Using a Bull Team – Mitigating risk in breeding

by Professor Donagh Berry, Statistical Geneticist, Animal and Grassland Research & Innovation Centre, Teagasc Moorepark
Breeding is a bit like horse racing – the 3/1 favourite is the bull that comes from a good pedigree proven to often produce good females while the 50/1 is analogous to the low reliability high index bull. One can play it safe-ish with the favourite, but the favourite doesn’t always win – one could take a chance and bet on the 50/1 and if it is placed (i.e., not necessarily the best but sufficiently high) then the rewards are greater. So what impacts the decision to bet on either? Financially would you be better off betting on just the favourite, or betting each way on four of the 50/1 – the equivalent in breeding is using a single high reliability bull or using a team of lower reliability bulls. The answer lies in probability theory.

What is reliability?
The genetic evaluation process, using sophisticated statistical techniques, provides the best estimate of an animal’s genetic merit based on the available data on the animal itself, its pedigree, and its descendants. The confidence in this best estimate is reflected by the corresponding reliability of the proof. Reliability varies from zero to one. In the absence of information on any descendants or on the animal itself, the reliability of a non-genotyped animal is quarter the reliability of its sire plus quarter the reliability of its dam; the EBI reliability of most newborn calves is approximately 32%. As the quantity of information available on the animal and/or its relatives grows then the reliability improves. The reliability therefore provides information on how much the proof of an individual can vary from the published estimate as more data accumulates. Figure 1 shows the 95% confidence interval for the EBI an animal with different reliability values; this interval depicts where the true EBI of the animal may actually lie relative to its published value but 5% of the time the true EBI may actually be outside this range. For example, for a bull with a published EBI of €300 and corresponding reliability of 30% (equivalent to parental average), several years later, once the bull has accumulated many hundreds of daughters, his EBI could lie anywhere from €120 to €480; 2.5% of the time, his EBI could actually be >€480 and 2.5% of the time his EBI could actually be <€120. If the bull reliability was 90% instead of 30%, his EBI several years later has a 95% probability of being between €232 and €368 and thus a lot tighter range; nonetheless the EBI of high reliability bulls can still fluctuate over time. Similar confidence intervals can be derived for all traits. Figure 2 illustrates the same concept for any of the type traits or composite traits including overall type where the published proof is 0; for a bull of 50% reliability for any type trait, his true genetic merit for that type trait could be anywhere between ±1.39 of his published proof. This phenomenon is the same across the world no matter what country or what species.

Figure 1

Figure 1. Range within which the true EBI of a bull could lie if his published EBI is €300 and his reliability varies from zero to 100%

Figure 2

Figure 2. Range within which the true genetic merit for any type trait or composite trait of a bull could lie if his published proof is 0 and his reliability varies from zero to 100%

Which bull should I chose – a high index bull with low reliability or a lower index bull with high reliability?
As a purist geneticist, the answer is simple – the higher index bull since the estimate of genetic merit of each bull is the most accurate estimate. At a practical level, the answer depends on how risk-averse the farmer is; a risk averse farmer (or any investor) who prefers a lower return on investment with known risk (e.g., the lower index bull with higher reliability) than a higher return on investment with more risk (i.e., higher index bull with lower reliability). The decision is a function of both 1) the difference in the published index value between the two bulls compared, and 2) the difference in reliability of the two bulls. An example of such a scenario is in Figure 3 for a bull with an EBI of €260 and reliability of 90% (e.g., daughter proven bull) versus a bull with a EBI of €300 and a reliability of either 50%, 70% or 80% (i.e., genomic bull or team of genomic bulls). For the €260 EBI bull with 90% reliability, his true EBI could lie between €192 and €328 (depicted by red line in Figure 3). For the €300 EBI bull with 50% reliability, his true EBI could lie between €148 and €452 (depicted by blue line in Figure 3). Clearly therefore there is some probability that the lower EBI bull could in fact be truly better than the higher EBI bull (with low reliability); this probability is in fact 32% in this example. The probability of the lower EBI bull being truly superior to the higher EBI bull reduces as the difference in EBI between the bull increases but also as the reliability of the higher EBI bull increases. This is illustrated in Figure 4 for different combinations of differential in EBI between bulls and the reliability of the higher EBI bull(s). From Figure 4 is can be deduced that, if using a team of higher EBI bulls with 90% reliability, the probability that a 90% reliability bull is truly better than this team is 21% if the difference in EBI is just €40 but only 2% if the difference in EBI is €100. In other words, if there is a difference in EBI of €40 between two bulls each 90% reliability there is a 79% (i.e., 100% minus 21% from the example above) probability that the higher EBI is actually better.

Figure 3

Figure 3. Probability distribution of the true EBI of a 90% reliable bull with a EBI of €260 (red line) versus the probability of the true EBI of a bull of either 50% reliability (blue line), 70% reliability (black line) or 80% reliability (green line) all with an EBI of €300.

Figure 4

Figure 4. Probability that the true EBI of a less reliable bull (varying in reliability from 50% to 90%) is less than the true EBI of a 90% reliability bull when the difference in EBI between the two bulls varies from €40 to €110.

Bull teams as a strategy to overcome low reliability
The principle underpinning genetic evaluations is that an animal’s proof has an equal probability of going up as it does of going down; this can be summarised therefore into two possible outcomes 1) up, or 2) down. This is equivalent to tossing a coin – the outcome can be either a herds or a tails. If you toss a coin twice there is a 25% probability you will get two heads (assume heads is the same as a bull dropping so therefore a 25% chance that your both bulls will drop). If you toss a coin three times the probability of 3 heads (i.e., all three bulls dropping) is 23 or 12.5%; for 4 bulls the probability is 24 or 6.25% and so on. Therefore, the larger the bull team, the lower the likelihood of being very unlucky (and of course the lower the probability of being very lucky when all bulls go up). This however assumes all coin tosses are independent of each other (i.e., what outcome you got in the last toss does not affect the current toss) – this is not necessarily the case for bulls where some bulls could originate from the same sire. If this common sire himself is low reliability, and his proof drops, then all his progeny will automatically drop. Therefore, the calculations to estimate the reliability of a bull team were revised to account for relationships among the bull team members. Many farmers took on board the recommendation to use a team of at least 4 bulls in their breeding program; however, the bulls were not always equally used on the same farm and this compromises the reliability. To illustrate this point, take a team of 4 bulls each 50% reliability; if 1 bull was used on 99% of the cows then logically the reliability of the “team” of bulls is close to 50% (i.e., the farmer more or less used just one bull) and not the 87.5% reliability that would have materialised if the 4 bulls were used evenly. Therefore, the calculation of bull reliability was further updated to account for unequal usage.

Does using a bull team noticeable increase variability in the progeny?
In short, no! The sire only contributes 25% to the genetic variability in his daughters; the dam contributes a further 25%, with how the DNA is randomly inherited between parent-offspring contributing the remaining 50%. A great example of this is Etazon Slogan and Etazon Addison who are full brothers but genetically very different. Therefore, using a single bull reduces the genetic variability relative to a huge team of bulls by only 25%; however, for traits like fertility, only 3% of the observed variability in similarly managed animals is genetic, so therefore the actual difference observed on farm is <1%. Remember also that variability is key to genetic gain.

Risk is part and parcel of farming and breeding is no exception. Strategies such as the use of bull teams can reduce the risk of breeding programs without noticeably increasing the heterogeneity of the herd. Advise on bull team usage has been updated in light of observations of farmer habits and the availability of related bulls in AI. These updates are incorporated into the revised sire advise.

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