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 pi, and the probability that the second originates from genotype j is pj. The probability that these two genes originating from the orchard genotypes i and j are identical by descent (IBD) is θij. 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.