Genetic Value Analysis

The genetic value analysis proceeds according to the following steps:

1. First, the average of all pairwise kinship coefficients are calculated for each living animal in the breeding colony relative to every other living animal in the colony according, to the algorithm of Lange (1997). The grand mean kinship in the breeding colony is then calculated from the distribution of individual mean kinships, along with other summary statistics describing this distribution.

2. Second, measures of individual mean kinship for each animal are then calculated in terms of standard deviates from this grand mean kinship, as z = (x-μ)/σ, i.e., "z-scores", in which x is the estimate of individual mean kinship, μ is the grand mean kinship, and σ is the standard deviation of the distribution of all individual mean kinship values of living animals in the colony.

   These z-scores indicate the extent and direction to which each animal's individual mean kinship deviates from the grand mean kinship in the colony. An animal having a positive z-score has individual mean kinship that lies above the colony grand mean kinship, suggesting that this animal's genome is over-represented in the colony, making the animal of lesser genetic value than others with negative z-scores. Conversely, an animal having a negative z-score has individual mean kinship that lies below the grand mean kinship, suggesting that this animal's genome is underrepresented in the colony, making the animal of greater genetic value than animals with positive z-scores.

3. Third, genome uniqueness values are calculated using a gene-drop simulation according to MacCluer et al. (1986) and Ballou & Lacy (1995), by assigning unique alleles to all pedigree founders, and simulating their segregation throughout the pedigree according to Mendelian rules. Genome uniqueness is a measure of the probability that an animal possesses founder alleles that are carried by at most x animals in all, counting the animal itself (the application offers 1-5, default 4), and thus are rare and at risk of being lost from the population. A range of 100 to 10,000 simulations may be selected. A minimum of 1,000 simulations is recommended, and 1,000 is the default. A genome uniqueness threshold value between 1 and 5 should also be selected, as desired.

   Because genome uniqueness is estimated from a finite number of gene-drop iterations, each value carries a sampling standard error (the guSE column), which shrinks roughly in proportion to one over the square root of the number of iterations; the default of 1,000 iterations gives a sampling error below one percentage point on the pedigrees we have examined. Keep two ideas separate: the standard error tells you how precise the genome uniqueness number is, while what actually decides which animals are selected for breeding is the order in which they are ranked. A small standard error does not by itself mean that order has settled. The gvaConvergence() function checks how many gene-drop iterations a given pedigree needs for the selection order to stop changing.

4. Following the calculation of mean kinship, related z-scores, and genome uniqueness for all animals, animals are ranked from the highest genetic value (ranking = 1) to the lowest. The Ranking Scheme control offers two schemes:
   • Combined (kinship - uniqueness), the default: each animal's mean kinship minus its genome uniqueness is ranked from smallest to largest, so animals with low mean kinship and high genome uniqueness rank highest. Animals whose value is Undetermined (see below) are ranked last.
   • Categorical (priority order): animals are sorted into tiers, in this order, with the "Genome uniqueness first" priority axis (choosing "Mean kinship first" swaps tiers ii and iii):
     1. Imported animals (both parents unknown, with a recorded origin) are ranked highest, followed by
     2. All animals with greater than 10% genome uniqueness (the high-uniqueness cutoff), ordered first by genome uniqueness from largest to smallest values, and by z-score within the same genome uniqueness from smallest to largest values; followed by
     3. All remaining animals with a z-score of 0.25 or less (the low-kinship cutoff), ranked by z-score from smallest to largest values; followed by
     4. All other animals, ranked by z-score from smallest to largest values. Animals with both parents unknown and no recorded origin are labeled Undetermined and placed last, without a rank.

   Under either scheme, the value column labels each animal High Value (imported animals and those above the high-uniqueness or low-kinship cutoff), Low Value (all others), or Undetermined. Animals labeled High Value are considered to be of high genetic value, while animals labeled Low Value are not recommended for breeding, but may be suitable for research assignment or sale. Low Value animals are not highlighted; read the value column.

   This ranking scheme follows Vinson & Raboin (2015).

Breeding Group Formation

• In large colonies, most or all genetic management may take place primarily during development of the housing/breeding group. A genetic value analysis may be used as the basis for creating potential new breeding groups that will maximize genetic diversity within the colony as a whole.
• When using the results of a genetic value analysis to develop new breeding groups, it is important to recognize that animals of high genetic value may still be closely related to other high-value animals, and that genetic diversity in the colony can be greatly reduced if relatives are allowed to produce viable offspring.
• Following a genetic value analysis of all breeding colony animals, the candidates for potential new breeding groups are chosen as the highest-ranked animals (by default), the animals not labeled Low Value, or every animal in the pedigree. In this analysis, potential new breeding groups are formed based on relationships that must be excluded, the threshold value of within-group relatedness that may be tolerated, relationships that can be safely ignored, and any additional specific group criteria. For example, with a threshold of 0.015625 (second cousin), relatedness at or above second cousin between breeding males, and between breeding males and females, is of concern; the application's default threshold is 0.25. Relatedness between breeding adults and animals under 1 year of age, or between females of any age, might be ignored, depending on the social group structure desired.
• This algorithm will assign randomly-selected animals to hypothetical groups, with the constraint that they cannot be related at the specified threshold level or greater to animals already assigned to the group. This process is repeated for the chosen number of simulations (10 by default in the application; raise it for a final run) to sample the collection of possible groups that can be formed from the set of candidate animals being considered. Upon completion, this algorithm will return the best set of groups, defined as the set with the largest minimum group size.