Maintenance of genetic diversity in subdivided populations using genomic coancestry matrices

Abstract

For both undivided and subdivided populations, the consensus method to maintain genetic diversity is the Optimal Contribution (OC) method. For subdivided populations, this method determines the optimal contribution of each candidate to each subpopulation to maximize global genetic diversity (which implicitly optimizes migration between subpopulations) while balancing the relative levels of coancestry between and within subpopulations. Inbreeding can be controlled by increasing the weight given to within-subpopulation coancestry (λ). Here we extend the original OC method for subdivided populations that used pedigree-based coancestry matrices, to the use of more accurate genomic matrices. Global levels of genetic diversity, measured as expected heterozygosity and allelic diversity, their distributions within and between subpopulations, and the migration pattern between subpopulations, were evaluated via stochastic simulations. The temporal trajectory of allele frequencies was also investigated. The genomic matrices investigated were (i) the matrix based on deviations of the observed number of alleles shared by two individuals from the expected number under Hardy-Weinberg equilibrium; and (ii) a matrix based on a genomic relationship matrix. The matrix based on deviations led to higher global and within-subpopulation expected heterozygosities, lower inbreeding and similar allelic diversity than the second genomic and pedigree-based matrices when a relatively high weight was given to the within-subpopulation coancestries (λ ≥ 5). Under this scenario, allele frequencies moved only slightly away from the initial frequencies. Therefore, the recommended strategy is to use the former matrix in the OC methodology giving a high weight to the within-subpopulation coancestry.

Keywords: allele frequency changes; allelic diversity; expected heterozygosity; genomic coancestry; optimal contributions; subdivided populations.

FIGURE 1

Diagram of the steps given to generate the base population in scenarios with different population structures: Equal (a, all subpopulations were equally related) and Unequal (b, subpopulation 1 was genetically differentiated and more inbred than the other four subpopulations).

FIGURE 2

Average frequency of the minor allele (MAF) in the global population (left panels) and in subpopulation 1 (right panels) across generations when contributions are optimized using pedigree‐based (Ɵ _PED ), Li and Horvitz (Ɵ _L&H ) and VanRaden (Ɵ _VR2 ) coancestry matrices and two different weights are given to the within‐subpopulation coancestry (λ = 1 and λ = 5), for scenarios with Unequal population structure. Matrices Ɵ _L&H and Ɵ _VR2 were computed using global (subscript “_g”) or subpopulation initial allele frequencies (subscript “_s”).

FIGURE 3

Number of individuals sent to and received by subpopulation 1 across generations when contributions are optimized using pedigree‐based (Ɵ _PED ), Li and Horvitz (Ɵ _L&H ) and VanRaden (Ɵ _VR2 ) coancestry matrices and two different weights are given to the within‐subpopulation coancestry (λ = 1 and λ = 5), for scenarios with Unequal population structure. Matrices Ɵ _L&H and Ɵ _VR2 were computed using global (left panels) or subpopulation initial allele frequencies (right panels).