PT  - JOURNAL ARTICLE
AU  - Armando Arredondo
AU  - Josué Corujo
AU  - Camille Noûs
AU  - Simon Boitard
AU  - Lounès Chikhi
AU  - Olivier Mazet
TI  - Exact calculation of the expected SFS in structured populations
AID  - 10.1101/2023.05.10.540112
DP  - 2023 Jan 01
TA  - bioRxiv
PG  - 2023.05.10.540112
4099  - http://biorxiv.org/content/early/2023/05/12/2023.05.10.540112.short
4100  - http://biorxiv.org/content/early/2023/05/12/2023.05.10.540112.full
AB  - The Site Frequency Spectrum (SFS), summary statistic of the distribution of derived allele frequencies in a sample of DNA sequences, provides information about genetic variation and can be used to make population inferences. The exact calculation of the expected SFS in panmictic population has been derived in the Markovian coalescent theory for decades, but its generalization to the structured coalescent is hampered by the almost exponential growth of the states space. We propose here a complete algorithmic procedure, from how to build a suitable state space and sort it, to how to take advantage of the sparsity of the rate matrix and to solve numerically the linear system by an iterative method. The simplest case of the symmetrical n-island is then processed to arrive at a ready-to-use demographic parameters inference framework.Competing Interest StatementThe authors have declared no competing interest.