Expectation of the Site Frequency Spectrum

TL;DR

This paper reviews the expected behavior of the site frequency spectrum in population genetics, explaining why adding more sequences extends the spectrum without altering existing entries under neutral conditions.

Contribution

It provides a detailed explanation of the reasons behind the invariance of the spectrum's entries when increasing sample size under neutrality.

Findings

Adding sequences extends the spectrum without changing existing entries.

The expected spectrum remains stable under neutrality and constant population size.

The paper clarifies the mathematical reasoning behind this phenomenon.

Abstract

The site frequency spectrum describes variation among a set of n DNA sequences. Its i'th entry (i=1,2,...,n-1) is the number of nucleotide sites at which the mutant allele is present in i copies. Under selective neutrality, random mating, and constant population size, the expected value of the spectrum is well known but somewhat puzzling. Each additional sequence added to a sample adds an entry to the end of the expected spectrum but does not affect existing entries. This note reviews the reasons for this behavior.