The identity by descent process along the chromosome

Area of Science:

• Population Genetics
• Statistical Genetics
• Genomic Analysis

Background:

• Identity by Descent (IBD) states at a locus encapsulate genealogical information for a cohort.
• Understanding the stochastic process of IBD states across the genome is crucial for genetic studies.
• Previous work indicates the need for expanded state spaces to preserve the Markov property when analyzing IBD dynamics.

Purpose of the Study:

• To present a general, iterative method for deriving transition matrices of Markov chains modeling IBD state dynamics.
• To demonstrate how this method reduces the necessary state space size for genomic IBD analysis.
• To illustrate the application of the proposed method with two specific examples.

Main Methods:

• Development of a general iterative method for calculating transition matrices for IBD state Markov chains.
• Focus on a recursive approach to transition matrix derivation across genomic positions.
• Application and validation of the method through two distinct case studies.

Main Results:

• The proposed iterative method effectively derives transition matrices for IBD state stochastic processes.
• This approach leads to a significant reduction in the required state space size compared to traditional methods.
• The method's utility is confirmed by successful application in two illustrative examples.

Conclusions:

• The developed iterative method offers an efficient way to model genome-wide IBD state transitions.
• This technique simplifies the analysis of genealogical information across populations by reducing state space complexity.
• The findings provide a valuable tool for advancing research in statistical and population genetics.