Population Genetics II: Reducing High Gene Frequencies
Suppose you have an undesirable recessive gene that is affecting most of a population. This gene is clearly not lethal in the normal sense, as there is no way that a naturally lethal gene can exceed a gene frequency of 50% (every animal in the breed a carrier, and that is unlikely unless there is strong selection against both homozygotes.) But it can easily be a gene which affects health (e.g., deafness, blindness, bleeding tendencies, metabolic disorders) but does not appear obvious to the eye of the breeder without tests. It is possible for such an undesirable recessive to affect an entire breed; and once this happens it is not possible to eliminate the condition without crossing to another breed. For breeds which have not quite reached this 100% frequency, then, it is of extreme importance to preserve the normal gene.
Suppose we start with a breed gene frequency of 95%. We will again assume random breeding, modified only by the breeding strategy of the breeders. With a 95% gene frequency, we would expect 90.25% affected, 0.25% genetic clears, and about 9.5% carriers, for an unaffected rate of slightly less than 10%. (In practice, some breeders will normally have been testing and removing carriers, so the fractions of affecteds and clears will increase at the expense of carriers.) We assume that in any generation we want to remove no more than 10% of the gene pool due to this single gene. The exact value of 10% can be argued - it should depend on the severity of the unwanted gene - but removing much more than 10% in a single generation due to a single gene can have dangerous effects on the overall genetic diversity of the breed.
In the first few generations, you forget about selection against the undesirable gene and concentrate - hard - on selection for the normal gene. In effect, unaffected status - be it carrier or simply non-affected - is treated as an extremely positive virtue and bred for. Almost all unaffected dogs should be bred, and they should be bred to the best mates available. This means that owners of top quality dogs must be willing to mate them to bitches which are of poor quality by show standards if these bitches are non-affected. Affected, poor-quality offspring of such matings can and should be removed from the breeding pool; non-affected offspring, like their non-affected parent, should be kept in the gene pool. A more difficult goal is to get owners of top quality bitches to mate them at least once in their lives to the best non-affected male available. The goal at this point is to increase the number of carriers at the expense of affecteds. Unfortunately the show ring provides no reward for this kind of long-range thinking.
How fast will this have an effect? It depends on how strong the selection for non-affecteds is, and how rare non-affecteds are to start with.
It is clear, however, that it will take some time to get a reasonable spread of K genes in the breed (remember most of the breed starts out kk) especially if we want those K genes to come from as wide a range of individuals as possible. Note that at this time we are distinguishing only between affected (kk) and non-affected Kk and KK) individuals. To a first approximation, the percent of affected individuals is the square of the gene frequency. (This is exact only for random breeding.) The gene frequency is then the square root of the percent of affected individuals in the breed. This is an easy calculation on a $10 pocket calculator - punch in the fraction of affecteds as a decimal (e.g., 70% is put in as 0.70) and hit the square root key. (In this case the gene frequency is about 0.84 = 84% - the gene frequency will always be greater than the percent of affecteds.)
By the time the gene frequency has dropped to around 80% (64% affecteds) some mild selection against affecteds should be added to the mix. Affected to affected breedings should be looked on with an increasingly critical eye - not actually banned yet, but limited. Affected dogs (both sexes) without any great virtues to offer should be removed from the gene pool.
As the gene frequency continues to drop, the selection against affecteds should grow stronger. Actual removal of all affecteds should wait until the observed frequency of affecteds drops below the critical value of 10% (gene frequency about 32%), but affected to affected breedings should be eliminated and non-affected to non-affected breedings encouraged as far as possible. At this stage it is premature to worry about carriers, but an affected dog should have really great virtues to offer if it is kept in the breeding pool. Once the gene frequency drops below about 30%, it is safe to start removing all affected individuals from the breeding pool. By this time, 90% of the animals in the breed will be non-affected, and there should be no problem in finding good non-affected mates.
Until now, we have assumed that we cannot differentiate KK from Kk - both are simply non-affected. In most cases, however, there are ways of identifying carriers. The simplest is simply to continue to test for the condition, and pay attention to normal breeding results. If a breeding produces any affected individuals, both parents are carriers and non-affected littermates have 2 chances out of three of being carriers. One in three of the littermates, however, are genotypic normals. Thus the littermates of affected pups, if of exceptional type otherwise, should be tested for carrier status. If such an animal tests as a genetic normal, it cannot pass on the gene for the problem, even though a littermate was affected.
Testing for carrier status beyond what comes out of normal breeding has changed sharply in the last few years. The old method (still needed for some genes) is to breed the questionable dog to an affected one. Some affecteds will still be produced at this stage, and some should be retained for test breeding if that is necessary. This type of test breeding, however, has considerable uncertainty and required several known carrier offspring to be produced (around 10) before a dog could be pronounced to be a non-carrier with a reasonably high degree of confidence. In fact, a dog could never be proven to be a non-carrier; it could only be demonstrated that he could not be proved to be a carrier.
Increasingly, gene sequencing is offering an alternative in determining carrier status. This has great advantages over test breeding: no carriers or affected dogs need be produced to determine the status of the dog, and the production of affected individuals can be entirely avoided if the carrier status of all individuals in the breeding population is known. It does produce problems as well: the temptation is to say that no carriers should be bred right from the start, when a large number of dogs, could be removed due to a single gene. Suppose that the test becomes available when the fraction of affected individuals in the breed is on the order of 4%. This corresponds to a gene frequency of 20% and a carrier frequency of 32%. Even with an affected frequency of 1% we can expect a carrier frequency of 18%. Yet we do not want to elminate more than 10% of the breed due to this single gene. How do we prodeed?
We can avoid producing affecteds by breeding carriers only to dogs genetically tested as non-carriers - genetic normals. This in itself, however, does nothing to reduce the gene frequency. For the best benefit of the breed as a whole, the avoidance of carrier to carrier matings should be accompanied by some selection against carriers, but not by actual elimination of carriers from the gene pool when such elimination would lead to too rapid a restriction of the gene pool A limitation on the number of litters produced by carriers would be appropriate, as would removal of those carriers whose virtues could be found in non-carriers. Figure 3 in part I of this series shows how rapidly selection will reduce the gene frequency using this strategy. Probably the initial approach would be to allow carriers to reproduce at around 90% of their expected rate, then reduce the reproductive rate with each generation until the carriers make up less than 10% of the population. At that point the remaining carriers could be removed from the breeding pool.
How long should testing continue? Certainly as long as occasional affecteds are being produced. More practically, offspring from normal to normal breedings should all be normal. Until the test is throroughly established, breeding stock from normal to normal breedings should still be checked, but carrier status for these dogs is not expected. Once the test is fully validated, all pups from matings involving a carrier as a parent should be tested. Once all carriers are removed, in theory no more testing is needed - but to catch any new mutations, it is still a good idea to check widely used animals - any dog bred to produce more than two litters a year, I would say. Also all relatives of any affected pups that show up after the gene is apparently eradicated.
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sbowling@mosquitonet.comLast updated April 7, 2010
