title: The SMM model as a boundary value problem using the discrete diffusion equation.
abstract: A generalized single-step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.
authors: NASA Langley Research Center, MS 488, Hampton, VA 23681, USA. joel.f.campbell@nasa.gov
authors: Joel
authors: J
authors: Campbell
mesh_terms: D000465:Algorithms; D040961:Genetic Drift; D006801:Humans; D018895:Microsatellite Repeats / Q000235:genetics; D008957:Models, Genetic; D009154:Mutation; D016011:Normal Distribution