title: Revisiting the diffusion approximation to estimate evolutionary rates of gene family diversification.
abstract: Genetic diversity in multigene families is shaped by multiple processes, including gene conversion and point mutation. Because multi-gene families are involved in crucial traits of organisms, quantifying the rates of their genetic diversification is important. With increasing availability of genomic data, there is a growing need for quantitative approaches that integrate the molecular evolution of gene families with their higher-scale function. In this study, we integrate a stochastic simulation framework with population genetics theory, namely the diffusion approximation, to investigate the dynamics of genetic diversification in a gene family. Duplicated genes can diverge and encode new functions as a result of point mutation, and become more similar through gene conversion. To model the evolution of pairwise identity in a multigene family, we first consider all conversion and mutation events in a discrete manner, keeping track of their details and times of occurrence; second we consider only the infinitesimal effect of these processes on pairwise identity accounting for random sampling of genes and positions. The purely stochastic approach is closer to biological reality and is based on many explicit parameters, such as conversion tract length and family size, but is more challenging analytically. The population genetics approach is an approximation accounting implicitly for point mutation and gene conversion, only in terms of per-site average probabilities. Comparison of these two approaches across a range of parameter combinations reveals that they are not entirely equivalent, but that for certain relevant regimes they do match. As an application of this modelling framework, we consider the distribution of nucleotide identity among VSG genes of African trypanosomes, representing the most prominent example of a multi-gene family mediating parasite antigenic variation and within-host immune evasion.
authors.affiliation: Instituto Gulbenkian de Ciência Oeiras, Portugal. Electronic address: egjini@igc.gulbenkian.pt.
authors.forename: Erida
authors.initials: E
authors.lastname: Gjini
authors.affiliation: Institute of Biodiversity, Animal Health and Comparative Medicine, College of Medical, Veterinary and Life Sciences, University of Glasgow, Glasgow, United Kingdom; The Boyd Orr Centre for Population and Ecosystem Health, University of Glasgow, Glasgow, United Kingdom; Wellcome Trust Centre for Molecular Parasitology, Institute of Infection, Immunity and Inflammation, University of Glasgow, Glasgow, United Kingdom.
authors.forename: Daniel T
authors.initials: DT
authors.lastname: Haydon
authors.affiliation: Wellcome Trust Centre for Molecular Parasitology, Institute of Infection, Immunity and Inflammation, University of Glasgow, Glasgow, United Kingdom.
authors.forename: J
authors.initials: J
authors.lastname: David Barry
authors.affiliation: School of Mathematics and Statistics, College of Science and Engineering, University of Glasgow, Glasgow, United Kingdom; The Boyd Orr Centre for Population and Ecosystem Health, University of Glasgow, Glasgow, United Kingdom.
authors.forename: Christina A
authors.initials: CA
authors.lastname: Cobbold
mesh_terms: D000818:Animals; D000953:Antigens, Protozoan / Q000235:genetics; D005075:Biological Evolution; D005785:Gene Conversion / Q000235:genetics; D017125:Genes, Protozoan / Q000235:genetics; D014644:Genetic Variation; D005828:Genetics, Population; D008957:Models, Genetic; D005810:Multigene Family; D009154:Mutation; D017354:Point Mutation; D012641:Selection, Genetic; D013269:Stochastic Processes; D014345:Trypanosoma / Q000235:genetics / Q000276:immunology
chemical_list: D000953:Antigens, Protozoan
keywords: Gene conversion; Identity distribution; Mutation rate; Trypanosome antigen archive; Wright-Fisher model