Arthur Zwaenepoel 2021 arzwa@psb.vib-ugent.be

TwoTypeDLModel

Inference for a two-type branching process model of gene family evolution by duplication and loss. The main aim is more realistic estimation of gene duplication and loss rates from gene family data (see the associated preprint here). The method for computing transition probabilities is based on the work of Xu et al. (2015) on the Birth-Death-Shift process.

The model is a two-type continuous-time branching process with stochastic dynamics that could be schematically represented as

1 → 12   with rate λ
1 →  ∅   with rate μ₁
2 → 22   with rate λ
2 →  ∅   with rate μ₂ > μ₁ and μ₂ > λ + ν
2 →  1   with rate ν

A special case of this model that may be of interest is the μ₁ = 0 case. The case μ₁ = ν = 0 corresponds to a linear birth-death immigration process incremented by one with immigration and birth rate λ and death rate μ₂.

Here we can roughly think of the number of type 1 particles denoting the number of groups of redundant genes in a family, or the number of more or less essential genes per family, while the number of type 2 particles reflects the number of excess genes per family. The most important aspect of the model is that type 2 genes get lost at a higher rate than type 1 genes, and that type 2 genes can get established (capturing the processes of 'complete' sub- and neofunctionalization) and become stably incorporated type 1 genes.

For more information, consult the documentation

Reference

A two-type branching process model of gene family evolution
Arthur Zwaenepoel, Yves Van de Peer
bioRxiv 2021.03.18.435925; doi: https://doi.org/10.1101/2021.03.18.435925