schematic representation of the mating system is depicted in figure 1.

A proportion of purebred female of Breed A (adapted to the environment) is mated to sires of Breed B. The F1 progeny of that mating, bulls, and heifers, are removed from the purebred herd and incorporated into the commercial herd. F1 sires are mated to the commercial cows, originally of Breed A, in successive generations until all the females in the commercial herd are of genetic composition like the F1. The modified F1's is represented within brackets [F1]. The female progeny from the commercial herd are kept as replacements, while the males go to market. In any generation, new unrelated F1 sires are used. It can be said that the mating system tries to absorb or grade up to [F1]. The expected composition of successive generations at equilibrium has been developed with that of the rotation to allow comparisons.

Rotation: First, let us call the (ec3) fraction of genes from the parental breed in the n^th generation and the fraction of genes from the maternal grandsire in the same generation of any progeny of rotation mating.(ec4)

Then:

Or

but 𝑌 0 =1 in the purebred population, then in general:

while, (1)

Table 1 summarizes the application of this general formula to fill the genetic composition of the herd in the successive generations of rotational crosses.

Modified [F1]: By analogy in Modified [F1] 𝑌 𝑛 is the fraction of genes from the newly introduced breed carried by the progeny in generation n; then in general (2)

Table 2 summarizes the application of these general formulas to fill the genetic composition of the herd in the successive generations of "Modified [F1]".

As can be seen from table 2, the genetic composition of the population at equilibrium resembles that of the first generation of interse mating. The properties of such a population must be studied in more detail.

(1) The simplicity of management: At the commercial level, the system performs as simply as does any pure breeding system. Only one breed of sires is used, allowing for entire herds in the small operations. The system also provides for their replacement females. Still, F1 sires must be provided from elite herds located at accessible areas, where AI increases the ability to capitalize on genetic progress in the progenitor breeds, under the prevailing conditions.

(2) Flexibility: It is one additional advantage of the proposed system. Change in the exotic breed due to adjustment of the performance of the products following changes in environmental conditions, the market, and the goals is relatively simple and in no way affects the development of the system, reducing the risk mentioned above. The flexibility available through crossbreeding to match performance levels to specific conditions must also be considered a real advantage (^{Long, 1980}).

(3) The adaptability of the parents: As has been indicated, a primary consideration for crossbreeding is the possibility of combining useful traits quickly in an individual. The main objective of using crossbreed bulls is to combine in an animal the adaptability of the tropical breed and the improved performance of the exotic, hoping to obtain an animal able to work in adverse conditions, but that simultaneously transmits to his progeny desired genes for beef production. F1 Zebu x European bulls have proven to be suitable as mentioned by ^{Neville et al. (1985}) on "the comparison of SB (purebred) and F1 bulls for reproductive and progeny performance… there were no differences (P>.05) among the four sire groups for the proportion of cows exposed that had a calf, had a live calf or weaned a calf." The adaptability of the female, on the other hand, is guaranteed if their genetic potential for mature size and particularly for milk production, is maintained within limits coupled with the level of nutrition (^{Plasse, 2000}). As stated by ^{Willham (1972}), "If low-quality roughage that can be harvested only by the cow is considered, milk production in excess of growth demands by the calf seems of little economic value." The cow adaptability depends, to a large extent, on the exotic breed, which is chosen to be incorporated in the population.

(4) The efficiency - the ability to produce an output without waste: As indicated by ^{Cartwright (1970}), rather than individual performance, the whole system performance must be considered when comparisons between systems must be made. Following the scheme indicated by Cartwright et al. (1975), some comparisons between the main alternatives made in a previous paper, are included here because of their importance. Although the rotational cross seems to be more useful for exploiting hybrid vigor, the last four columns of table 3 can make a difference in the profitability of the proposed system.

(5) The exploitation of Heterosis: Following ^{Willham's (1970}) approach to genetic consequences of crossbreeding, some properties of such a population can be estimated. Considering a single locus with two alleles L1 and L2 and two breeds A and B, that have gene frequencies p:q and p+Δp:q-Δp.

; where µ _AB is mid parent value,

where µ _F1 is the mean of the reciprocal crosses µ _A.B and µ _B.A; a is the average effect of a gene substitution, and d is the dominance deviation from the homozygote average.

Then, heterosis is defined as the difference between the mean of the cross and the average of the parents and is equal to:

For this locus to show heterosis, it is required both a difference in allele frequencies between the populations (Δp ≠ 0) and positive dominance (d > 0).

Then, the genetic array of the crossbreed F1 sire is

and the mean of the first-generation crossing A females and F1 males can be developed

then, heterosis:

We have estimated as the fraction of genes from the newly introduced breed in the progeny of generation n. This same fraction remains of the difference between gene frequencies at the locus level. Then in general, means and heterosis from the mating of F1 sires with the crossbred females of generation n can be calculated as follows:

Genetic array:

Males:

Females:

Genotypic array

Heterosis:

(4)

The level of heterosis depends on the fraction of the squared difference in gene frequency remaining and the degree of dominance minus the additive component of the differences.

By analogy, table 4 summarizes the application of these general formulas to fill the gene frequencies and expected heterosis of the herd in the successive generations of "Modified [F1]" cross.

The expected heterosis from the system in equilibrium is equal to that of an interse mating. However, it is necessary to indicate that while synthetics reach their maximum level of heterosis in the first generation of crosses, Modified Absorption to [F1] behaves in the opposite direction, the level of heterosis increases in successive generations as the coefficient of Δp increases. That can be a disadvantage if maximum production potential is desired rapidly, but it could be an advantage if the selection is applied simultaneously. It also gives time to the breeder to provide the appropriate environment required to match the new genotype tested. On the other hand, when epistatic effects are essential components of heterosis, F1 sires can make partial use of this advantage. If recombination is low enough and selection is applied, the initial disequilibrium between repulsion and the coupling phases may persist for several generations with the additional heterotic advantage. Furthermore, as heterosis in sire reproductive performance is important, it could represent an additional advantage of this system over the rotation.

(6) Loss of heterosis due to renewed inbreeding: As the population is maintained open, unrelated sires can be used to generate F1 sires, in every generation. Then, the probability of heterosis losses due to renewed inbreeding is small if nonexistent.

(7) Selection for the additive traits: As said before, F1 sires must be provided from elite herds where AI is available, capitalizing on the genetic progress in the progenitor breeds. Then, selection among the purebred herd that generates the F1 sires will have similar results that they would have under purebred mating. ^{Willham (1970}), discussed how selection response in crossbreds is lower than that obtained when selecting among purebreds or advanced generations of interse mating. However, the heritability of a trait is a ratio between the additive and total phenotypic variances. Although the dominance and epistatic components of variance are increased in the crossbred, the additive component is also increased. ^{Stonaker (1973}) has found that heritabilities are somewhat higher in crossbreds rather than in purebreds.

Since crosses are generally less variable, this higher heritability is probably the result of a smaller environmental and a more significant genetic contribution to the difference. Additionally, Sires in Breed B might be selected mainly on additive merit based on their progeny from cows of Breed A.

If nonadditive effects contributed to their ranking on the EBV, then the Sires selected in Breed B would be chosen in part for their genetic differences from Breed A. Thus, the long-term effects of selection in the two breeds would be for genetic divergences, and hence the enhancement of heterosis between them.

4.1 Similarities

Comparing Composites and Modified [F1], it becomes evident that (1) both mating systems generate female replacements throughout the herd and (2) effectively exploit heterosis to a similar extent, given they are made of the same number of breeds. (3) 100% of the cowherd as well as of the calves marketed are crossbreds so, (4) if meticulously designed, females and males could be fully adapted to the conditions under which they will strive. (5) Minimum number of breeding pastures required is one.

4.2 Differences

However, some differences need to be highlighted: Modified [F1] overcome three fundamental requirements: (1) The use of F1 sires impede loss of heterosis due to renewed inbreeding, expand heterosis retention, do not interfere with selection for additive traits, and capitalize genetic progress in the parental breeds. (2) There is not a minimum herd size, a valuable attribute for the small rancher. (3) The flexibility available, through a change in the exotic breed, to match genetic potential to specific conditions of the environment, market, and goals.

Finally, a valid criterion to compare the advantages or disadvantages of the alternative matting systems is "previous experiences” in similar conditions. There are no experiences with the Modified [F1], but, as mentioned before, the literature contains just the successful trails while many failures stay undisclosed to the public. ^{Plasse (2000}) was very brave to admit, after several attempts, that he was not aware of any information that would allow him to recommend composites to livestock practice. So, in the absence of previous experience with the Modified [F1] system, more research on mating systems in beef cattle production is required.