A stochastic evolution model for residue Insertion-Deletion Independent from Substitution.
We develop here a new class of stochastic models of gene evolution based on residue Insertion-Deletion Independent from Substitution (IDIS). Indeed, in contrast to all existing evolution models, insertions and deletions are modeled here by a concept in population dynamics. Therefore, they are not only independent from each other, but also independent from the substitution process. After a separate stochastic analysis of the substitution and the insertion-deletion processes, we obtain a matrix differential equation combining these two processes defining the IDIS model. By deriving a general solution, we give an analytical expression of the residue occurrence probability at evolution time t as a function of a substitution rate matrix, an insertion rate vector, a deletion rate and an initial residue probability vector. Various mathematical properties of the IDIS model in relation with time t are derived: time scale, time step, time inversion and sequence length. Particular expressions of the nucleotide occurrence probability at time t are given for classical substitution rate matrices in various biological contexts: equal insertion rate, insertion-deletion only and substitution only. All these expressions can be directly used for biological evolutionary applications. The IDIS model shows a strongly different stochastic behavior from the classical substitution only model when compared on a gene dataset. Indeed, by considering three processes of residue insertion, deletion and substitution independently from each other, it allows a more realistic representation of gene evolution and opens new directions and applications in this research field.
Lèbre
Sophie
S
Equipe de Bioinformatique Théorique, FDBT, LSIIT (UMR UdS-CNRS 7005), Université de Strasbourg, Pôle API, Boulevard Sébastien Brant, 67400 Illkirch, France. lebre@dpt-info.u-strasbg.fr
Michel
Christian J
CJ
D003198:Computer Simulation; D019143:Evolution, Molecular; D054643:INDEL Mutation; D008957:Models, Genetic; D015233:Models, Statistical; D009711:Nucleotides / Q000235:genetics / Q000378:metabolism; D011336:Probability; D013269:Stochastic Processes
D009711:Nucleotides