# ZooEasy information in English

AVK
ZooEasy enables you to carry out very precise calculations of the AVK value. This value is calculated by using a 5 generation pedigree with a maximum of 62 ancestors. The number of different ancestors is often smaller because an animal has been used several times in a line. The more often this happens, the fewer different ancestors there will be, the higher the loss of ancestors and the higher the inbreeding coefficient.

Inbreeding calculation
With ZooEasy you will be able to perform extremely accurate inbreeding calculations. This part of ZooEasy has been realized in conjunction with Wageningen University. Dr. P. Bijma,

Professorial Chair in Breeding and Genetics, helped to develop this function. The theoretical background is described in the explanation.

Explanation
Contrary to the relationship coefficient which represents the genetic similarity between animals, the inbreeding coefficient is a number that is connected to individual animals. To understand the inbreeding coefficient some extra knowledge about genes is recommendable. The DNA of birds and mammals comes in pairs, which means that of each gene there are actually two. Because of this we call these gene pairs. Of each gene pair one of the genes comes from the mother and the other from the father. People and animals have a lot of these gene pairs. According to recent estimates human beings have approximately 40,000 of these gene pairs. The inbreeding coefficient represents the probability that both genes of a random gene pair are identical. The inbreeding coefficient thus states something about the genetic uniformity of an animal. An animal that has not mated with relatives has an inbreeding coefficient of zero. Both genes of a random gene pair are different for this animal. The inbreeding coefficient of a fully inbred animal is 1; both genes of a gene pair are always identical.

Inbreeding occurs when two animals of the same family are mated. The descendant of such a mating is thus inbred. Illustration 1 is an example of inbreeding. An animal (no. 3) is mated with his sister (no. 4), which has the same parents. A descendant (no. 5) is born from this mating. Animal no. 5 is inbred because both parents are related to each other. Animals that are related always have common ancestors. In this case the animals no. 1 and 2 are both ancestors (parents) of animal no. 3 and of animal no. 4, so animals no. 3 and 4 are related to each other. When animals sharing one or more common ancestors mate, there is a chance that both animals pass on the same gene (that originally comes from the common ancestor) to their descendant. Therefore, there is a chance that the descendant will receive a gene pair with two identical genes, which means that the descendant is inbred. In illustration no. 1 this is represented by a gene (A) of animal no. 1. In this illustration the gene is passed on to both animals no. 3 and 4 and subsequently animals no. 3 and 4 pass this on to descendant no. 5. The inbreeding coefficient of animal no. 5 is the probability that animal no. 5 indeed receives two identical genes. In this example the inbreeding coefficient equals 0.25 which means that there is a probability of 25% for animal no. 5 having two identical genes.

Animals that are not related to each other don't have common ancestors, which means that they won't pass on the same gene. The descendant therefore is not inbred when two animals mate that are not relatives of each other. In other words: the inbreeding coefficient for this animal is zero. In general the inbreeding coefficient of a descendant equals half the relationship coefficient of its parents. If an animal mates with his own full sister this will result in a descendant with an inbreeding coefficient of 0.25 due to the fact that the relationship coefficient connected to full brothers/full sisters amounts to 0.50.

The base level
In all animal populations the average inbreeding coefficient increases steadily. If a population starts with all animals having an inbreeding coefficient equaling zero, the average inbreeding coefficient will have become larger than zero after a few generations. The inbreeding coefficient in Illustration 1 is valid for a population with an average inbreeding level that equals zero. If a population has already reached a certain inbreeding level, the inbreeding coefficients will be higher. e.g. If the population in Illustration 1 has already reached an average inbreeding level of 0.2, the inbreeding coefficient of animal no. 5 equals 0.2 + 0.25 × (1-0.2) = 0.4. This 0.2 represents the base level, 0.25 represents the inbreeding coefficient for animal no. 5 if the population would not have been inbred and 1-0.2 is the increase still possible for the inbreeding coefficient (1 is the maximum value). The base inbreeding level equaling 0.2 the relationship coefficient between animals 3 and 4 equals 2 × 0.2 + 0.5 × (1-0.2) = 0.8. In general, the relationship coefficient is twice as high as the inbreeding coefficient, which explains the calculation 2 × 0.2. The outcome 0.5 is the relationship coefficient between 3 and 4 if the population would not have been inbred.

 Animal Father Mother Gene ------------------------------------------ 1 - - AB 2 - - CD 3 1 2 AC 4 1 2 AD 5 3 4 AA

Illustration 1: Blood line with 5 animals. The genes of a random gene pair are indicated by the italic letters A up to and including D. e.g. Animal no. 1 has two genes, A and B. The blood line illustrates how gene A is passed on via animals no. 3 and 4 to animal no. 5 because of which animal no. 5 is inbred. In this blood line the inbreeding coefficient of animal no. 5 equals 0.25. This means that the probability of animal no. 5 having two the same genes equals 0.25. The blood line illustrates that animal no. 5 was inbred by gene A, but one of the other genes B, C or D could have been responsible for this just as well.

Relationship coefficient
The relationship coefficient of two animals can be established by entering the registration numbers of both animals. When you click the OK button, ZooEasy will establish the percentage.

This part of ZooEasy has been realized in conjunction with Wageningen University. Dr. P. Bijma, Professorial Chair in Breeding and Genetics, helped to develop this function. The theoretical

background is described in the explanation.

Explanation
The relationship coefficient between two animals indicates how much these two animals resemble each other genetically. A relationship coefficient equaling zero means that the animals do not

resemble each other at all. The relationship coefficient between two animals that are not related in any degree thus equals zero. The relationship coefficient of two identical twins equals 1, because identical twins are genetically identical. The relationship coefficient between two animals depends on the number of genes these animals have in common. e.g. The relationship coefficient of father and daughter equals 0.5 because the father passes half of his genes on to his daughter. (Of course, the other half is passed on by the mother). For the same reason the relationship coefficient between mother and daughter equals 0.5 and between grandmother and daughter 0.25. The relationship coefficient between full brothers and full sisters equals 0.5. Full brothers and full sisters receive half of their genes from each of their parents, however, not exactly the same half. On average full brothers and full sisters share 50% of the same genes.

From a statistical viewpoint the relationship coefficient between two animals can be considered as the contribution of the genetic variation these animals have in common. Let's assume that a characteristic (e.g. the body weight) has a hereditary coefficient of 0.3. This would mean that the total variation that you observe between animals is for 30% caused by hereditary differences between animals. The total variation two full brothers and sisters have in common is determined by the relationship coefficient and inbreeding coefficient. In this example they have 0.3 x 0.5 = 0.15 = 15% of the total variation in common. This means that full brothers and full sisters have 15% of the differences, which can be observed between animals in common. e.g. If one of both animals is heavier than average, you would expect the other to be heavier than average too. This, however, is something you don't know for sure, because there is still a variation of 85% these animals do not have in common.

 Composition relationship-coefficient Identical twins 100% Brothers with full sister 50% father-daughter or mother-son 50% brother with half-sister 25% descendant-grand parent 25% uncle-niece or aunt-nephew 25% double nephew-niece1 25% single nephew-niece2 12,5% animal-great grand parent 12,5%

1 Double nephew-niece is a breeding pair where both of the fathers are full brothers and where the mothers are full sisters too.

2 Single nephew-niece is a breeding pair where only two of the four parents are full-brothers or full-sisters.