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