The correlation between relatives with assortative mating

Area of Science:

• Quantitative Genetics
• Statistical Genetics
• Population Genetics

Background:

• Phenotypic assortative mating influences the correlation between relatives.
• Understanding these correlations is key to estimating heritability accurately.
• Previous models often had restrictions on genetic architectures.

Purpose of the Study:

• To calculate the equilibrium correlation between relatives under phenotypic assortative mating.
• To determine if Fisher's formulae for correlation between relatives hold without restrictions on the linkage map.
• To validate genetic models for traits influenced by additive loci without dominance and uncorrelated environmental factors.

Main Methods:

• Calculated equilibrium correlations for various close relatives.
• Assumed bivariate normal distribution for spouse phenotypes.
• Assumed normally distributed heredity and environmental factors.
• Assumed linear regression of phenotype/genotype on relatives' phenotype/genotype.

Main Results:

• Fisher's formulae for the correlation between relatives were found to hold true.
• The validity of these formulae was confirmed without restrictions on the linkage map.
• The results are consistent with assumptions of additive gene action and normally distributed traits.

Conclusions:

• The study validates the general applicability of Fisher's formulae in quantitative genetics.
• Assumptions regarding genetic and environmental distributions simplify but do not limit the core findings.
• This work provides a robust theoretical framework for analyzing relatedness in populations with assortative mating.