کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4498907 1319004 2007 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Singular solutions of the diffusion equation of population genetics
موضوعات مرتبط
علوم زیستی و بیوفناوری علوم کشاورزی و بیولوژیک علوم کشاورزی و بیولوژیک (عمومی)
پیش نمایش صفحه اول مقاله
Singular solutions of the diffusion equation of population genetics
چکیده انگلیسی

The forward diffusion equation for gene frequency dynamics is solved subject to the condition that the total probability is conserved at all times. This can lead to solutions developing singular spikes (Dirac delta functions) at the gene frequencies 0 and 1. When such spikes appear in solutions they signal gene loss or gene fixation, with the “weight” associated with the spikes corresponding to the probability of loss or fixation. The forward diffusion equation is thus solved for all gene frequencies, namely the absorbing frequencies of 0 and 1 along with the continuous range of gene frequencies on the interval (0,1)(0,1) that excludes the frequencies of 0 and 1. Previously, the probabilities of the absorbing frequencies of 0 and 1 were found by appeal to the backward diffusion equation, while those in the continuous range (0,1)(0,1) were found from the forward diffusion equation. Our unified approach does not require two separate equations for a complete dynamical treatment of all gene frequencies within a diffusion approximation framework. For cases involving mutation, migration and selection, it is shown that a property of the deterministic part of gene frequency dynamics determines when fixation and loss can occur. It is also shown how solution of the forward equation, at long times, leads to the standard result for the fixation probability.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Theoretical Biology - Volume 247, Issue 4, 21 August 2007, Pages 849–858
نویسندگان
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