Prediction of multilocus identity-by-descent

Area of Science:

• Population Genetics
• Statistical Genetics
• Genomics

Background:

• Previous methods for predicting identity-by-descent (IBD) probabilities were limited to a few loci or relied on approximations.
• Extending IBD prediction to multiple loci is crucial for understanding genetic relatedness and disease associations.

Purpose of the Study:

• To develop a precise and computationally efficient method for predicting multi-locus IBD probabilities.
• To provide simple formulas applicable to various population genetics scenarios, including bottlenecks and migration.

Main Methods:

• Developed a "chain rule" based on exact two-locus IBD probabilities, generalizing to multiple loci.
• Derived formulas for non-IBD probabilities (X(123...k)) using a recursive relationship.
• Introduced an approximate recurrence formula for improved robustness with mutation.

Main Results:

• The proposed chain rule provides highly accurate predictions of multi-locus IBD and non-IBD probabilities.
• Formulas are functions of population size, time, and genetic map distances.
• The method shows high precision under bottlenecks and migration, with slightly reduced accuracy in the presence of mutation.

Conclusions:

• The new formulas offer a precise and practical approach to multi-locus IBD prediction in population genetics.
• The method can be applied to identify quantitative trait loci (QTL) by relating IBD to identity-by-state at markers.
• The combination of chain rule and recurrence formula provides explicit equations for non-IBD in genomic regions.