Relationship and inbreeding
Measurement of F coefficient (consanguinity) in a population can be considered as a measure of the increase in the proportion of homozygous individuals following an inbreeding mating (between relatives) [3].
The coefficient of consanguinity F can be calculated with the following methods: 1) pedigree 2) run of homozigosity (ROH); 3) genomic kinship matrix; 4) SNP genotyping [4, 5]. Inbreeding can occur in small closed populations due to mating between related animals. In a closed population, the decrease in the fraction of heterozygotes from one generation to the next may be referred to as ΔF. This value varies in relation to the size of the population: ΔF = 1 / 2Ne where Ne is the effective number or effective size of the population. In a population, Ne depends on the number of males (Nm), and on the number of females (Nf), in the following relationship:
The inbreeding coefficient, at a given t generation, can be calculated as a function of ΔF and t as:
which shows the decrease (ΔF) of heterozygotes that occurs at each generation following inbreeding [6]. Lewis et al. [7] reported for 221 breeds of the UK Kennel Club a Ne that varies between 23.8 of the Manchester terrier breed to 918 of the Borzoi breed and an average value of F equal to 0.06. The deleterious effects of inbreeding are universally known. They can be summarized briefly in the increase in the frequency of all genetic defects and abnormalities (reproductive sphere, resistance to diseases, longevity, etc.). These findings are based on the results of experiments carried out on different breeds and for several generations. Leroy et al. [8] showed that the increase in inbreeding in the population has an effect on individual survival and litter size of different breeds.
Deleterious effects begin to occur when the value of F is about 0.375. Lower values are not to be considered dangerous. It is worth noting that this is the level of inbreeding that is achieved in only two generations of full sibling mating. For this reason, it is recommended to avoid mating between close relatives. Consanguinity is influenced by the number of individuals used per generation [9]. As a general rule, individuals whose numbers are lower in the breeding population they exert a proportionately greater effect on consanguinity. This is true both in relation to the male/female ratio (depend more on the number of males) and the different numbers of breeders in the various generations. The actual number of breeding animals is the parameter used in small populations to determine the expected inbreeding coefficient. Since the less numerous sex is the most important, the actual number of the population can be calculated even if the number of the larger sex is not known (e.g. 2 males and the number of females is assumed to be infinite: 1/Ne = 1/ 4Nf = 1/4 (2) =1/8 * F = 1/16 = 0.0625). The family size is the number of offspring in each family who become parents in the next generation. In ideal conditions, the size of the population will remain constant in subsequent generations if each parent is replaced by another individual. In this case, the average number of offspring per parent is equal to 1 with an average family size of 2 (two parents). The Ne is also function of the variance of the family size. If males mate with more than one female, the number of offspring and thus the variance of the family size will differ between the two sexes. Several measures can be implemented to keep consanguinity within acceptable limits in the population: increase the number of breeders; mating of one male with a female (since the number within the sexes is the same, Ne will be maximized), reduce the variance size of the family (for a constant number of offspring for each family, the variance is equal to 0 and the Ne is double); avoid mating between siblings or cousins; avoid mating individuals in generations that overlap as inbreeding increases. If the management program includes the genetic improvement of one or more characters, selection must be carried out using selection indices that take into account of the level of relationship. The goal is to find the optimal number of offspring for each breeding animal and determine if a young animal (a candidate for selection) should be selected for breeding or not. This is done in an optimal way using the software EVA [10] that guarantees the achievement of the genetic progress and the maintenance an optimal genetic diversity in the population.4.