Computing Mean Kinship

The 'mean kinship' of an individual with respect to a group is the mean of its kinship coefficient with every other member of the group, including itself.

Its a measure of the relatedness of an individual to the rest of the group.

How To Calculate Mean Kinship

Computing mean kinships for a group of individuals requires the construction of a relationship matrix ('A') for the individuals concerned and their ancestors (to a chosen depth or ancestry, or all available ancestry). Then, for each member of the group for which the report is compiled, the kinships between that member and every other member of the group (including itself) can be summed and averaged.

Creating a relationship matrix ('A') for a large number of individuals together with their ancestors can be a computationally enormous task involving a huge amount of memory, because it requires a matrix that is proportional in size to the square of the total number of individuals and their ancestors involved.

It is relatively easy to run out of memory when the report many individuals and their ancestors. E.g. if there are 100,000 individuals and ancestors that would require a matrix with 10,000,000,000 i.e. 10 billion entries. This is beyond the realistic memory capacity of most desktop computers. For this reason it is necessary to restrict the report where possible, by reducing the number of individuals for which the report is compiled and/or reducing the depth of ancestry included in the analysis.

Gene Diversity - Averaging Mean Kinship

The mean of the mean kinships for a breeding population results in a single value that expresses the overall relatedness of that population. The lower this value, the less related the members of the breeding population are to each other.

This can also be expressed as a value called 'Gene Diversity' (GD), which is defined as 1 minus the mean of the mean kinships. Which means the higher the GD, the better.

The Extended of Breeders Assistant can rank prospective matings in order to minimize the mean kinship in the resultant offspring. Video

Minimizing Inbreeding

Breeders Assistant can also be used to rank prospective matings according to the resulting inbreeding. I.e. it can take a group of breeding males and females and compute the inbreeding that would result from thousands of potential matings, listing the results in increasing order of offspring inbreeding. Video

Displayed Columns

The columns displayed by default include:

Mean Kinship (symbol MK) - the mean of the kinship of the individual with every other individual in the breeding group, including itself, for which the report was compiled.

Inbreeding Coefficient (symbol F) - computed using all the ancestry that was specified.

Genome Uniqueness (symbol GU) - an estimation of the probability that an animal contains founder alleles not present in any other single (normally) animal within the group for which the report has been compiled. This latter point is crucial to understand - the whole purpose of the GU measure is to identify animals within the breeding population that are likely to carry genes from founders where there is little or no representation of those genes in other members of the breeding population. GU can be factored into mate selection decisions when prioritizing prospective matings using gene diversity metrics. Informally, if an animal is the only one carrying a particular founder's genes, then you'd likely want to breed from that individual so as not to lose those genes from the population forever.

Full Generations (symbol GF) - the number of generations of ancestors that are 'full' - i.e. all ancestors given (within the depth of ancestry under consideration).

Max Generations (symbol GM) - the maximum depth of ancestry at which ancestors were found - (within the depth of ancestry under consideration). It is possible for this to exceed the #generations chosen if the group of animals for which it is compiled also includes some of their ancestors. E.g. if you have two animals in your database called, say 'Fred' and 'Bert', where 'Bert' is the sire of 'Fred', and you chose to do the analysis for just 2 generations, then because 2 generations of Bert's ancestors are traced, it means that ancestors will have been seen for 'Fred' 3 generations back.

Equivalent Complete Generations (symbol ECG) - a measure of the completeness of the pedigree. It is the sum total of the proportion of the ancestors that were traced at every generation at which ancestors were found (including, possibly, ancestor generations beyond those requested, for the same reasoning as given for Max Generations). E.g. if both parents are present that contributes 1 to the ECG value. If 2 grandparents are present that would add 0.5 to the ECG (i.e. 2/4). If 3 great-grandparents are present that would add 0.375 to the ECG (i.e. 3/8). Etc.

Pedigree Completeness (symbol PC) - another measure of the completeness of the pedigree. It is the sum total of the proportion of the ancestors that were traced at each generation, divided by that number of generations, shown as a percentage. E.g. if you were to request 3 generations of ancestors be included, then for an animal where both parents are present (i.e. proportion 1.0), 2 grandparents are present (proportion 0.5), and 3 great-grandparents (proportion 0.375) then the PC value would be (1.0 + 0.5 + 0.375) ie 1.875 divided by 3 which is 0.625 or 62.5%.

Pedigree Completeness Index (symbol PCI) - this is yet another measure of the completeness of the pedigree, and probably the most useful. It is the harmonic mean of the PC values for the parents of an animal, so long as both parents are present, otherwise it is zero. Because it is the harmonic mean it weights the result to the lower of the parent PC values. This value is computed using the method of MacCluer et al ("Inbreeding and Pedigree Structure in Standardbreed Horses", Journal of Heredity 1983, 74:394-399). PCI can be useful when deciding how much importance to give to an inbreeding value. Informally, if insufficient ancestry is available then a low inbreeding coefficient is not a reliable guide to the true level of inbreeding. When selecting prospective matings by inbreeding Breeders Assistant can use weightings for the sire and dam PCI values in the overall ranking. A threshold can also be specified to exclude prospective matings which have a PCI value below a given value.

Computing Mean Kinship

How To Calculate Mean Kinship

Gene Diversity - Averaging Mean Kinship

Minimizing Inbreeding

Gene Diversity Metrics

Displayed Columns

Mate Selection Matrix With Inbreeding Minimization