Poisson adjacency distributions in genome comparison: multichromosomal, circular, signed and unsigned cases

Area of Science:

• Genomics
• Bioinformatics
• Evolutionary Biology

Background:

• Common adjacencies of genetic markers measure genome similarity.
• This measure is crucial for inferring evolutionary relatedness and phylogenetic relationships.
• Statistical tests using marker order require understanding the probability distribution of adjacencies.

Purpose of the Study:

• To derive probability distributions for the number of adjacencies across various genome types.
• To provide a basis for statistical tests to detect evolutionary signals in marker order.
• To analyze both signed/unsigned and circular/linear, single/multichromosomal genomes.

Main Methods:

• Derivation of probability distributions for different genome types.
• Utilizing generating functions for single-chromosome genomes to calculate exact counts.
• Employing probability approaches for multichromosomal genomes to determine expectations and variances.
• Deriving limiting distributions for the number of adjacencies.

Main Results:

• Exact counts are calculable for single-chromosome genomes using generating functions.
• Expectations and variances are precisely determined for multichromosomal genomes.
• Limiting distributions for unsigned genomes follow a Poisson distribution with parameter 2.
• Limiting distributions for signed genomes follow a Poisson distribution with parameter 1/2.

Conclusions:

• The derived probability distributions are essential for robust statistical testing in comparative genomics.
• The study provides a unified framework for analyzing genome similarity across diverse genomic architectures.
• Findings contribute to a deeper understanding of evolutionary processes through comparative genome analysis.