کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6372212 1320035 2007 47 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Exact solution of the multi-allelic diffusion model
موضوعات مرتبط
علوم زیستی و بیوفناوری علوم کشاورزی و بیولوژیک علوم کشاورزی و بیولوژیک (عمومی)
پیش نمایش صفحه اول مقاله
Exact solution of the multi-allelic diffusion model
چکیده انگلیسی

We give an exact solution to the Kolmogorov equation describing genetic drift for an arbitrary number of alleles at a given locus. This is achieved by finding a change of variable which makes the equation separable, and therefore reduces the problem with an arbitrary number of alleles to the solution of a set of equations that are essentially no more complicated than that found in the two-allele case. The same change of variable also renders the Kolmogorov equation with the effect of mutations added separable, as long as the mutation matrix has equal entries in each row. Thus, this case can also be solved exactly for an arbitrary number of alleles. The general solution, which is in the form of a probability distribution, is in agreement with the previously known results. Results are also given for a wide range of other quantities of interest, such as the probabilities of extinction of various numbers of alleles, mean times to these extinctions, and the means and variances of the allele frequencies. To aid dissemination, these results are presented in two stages: first of all they are given without derivations and too much mathematical detail, and then subsequently derivations and a more technical discussion are provided.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Mathematical Biosciences - Volume 209, Issue 1, September 2007, Pages 124-170
نویسندگان
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