Affiliation:
1. Centre for Computational Systems Biology, Fudan University, Shanghai 20433, People's Republic of China
2. Department of Mathematics, Suzhou University, Suzhou 215006, People's Republic of China
Abstract
Abstract
A numerical method is presented to solve the diffusion equation for the random genetic drift that occurs at a single unlinked locus with two alleles. The method was designed to conserve probability, and the resulting numerical solution represents a probability distribution whose total probability is unity. We describe solutions of the diffusion equation whose total probability is unity as complete. Thus the numerical method introduced in this work produces complete solutions, and such solutions have the property that whenever fixation and loss can occur, they are automatically included within the solution. This feature demonstrates that the diffusion approximation can describe not only internal allele frequencies, but also the boundary frequencies zero and one. The numerical approach presented here constitutes a single inclusive framework from which to perform calculations for random genetic drift. It has a straightforward implementation, allowing it to be applied to a wide variety of problems, including those with time-dependent parameters, such as changing population sizes. As tests and illustrations of the numerical method, it is used to determine: (i) the probability density and time-dependent probability of fixation for a neutral locus in a population of constant size; (ii) the probability of fixation in the presence of selection; and (iii) the probability of fixation in the presence of selection and demographic change, the latter in the form of a changing population size.
Publisher
Oxford University Press (OUP)
Reference30 articles.
1. Solutions of the forward diallelic diffusion equation in population genetics.;Barakat;Math. Biosci.,1978
2. A non-standard evolution problem arising in population genetics.;Chalub;Commun. Math. Sci.,2009
3. Some genetic problems in natural populations. Proc. Third Berkeley Symp. Math. Stat. and Prob.;Crow,1956
4. Applied Numerical Linear Algebra
Cited by
28 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献