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  • Jan Iving

COI – the Co-efficient of Inbreeding, does it matter?

There is considerable confusion about Co-efficient of Inbreeding. Alas, sorry, this article probably will not unravel all the mysteries, but it may clarify the scene in your mind just slightly. The idea for an article was spurned by most sites/programs not spelling out which formula they use and over how many generations the COI is calculated.

THE FORMULAS Most programs and registers seem to use Wright, but there are other methods that can be used to calculate inbreeding, and Wright’s formula also has variations.

Wright’s Equation and Hardiman’s Method are both based on the principle that the inbreeding of an individual is one half the relationship of its sire and dam, however the calculations involve different data and so the inbreeding coefficients produced by them are not interchangeable and should not be compared with each other. Wright’s Equation is haphazardly calculated to any number of generations, whereas Hardiman’s Method is always calculated to five generations.

Wright’s Equation considers duplicated ancestors only if they are common to both sire and dam, whereas Hardiman’s Method considers all duplicated ancestors. It should be noted here that an inbreeding coefficient is of little value without a standard with which it can be compared, so the proposed Register of Inbreeding Coefficients will be used to calculate a breed average for comparison. from

Essentially Wright considers all duplicate entries within the pedigree (however many generations one chooses to look at), while Hardiman considers all inbred ancestors, so in effect you can imagine that Hardiman will be a truer indication of the likely reduction in a gene pool of whatever gene you are focusing on. Which establishes that there is a difference, and probably a big difference, in the result of the two calculations. Hardiman also has the probable advantage in that the number of generations to limited to the more recent ancestral generations so a) we can better assume we know what issues or advantages these ancestors have to offer b) the data is likely to be more accurate as I have seen some Wright’s calculation programs just accept ancestral blanks in a pedigree. Actually I don’t know that the dog world has caught up with the Hardiman equation as yet.

Hardiman’s is 2000, but there have been plenty of other formulas offered over the years: 1948 Malecot 1962 Kudo Kudo and Sakaguchi version of Kudo taking into account X borne genes also 1997 Ballou

THE IDEA BEHIND COI For close to 100 years (1920s) breeders have had the option of using the Coefficient of Inbreeding. The COI is the mathematical representation of the likelihood that the progeny of a mating will have two copies of the same recessive gene or same dominant gene – in ‘genetic speak’ aa or AA. Just as the hip assessment scheme, particularity the BVA based ones that combine scores on various attributes that demonstrate hip dislocation disease, is a gauge for breeders and owners to ‘visualize’ the chances of a serious hip dislocation being an issue and causing significant pain.

The COI will give the astute breeder a value figure on the likelihood of an individual (or individuals in a litter) of having a recessive gene expressed, or a autosomal dominant gene expressed, so in fact the individuals being, say, either aa or AA. COI is best understood for the consideration of recessive genes, a classic example in Clumbers is the mutation that leads to PDP1 deficiency. For an individual to express (show, have) a recessive disease (or virtue!) that individual must acquire the same recessive gene from both parents, one from each parent. The ‘problem’ with recessive genes is that they can lurk in a population without being expressed (where the individual is aa so the point is expressed, rather than Aa where the individual is a carrier but unaffected) for many, many generations. So breeders can sometimes assume the recessive fault or virtue has been bred out – but one day new individuals start to appear with the virtue or disease, as an Aa and Aa are bred together and aa individuals happen to be born and grow up! On the general scatter theory of wide open pedigrees, geneticists can offer breeders the greater certainty that a recessive (or dominant) gene won’t appear in the individuals by reducing the number of likely carriers in the pedigree, ‘outsiders’. It is a stab in the dark concept, but one that works quite nicely. There is no certainty that other individuals not previously used in a kennel won’t also be ‘secret’ carriers of the same problem or virtue gene, but like tossing a coin statistics can help.

Most dog breeds were developed and evolved by inbreeding, inbreeding concentrates within the individuals the ‘desirable’ attributes, and naturally to concentrate the desirable attributes the same dogs can and sometimes do also have less than desirable attributes concentrated, so the relative population of the ‘danger’ gene in the breeding stock can rise.

So a breeder taking into account and respecting a need for a low value COI can shunt opportunities in their favour, the COI is a tool, and a useful tool – the use of a single figure clarifies what is on the pedigree and will even ‘highlight’ unsuspected inbreeding that a reader can often miss seeing when viewing a pedigree – there are a lot of names on a pedigree chart!

THE EFFECT/AFFECT OF THE NUMBER OF GENERATIONS IN THE CALCULATION Generally breeders are offered Wright’s Co-efficient of Inbreeding, and generally you aren’t told the actual formula used, which could lead to variations in COI, and sometimes you are not told how many generations are included which again can alter the COI.

Certainly trying to compare the Kennel Club’s ‘all known ancestors’ back to the early 1980s for however many documented generations to a 10 generation home computer program can give different results. I run Breedmate and for an individual, and as an example I came up with

4 generations 3.27% 5 generations 4.54% – so conforms to the current Swedish recommendations 6 generations 6.37% 7 generations 7.75% 8 generations 8.72% 10 generations 15.82% 15 generations 28.28% 20 generations 32.53%

wow, well obviously while in this dog (actually it was a proposed mating and hasn’t been undertaken yet) the immediate (typical four generation pedigree) is relatively not inbred, the ancestors beyond are probably the same, which actually is going to be very likely in a number of breeds, or breeds that have used a few fashionable parents, as well as Clumbers.

Anyway, the point I wanted to make is that the number of generations can and do affect the COI.

WHAT IS GOING OUT THERE THE KENNEL CLUB (UK) I was unable to see anything on their newly released (2011) Mate Select (possibly because the server was not responding well on my first play around), so asked I them. Jeff Sampson their top breeding and health consultant wrote, “The calculation of COIs uses data drawn from the KC electronic database which effectively goes back to the early 1980s for most dogs. All of the available information is used to calculate an individual COI, but the precise amount of information will vary from dog to dog. When you use the programme to calculate an individual dog’s COI the right hand panel of the report will give the number of generations considered when calculating the COI. The only time where this will change will be if an imported dog appears in a pedigree and this is because when we register an imported dog we usually only have a 3 generation pedigree available.” (private email 7-6-11)

THE SWEDISH BREEDING RECOMMENDATION Calculation of inbreeding is a purely mathematical process, based on the fact that every individual of 50% is related to his father and mother, ie, one half of their genes comes from each parent. The actual inbreeding may be higher or lower than the theoretical calculated, everything depends on the circumstances and the choice of starting point for the calculations. For the calculation formulas refer to basic textbooks on breeding.

Calculation of inbreeding by hand is laborious and full of risks for error, especially when pedigrees are complex and calculation is ​​over many generations. It is therefore best to use computer programs that work with established or finished pedigree databases. The Dog Registry of SKK Rasdata is one such list, but it goes no further back than the beginning of the 1970s. It is therefore not meaningful to calculate inbreeding for more than about five generations based on SKC computerized pedigree data. The current design has therefore inbreeding estimates standardized to include the last five generations. Note that this means that the calculations can be very incomplete in older dogs and dogs with incomplete pedigrees. Google translation and my tidying of

Most elementary genetics books have instructions for calculating the inbreeding coefficient from the pedigree. (For more information, see Dr. Armstrong’s site, Significant Relationships.) However, these procedures have two major limitations. First, they are not really designed for cases where there are multiple common ancestors, though they can be used separately for each common ancestor and the results added. Second, they become impossibly complex as the length of the pedigree increases. It is by no means uncommon in dogs, for instance, to have pedigrees which can be researched in the AKC stud book and the KC Gazette and which go back to foundation dogs born around the turn of the century – perhaps 30 or even 40 generations earlier. With this type of long pedigree, foundation animals may appear a million times or more in the pedigree.

With this in mind, a computer program called GENES was developed by Dr. Robert Lacy for the calculation of the inbreeding coefficient, kinship coefficients among animals in the breeding pool, percent contributions of varying founding ancestors, and related output, assuming full pedigrees to the foundation stock were available for all animals currently in the breeding population. For captive breeding populations, the less inbreeding the better, and this is the way the program is used. from

BREEDMATE is available for home use, it allows you to calculate the COI (based on Wright’s equation) on a variable number of generations. Of course there are several other pedigree programs, you will get better value if you seek one that can detect when a generation is not fully recorded and one that allows you to alter the number of generations being assessed. Typical inbreeding percentages are as follows, assuming no previous inbreeding between any parents: Father/daughter, mother/son or brother/sister = 25% Grandfather/granddaughter or grandmother/grandson = 12.5% Half-brother/half-sister = 12.5% Uncle/niece or aunt/nephew = 12.5% Great-grandfather/great-granddaughter or great-grandmother/great-grandson =6.25% Half-uncle/niece or half-aunt/nephew = 6.25% First cousins = 6.25% First cousins once removed or half-first cousins = 3.125% Second cousins or first cousins twice removed = 1.5625% Second cousins once removed or half-second cousins = 0.78125%

SO WHAT SHOULD BREEDERS DO? The Kennel Club imply breeders should keep their COI on future litters below the breed’s average, and that was about 17% for Clumbers when the facility to check potential matings came online! The Swedish recommendation is less than 6.25% in five generations, and their research scientist wrote, There is not much you can do about the breeding work that has already been implemented. The aim is rather to avoid repeating past mistakes in future generations. It is therefore important to investigate what the expected increase of inbreeding will be from a planned mating rather than to analyze how inbred the mating partners are. A good basic rule is to avoid mating between individuals that are more closely related than first cousins. Cousin mating gives an estimated increase of inbreeding of 6.25% in the offspring. With access to the computerized calculation programs, it is relatively easy to check each potential pedigree as you like and make sure it stays down below that level. The procedures for mating planning, combined with inbreeding calculation, will give you control to limit inbreeding. The proposed cut off is not intended as an overall limit on the appropriate pairing, just as a boundary that should not be exceeded for individual matings. Ideally, the average rise of inbreeding in one strain does not exceed about 1% per generation.

To completely avoid any inbreeding is hardly possible, nor desirable. For properties that have a hereditary background it is inevitable that the best individuals in the breed are in some way related to each other. The quest to totally avoid any inbreeding would therefore pose immense difficulties and probably prevent a breeder from using the best breeding material. It can never be the goal of breeding selection and subsequent mating planning. In contrast, if the rise of inbreeding is kept low enough to reduce the loss of genes in each generation, breeders can then avoid undermining prospects for a future and meaningful breeding program. Per-Erik Sundgren, January 1999, from Google translation and my tidying of So, are dogs actually inbred compared to other domestic livestock, here are a few snippets from the internet to give you some idea.

Today, a limited number of animals in each breed serve as parents of highly influential sires in each generation. Wiggans, et al. found average inbreeding of 4.7% in Ayrshire cows, 3.0% in Guernsey, 2.6% in Holstein, 3.3% in Jersey, and 3.0% in the Brown Swiss breed. Are these numbers alarming? The critical issue is whether inbred dairy cows are functional under today’s management conditions and whether that functionality is compromised by less genetic diversity in the population. Cattle today are more inbred than their ancestors, but they are also much more productive. It would not be accurate to say that current levels of inbreeding are alarming. from

Apparently it is not uncommon for some purebred cat breeds to display COIs of about 30% Thoroughbreds are apparently usually less than 5% And if you are curious about other dog breeds, pop by the Kennel Club’s Mate Select selection and you can pull up their COI for a breed. Clumbers are at 17.7%, Sussex at 22.6%, German Shepherds 3.2%, Shetland Sheepdogs 5.8%, Cavaliers 5.2% WHAT ARE THE DOCUMENTED POTENTIAL PROBLEMS OF INBREEDING? Well of course you get the folk who say doom will descend and the breed will die out. But let’s look at documented issues in other forms of livestock where inbreeding has climbED rapidly and to a high level: ~Increased age before reproduction would occur in cattle The data comprised of 4127 lactations belonging to 1613 animals of FG, JG, FJG, JFG and BFG genetic groups, collected from Mahatma Phule Krishi Vidhyapeeth, Rahuri, (M.S.). The detailed inheritance charts of these animals born over a period of 29 years during 1972 to 2000 were prepared and inbreeding coefficient of individual animal was calculated. All the animals were grouped into six sub-groups as non-inbred, very distinct, distinct, moderate, close and very close inbred. The overall level of inbreeding during the study period was noticed as 7.03%. The inbred cows in the total herd were 38.46% in FG, 52.26% in FJG, 23.33% in JFG and 52.29% in BFG genetic groups. In JG genetic group none of the animal was found inbred. The effects of level of inbreeding was significant on age at first calving (P<0.01) in FJG genetic group only and remaining all the traits were non-significant in all the genetic groups. from INBREEDING AND ITS EFFECT ON REPRODUCTION TRAITS OF CROSSBRED CATTLE* R.L. Bhagat1, B.R. Ulmek and A.B. Pande2 Indian J. Anim. Res., 41 (3): 204 – 207, 2007

~Decrease in birth weight, increase of age at first delivery, increase in interval between deliveries in cattle Reyna Creole cattle in Nicaragua comprise about 650 purebred animals, and the breed has been shown to have a high level of inbreeding. To characterize the breed, as basis for a conservation program, information from two herds on birth weight (BW, n = 1097), age at first calving (AFC, n = 449) and calving interval (CI, n = 1,347) was analysed. Overall averages were 27.8 kg for BW, 37.4 months for AFC and 424 days for CI. Large differences between the herds were observed for all traits. Thus, there would be opportunities for management interventions to improve reproduction results. The heritability for BW was 0.34. For CI, the heritability of 0.20 and the additive genetic standard deviation of 36 days were comparatively high values. No genetic variation was found in AFC. Estimated inbreeding effects were associated with large standard errors due to the small size of the data and incompleteness of pedigrees. Nevertheless, significant effects were shown of dam inbreeding level on all traits. For each percentage of increased inbreeding, BW decreased by 0.06 kg, AFC increased by 3.5 days and CI increased by 1.4 days. The effects of the inbreeding level of the individual itself were not significant. The relatively good reproduction traits of Reyna Creole cattle shown in this study, despite high inbreeding levels, will be supplemented with a characterization of milk production traits. from Birth weight, reproduction traits and effects of inbreeding in Nicaraguan Reyna Creole cattle. Corrales R, Nasholm A, Malmfors B, Philipsson J. Trop Anim Health Prod. 2011 Aug;43(6):1137-43. Epub 2011 Mar 26.

~Decreased growth rates in sheep The aim of this study was to describe the population structure, inbreeding and to quantify their effect for different weights, of Santa Ines sheep. For this reason, 6490 data of production and 17,097 animals in the pedigree data set were utilized to evaluate birth weight (BW), weight at 60 days (W60) and weight at 180 days (W180). The genetic structure analysis of the population was realized by the software ENDOG (v.4.6.), resulting in some level of inbreeding for 21.72% of the animals in the pedigree data, being 41.02% the maximum value, and average of 10.74% for the inbred individuals. The population average inbreeding was 2.33% and the average relatedness was 0.73%. The effective number of ancestors was 156 animals and the effective number of founders was 211 individuals. A significant depressive effect of the inbreeding can be verified for all traits. The monitored parameters related with the genetic variability on this population must be constant in order to prevent the decrease in the genetic progress. The utilization of a program for directed mating in the present flock is an appropriate alternative to keep the level of inbreeding under control. from Population structure and inbreeding effects on growth traits of Santa Ines sheep in Brazil V.B. Pedrosa, M.L. Santana Jr., P.S. Oliveira, J.P. Eler, J.B.S. Ferraz in Small Ruminant Research Volume 93, Issue 2 , Pages 135-139, October 2010 And there are plenty more studies out there, but, and this is where the advice is springing from, inbreeding (without selection to avoid such issues) can easily lead to significant breed population issues such as late onset of breeding, decreased birth weight, decreased growth rate, and probably smallness of adult.

If you and allied breeders are witnessing ANY changes in onset of successful breeding (earlier or later), ANY changes in birth weight, or ANY changes in adult size and those individuals have a high COI, what are you going to do in the next generation? I hope you are not going to seek to continue to inbreed on that future generation.

Obviously the research into livestock is about reduced production and yield and I would not be surprised for diehard SHOW breeders to point this out to diehard working breeders with smaller dogs BUT don’t assume if you have larger Clumbers and inbreed you won’t be faced with some challenge or disadvantage to producing your own next generation if you are determined to inbreed again on this generation. Inbreeding is a TOOL and a tool to be used sensibly and wisely when appropriate – to use it unwisely and produce unhealthy or unthrifty pups in our modern times will mean this tool will be removed from our store of options – in fact in many countries the registries will no longer accept brother to sister, parent to offspring matings, the tool is already being chipped away because of the product of breeders not taking appropriate care and forethought.

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