Group coancestry of a population

Consider the gene pool of a seed orchard

Seed orchard

A seed orchard is an intensively-managed plantation of specifically arranged trees for the mass production of genetically improved seeds to create plants, or seeds for the establishment of new forests.-General:...

 crop or other source of seeds with parents. The gene pool is large as there are many seeds in a seed crop, so there is no genetic drift

Genetic drift

Genetic drift or allelic drift is the change in the frequency of a gene variant in a population due to random sampling.The alleles in the offspring are a sample of those in the parents, and chance has a role in determining whether a given individual survives and reproduces...

. 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 originate from the orchard genotypes i and j are identical by descent (IBD) is θ_ij. This is the Malecot's method of coancestry

Malecot's method of coancestry

Malecot's coancestry coefficient, f , refers to an indirect measure of genetic similarity of two individuals which was initially devised by the French mathematician Gustave Malécot....

(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, Θ, can be found by adding over all possible pairs of genes from N parents. Formula for the group coancestry (from which gene diversity can be obtained) of seed orchard crops.


Θ= p_ip_jθ_ij.

The group coancestry of a seed orchard crop can be divided in two terms, one for self-coancestry and one for cross-coancestry.


Θ= p_i²(1+F_i)/2 + p_ip_jθ_ij, the last summation excluding j=i.


Let’s consider a simple case. If the seed orchard genotypes are unrelated the second term is zero, if there is no inbreeding, the first term becomes simple. For no relatedness and no inbreeding, status number (N_S, effective number of parents) becomes

N_S = 1/ p_i²

Similar but less developed expressions has been used many times before, it has similarities to the concept of effective population size as defined by .