In the previous module, inbreeding and population substructure were introduced.  Population substructure can be dealt with in the same manner as inbreeding.  The 1996 National Research Council Report (NRC II) proposed using formulas 4.4a and 4.4b to deal with population substructure. Formulas analogous to those noted below (with theta) are used for the inbreeding coefficient, F. These formulas do not require that the subpopulations be distinct or mate at random.⁰⁷ The value of theta (θ) can be positive or negative, but must be less than or equal to 1.

Read about the inbreeding coefficient, F in this course.

• Homozygote: p _i² + p _i (1-p _i) θ_ii (formula 4.4a from the NRC II)

• Heterozygote: 2p _i p _j (1- θ_ij), i ≠ j (formula 4.4b from the NRC II)

The parameter θ can be defined as the probability that two alleles in different people, in the same subpopulation, are identical by descent.⁰⁵ Strictly the two alleles can originate from the same individual or, more likely, two different individuals. The value of θ can be determined for a given population. Generally, θ = 0.01 can be used for large populations, and θ = 0.03 for small, isolated populations.

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