The COI, or coefficient of inbreeding, measures how inbred a horse is on Horse Reality. More specifically, it measures the probability (or chance) that a horse inherits the same genetic traits from both parents because they share an ancestor. These traits could be rare, recessive colour alleles such as rabicano or very high conformation stat allele, and inbreeding could help to “fix” these wanted traits to make a better foal. However, it could also be a low fertility allele!
Note: Only Lipizzaners have the COI available to them at the moment. The COI is only available for horses migrated to the new horse/foundation system. The COI will also be introduced to the other horse breeds, once they get migrated to the new system.
¶ COI
All players can view the COI of a horse in the pedigree of the horse profile.
Players with a premium account will also be able to calculate the COI of a potential foal before breeding. This will be reassessed if additional inbreeding consequences ever get added to the game, and COI becomes more important*.
The COI formula that is used the most today by animal breeders, conservation, research, and Horse Reality was developed by Sewall Wright. The COI % measures the probability that a horse inherits the same allele from an ancestor shared by both parents. If you want to refresh how alleles and inheritance work, you can check our Inheritance 101 page on the wiki.
The COI is automatically calculated based on 16 generations (including the horse itself). However, the more recent (5-6) generations will have a stronger impact on the COI. The chance that a certain allele gets passed down for so many generations in a row, all the way from a shared ancestor 16 generations ago to a horse, is much lower and will therefore result in a lower COI. On the other hand, not including enough generations can underestimate the COI and its effects.
Since the COI measures the probability that a horse will get 2 of the same alleles from a shared ancestor, a higher COI means a higher chance the horse will be homozygous for a specific gene. For example, a COI of 10% means there is a 10% chance the horse inherited 2 copies of the same allele (=homozygous) from a shared ancestor.
Note: In real life, a COI of 10% would mean that
- There is a 10% chance the horse inherited 2 copies of the same allele from a shared ancestor
- We can expect 10% of the genes to be homozygous
However, while realistic, Horse Reality's genetic system is simplified compared to real life. Horses have more than 20.000 different genes, and a much larger number of possible variations. In-game, they have only 5 health stats, for example. Because of this, we might see that more than 10% is homozygous; especially in breeds with little colour variation.
Horses can of course also be homozygous for things with a COI of 0%. The parents can carry the same alleles and pass them on not because of a shared ancestor, but simply because of chance. Inbreeding increases the chance of being homozygous.
There are benefits to this:
- It “fixes” genetic traits - an allele carried by a shared ancestor, such as a rare recessive rabicano allele or a high stamina allele, becomes homozygous
- The horse becomes a more predictable producer - if the horse is homozygous, there is only 1 possible allele it can pass on
However, the same thing applies to unwanted traits. The benefits of a higher COI are accompanied by a higher risk of negative consequences
- The horse can become homozygous for other stats - it may “fix” a low fertility, conformation, GP or health stat while you are focussing on improving other stats
- It lowers genetic variability - if horses become more homozygous, you may lose certain colours in your herd or have a harder time improving or changing stats
- *In real life, inbreeding and a higher COI can lead to horses becoming homozygous for alleles that had no or little consequences when heterozygous, but that now lead to health consequences, defects, diseases etc. This is NOT in-game at the moment.
All benefits and risks considered, it's up to each player how they prefer to breed their horses, whether they want to take the COI into consideration or not, and what level of COI or inbreeding they use. The game can be played however you want.
Note: At the moment, there are no newly added health consequences or other penalties in-game because of the COI. It is a visual indicator only, that players can use however they wish.
¶ Calculation
The calculation of the COI is done automatically by Horse Reality, but if you would like to learn more about how it works and what's behind it, you can read this section to learn! If math is not your thing, you can safely move on to the next section, which visualises COI using pedigree examples.
The COI is a measure of inbreeding, but it essentially stands for the probability that a horse will inherit 2 copies of the same allele, from an ancestor shared by the dam and the sire. You can say that a horse is inbred when there is a (or multiple) loop(s) in the pedigree - you can go from the horse to a shared ancestor through the dam, and from the shared ancestor back to the horse through the sire. The number of different horses inside a loop (excluding the horse) is called “n”.
Every generation, there is a 50% chance that a specific allele from the shared ancestor gets passed down. This means that the probability of the foal getting the same allele through both parents is 0.5n: it needs to get passed on by all the horses in a loop to the foal. The more individuals there are between the horse and the common ancestor, the lower the probability gets. If the shared ancestor itself is also inbred, it will already have a higher chance of having 2 of the same alleles. The chance that the foal ends up with 2 copies of the same allele, becomes higher as a result. Therefore, the COI of the shared ancestors also needs to be included in the formula.
The COI formula adds up all the possible loops in the pedigree; in-game up to 16 generations. The formula that is used is the following:
COI = ∑0.5n.(1 + COIshared ancestors)
n = number of individuals in between the loop of horse → dam → common ancestor → sire → horse
∑0.5n = summing up all the possible loops
COIshared ancestors = COI of the shared ancestors
This might sound like complicated gibberish right now, but let's explain what this means in practice by using a couple of examples.
¶ COI examples
Let's explore what the COI means in practice using some examples. We'll follow the made-up alleles “A1/A”, carried by 1 horse, and use it to see how different ways of breeding influence the COI and presence of the allele.
The “A1” allele could be a rare, recessive colour such as rabicano or a very high conformation stat, and inbreeding could help to “fix” these wanted traits to make a better foal. However, it could also be undesired such as a low fertility or conformation stat.
¶ Example 1: half-siblings
The horse profile shows the pedigree up to the great-grandparent. Let's consider this foal with the following visible pedigree:
| Great -grandparent 1 | Great-grandparent 2 | Great-grandparent 3 | Great-grandparent 4 | Great -grandparent 1 | Great-grandparent 2 | Great-grandparent 5 | Great-grandparent 6 | Generation 4 | |
| Grandparent 1 A1/A |
Grandparent 2 A/A |
Grandparent 1 A1/A |
Grandparent 3 A/A |
Generation 3 | |||||
| Dam A1/A |
Sire A1/A |
Generation 2 | |||||||
| Foal - COI 12.5% A1/A1 |
Generation 1 | ||||||||
This foal has grandparent 1 on both sides of the pedigree, the parents are half-siblings. Grandparent 1 has the made-up alleles A1/A. Both the dam and the sire can pass on this grandparent's A1 allele. This way the foal could end up with two A1 copies from grandparent 1.
A breeding between half-siblings like this results in a COI of 12.5%. There is a 12.5% chance that the foal is homozygous (A1/A1 or A/A) from the shared ancestor.
The calculation is written out below, but you can again ignore it if it's not your cup of tea.
COI = ∑0.5n.(1 + COIshared ancestors)
n = 3 (dam, grandparent 1, sire)
COIshared ancestors = 0
COI = 0.53.(1+0) = 0.125 or 12.5%
¶
Example 2: Siblings
| Great -grandparent 1 | Great-grandparent 2 | Great-grandparent 3 | Great-grandparent 4 | Great -grandparent 1 | Great-grandparent 2 | Great-grandparent 3 | Great-grandparent 4 | Generation 4 | |
| Grandparent 1 A1/A B/B |
Grandparent 2 A/A B1/B |
Grandparent 1 A1/A B/B |
Grandparent 2 A/A B1/B |
Generation 3 | |||||
| Dam A1/A B1/B |
Sire A1/A B1/B |
Generation 2 | |||||||
| Foal - COI 25% A1/A1 B1/B1 |
Generation 1 | ||||||||
This foal has both grandparent 1 and grandparent 2 on both sides of the pedigree, the parents are full siblings. There are 2 shared ancestors: the dam and the sire can both pass on not just grandparent 1's alleles, but those of grandparent 2 as well. To represent this, the alleles B1/B have been added to the example.
A full sibling breeding like this, results in a COI of 25%. There is a 25% chance the foal is homozygous (A1/A1, A/A, B1/B1 or B/B) from the shared ancestors.
We already know from example 1 that with the shared grandparent 1, there is a 12.5% chance the foal is A1/A1 or A/A. Logically, there is now also a 12.5% chance that the foal gets B1/B1 or B/B from grandparent 2. To get the chance that the foal gets any 2 identical alleles from a shared ancestor, we can simply add this up to get 25%. This is also shown in the calculation (optional, as always):
COI = ∑0.5n.(1 + COIshared ancestors)
n1 = 3 (dam, grandparent 1, sire)
n2 = 3 (dam, grandparent 2, sire)
COIshared ancestors = 0
COI = (0.53 + 0.53) .(1+0) = 0.25 or 25%
¶
Example 3: Outcrossing
Let's see what happens when we breed these horses together:
| Great -grandparent 1 | Great-grandparent 2 | Great-grandparent 1 | Great-grandparent 2 | Great -grandparent 3 | Great-grandparent 4 | Great-grandparent 5 | Great-grandparent 6 | Generation 4 | |
| Grandparent 1 A1/A B1/B |
Grandparent 2 A1/A B1/B |
Grandparent 4 A/A B/B |
Grandparent 5 A/A B/B |
Generation 3 | |||||
| Dam - COI 25% A1/A1 B1/B1 |
Sire A/A B/B |
Generation 2 | |||||||
| Foal - COI 0% A1/A B1/B |
Generation 1 | ||||||||
There is some inbreeding in the dam's side of the pedigree: her parents are siblings. This gives her a COI of 25%, as we learned in example 2. It might sound contradictory at first, but the foal in this example would have a COI of 0%! We don't just count any repeated ancestors, but ancestors shared by both parents. Great-grandparents 1 and 2 are only on the dam's side of the pedigree.
Even if the dam is homozygous A1/A1, introducing an unrelated sire means there is no chance the foal will inherit both alleles. The foal will have only 1 allele coming from the shared ancestors of the dam.
This is called outcrossing. Breeding the dam to an unrelated sire reduces homozygosity and introduces new genetic traits.
¶ Example 4: Outside the visible pedigree
Let's take the same pedigree as in example 1, but this time, with an extra generation included. This won't be visible on the horse profile pedigree, but it can still contribute to the COI.
| 1 2 A1/A |
1 2 A1/A |
3 | 4 | 5 | 6 |
|
1 2 A1/A |
1 2 A1/A |
9 | 10 | 11 | 12 | Generation 5 | |||
| Great -grandparent 1 A1/A |
Great-grandparent 2 A1/A |
Great-grandparent 3 | Great-grandparent 4 | Great -grandparent 1 A1/A |
Great-grandparent 2 A1/A |
Great-grandparent 5 | Great-grandparent 6 | Generation 4 | ||||||||
| Grandparent 1 - COI 25% A1/A1 |
Grandparent 2 A/A |
Grandparent 1 - COI 25% A1/A1 |
Grandparent 3 A/A |
Generation 3 | ||||||||||||
| Dam A1/A |
Sire A1/A |
Generation 2 | ||||||||||||||
| Foal - COI - 15.625% A1/A1 |
Generation 1 | |||||||||||||||
We know from example 1 that, without generation 5, the foal would have a COI of 12.5%. However, this time we need to add the COI of Grandparent 1 into the mix as well. Grandparent 1 is the result of a full-sibling breeding. In example 2, we learned that this results in a COI of 25%. Using the COI formula, this gives us a COI of 15.625%. There is a 15.625% chance that the foal is homozygous (A1/A1 or A/A) from the shared ancestor.
We can see that because Grandparent 1 was already inbred himself, this increased the COI of the foal. In example 1, the grandparent could only be A1/A. In this example, there's also a chance of him being A1/A1 (or A/A). If this were the case, he could only pass on A1. Naturally, this would increase the chance the foal would get A1/A1, too. If we didn't include generation 5, we would have underestimated the COI value.
It highlights that not just the visible pedigree is important for the COI. We can also note, however, that the COI only increased a little bit - from 12.5 to 15.625. The inbreeding in generation 5 is further away from the foal and impacts the COI less as a result. If we go back even further, the influence will be even smaller.
COI = ∑0.5n.(1 + COIshared ancestors)
n = 3 (dam, grandparent 1, sire)
COIshared ancestor = 0.25 (COI grandparent 1)
COI = 0.53.(1+0.25)
COI = 0.125 * 1.25 = 0.15625 = 15.625%
¶ Changelog
- The COI was added to the game on January 15th, 2025[1]
¶ References
- https://v2.horsereality.com/news/206/release-notes-coefficient-of-inbreeding
- Laboratory of Veterinary Genetics; https://labgenvet.ca/en/horse-genetics-4-1-inbreeding-calculator-detailed-instructions-and-interpretation/; Access: January 2025
- P. van Eldik et. al, Possible negative effects of inbreeding on semen quality in Shetland pony stallions, 2005
- Wade et al., Genome sequence, comparative analysis and population genetics of the domestic horse (Equus caballus), 2013