The Theory of Optimal Contributions, inbreeding, and TGRM™

Modern breeding programs are using technologies that have accelerated the rate at which genetic improvement can be made. One of the consequences of rapid genetic progress using technologies such as BLUP and genetic markers is the acceleration of inbreeding. These technologies rely heavily on the relationships between individuals to infer genetic merit. This results in more accurate genetic information, and also reflects the genetic fact that individuals with similar ancestry also have similar genetic values. A consequence of this, aside from increasing genetic progress, is to increase the probability of selecting individuals that are more related to each other.

Once this was clearly understood, considerable scientific effort was focused upon methods to manage how quickly inbreeding accumulated. A key approach emerged that considered the concept of coancestry; how related individuals are to each other. This has become known as Optimal Contributions Theory. In contrast to coancestry, inbreeding is a measure of how similar the pairs of alleles across the genes are within an individual. A simple way to think about coancestry and inbreeding is to think about two individuals who are related (the share coancestry). If they are mated, there will be inbreeding in their progeny. Two unrelated (no shared coancestry) individuals will produce progeny with zero inbreeding.

We now have formal methods of measuring "coancestry", and given a list of animals and how they are mated, we can measure the rate at which we would expect coancestry to increase. We need to know who will be selected, and how often each individual is to be used. The concept can be illustrated again with an example. If an individual that is unrelated to all other individuals is used only once, it has very little chance to contribute its genes to the next generation, and therefore will not contribute very much coancestry. However if the same individual contributes many progeny, then it has the potential to contribute very highly to future generations, and therefore would have higher coancestry in future and we would expect the coancestry of the population to increase.

The difference between coancestry and inbreeding, and their effects on future inbreeding, can be illustrated with an extreme example. Suppose all of the progeny come from a single but unrelated sire (no coancestry between the sire and the dams). All of the progeny will have zero inbreeding, but will share the same sire, and therefore share their coancestry. If you wanted to breed from those progeny, they would all be related through the sire, and any and all matings between them would result in inbred progeny, even though they are not inbred at all. This also illustrates the point that avoiding close matings, that is to only avoid inbreeding, is not an effective way to manage coancestry, that is to avoid future inbreeding! The most effective way to manage future inbreeding is to manage coancestry. Optimal Contributions can do this.

The science of Optimal Contributions has given us two important concepts we can apply:

  • given the number of matings for each male and female parent, we can calculate the rate of coancestry (should we proceed to mate them or have already mated them) - this means that for any mating list, we can calculate the relevant coancestry figures (we need the pedigree to do this)
  • the rate of coancestry can be held constant (resulting in a linear rate of inbreeding) and therefore can be managed in concert with maximising genetic progress - we call the range of possible combinations of genetic progress and coancestry the frontier of genetic gain and coancestry. This means sustainabile genetic progress and sustainable genetic improvement programs.

TGRM™ is the first practical application of Optimal Contributions Theory.