If the exact mode of inheritance of a trait is known, including the number of genes involved and whether the allele(s) for the trait are dominant, recessive, etc. then it is possible to mathematically calculate exact probability that the dog under consideration is either affected or a carrier. Unfortunately, we do not have this information for most of the genetic diseases we encounter in Aussies.
While we can't determine precise probabilities, there is a useful approach to the problem via a variation of the "percentage of ancestry" calculation. Percentage of ancestry is usually used to determine how much a particular dog or bitch has contributed to a pedigree. A parent contributes 50%, a grandparent 25%, and so on. If a particular animal appears multiple times, the values for the different generations in which the name appears are added to reach the final result.
Examples:
Blue is a grandsire and a great grandsire.
25 + 12.5 = 37.5 percentage of ancestry.
Lady is great grand dam twice and great-great grand dam three times.
(2 x 12.5) + (3 x 6.25) = 43.75 percentage of ancestry
Blue falls somewhere between a grandparent and a parent in the amount he has potentially contributed to the pedigree and Lady is very nearly at the level of a parent. I say "potentially" because we cannot know exactly which genes came down through the intervening generations. It may be everything the individual passed to it's immediate descendant or it may be nothing. In most cases actuality will hover somewhere around the percentage of ancestry figure.
A percentage of ancestry value of this type cannot exceed 50% because of gender. No bitch or dog could be behind more than half of the possible lines of descent in a pedigree. If you come up with a number greater than 50 in this kind of calculation, you have made an error.
Using percentage of ancestry for determining the likelihood of producing a particular trait is somewhat different. Instead of looking for a particular name, you are looking for any dog that is likely to have genes for the trait under consideration.
We cannot know the genotype of every dog in the pedigree and, except for dominant traits, noting only those dogs that expressed the trait would lead to an understated result. In the case of severe faults or genetic defects, such individuals usually will not be bred so the typical pedigree will have no ancestors who exhibited the trait. If an affected individual is in the pedigree, however, it will certainly have contributed genes for that trait to the next generation and those genes may have been passed further along the line.
If a dog or bitch has affected offspring then, with very few exceptions (things proven to be single-gene simple dominant or X-linked traits,) both parents will have contributed genes to produce the trait. If they have done it once, they could do so again, depending on what genes were contributed by their mates.
It is very likely that you may not have been able to find out whether a particular dog had actually produced the trait you are concerned about. However, you might have found out about one or more grandpups which had the trait, indicating that the dog on your pedigree might have carried gene(s) for it. I refer to these dogs as "suspect" carriers. Such dogs should be considered, but should not be given the same weight as dogs that actually exhibited the trait or were known to produce it. Another reason to include suspects is as a way of considering the "breath of pedigree" necessary for evaluating risk of producing polygenic traits like hip dysplasia while working with a typical pedigree that contains the names of direct ancestors only.
Going farther back from an identified affected individual than grandparents, begins to get very tenuous. More distant ancestors are less and less likely to have contributed the necessary genes. Consideration of them makes the calculation more cumbersome for very little added benefit. It can also become misleading. For instance, if a frequently used sire who had no affected offspring or grandpups and who also happens not to actually carry genes for the trait appears numerous times in the pedigree, this can unreasonably inflate the result.
How many generations you should go behind your subject dog depends on a number of factors. If the trait is easily recognized (color, coat type) or readily discussed (dentition) or if information is readily available (performance records), three generations might be enough. However if the trait is one people don't consistently check for and may therefore have missed or which they may not mention for fear of stigma, then five generations may be more revealing. Five or six is the maximum to review. Beyond that the likelihood that the trait has been passed down and nobody has made any note of it becomes rather tenuous.
Since I use this process to look for risk of hereditary defects and diseases, I first check three generations and make note the affecteds, carriers and suspects that I find. I then check an additional two generations to see if any of the noted traits are connected with those ancestors. For our breed's more serious and common problems (cataracts, epilepsy and hip dysplasia) I check a full five generations because information on affected individuals often will not have been made available to others and a longer pedigree can be more revealing.
When you begin to mark the pedigree. Start with the subject dog and move back along each line of descent. Once you find an individual connected to a particular trait, note whether it was affected, carrier or suspect. Do not proceed any farther along that particular line. You have found the most recent connection and noting more distant ancestors along that line will inaccurately inflate your result. If you have checked only three generations to determine which traits to check further for, follow only those lines of descent into the 4th generation and beyond on which you have not already identified a suspect individual.
Example: You find a grandparent that was an iris coloboma carrier and a great-grandparent that was a suspect carrier. When you look at the additional generations, disregard those lines that fall behind the grandparent and great grandparent you have already identified.
Note: Do not let names of the dogs confuse you. You are considering only connection to the disease and position in the pedigree. Examples:
- If the suspect great grandparent also appears in the 4th and 5th generations, you must note it there, too, unless the appearance is behind the already identified carrier grandparent.
- If the dam of that carrier grandparent, who is necessarily a suspect, appears in the 4th generation on another line of descent—other than behind the already noted suspect great-grandparent—then it should be noted.
Once every known connection to the trait has been noted on each line of descent, it's time to determine how much risk the subject dog has for the trait. This method will not give you separate consideration for whether the dog might have the trait as opposed to merely carrying it. Since we don't have any way of knowing exactly what genes came down with polygenic traits and those of undetermined inheritance, there is no way to do this. What the calculation will give you is a percentage of ancestry based on the trait, as opposed to a particular individual.
The values used below are those I use in determining level of risk. They are not meant to represent precise probability. Rather they are a method of consistent comparative ranking. Who's higher and who's lower, with lower being preferable for undesirable traits like hereditary disease. If you were doing this for desirable traits, you would want high numbers.
I give affected individual who appear in the parent generation a value of 100. They have the genes because they exhibit the trait. Since they are affected they will pass genes on to each of their offspring. Even in the case of polygenic traits, the offspring will each get at least a little bit from that parent. If the affected appears as a grandparent, its value is 50, 25 for a great grandparent, and so on.
Carriers also have the genes, but in addition will have sufficient other versions of those genes that they do not themselves have the trait. Some of their offspring will get the versions you want and some will get the ones you don't. I value a carrier parent at 50, a carrier grandparent at 25, etc.--half the value I assign to an affected.
Suspects are even less likely to provide genes for the trait under investigation. I therefore value them a quarter of what I value an affected. A suspect parent would be 25, a grandparent 12.5, and so on.
Since gender is not an issue in this kind of search, values over 50 can easily result. It is also possible to get values over 100 (e.g. an affected parent bred to the daughter of a carrier would score 125.) Even though it is similar to and based upon percentage of ancestry, the result is not a percentage calculation.
I use these numbers for the purposes of determining relative risk only. Thus far I have not provided them to people for whom I do analysis because they could too easily interpreted as precise probability estimates. However, for knowledgeable users the information could be of value and I am considering starting to use the scores in conjunction with some of our thornier problems like epilepsy and cataracts, where so many animals are high risk.
Prior to now, I have been using the following classifications of scores:
75+ Very significant
50 – 74 Significant
25 – 49 Moderate
13 – 24 Low
1 – 12 Very Low
0 Unlikely
Very significant is roughly equivalent to having at least carrier parent and a carrier grandparent. Significant is equivalent to having at least a carrier parent, moderate a carrier grandparent, low a great grandparent, and very low a great great grandparent. The picture is rarely so simple, however.
A pedigree a reviewed recently for epilepsy had a suspect parent, a suspect great grandparent, and five suspects on the 5th generation. This resulted in a moderate risk estimate (score of 39.) If the suspect parent had been clean and had no connections to epilepsy in the dogs behind it the score would only have been 14, or low risk.
I don't usually bother to list things for which I find no connections (score=0), but if people ask me about such an item, I say it is "unlikely." I use this term because I know I don't have all the information. I may not know about the connection or the suspicious ancestors are so far back I didn't note them, therefore there is a possibility that the genes might be there. Never say never.
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