Seed production and gene diversity

Genetic diversity is often a major consideration in e g forest crops.

Consider the gene pool of a seed orchard crop. The gene pool is large as there are many seeds in a seed crop, so there is no genetic drift. The probability that the first gene originates from genotype i in the seed orchard is p_i, and the probability that the second originates from genotype j is p_j. The probability that these two genes originating from the orchard genotypes i and j are identical by descent (IBD) is θ_ij . Thus the coancestry (or "coefficient of kinship"; "coefficient of relationship" is a similar measure which can be computed) between genotype i and j. The probability that any pair of genes is IBD can be found by adding over all possible pairs of genes from N contributorsFormula for the group coancestry (from which gene diversity can be obtained) of seed orchard crops.

$\sum _{i=1}^{N}\sum _{j=1}^{N}$  pipjθ.

The group coancestry of a seed orchard crop can be divided in two terms, one for self-coancestry and one for cross-coancestry. Similar expressions has been used many times before, it has similarities to the concept of effective population size as defined by .