Using mathematical constraints to explain narrow ranges for allele-sharing dissimilarities

Area of Science:

• Population Genetics
• Human Genetics
• Statistical Genetics

Background:

• Allele-sharing dissimilarity (ASD) statistics measure genetic differentiation between individuals or populations.
• Understanding the mathematical constraints on ASD is crucial for interpreting genetic variation patterns.

Purpose of the Study:

• To investigate the mathematical bounds of two ASD statistics (D1 and D2).
• To determine how allele frequencies constrain expected ASD values.
• To explain empirical observations of limited genetic variation range in human populations.

Main Methods:

• Calculating the expected value of ASD statistics based on allele-frequency distributions.
• Analyzing the bounds of expected ASD as a function of the most frequent allele's frequency.
• Comparing intra-population and inter-population ASD constraints.

Main Results:

• The expected ASD values are constrained by allele frequencies, resulting in a range narrower than [0,1].
• Bounds on expected ASD were derived in terms of the most frequent allelic type's frequency.
• Mathematical constraints help explain the empirically observed narrow range of human genetic variation.

Conclusions:

• Allele frequencies impose significant mathematical constraints on expected allele-sharing dissimilarity.
• These constraints provide a theoretical basis for the relatively narrow range of genetic variation observed in human populations when averaged across loci.